A Dark, Misleading Force

By Sean Carroll | December 10, 2007 12:22 pm

Certain subsectors of the scientifically-oriented blogosphere are abuzz — abuzz, I say! — about this new presentation on Dark Energy at the Hubblesite. It’s slickly done, and worth checking out, although be warned that a deep voice redolent with mystery will commence speaking as soon as you open the page.

But Ryan Michney at Topography of Ignorance puts his finger on the important thing here, the opening teaser text:

Scientists have found an unexplained force that is changing our universe,
forcing galazies farther and farther apart,
stretching the very fabric of space faster and faster.
If unchecked, this mystery force could be the death of the universe,
tearing even its atoms apart.

We call this force dark energy.

Scary! Also, wrong. Not the part about “tearing even its atoms apart,” an allusion to the Big Rip. That’s annoying, because a Big Rip is an extremely unlikely future for a universe even if it is dominated by dark energy, yet people can’t stop putting the idea front and center because it’s provocative. Annoying, but not wrong.

The wrong part is referring to dark energy as a “force,” which it’s not. At least since Isaac Newton, we’ve had a pretty clear idea about the distinction between “stuff” and the forces that act on that stuff. The usual story in physics is that our ideas become increasingly general and sophisticated, and distinctions that were once clear-cut might end up being altered or completely irrelevant. However, the stuff/force distinction has continued to be useful, even as relativity has broadened our definition of “stuff” to include all forms of matter and energy. Indeed, quantum field theory implies that the ingredients of a four-dimensional universe are divided neatly into two types: fermions, which cannot pile on top of each other due to the exclusion principle, and bosons, which can. That’s extremely close to the stuff/force distinction, and indeed we tend to associate the known bosonic fields — gravity, electromagnetism, gluons, and weak vector bosons — with the “forces of nature.” Personally I like to count the Higgs boson as a fifth force rather than a new matter particle, but that’s just because I’m especially fastidious. The well-defined fermion/boson distinction is not precisely equivalent to the more casual stuff/force distinction, because relativity teaches us that the bosonic “force fields” are also sources for the forces themselves. But we think we know the difference between a force and the stuff that is acting as its source.

Anyway, that last paragraph got a bit out of control, but the point remains: you have stuff, and you have forces. And dark energy is definitely “stuff.” It’s not a new force. (There might be a force associated with it, if the dark energy is a light scalar field, but that force is so weak that it’s not been detected, and certainly isn’t responsible for the acceleration of the universe.) In fact, the relevant force is a pretty old one — gravity! Cosmologists consider all kinds of crazy ideas in their efforts to account for dark energy, but in all the sensible theories I’ve heard of, it’s gravity that is the operative force. The dark energy is causing a gravitational field, and an interesting kind of field that causes distant objects to appear to accelerate away from us rather than toward us, but it’s definitely gravity that is doing the forcing here.

Is this a distinction worth making, or just something to kvetch about while we pat ourselves on the back for being smart scientists, misunderstood once again by those hacks in the PR department? I think it is worth making. One of the big obstacles to successfully explaining modern physics to a broad audience is that the English language wasn’t made with physics in mind. How could it have been, when many of the physical concepts weren’t yet invented? Sometimes we invent brand new words to describe new ideas in science, but often we re-purpose existing words to describe concepts for which they originally weren’t intended. It’s understandably confusing, and it’s the least we can do to be careful about how we use the words. One person says “there are four forces of nature…” and another says “we’ve discovered a new force, dark energy…”, and you could hardly blame someone who is paying attention for turning around and asking “Does that mean we have five forces now?” And you’d have to explain “No, we didn’t mean that…” Why not just get it right the first time?

Sometimes the re-purposed meanings are so deeply embedded that we forget they could mean anything different. Anyone who has spoken about “energy” or “dimensions” to a non-specialist audience has come across this language barrier. Just recently it was finally beaten into me how bad “dark” is for describing “dark matter” and “dark energy.” What we mean by “dark” in these cases is “completely transparent to light.” To your average non-physicist, it turns out, “dark” might mean “completely absorbs light.” Which is the opposite! Who knew? That’s why I prefer calling it “smooth tension,” which sounds more Barry White than Public Enemy.

What I would really like to get rid of is any discussion of “negative pressure.” The important thing about dark energy is that it’s persistent — the density (energy per cubic centimeter) remains roughly constant, even as the universe expands. Therefore, according to general relativity, it imparts a perpetual impulse to the expansion of the universe, not one that gradually dilutes away. A constant density leads to a constant expansion rate, which means that the time it takes the universe to double in size is a constant. But if the universe doubles in size every ten billion years or so, what we see is distant galaxies acceleratating away — first they are X parsecs away, then they are 2X parsecs away, then 4X parsecs away, then 8X, etc. The distance grows faster and faster, which we observe as acceleration.

That all makes a sort of sense, and never once did we mention “negative pressure.” But it’s nevertheless true that, in general relativity, there is a relationship between the pressure of a substance and the rate at which its density dilutes away as the universe expands: the more (positive) pressure, the faster it dilutes away. To indulge in a bit of equationry, imagine that the energy density dilutes away as a function of the scale factor as R-n. So for matter, whose density just goes down as the volume goes up, n=3. For a cosmological constant, which doesn’t dilute away at all, n=0. Now let’s call the ratio of the pressure to the density w, so that matter (which has no pressure) has w=0 and the cosmological constant (with pressure equal and opposite to its density) has w=-1. In fact, there is a perfectly lockstep relation between the two quantities:

n = 3(w + 1).

Measuring, or putting limits on, one quantity is precisely equivalent to the other; it’s just a matter of your own preferences how you might want to cast your results.

To me, the parameter n describing how the density evolves is easy to understand and has a straightforward relationship to how the universe expands, which is what we are actually measuring. The parameter w describing the relationship of pressure to energy density is a bit abstract. Certainly, if you haven’t studied general relativity, it’s not at all clear why the pressure should have anything to do with how the universe expands. (Although it does, of course; we’re not debating right and wrong, just how to most clearly translate the physics into English.) But talking about negative pressure is a quick and dirty way to convey the illusion of understanding. The usual legerdemain goes like this: “Gravity feels both energy density and pressure. So negative pressure is kind of like anti-gravity, pushing things apart rather than pulling them together.” Which is completely true, as far as it goes. But if you think about it just a little bit, you start asking what the effect of a “negative pressure” should really be. Doesn’t ordinary positive pressure, after all, tend to push things apart? So shouldn’t negative pressure pull them together? Then you have to apologize and explain that the actual force of this negative pressure can’t be felt at all, since it’s equal in magnitude in every direction, and it’s only the indirect gravitational effect of the negative pressure that is being measured. All true, but not nearly as enlightening as leaving the concept behind altogether.

But I fear we are stuck with it. Cosmologists talk about negative pressure and w all the time, even though it’s confusing and ultimately not what we are measuring anyway. Once I put into motion my nefarious scheme to overthrow the scientific establishment and have myself crowned Emperor of Cosmology, rest assured that instituting a sensible system of nomenclature will be one of my very first acts as sovereign.

CATEGORIZED UNDER: Science, Science and the Media
  • http://pantheon.yale.edu/~pwm22/ Peter Morgan

    If I define a force as anything that causes a (macroscopic, non-quantum mechanical) test particle not to follow the geodesics of the geometry of space-time, is the “Dark, Misleading Force” a force on that definition? If not, why not? Or do you find this definition misleading in this cosmological context?

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    It’s certainly not a force by that definition. Galaxies are following geodesics.

  • Jason M. Hendler

    I love your description of a “smooth tension”, because, to me, it seems similar to surface tension, like watching dishsoap coalesce grease into perfect circle of your dishpan.

    As stated previously, I believe that there is only one force – entropy, which reveals itself nicely in a “smooth tension” / surface tension sort of way. The clusters of galaxies and the “fibers” in between with large “bubbles” of empty space look so much like the interaction of tensions with entropy determining it all.

  • http://scilearn.blogspot.com/ Freiddie

    So that’s why my mind got stuck when I was reading that sentence… Anyway, that also explains why dark energy is never called dark force (I asked this in Bad Astronomy).

  • http://pantheon.yale.edu/~pwm22/ Peter Morgan

    Re my 1 and 2: So dark matter makes the geodesic geometry different from what it would be if there were no dark matter. What would be wrong with saying, on a local level, that the “dark force” on a test particle is proportional to the mass of the test particle? Or test galaxy? Alternatively, hedging in a slightly cute way, that the dark force is as much a force as gravity is?
    Saying that gravity is a force is an empirically effective way of talking about local physics — to pretty good accuracy at most human scales — so presumably we could equally well talk about the dark force, provided we define the empirical scale we are talking about to be in the galactic cluster range, but we could not talk about a dark force on global, universal scales?
    I suppose that this may run up against realist ontological objections from some that geometry is “real” but gravitational force is not. I would have to more-or-less agree with that objection because of the advance of the perihelion of Mercury and the other experimental tests of GR. At what scale is an experimentally based objection against thinking in terms of a dark force very clear?

  • Jason Dick

    Peter Morgan,

    What we typically mean by a new force is a new interaction between two test particles. That is, if we took, say, two protons and put them near one another, then they would primarily have a gravitational attraction and an electrostatic repulsion. The gravitational attraction is mediated by an exchange of gravitons, while the electrostatic repulsion is mediated by the exchange of photons.

    A “fifth force” would be something that acts in much the same way: as some function of distance, it would contribute some amount to the attraction or repulsion that any two test particles feel. It would couple to its own sort of charge as well, and thus would not, in general, behave identically to any known force (if it did behave identically, then it could never be disentangled from a known force: for example, if it behaved just like gravity then we might merely treat it as being a different species of graviton, for example).

    Dark energy isn’t anything like this (neither is dark matter). It’s not, so far as we know, some new particle that is mediating some new attraction or repulsion between two test particles. Instead, it appears to be just some different stuff that is sitting around, and which interacts, through gravity, with other particles. Another way of looking at it is instead of having our two test particles have some new attraction or repulsion mediated by some new, unknown particle, we have some number of test particles that we can detect through more direct means (e.g. photons, protons, electrons) interacting with other test particles that we cannot see directly. It’s very much akin to how we know about neutrinos: neutrinos are, for all intents and purposes, completely invisible, but they are produced in weak interactions and cause weak interactions to occur. As a result, we can detect their influence by observing the behavior of test particles that we can observe.

    The same is the case for dark matter and dark energy: it’s not the same stuff interacting in different ways, but new stuff that we can only observe indirectly.

  • BG

    Sean, if DE is a cosmological constant couldn’t you choose to absorb it into the left-hand side of Einstein’s equation rather than put it in the stress-energy tensor? Equivalently, in the Newtonian limit can’t you absorb the Lambda term into a redefinition of the potential? And if you do so, isn’t it OK to talk about it as some inherent part of the gravitational “force”, a part that is “unexplained” and a “mystery”? None of the text you quoted really claims that it’s a new fifth force.

    And are you aware of some new evidence that dark energy really is “stuff” rather than a modification to gravity or something? Saying “dark energy is definitely stuff” sounds at least as misleading to me as “dark energy is an unexplained force”.

    I’m totally with you about “negative pressure”, though. Even among scientists it seems to create way more misunderstanding than it should.

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    BG, it doesn’t matter whether you put the cosmological constant on the left-hand side or the right-hand side of the equation; it’s still the vacuum energy. The reason why the universe is accelerating might very well be a modification of general relativity, but it’s still gravity, not a new force. (Gravity didn’t stop being gravity when GR replaced Newton’s theory, for example.) In that case you should just say that dark energy doesn’t exist, which is not what they were getting at.

  • George Musser

    Sean, this is a very helpful comment and I need to be more careful about this terminology myself. A few questions for the fastidious:

    1. Is it correct to say that astronomers discovered dark energy, be it stuff or force? They discovered acceleration and have attributed it to dark energy, among other possibilities that you yourself have talked about.

    2. Should we be using “force” or “interaction”, the former being a special case of the latter?

    3. Should we really identify the fermion/boson distinction with the stuff/force distinction? Bosons can interact with one another and fermions can agglomerate to act as bosons.

    4. Leaving the domain of fundamental physics, the concept of force is more protean and frame-dependent. For example, the force of gravity that we common measure isn’t just gravitation. Indeed, “force” is a term of convenience. A phenomenologist might indeed attribute cosmic acceleration to an antigravity force.

    George

  • http://tyrannogenius.blogspot.com Neil B.

    Sean and others have some good points, but I don’t like the idea in glib GR talk of dismissing “forces” caused by gravitation in lieu of natural motion in space-time. That is true in some context, but really: if I have two masses separated by a rod, the rod certainly acts compressed by real forces. You can talk about what the masses would have done had the rod not been there, but since it is, the sophistic discussion of geodesics etc. doesn’t negate the fact that effectively the masses exert forces on each other for all practical purposes. Presumably th same point applies to dark energy, which is like a density with negative value for producing a field where g = (4/3)pi*rho*r. Since dark energy intrinsically and uniformly fills space (?) it could be distinguished from effects due to matter density: If I can evacuate a large region of space, I should measure a little bit of tension if masses have a string between them and the DE effect outweighs their mutual attraction. If the magnitude of DE keeps getting bigger, then indeed electrons would eventually be stripped from nuclei, and presumably even nuclei would be shredded some day in the very far future. Someone suggested that could generate energy, and brought up conservation issues (but it’s so hard to define total energy when gravity is present, true? What about the claim that space-time curvature doesn’t really have the same machinery as E&M for defining “energy” in flight as it were, for gravitational radiation? Doesn’t that cause conservation problems because we want to say, when rotating neutron stars etc. lose energy of motion by radiation, it is then “present” in the expanding gravitational waves?

    BTW, those interested in such issues could consider or reconsider the thought experiment I posed in the thread Thanksgiving about hard containers impeding space contraction, such as #3,5,6 and a final thought in #35:
    There are contradiction problems if you try to imagine what happens to all the bodies in expanding/contracting universes if some things are impeded by material barriers/obstructions and other things just move like dust in free fall.

    BTW as I understand it, the net gravitational effect is all that matters (heh) for making space curvature, not whether it’s from matter or DE etc. Note that if space is really open and infinite, people *just* like us are having this same discussion e.g. about 10^800 light-years away, and so on ad infinitum…

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    George:

    1) I don’t mind saying that astronomers discovered dark energy, or even that they’ve discovered the cosmological constant, depending on the level of precision for which one is aiming. The truth is that they’ve discovered the acceleration (and spatial flatness) of the universe. The best (but not only) explanation for that is dark energy, and the leading (but not only) candidate for that is the cosmological constant. But I don’t especially object to speaking as if the most likely scenario is the one you’ve found, depending on how much detail you are trying to go into. Being rigorously correct in every single statement you make is a recipe for never being understood. What I object to is being wrong for no good reason.

    2) That just depends on the circumstances. Both “force” and “interaction” are perfectly good words in context.

    3) The fermion/boson distinction is not precisely the stuff/matter distinction, as I did try to make clear. Arguably I shouldn’t even have brought it up at all, but it’s an example of a rigorous modern concept that matches pretty well with a venerable more primitive concept.

    4) This one I don’t understand. What do you mean by a phenomenologist? If you mean someone who sticks just to what we observe, they should be talking in terms of luminosity distances and redshifts, not in terms of forces. Anyone who speaks of forces does so in the context of a theory, and in all the theories I know of, the force responsible for the acceleration of the universe is gravity.

  • George Musser

    Sean, regarding #4: All I’m saying is that there are different levels of explanation and it’s not always convenient to talk strictly in terms of fundamental interactions. When I let go of my pencil and it hits the desk, I suppose I should be saying that the desk hit it, but FAPP I talk about a force of gravity pulling things downward. Similarly, why not talk about a force of antigravity — as astronomers did before “dark energy” entered circulation — as long as we’re clear that we don’t mean a new fundamental interaction?
    George

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    I have no objection to attributing the fall of your pencil to the force of gravity. It’s useful, if imprecise, language. (I’ve never been a stickler about “centrifugal force,” either.)

    But I would object if you dropped your pencil on the Moon, and on Mars, and into the black hole at the center of the galaxy, and then claimed that you had found a handful of new forces of nature. It’s the same force in every case — gravity. Dark energy is exactly the same. It’s a new source for gravity, just one that happens to make test bodies move apart rather than together. Calling it a new force isn’t just sloppy, it’s actively incorrect and misleading.

  • George Musser

    True, and highly nontrivial. Finding unity in variety is the heart of physics.
    George

  • Ellipsis

    Sean — if you are considering the Higgs to be a fifth force as per the above, then I would think you would consider quintessence, if quintessence were the cause of dark energy, to also be a fifth (or rather sixth) force, no…?

  • Jason Dick

    Ellipsis,

    Dark energy might indeed mediate an as yet unknown force. Its affect on the acceleration, however, would have nothing to do with this. So it would still be misleading to call it a force.

  • Pingback: Dark Energy and Me

  • Ellipsis

    Jason — I only brought it up because Sean mentioned that he sometimes liked to consider the Higgs a fifth force. I think if one were to take that view (which I wouldn’t myself, but agree that it’s not off the wall), then in that case quintessence (if it exists) would also fall into the additional force category, being that it’s another scalar field, in a fairly similar manner to the Higgs. Would you disagree?

  • John Merryman

    If space is what is actually expanding, wouldn’t the speed of light be increasing as well? Say two galaxies are 100 lightyears apart, if the universe expanded to twice its size, it would still take light only 100 years to cross that space, because if it now takes 200 years to cross that space, that isn’t expanding space, that’s increasing distance in stable space. This raises two issues; If the speed of light did increase, how would we even know it expanded, as the increased speed of the light would require increased energy and wouldn’t this speeding up blueshift the spectrum and eliminate any redshift?
    Otherwise, if it is increasing distance in stable space and all galaxies appear redshifted directly away from us, it would mean we are at the center of the universe.
    Gravity curves space because light traveling across it is bent inward from what would otherwise be a straight line. As gravity collapses mass, radiation expands the constituent energy. Are we really sure the effect of all the radiation crossing space doesn’t have the opposite effect on a particular beam of light? Since it isn’t being pulled toward a gravitational vortex, it isn’t curved, but would it be redshifted, since the cause is evenly distributed? A prism bends light, but we don’t say space is curved. An optical effect would explain redshift without the Milky Way being at the center of the universe. It would also eliminate the need for dark energy. The further light traveled, the more the effect would be compounded and eventually the source would appear to be traveling away at the speed of light, which would put anything beyond that over the horizon line.

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    Ellipsis– Quintessence could certainly mediate another force, as I mentioned in the post. But (as Jason says) that’s not what anyone has claimed to have discovered, and it may not even exist. And in particular, the thing that is making the universe accelerate is not the 5th force mediated by the hypothetical quintessence field — it’s the energy density of the dark energy.

  • Lawrence Crowell

    To call the Higgs field a fifth force might have to be qualified. Gauge fields have vector or chiral connections A on a principal bundle that under the action of the differential operator give F = dA + a/A, where F is a two-form who’s components are the fields, such as electric and magnetic fields in that case of EM. The Higgs field is an n-tuplet of scalar fields which have a quartic potential. A component of the Higgs field is absorbed (Goldstone boson) which restricts the local gauge freedom of a field. That breaks the symmetry of the gauge field, such as with the standard electroweak model.

    What follows is a bit long and somewhat technical, but it indicates my thinking about some of the physics lore common today, which frankly I think is beginning to sound like the luminiferous aether of the 19th century. The term negative pressure in a sense is a matter of “culture.” It stems from the definition of the momentum-energy tensor

    T^{ab} = (e + p)U^aU^b + pg^{ab},

    For e energy density and p pressure. The energy density is identified by some as the zero point energy of quantum mechanics, which I will get to below, and p is a pressure associated with this ZPE. If we identify the trace of this as the cosmological constant we get / = k(e + 3p). The gradient of the energy leads to a term that vanishes for p = -e, or where we get the infamous w = -1, and experimental data computed from WMAP data w = -1.02 {+/-.12/.19}. Not bad and it appears as if we are on to something.

    But not so fast!!! The condition that w = -1 is a local condition, whether this pertains globally is unclear. There is a little business of Killing vectors which project onto momentum vectors p^a = mU^a, where U^a is a vector along the geodesic flow lines, so that K_ap^a = constant. A Killing vector exist along a direction if there is a constancy defined along that variable. In a stationary metric we do have a Killing vector K_t, which when projected on a momentum four-vector give K_tE = constant. This pertains for a black hole, but not a cosmology. The metrics for cosmologies are time dependent and so there is not a defined timelike Killing vector. So what does p = -e or w = -1 buy you? It is a thermodynamic-like equation of state which constrains energy to momentum locally. Cosmologies will permit spacelike or momentum Killing vectors, and this equation applies locally. But we have no theorem which tells us whether this applies globally, or throughout the entire cosmology.

    There is also the issue of the ZPE. It would appear that in our modern world we have something analogous to the aether, and it is a basic problem in physics today. This is the quantum vacuum, or zero point energy. This emerges as a consquence of quantization. The Hamiltonian for the classical harmonic oscillator is

    H = 1/2m(p^2 + m^2 omega^2 q^2)

    for omega the frequency of motion for the harmonic oscillator of mass m. The standard quantization procedure is to construct the operators

    a = sqrt{hbar/2m omega}(m omega q + ip),
    a^* = sqrt{hbar/2m omega}(m omega q – ip),

    where * = dagger, which gives the Hamiltonian for the quantum system

    H = hbar omega/2(a^*a + aa^*).

    By the addition of hbar omega/2(a^*a – a^*a) = 0 this may be converted to the form

    H = hbar omega(a^*a + 1/2).

    The energy eigen-states for this operators are a ladder |n>, n = 0, 1, 2,… infinity, where for the zero state the expectation of the Hamiltonian on this vacuum has an energy hbar omega/2. The harmonic oscillator is used as the solution to many quantum wave problems, where a field in space or spacetime is modelled as a harmonic oscillator at every point. The index n corresponds to the number of particles in the system. For n = 0 the quantum system is a vacuum. Since relativistic fields occur for a range of momenta p , where each has its operators a(p), a^*(p), the vacuum state then has a zero point energy (ZPE) given by a

    E = sum hbar/2 int_0^infinity d omega(p).

    The vacuum then in principle has an infinite amount of energy.

    Often this ZPE is dropped since it contributes nothing to most physics. One way this is done is to say that we can commute the operator a past a^* to drop the term. This sounds a bit like cheating, but since the ZPE contributes nothing to physics this move causes no “harm.” We might think back to the classical harmonic oscillator and write it as

    H = 1/2m(p^2~+~m omega^2 q^2) + i omega/2(qp – pq).

    The imaginary term might be objected to since classical mechanics involves real variables, but this term is classically zero. So this Hamiltonian is identical to the standard Hamiltonian, and we may then quantize this Hamiltonian to obtain H =hbar omegaa^*a, and the hbar omega/2 term is removed. The ZPE has been eliminated by treating the classical Hamiltonian in a particular way. This tends to show that abolute energy values are not important, relative energy differences are. Each E_n = hbar omega n energy eigenvalue is relative to the vacuum energy, which we may set to zero. By the same token a voltage is measured across a component, never at a point on a circuit. So the ZPE can be seen are mostly an artifact of quanitzation, and its physical contribution negligable or nonexistent.

    One might then ponder what happens with gravity? After all if this ZPE turns out to exist then it should have a gravity component. We might think of there being gravitons which couple to the vacuum, and at least in a linearized sense there are these quantized spin-2 pp-waves which couple to loops and other stuff common to the perturbative theory in QED. Maybe, but the problem is that if one naively takes the ZPE stuff an computes it contribution to the cosmological constant, and it is huge. Particularly if we assume that quantum gravity fluctuations near the Planck scale are &R ~ 1/L_p^2 this curvature is ~ 10^{68}cm^{-2} and the expected cosmological constant is 123 orders of magnitude from what it is currently estimated to be. Getting rid of the ZPE as above might be convenient if the cosmological constant were indeed zero, but we are finding that it is not zero. It is small, but not zero. This muddies up the story considerably. I believe it was Lord Kelvin who commented that everything was figured out, except that annoying problem of blackbody radiation and the vanishing of the aether by Michelson & Morely. Might it be that we are bumping into certain limits of what current physics can deliver?

    I will make this as brief as possible. The Hamiltonian constraint in ADM relativity H = 0 in the canonical quantization leads to Hpsi[g] = 0, which is similar to a Schrodinger equation. If you add a harmonic oscillator field to this system it has eigenvalues which give a stationary phase condition. Then we have that there is a Schrodinger equation

    iK_tPsi[g] = HPsi[g], i = sqrt{-1}

    for K_t = &/&t. So we have “manufactured” a time here by placing a scalar field on the spacetime manfolds. If the classical spacetimes (M, g) that are the configuration variables for the wave function(al) are stationary then K_t is a Killing vector. It turns out that not all configuration variables are classical spacetimes, but that I will forego for now. Now if you have an entanglement of wave functionals over different metrics then do we have a global K_t? No! And if we did it amounts to a violation of general covariance of general relativity, for it is a coordinate dependency on spaces. So we have a bit of a conundrum here in defining time and energy in quantum gravity as well as a problem of defining a global definition of energy in cosmology. These “breakdowns” are linked by a general principle.

    Lawrence B. Crowell

  • Lawrence Crowell

    The speed of light is a local thing. In your lab, which is in a flat spacetime, you will always measure the same speed of light. If you watched a light beam pass through a cloud of gas near a black hole you would see its course through the cloud just as laser beams or headlamps illuminate a fog. You would find the light speed apparently slowed down. There are of course a number of ways of looking at this, in particular since time on clocks near the black hole are slowed down you are witnessing an apparent slowing down due to the gravitational time dilation. A similar thing happens with inflationary cosmology. And indeed many distant objects in the universe we observe we could never send a signal to. They are beyond the cosmological horizon distance r = sqrt{3/ /}, in DeSitter cosmology, but their photons can reach us. It is somewhat similar to an observer in a blackhole beyond the Schwarschild radium who can see out, but can’t communicate out. For this reason the universe up to the deionization epoch we detect in the CMB is 70 billion light years away, while the timeline for the universe is 13.7 billion years. Mass-energy has been comoved away on the expanding space of the universe more than it has been moving away in the ordinary sense.

    Now here is a bit of a puzzle. If the universe is 150 billion lightyears across to the CMB deionization limit, but only 13.7 billion years in age, then we are causally disconnected from anything out there — we can’t induce an effect out there, the light from our galaxy emitted now will never reach those regions. Now focus in on the early rapid inflationary model, where there was a rapid accelerated expansion of the universe. In the same way most of the universe that tunnelled out of the vacuum or vacua were quickly diconnected causally, but yet the Higgian inflaton froze out gauge restrictions or broken symmetry “everywhere.” How could that have happened?

    Lawrence B. Crowell

  • Jason Dick

    Lawrence,

    During inflation, regions which were once causally connected rapidly grow to sizes much larger than the horizon size. This explains why things today which are causally disconnected (most of the observable universe) are still correlated: once they were causally connected, during the epoch of inflation.

    The picture of why this happens is pretty simple: during inflation, when the universe was dominated by a nearly constant energy density, the horizon size was nearly constant. But if the universe is expanding with a nearly constant horizon size, then any linear perturbation of any size quickly grows to be larger than the horizon, and the perturbation becomes causally disconnected from itself: it becomes “frozen.”

    Then, as the universe’s expansion slows down during the radiation and matter-dominated regimes, the horizon scale rapidly increases. So scales that were first generated during inflation, then expanded beyond the horizon size, re-enter the horizon.

  • Lawrence Crowell

    Agreed that during inflation the horizon, if we use a DeSitter radius r = sqrt{3/ /}, is smaller as / is much larger. There are plenty of models for / = /(phi, phi-dot) for phi a Higgsian inflaton field. During this period the Higgsian field is settling into it degenerate vacua, or some minima on the “landscape.” The so called phantom energy situation of the big rip forces r to decrease until it collapses in around averything, ripping even nucleons apart. The problem still remains though, for even if some measure of causal connection is restored after inflation, it is during the period where r is much smaller than the Higgs field set the vacuum expectation for fields of broken symmetry. There is also a problem with any idea that the universe had a vacuum of constant energy.

    From the momentum energy tensor

    T^{ab} = (e + p)U^aU^b + pg^{ab} (e = energy density)

    the covariant derivative of the energy density is simply the ordinary “gradient” or directional derivative

    nabla e = e_{,a}U^a = -(e + p)U^a_{;a},

    which has a curious dependency on the chart or coordinate system. So globally the covariance of this equation is either local or exists for some special circumstances. The p = -e ( or dark energy condition for w = -1) is apparent here which gives nabla e = 0. Now we can set this in a first law of thermodynamics setting with

    dU = -dW + dQ

    And set the “work” as pdV and the energy at equilibrium (the ZPE etc) as dQ and get

    dU = -pdV + edV

    and the volume may be thought of as evolving along a set of flow lines so its evolves by the geodesic equation. This is essentially another way of describing our equation for nabla e — which is not covariant, or is chart dependent. From a thermodynamic perspective the differentials are exact differentials that apply for closed systems. A cosmology in an eternal inflation is not a closed system in a strict thermodynamic sense. So these considerations are useful in a local setting, but we really have no theory which can tell us if they apply globally. Thus energy is really an ineffective concept in general relativity.

    The issue is similar to difference between the standard and Killing times with the accelerated observer. This is the situation which occurs for an accelerated observer who detects a thermal bath of radiation. The spacetime on the accelerated frame is calle the Rindler space as the causal region the observe can interact with is partitioned by horizons, or a split horizon along two different null direcitons. A Minkowski metric for the Rindler space is

    ds^2 = -x^2 dt^2 + g_{ij}dx^idx^j

    so that on ds = 0 we can find the spatial metric

    dc^2 = (g_{ij}/g_{tt})dx^idx^j, g_{ij}/g_{tt} = &_{ij}/x^2

    or Fermat metric which is a Poincare half-plane when restricted to two dimensions. Take this space and conformally fold it into a Poincare disk (again restricted to two dimensions) and you have the spatial metric for a DeSitter cosmology for r = 0 to sqrt{3/ /}. The two dimensional representation of this is seen in the Escher disk of tesselated figures that pile up near the edge of the disk. In Robert Wald’s book “Black hole thermodynamics … ” he discusses the Unruh radiation according to the deviation between standard time. Under this “map” this deviation between Killing and standard times manifests itself between timelike directions for different observers in the DeSitter cosmology. This then means that the vacuum state for the universe is not unitarily equivalent everywhere, where this is tied to coordinate dependent time directions on different charts of the spacetime. This is also one reason why there is Hawking-Gibbon radiation from the event horizon at r = sqrt{3/ /}.

    So we have a problem here with defining not only energy, but this appears connected with a unitary inequivalence of the vacuum in different regions of the universe, both now and during the early moments of inflation.

  • Jason Dick

    So we have a problem here with defining not only energy, but this appears connected with a unitary inequivalence of the vacuum in different regions of the universe, both now and during the early moments of inflation.

    Nope. You only need a small region of the universe to have nearly constant energy density in the right sort of field that can drive inflation (about one horizon scale at that time, which would have been ~10^-30m or so). Any inhomogeneities that exist will be blown so far apart so rapidly that they might as well not have existed at all: all that remain are the zero-point fluctuations in the inflaton field itself. So, in the context of inflation, you don’t need to worry about widely-separated points not being causally connected: all scales that we observe, even much larger scales than we observe, were within the horizon during the epoch of inflation.

    Naturally this only works if inflation lasts long enough.

  • Lawrence Crowell

    The region of space bounded by the horizon will have local regions of vacua which are not unitarily equivalent. If the horizon length is very small then these local regions of different vacua are proportionately smaller. This is what gives rise to Hawking-Gibbon radiation, analogous to the Hawking radiation from black holes. The matter and radiation we observe in the universe may have been generated by this process, along with some sort of symmetry breaking process and a CP violation which gave rise to a dominance of matter over anti-matter. Of course this happened when the horizon distance was very small, which then inflated out to its current distance.

    Lawrence B. Crowell

  • http://tyrannogenius.blogspot.com Neil B..

    Lawrence, folks: Isn’t it true, that the easy way to track the progress of light across the cosmos is to pretend that the scale of objects and speeds is shrinking, while the separations between galaxies (those stationary relative to the background radiation, the neo-standard of rest) stay the same? So, I imagine that c in my adjusted coordinate system is a function of time (the universal local time since the BB for any observer at that CBR standard), the inverse of the cosmic scale factor. Then I can track how it progresses. In a flat space this also allows to find apparent sizes, since we imagine photons to continue in straight lines by symmetry. (So, think of photons coming from opposite sides of a galaxt at time t1, then as the galaxy “shrinks” they continue as before – the distant galaxy will appear as big as if it was still only as far as when the light was emitted, as you might intuitively expect.)

    Presumably one can adapt this to tardyons by making adjustments for relativistic transformation (so that a particle emitted by me at 0.6c will have proper velocity addition as it passes a galaxy receeding at 0.001c etc., hence the galaxy finds it locally whizzing by at 0.6c – 0.00064c. IOW, the infinitesimal idealized velocity correction is gamma^(-2) times the simple Hubble factor.

  • http://tyrannogenius.blogspot.com Neil B..

    Note, that I meant “pretend” that galaxies are shrinking rather than imagine that the “actually are.” Hoyle and some others thought the two equivalent, but: suppose we imagine that “things” actually shrink with time, but that dynamical rules stay the same relative to the old standard. Then, a particle emitted and coasting through space would seem to speed up, since it be passing shrinking length standards while keeping much of its original velocity (or at least, even if the net result was not a velocity increase, inhabitants could tell the difference.)

  • Lawrence Crowell

    The spacetime is not flat, even if the space is flat. The Ricci curvature terms are of the form R_{00} = a” – 3(a’)^2, primes = time derivative and a the FRW radius, which means that even if the space is flat it’s extrinsic curvature with respect to how it is embedded in spacetime is not. So spacetime is not exactly flat. Galaxies are moving out not because they have a velocity as we normally think of it, but because the space they exist in is expanding outwards.

    The Hubble factor H enters into the cosmological constant as

    / = 3H^2(Omega)/c^2

    where we can set Omega =~ 1. For a radius r = sqrt{3/ /} the metric factor A = 1 – /r^2/3 is zero in the line element

    ds^2 = -Adt^2 + (1/A)dr^2 + r^2d(angular parts).

    For this line element one can compute curvatures and the rest and find that the spacetime is not flat.

    As it turns out it is not possible to find a quantum vacuum for a quantum field that is unitarily equivalent throughout the spacetime. As Wald points out with Unruh radiation the departures between the Killing time and standard time are a measure of this departure. This spacetime shares some features similar to the Rindler spacetime for an accelerated observer, and different observers will have different measures of time. The departures between these are involved with the lack of a single equivalent quantum vacuum for the cosmology. This is why it is that the cosmological event horizon has a thermal temperature, which is very very tiny. This is not to be confused with the CMB temperature, even though that may be ultimately due to the same physics during the inflationary phase.

    This may sound rather odd, but it is not possible to define energy conservation in a cosmology and there is really no univerally defined concept of time either. One person’s time “here” is different than “there.” The invariance of time translation is then not something which can be established globally. The generator of time translation by Noether’s theorem is the Hamiltonian (energy) and so this means that energy or energy conservation can’t be established globally.

    Lawrence B. Crowell

  • Jason Dick

    Actually, it is possible to define energy conservation, using the Hamiltonian formalism. Granted, I don’t know a whole lot about it, but supposedly it’s a valid construct there.

  • John Merryman

    Lawrence,

    The speed of light is a local thing. In your lab, which is in a flat spacetime, you will always measure the same speed of light. If you watched a light beam pass through a cloud of gas near a black hole you would see its course through the cloud just as laser beams or headlamps illuminate a fog. You would find the light speed apparently slowed down. There are of course a number of ways of looking at this, in particular since time on clocks near the black hole are slowed down you are witnessing an apparent slowing down due to the gravitational time dilation. A similar thing happens with inflationary cosmology.

    You are right, that the speed of light is a local effect and thus logical that it might slow near a black hole, but the expansion of the universe isn’t a local effect, presumably it is a universal effect, so wouldn’t the speed of light everywhere be increasing as the universe and the total space, local and otherwise, expands?

  • Jason Dick

    You are right, that the speed of light is a local effect and thus logical that it might slow near a black hole, but the expansion of the universe isn’t a local effect, presumably it is a universal effect, so wouldn’t the speed of light everywhere be increasing as the universe and the total space, local and otherwise, expands?

    The speed of light is only a well defined quantity locally. When talking about the speed of light far away from the observer, there is no objective method of stating what that speed is. So, in essence, it all depends upon what arbitrary method of estimating the speed you choose, just as long as you’re aware that an observer at the location that you’re actually measuring the speed would always measure the same speed of light that we measure.

  • Lawrence Crowell

    To paraphrase the statement about politics, “All physics is local.” The speed of light is something defined on a local frame. It applies on all local frames, but if you tried to measure the speed of light “there,” say by watching a pulse of light cross a nebula and illuminate the dust and gas as it goes, you might observe something different.

    There is a lot of mathematical structure to this involving local charts on a space (what is called a manifold) and how on the overlap of these charts there exist transformation functions and connection coefficients. This extends to gauge theories, such as electromagnetism, as well. If in one chart a wave function has one phase and in the other it has a slightly different phase then the change in this phase in a transformation between the charts determines fields. The transformation functions determine something called the vector potential A, which in an elementary setting can determine the magnetic field by B = curl A or the electric field E = -&A/&t. General relativity is similar to this, but the charts are not some internal phase but changes in the space or spacetime itself, which leads to curvatures — and curvatures define what we call gravity.

    So everything is built up from local regions or charts, and in relativity theory this is a flat spacetime frame. If the region is small enough it is flat, or approximately so. This is where you define what time is by your clock and where you measure the speed of light and observe the motion of bodies. Newton’s first law “presaged” this for, “A body remains in a constant state of motion unless acted on by a force,” means one must observe physics from these inertial frames.

    Then we come to the issue of cosmology, where we are trying to understand a global system, but one which is not globally flat or with a constant phase, and frankly does not even have a globally defined quantum vacuum. So we are saying “All physics is local,” and we are trying to understand a nontrivial global system — think globally, act locally.

    There are a few things we might consider. The entire cosmology is probably given by a grand path integral or partition function. The initial and final points of the path integral should be related by some grand-global transformation function, similar to a development operator or e^{iS} that maps the initial configuration to the final one. We might of course suppose that this development is some grand product of such objects which define the foliation of spaces in what we locally call “time.” The initial configuration is a fine grained set of many vacua with some sort of superselection rule. The final state is hard to know, for we will never observe it. Yet we can make some reasoned guesses. The accelerated universe, known by SN1 data and WMAP, means the universe will asymptotically approach a pure DeSitter cosmology. Further, Hawking-Gibbon radiation will cause the cosmological horizon to receed away to infinity. I am not considering phantom energy or big rip for various reasons. This means the target or attractor point in superspace for this is a Minkowski spacetime — a perfect void with zero mass-energy content inside.

    The reason for thinking about the ultimate fate of the universe is that if the final point is a Minkowski space (at conformal infinity, with AdS/CFT etc), then this gives us an anchor we understand. A Minkowsi space is one with a globally defined time, the speed of light is uniform everywhere and so forth. This is the configuration of maximal entropy as well, for all information about the universe prior is completely lost, which is S_{max} in a Shannon-Khinchin sense. Then there is the initial state defined by a fine grained set of distinct and inequivalent vacua. All we need to do is find a grand transformation principle that links the two.

    As a bit of a final side note, Christianity is based on the idea that light triumphs over dark. Hmmm…., given what we might suppose about the future of the universe, stars will wink out, things are absorbed into black holes, black holes quantum decay in 10^{100} years and so forth, and if “at infinity” the whole thing ends up in a perfect Minkowskian void, then I’d say darkness wins.

    Lawrence B. Crowell

  • John Merryman

    Jason, Lawrence,

    The speed of light is only a well defined quantity locally. When talking about the speed of light far away from the observer, there is no objective method of stating what that speed is. So, in essence, it all depends upon what arbitrary method of estimating the speed you choose, just as long as you’re aware that an observer at the location that you’re actually measuring the speed would always measure the same speed of light that we measure.

    The reason for thinking about the ultimate fate of the universe is that if the final point is a Minkowski space (at conformal infinity, with AdS/CFT etc), then this gives us an anchor we understand. A Minkowsi space is one with a globally defined time, the speed of light is uniform everywhere and so forth. This is the configuration of maximal entropy as well, for all information about the universe prior is completely lost, which is S_{max} in a Shannon-Khinchin sense. Then there is the initial state defined by a fine grained set of distinct and inequivalent vacua. All we need to do is find a grand transformation principle that links the two.

    I realize there are limits on what we can measure, but according to theory, if two galaxies are 100 million lightyears apart now, when the universe has expanded to twice its current size, are they still one hundred lightyears apart, since the lightyear is our most fundamental measure of interstellar and intergalactic space, or are they 200 lightyears apart?
    As I see it, both answers cause problems for Big Bang/Inflation theory. If they still appear 100 million lightyears apart, then how can we say the space is expanding, since our most basic ruler is expanding along with it? Would it even redshift if the speed of light increases along with the expansion?
    On the other hand, if they are 200 million lightyears apart, that’s not expanding space, that’s increasing distance in stable space and this raises a series of issues. For one thing we would appear to be at the exact center of the universe. That would be on the list of internal problems. On the list of external problems, pre-existing space would be subject to quantum energy and the inflation stage in this sea of energy would burn everything to a crisp, to say the least.

    As for Inflation; Why did it slow down to the observed rate of expansion? It would seem the inertia of this stage would need something more then observed gravity to brake it down to the current rate.

  • John Merryman

    Lawrence,

    As a bit of a final side note, Christianity is based on the idea that light triumphs over dark. Hmmm…., given what we might suppose about the future of the universe, stars will wink out, things are absorbed into black holes, black holes quantum decay in 10^{100} years and so forth, and if “at infinity” the whole thing ends up in a perfect Minkowskian void, then I’d say darkness wins.

    People can be like bugs in the night. We head for the light. Sometimes it’s best to go with the herd. Sometimes it’s best to go the other way. Fortunately we have somewhat more brains then bugs do.

  • Lawrence Crowell

    The galaxies at 100 million light years at time = T will be at more than 200 million light years at time = 2T, where here the time is measured by the Hubble relation and distance. That distance is then given by Cepheid variables or SN1 or … .

    The rapid rate of expansion was stopped because we might think of the space itself as expanding. Now there are some problems with this, for this viewpoint runs into subtle problems with covariance.

    As for “the dark,” well we humans are afraid of the dark. It is a strange factor in our species. And if you have ever been in the wilderness at night it can be really dark and disorienting. Right now with Hannukah and Christmas and what was call Sol Invictus the idea was at the solstice to build fires to try to bring back the light. Lighting menorahs or Christmas trees and so forth goes back to some ancient ideas and some psychological aspects of us two legged biological misfits.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    he galaxies at 100 million light years at time = T will be at more than 200 million light years at time = 2T, where here the time is measured by the Hubble relation and distance. That distance is then given by Cepheid variables or SN1 or … .

    That’s what I thought and it does raise the question of what dimension of space lightspeed is measuring. Conventional Dppler effect isn’t about expanding space, it’s about increasing distance in stable space. The train is heading down the tracks, the tracks are not being stretched. The same would seem to apply here, in that lightspeed represents the tracks. So how is it that we say that “space” is expanding, when our most basic measure of space isn’t?

    The rapid rate of expansion was stopped because we might think of the space itself as expanding. Now there are some problems with this, for this viewpoint runs into subtle problems with covariance.

    In a lot of cases, it’s the subtle details that are trying to tell us that some initial navigational errors have us off course and reviewing what has been done, before continuing to dig ourselves in further, is wise.

    As for “the dark,” well we humans are afraid of the dark. It is a strange factor in our species. And if you have ever been in the wilderness at night it can be really dark and disorienting. Right now with Hannukah and Christmas and what was call Sol Invictus the idea was at the solstice to build fires to try to bring back the light. Lighting menorahs or Christmas trees and so forth goes back to some ancient ideas and some psychological aspects of us two legged biological misfits.

    There are some definite motivational impulses at work here. I think that “seasonal affective disorder” is a natural psychological gearshift between fat and happy summer and downshifting for the climb through winter.

  • Lawrence Crowell

    Measurements of distant galaxies is a Doppler shift, but that in general is a gravitational Doppler shift. For a black hole a light source near the horizon will have a gravitational Doppler shift. With cosmology a similar redshifting occurs due to the curvature of spacetime.

    When it comes to the halting of inflation, think of a balloon expanding as gas is forced into it. Now assume that this balloon is being inflated by a helium pressure tank. It inflates rapidly and then the valve is cut off so it stops or inflates at a much slower rate. The rapid exponential inflation of the universe pushed the nascent cosmology from a little sphere smaller than a nucleus to something maybe several meters in radius, and then as the Goldstone analogue of the Higgs field (here the inflaton) was absorbed the inflationary pressure stopped. The space or manifold then expanded onward from there. In part this is one reason that the observable universe may constitute one part in 10^{50} of the whole thing.

    Lawrence B. Crowell

  • http://tyrannogenius.blogspot.com Neil B.

    Lawrence, thanks a lot for your erudite discussions of cosmology issues. I see stuff about you on the Internet, but no clear main web page – let us know if you have one. I think, that in the Robertson-Walker metric one can indeed track the progress of photons in the manner I stated (and sure, that is based on the idea of space expanding and not of ordinary velocity differences – so maybe I screwed up the issue regarding sub-c particle progression.)

    I wonder what you think of the thought experiment I posed in the thread “Thanksgiving” about hard containers impeding space contraction, such as #3,5,6 and a final thought in #35:

    There are contradiction problems if you try to imagine what happens to all the bodies in expanding/contracting universes if some things are impeded by material barriers/obstructions and other things just move like dust in free fall.

    I meant, things like space being filled with hard balls with little test masses in the middle: when the balls crunch together, symmetry implies that the central masses should stay in each center, yet from a local Newtonian approximation, the test masses farther from a “favored” central mass should continue moving toward it, etc, (IOW, it can’t be consistent.) And, even if we accept some consistent way in GR to keep things symmetrical if there is a uniform distribution of such extended objects, what about local variations, such as a large region of balls closer together than the rest? The behavior has to be consistent with Newtonian expectations at some extent of distribution, which brings up interesting questions of how the two realms transition.

  • John Merryman

    Lawrence,

    Measurements of distant galaxies is a Doppler shift, but that in general is a gravitational Doppler shift. For a black hole a light source near the horizon will have a gravitational Doppler shift. With cosmology a similar redshifting occurs due to the curvature of spacetime.

    I have no trouble with redshift due to the “curvature of spacetime.” I disagree that it is due to objective recessional velocity.
    I certainly never set out with the intention of questioning modern physics, since my original motivation was learning the givens in this transitory life. The point where I started to question how it is postulated was learning that for the universe to be as stable as it is, Omega had to be very close to, if not equal to 1. If the expansion of space is being balanced by the contraction of gravity, then it seemed logical to assume the universe as a whole is not expanding, as gravity would neutralize the expansion effect. So it seemed the most logical reason these two effects would be in equilibrium was that there was a convective system of sorts and they were opposite sides of a larger cycle.

    Yes, the light of distant sources appears redshifted, but if this is due to the curvature of spacetime, then it is an effect similar to trying to walk up the down escalator. The space may be expanding, but it is also contracting into gravitational wells at the same time. The balloon has holes in it. The pressure of this expansion isn’t causing some larger expansion because we are not measuring the pressure lost to gravity.
    To put this in the analogy of gravity as a ball on a rubber sheet; Where there is no ball, the sheet is not flat but rises in gentle hills, that if were bulldozed into those gravity wells, would yield flat space. Thus Omega=1.
    Light is redshifted when it travels over these hills of spacetime curvature and the longer it travels on the hills and doesn’t fall into the wells, the more it is redshifted. Since this effect compounds, the further light travels, the faster the source appears to recede. Eventually it is redshifted enough that the source appears to recede at the speed of light and any source past this point is over the horizon line of visibility.
    I put “curvature of spacetime” in parentheses because it is the vortex of gravity which causes curvature, as well as contraction, but since the expansion effect is evenly distributed across space, it doesn’t “curve” around anything, it just expands. That’s why it is redshifted. To me, this is the cosmological constant and the whole Big Bang/expanding from a point scenario and all the patchwork required to hold it together, is based on an incomplete picture.
    The result is also a much less complex picture, as Inflation and Dark Energy are two factors that would be unnecessary.
    If we were to futher extend the analogy of a convective cycle, galaxies and the black holes at their center would be gravitational storms around the eye, with whatever falls in being ejected as charged particles out the poles. While the CMBR, up to 2.7K, would be the stable level of radiation in the atmosphere of space, below its dew point. Above this and it starts to condense back out as the most elemental forms of gravitational contraction and eventually what might be considered mass.

  • Lawrence Crowell

    I think there is a bit of confusion. John Wheeler called gravitation geometrodynamics, in that it is the dynamics of space, which defines a foliation in spacetime. So in the case of a cosmology we might think of points in space as dynamically receeding away from each other. Any particle in the space get dragged along for the ride, and in fact that is exactly what is happening for it is a form of frame dragging. It is in this way that an expanding universe is measured by a gravitational redshift.

    The term geometrodynamics is confusing, for really general relativity determines curvatures and intervals involved with relationships between particles. General relativity does not do this really with points, for if it were to do this the theory would not be generally covariant by specifying a point by point coordinate dependent map. Yet we can help but use the idea of there being points moving away from each other.

    The bit above about little gravitational wells, those are what galaxies are bound within. This is what keeps galaxies from flying apart due to the expansion of the universe.

    Lawrence B. Crowell

  • Lawrence Crowell

    Neil B. on Dec 12th, 2007 at 8:58 am
    Lawrence, thanks a lot for your erudite discussions of cosmology issues. I see stuff about you on the Internet, but no clear main web page – let us know if you have one.

    ————–

    No I don’t have one, though I am intending to do so. I am just a bit lazy at this time.

    As for things impeding the expansion of space, in principle that can happen and there have been ideas about huge vacuum domain walls in the universe. I am not a partisan of these ideas, but very dense or massive objects can stop the expansion of space. In fact enough mass added to the universe, say by God, would halt the expansion of the universe and cause it to recollapse.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    So in the case of a cosmology we might think of points in space as dynamically receeding away from each other. Any particle in the space get dragged along for the ride, and in fact that is exactly what is happening for it is a form of frame dragging. It is in this way that an expanding universe is measured by a gravitational redshift.

    This goes back to my point about why doesn’t the speed of light increase, as space is expanding? Evidence for expansion is the redshifting of lightwaves, yet the speed of light is stable, so it would seem space suffers from schizophrenia.

    Possibly the problem is defining space in terms of its contents. We say space is curved because light passing a gravitational body is bent around it. On the other hand, energy and mass may be drawn into a gravity well, but the well doesn’t shrink because there is always new energy and mass being captured. Maybe the same is true for expanding space, in that while it may take a particular photon longer to cross intergalactic space, due to expansion/negative curvature/cosmological constant/constant waves of radiation from all sources and directions/whatever, the actual distance doesn’t increase, because this space, as defined by its contents, is also falling into these gravity wells. Sort of like it takes more steps to climb up the down elevator, but the floors are not actually moving apart.

    Geometry assigns zero to the neutral dimension of geometric forms, ie. points, lines and planes, but that is actually a virtual dimension. Any number multiplied by zero is zero, so the real geometric zero would be empty space, not any particular point. While geometry defines space, it doesn’t create it. The absolute isn’t a point, it’s the potential for any point. Empty space.

  • Garth Barber

    This goes back to my point about why doesn’t the speed of light increase, as space is expanding? Evidence for expansion is the redshifting of lightwaves, yet the speed of light is stable, so it would seem space suffers from schizophrenia.

    There is a crucial difference between the speed of an object through space-time and the expansion of space-time itself.

    The speed of light is determined locally.

    If you compare the time taken for a radio signal to come from a spacecraft with that predicted from its orbital ephemeris and then repeat when the signal has to pass close by the Sun you find in the latter case a extra delay has crept in.

    This delay might be thought to indicate that the speed of light has reduced, however in GR it is explained by an increase in radio-path length caused by the curvature of space-time around the Sun.

  • http://tyrannogenius.blogspot.com Neil B.

    This question may have been lost upthread, so again: is it so, we can track the progress of light in the cosmos by the device of pretending that objects shrink, stay in the same place, and the speed of light decreases according to the scale factor? This leads to a specific rate of travel relative to cosmic time (the time ticked since BB by the “stationary” galaxies, which presumably all see average isotropic CBR etc.) I wonder: would the difference between “space expanding” and “actual recession” be shown by whether relativistic velocity addition applied? I mean, if I shot a bullet away at 0.995 c etc, and it passed by a galaxy receding by expansion at 0.01c, would the galaxy consider (by its own standards, kinetic energy equivalence, etc.) that bullet now to be going at 0.995 (relativistic minus) 0.001c = 0.99499, or only at 0.985c (or maybe I neglected further corrections, but which standard applies to that part of the result)?

    Oh, pardon me to anyone I or others offended with mere, uninformed “cocktail party physics” chatter like this about philosophically deep and contentious foundations, while they labor here on very specific and clearly stated physics problems like band structure in semiconductors, bunching and antibunching of photons, branching ratios for bottom mesons, etc. :-|

  • Lawrence Crowell

    I second Barber’s comment. The speed of light is something measured in a local frame. We might better think of there being a spacetime curvature that on any local frame results in space being stretched out as measured by the local observer’s time.

    The thing that is a bit strange is the we have the Einstein field equation

    G_{ab} = -kT_{ab} + /g_{ab},

    and if the T_{ab} = 0 then we are left with G_{ab} = /g_{ab}if / = 0 then under the reversed trace it is easy to show that R_{ab} = 0, but for / =/= 0 we have an Einstein space where the Ricci curvature is proportional to the metric. We then go off and say that / = tr(T_{ab}) and assign an energy density and pressure and so forth as if it is a material momentum energy tensor — when it really is not. The problem is that the vacuum is not a “fluid,” or once we start thinking that way we may have jumped into some sort oflatter day aether idea.

    This is a part of Sean’s critique of the idea of a negative pressure. The Einstein field equation is nabla-field = source, common to all field equations. But really there is no source, but instead the space is Einsteinian. So there is not in the strict sense a negative pressure which “causes” the accelerated expansion of the cosmology.

    Lawrence B. Crowell

  • http://foranewageofreason.blogspirit.com Andrew Daw

    A “dark misleading force” that could explained given a cosmology based on a causal theory of quantum mechanics?

    So one can think that describing enough details of a cause acting in addition to the forces to account for quantum wave, spin and entanglement could finally explain how matter can persist as atoms and molecules despite the forces acting within and upon it.

    And then one could ask might not such causal quantum theory explain the large scake structure of the universe without the need for the dark matter that hasn’t been directly detected despite 20 years of experiments?

    And then suppose a theory of such a casuse that would act universally and nonlocally in addition to the forces could explain the close relationship between galaxy rotation described by Milgrom’s law and the acceleration in the expansion of the universe, as mentioned by Lee Smolin in his book The Trouble with Physics pp 210-2?

  • Lawrence Crowell

    If you are watching two objects traveling at relativistic velocities an observer on one of those objects would observe the second moving at a velocity as given by “boosting” to that frame. This results in the relativistic addition formula. If the two objects are moving at velocities u and v and you boost to the object with velocity u you would see the second object move at

    v’ = (v – u)/(1 – u^2/c^2).

    Now this is for special relativity, but for galaxies with modest values of z this works well enough. So if u = .8c and v = .9c then

    v’ = (.9 – .8)c/(1 – .64) = .28c.

    So on the frame travelling at u = .8 you’d see the object travelling at v = .9 relative to the original frame moving with velocity .28c. I’ll leave it as an exercise to consider the particular case above.

    The dark mysterious force is really a manifestation of spacetime being an Einstein space. In this case the Ricci curvature is equal to a constant times the metric. This is why there is a subtle issue of assigning the accelerated expansion as due to a negative pressure. To do so is to assign this to a source of gravitation or curvature, which is not entirely the case. The origin of this, to use that language which is not entirely appropriate, may be due to the quantum substructure of spacetime. The idea of a negative pressure suggests this as well, for there it is associated with the zero point energy of the vacuum. Though I think there are questions about the reality of this ZPE and our exploitation of this to model the cosmological constant, where it has pressures and the rest, I think illustrates something very incomplete about our understanding of this problem.

    Lawrence B. Crowell

  • John Merryman

    Garth,

    If it’s space expanding, it is local.

    Lawrence,

    The problem is that the vacuum is not a “fluid,” or once we start thinking that way we may have jumped into some sort oflatter day aether idea.

    This is a part of Sean’s critique of the idea of a negative pressure. The Einstein field equation is nabla-field = source, common to all field equations. But really there is no source, but instead the space is Einsteinian. So there is not in the strict sense a negative pressure which “causes” the accelerated expansion of the cosmology.

    Einsteinian space measures the medium, not the geometry. Spacetime may curve, but it’s the light we measure.

  • http://www.gregegan.net/ Greg Egan

    There’s a very simple result based on symmetry and Killing’s theorem that yields all cosmological redshifts (whether for photons or material particles) in one stroke. (See e.g. Wald’s General Relativity section 5.3)

    The result of this is, for any object in free fall:

    p_2 / p_1 = a(t_1) / a(t_2)

    where p is the momentum of the object, measured by an observer at rest in the cosmological coordinates, and a(t) is the scale factor for the universe.

    It makes no difference whether the object is a photon or a meteor, how far it travels, and what a(t) does between t_1 and t_2 (so long as it’s a smooth function that remains positive); in a homogeneous, isotropic universe this result will always hold exactly.

    Killing’s theorem gives the relationship between the tangent to a geodesic and a direction that generates a symmetry. For example, suppose you are travelling along a great-circle route on the surface of the Earth, at a uniform speed. At any given latitude, theta, consider the component of your velocity that points east-west, and call it e(theta). It’s not hard to verify that:

    e(theta) r(theta) = constant

    where r(theta) is the radius of the circle of latitude. This in turn means that:

    e_2 / e_1 = r(theta_1) / r(theta_2)

    What’s more, this result will still hold if we replace the spherical surface of the Earth with any surface of revolution, however weird and complicated. So long as you follow a geodesic at a uniform speed, the component of your velocity in the direction that generates the surface of revolution will be “red-shifted” exactly in inverse proportion to the radius of the circle of revolution you’re on.

    In both cases, it’s the same simple underlying geometrical principle.

  • John Merryman

    Greg,

    The problem isn’t with the math for measuring redshift, but the reality of what is being measured. As you describe it, redshift is due to the classic Doppler Effect of motion in a stable medium/geometry causing light/sound waves to be shifted(red or blue) relative to the rate the source is receding/approaching. The problem with applying this concept to cosmological redshift is that if it is classic Doppler Effect, where the redshift is caused by recessional velocity in a stable medium/geometry of space, then it would appear that we/the Milky Way, are at the center of the universe, because all the other galaxies appear to be directly redshifted away from us. Big Bang Theory was amended by saying that it is space itself that is expanding and everything is the center of its own perspective. This is a reasonable solution, except for the point I’ve been raising, that if space is expanding, then our most fundamental measure of it, the speed of light should expand along with it, otherwise C is measuring a stable, not an expanding dimension of space. The solution really does lay at the heart of Relativity, as Lawrence keeps hinting at, but as it is currently formulated, Relativity Theory hasn’t fully escaped classical concepts of time and space. As I keep pointing out, three dimensions are a coordinate system, not space itself and every clock is its own dimension of time, since time is a consequence of motion, not the cause of it. What this means is that cosmological redshift is due to relativistic effects, ie. a cosmological constant, which is, just as Einstein originally proposed it, a balance to gravity that results in a stable universe, not one which is actually expanding or contracting.

  • http://www.gregegan.net/ Greg Egan

    As you describe it, redshift is due to the classic Doppler Effect of motion in a stable medium/geometry causing light/sound waves to be shifted(red or blue) relative to the rate the source is receding/approaching.

    That’s not “as I describe it” at all. Cosmological redshift is best described in terms of expanding space, and I have no idea why you imagine that I’m describing it in terms of relative motion. As others have explained, and as I entirely agree, relative motion is a poorly defined concept for objects separated by cosmological distances.

    This is a reasonable solution, except for the point I’ve been raising, that if space is expanding, then our most fundamental measure of it, the speed of light should expand along with it, otherwise C is measuring a stable, not an expanding dimension of space.

    Whether you think the speed of light “should” or “should not” increase as part of your notion of what it means for space to expand is beside the point. The thing is, there is a perfectly coherent notion of space expanding without the speed of light changing, and that notion is the one asserted by cosmologists. This is clearest in the case of a finite universe, when you can talk about the total volume of the universe at any instant of cosmological time, and that volume is increasing. The speed of light stays the same, and as a consequence the transit time for light between any two galaxies increases. This notion of expansion is perfectly coherent as an idea, and perfectly consistent with observation.

    What this means is that cosmological redshift is due to relativistic effects, ie. a cosmological constant, which is, just as Einstein originally proposed it, a balance to gravity that results in a stable universe, not one which is actually expanding or contracting.

    I’m sorry, but this is simply false. General relativity makes perfectly clear predictions for redshift in a stable universe where a cosmological constant balances gravity: it says that there are none. So there are no relativistic effects in the situation your propose that would explain the observed redshifts.

  • Lawrence Crowell

    Killing vectors are problematic in cosmology. If a spacetime has a Killing vector K = K^a nabla_a, then the Killing theorem is that K as a differential operator acts on the metric as

    K*g_{ab} = 0,

    which is defined according to the Lie derivative. For the metric as a two-entry device:

    g_{ab} = g(X_a,X_b)

    K*g_{ab} = Lie_K g(X_a,X_b) = 0.

    Now that we have set that up let us consider a line element for a cosmology. The FRW type of line element

    ds^2 = g_{ab}dx^a dx^b

    ds^2 = -dt^2 + R^2(dr^2 + r^2 d(angular stuff)^2),

    where R is the “radius” with R = R(t). Now let us propose there exists a timelike Killing vector K_t = A(&/&t), & = partial. It is not hard to see that this K_t will not give zero on the metric! So there is no time-Killing vector. Now the Killing vector projects onto the geodesic flow-lines in the space. A timelike Killing vector will project on the energy component of a four momentum so that K_t E = constant. But we can’t impose this on the above cosmology.

    As strange as this might appear it means that energy conservation can only be said to be a local effect. Now, when it comes to the “dark energy,” there is the equation of state e = -p, for p a pressure. The pressure term is spacelike and it is possible to say, “Well a spatial Killing vector K_i can be found, and so I will then say that e = -p imposes an energy conservation on the cosmology.” But before we start drinking shots of tequila over our cosmic coup, remember that e = -p is artificial in a way. We are treating the cosmological constant as a field source, which removes the Einsteinian condition of the manifold (spacetime) and thus violates some aspects of general covariance. So our identification e = -p can only at best be a local result and not one which pertains to the whole cosmology.

    This is a bit odd, for in physics we are taught all sorts of nice things about energy conservation. But in cosmology it turns out that energy conservation is not something which can be well established. We have a notion of time, and the standard logic is that the generator of time is the Hamiltonian, or energy. Think in quantum mechanics where exp(-iHt) is the time development operator and so forth. Yet here we see that the idea of global energy conservation can’t be substantiated, and the definition of time in cosmology is local as well.

    Lawrence B. Crowell

  • http://www.gregegan.net/ Greg Egan

    So there is no time-Killing vector.

    No, but the spacelike Killing vector does a perfectly good job at deriving the cosmological redshift, which was what I was using it for.

    The lack of a global energy in GR — except in asymptotically flat spacetimes — is just one of many headaches for quantum gravity, but classical cosmology gets along just fine without it.

  • Lawrence Crowell

    I looked at your discussion above, and it does appears as if you are appealing more to momentum Killing vectors, in that the ratio of momenta are going to be given by the reciprocal of their ratio Killing vector components.

    As for this being a problem for quantum gravity, that depends. In one way this lack of global energy might be seen as an ally.

    Lawrence B. Crowell

  • John Merryman

    Greg,

    Cosmological redshift is best described in terms of expanding space,

    Is that due to other galaxies redshifted as if they are all moving directly away from the Milky Way?

    The thing is, there is a perfectly coherent notion of space expanding without the speed of light changing, and that notion is the one asserted by cosmologists. This is clearest in the case of a finite universe, when you can talk about the total volume of the universe at any instant of cosmological time, and that volume is increasing. The speed of light stays the same, and as a consequence the transit time for light between any two galaxies increases. This notion of expansion is perfectly coherent as an idea, and perfectly consistent with observation.

    Increasing volume isn’t proof of expanding space, since space outside this volume logically becomes space inside it. Do cosmologists know so much that they can categorically say that space doesn’t exist, except as the carpet of this proposed expanding universe rolls out? The fact that the speed of light doesn’t change is proof that space as measured by C and that inside the bubble of an expanding universe are not the same. So which defines the real dimensions of space, that which is stable, or that which is expanding?

    So there are no relativistic effects in the situation your propose that would explain the observed redshifts.

    That’s the hitch. Because there is no relativistic explanation for why light would be redshifted, current cosmology assumes the entire universe is expanding. In order to support this assumption, increasingly exotic formulae are conceived to explain the various loose ends, from Inflation to Dark Energy. Yet all it would take to knock the whole house of cards down would be an explanation for relativistic redshift. Since gravity causes space to contract and mass eventually breaks down and radiates the energy back out, I suspect it would have something to do with the effect of radiation on light waves. Of course, it’s much easier to go along with the crowd, especially if you are trying to make a living at this, but it is a hobby for me, so I have the freedom to consider all the options.

  • Lawrence Crowell

    A few points to J.M’s post. There is no space that the universe is expanding into. There is no boundary to the universe which demarks some sort of “front” for the expansion of the universe.

    To say there is no relativistic explanation of redshift probably needs to be qualified. The redshift is not strictly a special relativistic motion of bodies, though that can be used as an approximation for galaxies somewhat local to ours. The expansion of space is a matter of general relativity, so in that sense it is a relativistic effect.

    Einstein originally imposed the cosmological constant and the term /g_{ab} as a way of keeping the universe static. One must realize that in 1915-20 the universe was thought to be the galaxy, and debate raged about whether galaxies, Messier objects, were just more local nebua. So Einstein’s assumption was that the universe was some sort of static space. Hubble came along as showed not only were galaxies beyond the Milky way, but that they were expanding away. Einstein revoked his /-term and called it his greatest blunder. Now the term is being resurrected in a different guise.

    In a static universe with / set to keep things stationary there would be no redshift, and Hubble’s observation of galactic redshift blew the static cosmos idea to bits — literally in a big bang.

    Lawrence B. Crowell

  • http://www.gregegan.net/ Greg Egan

    John

    There’s a moderately useful, but not perfect analogy which goes like this:

    Big Bang = South Pole
    Time = angle from south pole to some circle of latitude
    Universe at a given cosmological time = some circle of latitude
    World line of a galaxy = some meridian
    World line of a free-falling body moving from galaxy to galaxy = portion of a great circle other than a meridian, but inclined closer to a meridian than to the circles of latitude
    Velocity someone in a galaxy measures for free-falling body that leaves or enters that galaxy = tan(angle between the meridian for the galaxy and the great circle for the free-falling body)

    This is an aid to visualising some of the concepts in cosmology, but it doesn’t function as a precise computational tool. Also, at the risk of stating the obvious, the interior of the Earth and the space around the Earth in this analogy don’t correspond to anything. The universe isn’t curved by being embedded within some larger, flat, higher-dimensional space; it’s just intrinsically curved.

    Is that due to other galaxies redshifted as if they are all moving directly away from the Milky Way?

    Galaxies are moving away from each other in the sense that meridians on the Earth are moving away from each other. It takes longer to travel from 10 deg W to 20 deg W as you move away from the south pole and get closer to the equator, because the circles of latitude are getting larger.

    As I mentioned in #50, there’s a nice analogue of redshift: your east-west component of velocity drops as you move from the antarctic towards the tropics along an inclined great circle, becoming multiplied by the ratio of the circumference of the circle of latitude you left behind (i.e. the size of the universe when you left) to the circumferences of the circle of latitude you’ve arrived at (i.e. the size of the universe when you reach your destination). Something analogous happens to momentum in the real universe.

    If you try to construct paths on a plane that match this behaviour in detail, you’ll find that you can’t (as map-makers have known for centuries). Similarly, you can’t match the detailed behaviour of galaxies by positing that they are just moving away from each other in some pre-existing flat, empty space.

    Increasing volume isn’t proof of expanding space, since space outside this volume logically becomes space inside it.

    In the analogy, circles of latitude get bigger, but there is no “space outside them” which is being converted to “space inside them”. That is what is meant by expanding space.

    So which defines the real dimensions of space, that which is stable, or that which is expanding?

    It’s actually very simple: all local ways of measuring distance will agree on the result. At 85 degrees South, let a billion people spread out evenly on the circle of latitude measure the distance to their neighbour by any sensible means. Because there’s little curvature on that scale (a distance of about half a millimetre from neighbour to neighbour), the result will be virtually independent of their strategy. For example, they can send a great circle to their neighbour at a 45-degree angle to their meridian, and have the neighbour respond the same way, and then they halve the distance they travelled along their own meridian between sending out this “light signal” to their neighbour and getting a reply. When all the inter-neighbour distances are summed, that is an excellent estimate of the size of the circle of latitude (aka size of universe).

    When they repeat the experiment at 80 degrees South, they will get a larger inter-neighbour distance, and hence a larger total size for the circle of latitude.

    Note that the role of the fixed speed of light here is played by sending out the great circle at an angle of 45 degrees each time. This won’t give sensible results over vast distances, but for checking on your neighbour half a millimetre away it will work extremely well.

    Yet all it would take to knock the whole house of cards down would be an explanation for relativistic redshift.

    What you mean by this (for people who haven’t followed previous comments closely — if in fact there is anyone but the two of us still bothering to read the soggy dregs of this thread at all) is “an explanation for relativistic redshift in a static universe“.

    The hitch, for you, is that we already know how relativity works, and that it doesn’t predict redshift in a static universe. So rather than using the adjective “relativistic” here, you really ought to be saying “completely new theory of space, time and gravity which explains all other observations, and gives a redshift in a static universe”.

    Of course, it’s much easier to go along with the crowd, especially if you are trying to make a living at this, but it is a hobby for me, so I have the freedom to consider all the options.

    You’re free to consider options, but you’ve neither described a coherent alternative theory of space, time and gravity, nor motivated any need for such a theory. If you ever do come up with a testable alternative theory that can be used to make numerical predictions of what people will measure in any situation, then maybe someone will be willing to put it to the test. Right now you’ve neither provided that theory nor identified any need for it.

  • John Merryman

    Lawrence,

    Einstein originally imposed the cosmological constant and the term /g_{ab} as a way of keeping the universe static. One must realize that in 1915-20 the universe was thought to be the galaxy, and debate raged about whether galaxies, Messier objects, were just more local nebua. So Einstein’s assumption was that the universe was some sort of static space. Hubble came along as showed not only were galaxies beyond the Milky way, but that they were expanding away. Einstein revoked his /-term and called it his greatest blunder. Now the term is being resurrected in a different guise.

    In a static universe with / set to keep things stationary there would be no redshift, and Hubble’s observation of galactic redshift blew the static cosmos idea to bits — literally in a big bang.

    Einstein originally proposed the cosmological constant because his calculations showed that gravity would cause the entire universe to collapse to a point, so he added an arbitrary factor to balance it. Since gravity is contraction, the CC is effectively an expansion. That it was resurrected to explain dark energy would seem to prove this is accepted.
    If one is only looking at bodies in the local galaxy, it would make sense to estimate they are all falling into a vortex. All those other galaxies are also gravitational wells, pulling mass and its attendant spacetime into the central black hole. So this is a shrinking of spacetime. Redshift shows the spacetime between galaxies is expanding. If we have contraction and expansion and they are roughly in balance, as in the concept of Omega=1, as was explained by Hawking, in ABHoT, (Tests by COBE and WMAPP seemed to show this balance exists.) then where is the additional expansion for the entire universe to expand? It would seem from this perspective, that Hubble found Einstein’s Cosmological Constant. It just happened to be between galaxies, not in them. Given that what Peremutter, et al, found in ’98, as well as subsequent studies, redshift matches the predictions for a cosmological constant far better then it did for any predictions based of Big Bang theory.

    Greg,

    It’s not that I don’t have a reasonably good understanding of Big Bang theory. I’ve been following its evolution since the ’70′s and took for granted that it was a sensible explanation of the universe. It was reading Hawking’s ‘Brief History of Time,’ in’89, where he gave a short description of Omega, that I began to question it.

    there’s a nice analogue of redshift: your east-west component of velocity drops as you move from the antarctic towards the tropics along an inclined great circle, becoming multiplied by the ratio of the circumference of the circle of latitude you left behind (i.e. the size of the universe when you left) to the circumferences of the circle of latitude you’ve arrived at (i.e. the size of the universe when you reach your destination). Something analogous happens to momentum in the real universe.

    A compounding effect would also cause this, so that the further light travels, the faster the source appears to recede.

    In the analogy, circles of latitude get bigger, but there is no “space outside them” which is being converted to “space inside them”. That is what is meant by expanding space.

    This still doesn’t explain why the speed of light is stable, irrespective of the size of the universe. If all space is squeezed into that point at the south pole and expands from there, how is it that we have an extremely stable measure of space by which to measure the increasing distance???? If the entire universe was the size of a beachball and all space was squeezed into there, it should take light just as long to cross the same proportion of this space then, as whatever it has expanded to now, or it isn’t expanding space, it’s increasing distance. The speed of light is about 186 thousand miles a second, so whatever the age of the universe, it would seem a mile is a mile is a mile.

    What you mean by this (for people who haven’t followed previous comments closely — if in fact there is anyone but the two of us still bothering to read the soggy dregs of this thread at all) is “an explanation for relativistic redshift in a static universe”.

    That redshift is due to an expansion of space that is opposite the contraction of gravity, so that the two balance out and there is no overall expansion. (Thanks for taking the time to debate this. It’s more mentally engaging then the day job.)

    The hitch, for you, is that we already know how relativity works, and that it doesn’t predict redshift in a static universe. So rather than using the adjective “relativistic” here, you really ought to be saying “completely new theory of space, time and gravity which explains all other observations, and gives a redshift in a static universe”.

    It did predict the need for a cosmological constant to maintain a stable universe. It seems the effect of gravity contracting space gets completely overlooked in the glare of an expanding universe! If they are in rough balance, where does the additional expansion to increase the size of the universe come from???? It’s not a static universe, it seems to be a stable universe, where the space expanding between galaxies falls into galaxies!!!!

    You’re free to consider options, but you’ve neither described a coherent alternative theory of space, time and gravity, nor motivated any need for such a theory. If you ever do come up with a testable alternative theory that can be used to make numerical predictions of what people will measure in any situation, then maybe someone will be willing to put it to the test. Right now you’ve neither provided that theory nor identified any need for it.

    It isn’t a matter of testability, but of interpretation. Big Bang Theory predicted a completely different rate of expansion then what has been observed, but there is no questioning of theory, the predicted energy density of the universe is simply expanded several times over to fill the gap in the theory. If Bush had as much leeway as cosmologists, we would still be looking for WMD’s in Iraq!!! I suspect we will still be looking for dark energy several decades from now and spent enormous amounts of money doing so.

  • http://www.geocities.com/aletawcox/ Sam Cox

    I’ve been watching this thread develop- with interest.

    I believe a correct overall understanding of the geometry of the universe AND the relationship between the way the universe actually exists compared to the way it is observed and measured is the key to understanding dark energy.

    The Planck Realm is everywhere and is entangled with what we, from our frame of reference, call energy densitiy black holes of assorted “sizes”.

    If we add an additional three-space to the cosmic geometry (a slightly modified Schwarzschild “mirror geometry” with a Planck Realm, massed event horizon rather than a point mass) and assume space in the universe to be locally flat but marginally closed globally…Omega total 1.02, we obtain a universe which is finite in mass yet everywhere…there is nothing outside it.

    Because this two-sphere geometry has two sets of global coordinates which fit the GR equations, postitive and negative, within this model the big bang becomes the equivalent of a super massive white hole, and photons (which do work from an entropy standpoint), become the inverse of the singular Planck Realm- in which entropy is presently observed to increase.

    This universe we observe only exists on event horizon surfaces of varying sizes…as “particles” and bodies made of these energy density particles of varying sizes and composition…all based on the great proportion. At its heart, everything in the universe is singular, but depending on the coordinates from which the universe is observed, the universe might not seem to exist at all or be as vast as we observe it to be…13.7BLY in radius.

    A singular Earth would (and eternally does) have an event horizon surface the size of a golf ball, but its overall gravitational moment eternally remains 1G when measured 4,000 miles from its center, whether is is particulate as at our coordinates in space and time, or as it existed at the big bang- and will exist again, with the rest of the universe in the future.

    We observe motion and change-time- when we observe (cross-read) a general, everywhere proper time pulse of the universe which occurs 2.8 trillion times per Earth second, remotely in extreme gravitational time dilation. From our frame. we know relativistically that time is a quatity which is dependent on the relationships of events and observers, yet we fail to recognize the eternal nature of the whole…that everything…all information exists permanently, but is observed more “slowly” and sequentially from differing frames of reference.

    The distant universe which we see as progressively younger with “distance” and emerging from the big bang, is, within the second three space simultaneously collapsing to a singularity. From our frame, the universe is “eating itself alive” consuming itself progressively as black holes add to the cumulative mass of the dark energy Planck Realm at the overal expense of particulate existence.

    There is no stange “dark energy” at all. What we are observing is the process of simultaneous emergence from a big bang and collapse to singularity of the same universe. The effect: we, from our frame, observe an eternal existence as both a phenomenon of expansion and a cosmic contraction. The doppler effects are real. So is acceleration outward, just as our 4D particulate reality is real. Relativistically, the way we observe the universe IS our reality. We can build a technology on the way the universe is observed and measured. We occupy an accelerated frame of reference- and observe an Earth and universe which are, themselves the result of relativistic effects,

    At some point in “time” in the future, as the mass of our cosmic “hemisphere” increases, the Planck Realm wil rise to meet us. At a critical point, what we now observe as almost perfectly flat space will almost instantly cease to exist- and what is remaining of particulate reality with it. However, also simultaneously, the 3 space which has been filling with the matter and energy of our half of the universe will remain- as the universe always exists, everywhere and forever, preserving all information in CPT reversal. As quickly as our “hemisphere” dissappears, it will reappear in opposite polarity, in a hot big bang, pretty much as described in the standard model.

  • http://www.gregegan.net/ Greg Egan

    This still doesn’t explain why the speed of light is stable, irrespective of the size of the universe. If all space is squeezed into that point at the south pole and expands from there, how is it that we have an extremely stable measure of space by which to measure the increasing distance????

    How can we measure the fact that circles of latitude are getting bigger? Very easily: we use measuring rods, or we look at the return of “signals” that we bounce off our neighbours on different meridians at a fixed angle. Measuring rods measure metres, not degrees of longitude; they don’t expand as we move from the south pole towards the equator, conspiring to conceal the expansion of the circles of latitude from us.

    Equally, there is nothing to be puzzled about with the situation in cosmology — unless you’ve taken the universe-as-inflating-balloon metaphor too much to heart, and you imagine that all measures of distance are somehow painted in ink on the balloon.

    Distance doesn’t work like that. We do not define the kilometre as a fixed fraction of the total size of the universe. Although nobody these days would talk about a “standard measuring rod”, that’s only because some fields demand ultra-high precision; for everyday purposes there’s no reason we couldn’t define “one metre” as the length of a particular metal rod. Atoms, and rods made of atoms, do not get bigger as part of the cosmological expansion (nor does Brooklyn). Nor is the speed of light magically compelled to change in step with the expansion; why do you imagine that it would be? These measures of distance remain unchanged, while the universe grows larger.

    If you don’t like the phrase “space expanding” because it conjures up consequences for you that nobody is actually suggesting, well, go ahead and mentally call it something else. I’m happy to concede that “space expanding” is an imperfect, potentially confusing colloquialism. But the fact that you don’t happen to like a phrase isn’t enough to render the scenario for which cosmologists employ it logically flawed in any way.

    That redshift is due to an expansion of space that is opposite the contraction of gravity, so that the two balance out and there is no overall expansion.

    The trouble with this claim is that when an expansion and contraction balance out and leave no overall expansion, they also leave no overall redshift.

    It’s not a static universe, it seems to be a stable universe, where the space expanding between galaxies falls into galaxies!!!!

    You seem to have some misconception that galaxies could be “disposing of” the space that would otherwise be created by cosmological expansion. I’m afraid this just doesn’t work.

    Yes, the presence of matter in the universe acts to slow the expansion, and in the absence of a CC and with omega > 1 would eventually reverse the expansion and cause a collapse. But galaxies are not collapsing, or at least not on any timescale that would allow them to do what you suggest they’re doing.

    There are many individual red and blue gravitational shifts involved with the passage of light from a distant galaxy to us: the light climbs out of the gravitational well of a star, then a galaxy, then a galactic cluster, crosses inter-cluster space, then suffers blue shifts as it descends into our cluster, galaxy, solar system, and planetary gravitational fields. But the fact that the net result is a red shift means that there must have been a net expansion of the universe in the time it took for the light to reach us.

    It isn’t a matter of testability, but of interpretation.

    That’s dead wrong. What you propose would have observable consequences, and they are very different from what is observed. Apart from the overall killer that your model would actually lead to no cosmological red shifts, it would also imply that we on Earth would see significant blue shifts from everything else in the galaxy. That’s how a collapsing region of space would look.

    As for the nature of dark matter and energy, I have no stake in any particular outcome, and I’ll be interested in whatever does or doesn’t eventually show up. But however cynically you choose to view the positing of previously undetected forms of matter, you need to be aware that what you are suggesting is an even worse fit for the observational data than a Big Bang model without recourse to dark matter or dark energy. You’re not solving any problem, you’re just making the discrepancy far worse.

  • http://www.gregegan.net/ Greg Egan

    Sam

    As a mere mortal, I can only handle one Einstein at a time, so I’ll have to resist the temptation to give a detailed review of your truck-load of cosmic wisdom.

  • rw

    Greg, given good weed, we all become Einsteins and it often takes a good thrashing from a patient person like you before we learn that the things we view as problems with the orthodoxy are simply the product of our own lack of understanding.

  • Lawrence Crowell

    Some of this is coming in pretty fast and furious. I will try to make a few comments here that are as brief as possible.

    Things like distance and time are parameterizable. IN other words you can demark time with different units of “seconds,” say if we lived on mars or some other planet with a different frequency of orbit and so forth. We mark out months and weeks based on the lunar phase, but aliens on some other world might arrive at a different set of units. So how one chooses the unit of length or time is completely arbitrary and freely chosen by the observer or analyst. By extension the frame on operates on is a matter of choice as well.

    On of the nice things about electromagnetism is that the fine structure constant alpha = e^2/hbar c is a pure number ~ 1/137 with no units. No matter where you are this is the same.

    There is the bit about fractal geometry, where any subset is similar to a larger set or the whole set. The most rivial fractal is a straight line. Without units attached any segment of it looks like any larger or smaller segment. Much the same holds with time and distance. How there is the bit about the Planck distance, which can be found by equating the deBroglie wavelength of a black hole equal to its horizon circumference. This unit is

    L_p = sqrt{G hbar/c^3}

    Now this is an absolute unit of length, which even with arbitrary units reflects a discrete unit. There are similar units for time, Planck areas, even Planck voltages! Now if you rescaled the speed of light you would find that this unit is adjusted, but so would all the length scales you have. In doing so you find that Poincare’s curious observation holds: if the size of things were changed in some way how would you know it? So there is underlying this a conformal structure, which gets into Malcedena’s AdS/CFT and quantum holography and so forth.

    So the speed of light is simply the speed of light and it is what it is on any local frame is “fixed,” and any idea of adjusting in for a local frame is just some conformal shift which leads to an invariance. The speed of light is “stable,” though I am not sure what is meant by this, in that it is simply “fixed.” Also in a pure unit sense, say if we equate distance with time the speed of light is then “unitless,” and so similar to the fine structure constant is then simply a constant.

    Lawrence B. Crowell

  • http://tyrannogenius.blogspot.com Neil B.

    HeeHee – Yes rw I do appreciate Greg’s patience (and erudition) and must admit I too was rather too much a handful of a “weed-smoking” Cocktail Einstein. (Greg, I hope you can forgive me for truly being obnoxiously persistent about something I should have at least let go for a good while – maybe I should get a job at “Gitmo” and I wonder what do you Aussies think of Americans’ love of torture? I guess you’ve had your personal fill, heh.) You bring up what is a good subject, the popularization, teaching, and debate about science, and the interactions of experts, semi-professionals (like science-fiction writers who do know a lot about real physics ;-) ) and amateurs and semi-amateurs who have some education and interaction with the scientific world but aren’t up there yet or may never be (like me.)

    We can all do better in making these kinds of interactions. First, it is a bad temptation to tend to perceive that any “amateurish” sounding query is just clumsy ignorance of this or that (which it often is, but the good questions are all you have to bother with.) For example, my first point about gravitomagnetism was not based on the specific applicability to high speeds of the low-speed equations as was imagined, but rather on the symmetry requirement that the effects – whatever they were – of mass flowing one way should be canceled out by the same mass flow in the other direction. Well, maybe that is wrong too, but it isn’t the first kind of mistake that is explicitly warned against in a ready resource. Also, if someone wants to know how something fits into X framing of the issue, like “how does it fall relative to an actual structure” wouldn’t a good teacher first just answer that to get that satisfied, and then explain perhaps why it doesn’t in turn show Y (such as that the equivalence principle is thereby wrong, etc.)? When people present arguments using words like “acceleration” and different values for same under different conditions, that does involve semantics and needs elaboration. My mistake was to not retreat and work over the explanations and caveats right when shown them, not to have insisted to begin with that apparent contradictions and problems of meaning need to be resolved.

    I won’t give up on making points about physics, but will try to make the Socratic part more truly Socratic – there is indeed a role for that. (To ask good questions to bring forth explanations, which is not the same as claiming that such and such *is* the case, and yes even to press for what happens in such and such a case that you might think isn’t “relevant” etc.) I think that many of the questions posed by Sam Cox and John Merryman are starts at good expressions of Socratic method. All they need is to realize they aren’t demonstrating conclusions thereby, but stimulating you patient and helpful folks to explain why or why not, etc, for which we are grateful for your time, effort, and tolerance of irritation!

    Yet, I don’t agree that “the things we view as problems with the orthodoxy are simply the product of our own lack of understanding.” That presumes that orthodoxy must be right, and that is not warranted. More often, our thinking there’s a problem will be a misunderstanding, but it does not *have to be.* A non-specialist is unlikely to make headway in that regard, but the questions a good “student” can ask at least generate insight into what is confident, what isn’t (e.g. aren’t some of you arguing here over whether energy is really conserved in GR, how to define it, etc?)

    One thing though, you folks need to know and accept if you aren’t going to be big hypocrites. A bit of good weed and/or scientific degree/s makes many thinkers become Platos and think they are experts at framing or even making final judgments on all philosophical issues like whether the universe is contingent or ontologically self-contained, how to think about unobserved entities like “other universes”, God (as something responsible for the universe/s apart from any sectarian complications), the framing of the anthropic principle as a conceptual issue not just what physical laws are involved etc. Over and over again, I see the same folks (some of whom so wary and weary of “amateurs” poking into their physics turf) just digging and expounding heartily and very confidently into such frontier philosophical questions despite their makeshift handling of the issues and frequent offering of fallacious boners and ignorant misframings of every type. I can assure you, as someone who has studied some of that – many or most of you (and that includes very much the OPs here) have little idea of what you are talking about at the quality level. You don’t appreciate when a philosophical screwdriver can’t or shouldn’t be used to open a philosophical can, etc. In other words, I know how Greg feels but applied to philosophical reasoning instead of science.

    Ironically, I myself was getting irritated at amateurish digs at philosophical cases for God etc in the midst of metaphysical rambling about frontier physical questions, when I spouted off about “emperors not having clothes” – If you are going to use metaphysically loaded phrases like “illusion” to describe physical events, and remember that sort of phrase does *not* have rigorous physical content, then be prepared for a “philosophical” response in like manner. Some issues in science are like that.

    Please don’t tell me that studying science somehow automatically makes you an expert at general reasoning about issues etc – these issues require special concentration like other fields. Really, after seeing idiocies like “the cosmic teapot” around (see my take-down elsewhere if you want), it is clear that many of the neo-atheist skeptics (and yes I mean the big boys!) are philosophically illiterate, and I have had similar luck getting those I argue with to appreciate such things as Greg must feel he’s had a handful from me. How ironic.

    To elaborate on this issue that just about everybody else, in case you folks around here didn’t know: We don’t like physicists etc. thinking that they automatically make good philosophers, economists, theologians, political scientists, etc. Really, isn’t that “cocktail party” philosophy, economics, theology, politics, etc? But here I see all these posts about what God means, about why the world is friendly to the formation of life, of which candidate is better, etc – The OP and the commenters don’t show a lot of contrition and humbleness as I can see, about not being experts in those fields, although expecting such from others talking about science. (Ironically, our big brawl about gravity was in a thread titled “Over to You, Mitt”! Most of the argument was about the reasonableness of believing in a contingent versus self-sufficient universe, etc.)

    They go ahead a ply their weed-soaked or whatever form of amateurish expounding, apparently quite sure that they are doing quite intelligently. Really, I am irked by the gall of presumable non-physician Jason Dick to blithely expound on the “rationality” of something complex and out of his field like acupuncture, etc. (not to mention every philosophical question that ever comes up, in such good company!) OK, it’s a free for all and anyone can offer opinions on such topics, but don’t feel shocked when others want to play that game with scientific subjects. Sauce for the goose …

    Happy Holidays, whatever they are …

  • http://tyrannogenius.blogspot.com Neil B.

    Well, I must give some credit: many of the posts do pose non-science questions in good Socratic form, but I still see examples of presumption (“the answer happens to be no” etc.) In any case, the commenters are more the offenders of the sort I tweaked at here, than the OPs.

  • John Merryman

    Greg,

    I’m not Einstein and this isn’t new physics. Actually it is quite old physics, convection specifically. Heat expands until it cools off and cold contracts until it starts to heat back up. Is there any similarity between this and gravitation/radiation? I’m not a scientist. I’m a freaking farmer, for Pan’s sake! I like it simple. Ockham’s razor appeals to me.

    we use measuring rods, or we look at the return of “signals” that we bounce off our neighbours on different meridians at a fixed angle. Measuring rods measure metres, not degrees of longitude; they don’t expand as we move from the south pole towards the equator, conspiring to conceal the expansion of the circles of latitude from us.

    No, but if they are physical objects, they may well contract, subjected to extreme gravity. The topography of a sphere still doesn’t mean increasing distance and expanding space are the same thing, since it is the stable distance of the measuring rod that we use to measure this increase.

    Equally, there is nothing to be puzzled about with the situation in cosmology — unless you’ve taken the universe-as-inflating-balloon metaphor too much to heart, and you imagine that all measures of distance are somehow painted in ink on the balloon.

    I don’t. I’m using this to show why saying space expands because we can measure it, is really only increasing distance in stable space.

    We do not define the kilometre as a fixed fraction of the total size of the universe.

    No. Currently a kilometer is defined as a fixed fraction of the speed of light. So if two galaxies that were 100 million lightyears apart grow to be 200 million lightyears apart, that an increasing quantity of a stable measure.

    If you don’t like the phrase “space expanding” because it conjures up consequences for you that nobody is actually suggesting, well, go ahead and mentally call it something else. I’m happy to concede that “space expanding” is an imperfect, potentially confusing colloquialism. But the fact that you don’t happen to like a phrase isn’t enough to render the scenario for which cosmologists employ it logically flawed in any way.

    Cosmologists employed it to explain how the universe can expand without the Milky Way being at the center of the universe. Frankly I have no real problem with space expanding, or contracting, just as I have no problem with the speed of light slowing under various conditions. My problem is with the idea that the entire universe is expanding due to one side of this convective cycle being ignored.

    But galaxies are not collapsing, or at least not on any timescale that would allow them to do what you suggest they’re doing.

    I’m not saying they are collapsing, because they are constantly consuming more energy/mass and the time and space it defines. They are the bottom of the cycle, where mass contracts to the degree it heats back up and radiates out.

    But the fact that the net result is a red shift means that there must have been a net expansion of the universe in the time it took for the light to reach us.

    There is a redshift for the specific photons which interact with the collection plates on a telescope. To the extent this light is redshifted, it has lost energy. Did it lose this energy because the source is receding, or could there be other reasons? Every wave must fill an increasing volume of space, the further it travels from its source. Could there be an incremental interaction between crossing light waves? It wouldn’t take much, given the distances involved. If the universe isn’t expanding, then the expansion of space would possibly result in additional pressure on gravitational systems. Possibly the reason the outer bands of galaxies spin faster then Newton’s laws predict isn’t due to dark matter, or modified gravity, but from external pressure. The fact is that we don’t know what we don’t know and current cosmology has an awful lot riding on the only explanation for redshift being recession.

    Apart from the overall killer that your model would actually lead to no cosmological red shifts, it would also imply that we on Earth would see significant blue shifts from everything else in the galaxy. That’s how a collapsing region of space would look.

    It’s mass that collapses. Radiation expands. We see mass being pulled around gravitational vortexes. And we only see it due to the radiation escaping. If it was the radiation that was falling into gravity wells, then maybe it would be blueshifted. Radiation that can’t escape gravity isn’t blue, it’s black.
    Actually stars are the primary turnaround for mass being turned back into energy.
    Another problem with gravity being modeled as a curvature of spacetime, rather then as a property of mass is that if you go to the center of a massive object, the pressure is very great, but the gravity would balance out. Consider what this would mean if it were applied to galaxies. Possibly there is no gravitational body at the center, only extreme pressure. It would explain the jets of charged particles being ejected out the poles of galaxies.

    Lawrence,

    Things like distance and time are parameterizable. IN other words you can demark time with different units of “seconds,” say if we lived on mars or some other planet with a different frequency of orbit and so forth. We mark out months and weeks based on the lunar phase, but aliens on some other world might arrive at a different set of units. So how one chooses the unit of length or time is completely arbitrary and freely chosen by the observer or analyst. By extension the frame on operates on is a matter of choice as well.

    That’s why the speed of light is considered the most standard unit. That’s why the length of metric units are define relative to C, not the other way around.

    So the speed of light is simply the speed of light and it is what it is on any local frame is “fixed,” and any idea of adjusting in for a local frame is just some conformal shift which leads to an invariance. The speed of light is “stable,” though I am not sure what is meant by this, in that it is simply “fixed.” Also in a pure unit sense, say if we equate distance with time the speed of light is then “unitless,” and so similar to the fine structure constant is then simply a constant.

    So something measured as moving away on a scale of C is increasing distance relative to our most basic measure of space.
    As I recall, Inflation theory says space expanded at much faster then the speed of light because it was space itself that was expanding, carrying the light along with it. So it would seem that light was traveling faster then the speed of light. Prior to Inflation, would the speed of light be similar to what it is now?

    I’m not trying to be as hard-headed as I may seem, frankly I feel these are legitimate questions about a theory that seems far more inclined to make extreme projections when theory doesn’t meet observations, than to examine its own assumptions. That there is a deep psychological basis and history of situations where people, even very intelligent people, double down on bad hands, rather accept losses, makes me very leery. I can understand that those who take these ideas seriously think raising questions is bad form, but that is a danger sign in itself. Belief is a very powerful drug.

  • David Bennett

    Hi Sean. Quite frankly, seems to me that your remarks on negative pressure are a bit confused. The straw-man argument that you object to “negative pressure is kind of like anti-gravity” is certainly a problem, because it is wrong. Pressure is a source for gravity, and the gravitational force opposes the force due to the pressure of the field that is the source. The extra gravitational force due to the pressure of radiation gives rise to a stronger gravitational field in a universe dominated by radiation (i.e. relativistic particles), and it contributes to such things as black hole formation in relativistic fluids. With ordinary relativistic particles, the pressure adds to the attractive force due to gravity, but the pressure opposes the gravitational force. With dark energy, the situation is simply reversed. It is the “mechanical” dark energy force that “sucks” and the gravitational force due to the dark energy that is repulsive.

    I agree that you don’t really need the negative pressure discussion to consider the situation of a homogeneous and isotropic medium, but it becomes quite important if you consider models in which the dark energy is not homogeneous. It has been quite a while since I have worked in theoretical cosmology myself, but my sense is that there is a lot of confusion about this in the current dark energy literature. In particular, if you try to set up a field that gives rise to inhomogeneous negative energy, the inhomogeneity in the (negative) pressure will give rise to large non-gravitational forces that will likely convert some of the potential energy in the “dark energy” field to kinetic energy, which will give a contribution to the gravitational field of the opposite sign.

    Perhaps the best way to see the importance of “negative pressure” as a source of gravity is to consider the cases of topological defects that have tension (or negative pressure) in one or two dimensions: cosmic strings and domain walls, respectively. For a static cosmic string, the gravitational effects of the string energy density and tension exactly cancel, leaving no attractive or repulsive gravitational force. The spacetime outside the string is locally flat. However, it is not globally flat, and a circle around the string will yield 360 degrees minus a deficit angle proportional to the string tension.

    Domain walls provide an even more interesting example, and they are discussed in a very nice paper by Ipser and Sikivie (1984, Phys Rev D30, 712). The 2-d tension of the domain wall now dominates over the energy density and the overall force is repulsive. Observers on opposite sides of the wall feel a constant acceleration with respect to each other in the direction perpendicular to the wall. In the case of a localized wall, such as a sphere, observers near the wall see the same force as in the infinite plane wall case. But the wall tension causes it to collapse, and as it accelerates due to the tension, the potential energy stored in the wall is converted to kinetic energy, so the repulsive force goes away. An outside observer sees a Schwarzschild field (as she must due to the symmetry).

    So Sean, I hope that you will mend your ways and realize that the problem is not the use of the term “negative pressure” to describe the tension in the dark energy field. The problem is the failure to distinguish between the attractive “mechanical” force caused by the field tension and the repulsive gravitational force that this tension serves as the source for.

  • http://www.gregegan.net/ Greg Egan

    John

    I’m not Einstein and this isn’t new physics. Actually it is quite old physics, convection specifically. Heat expands until it cools off and cold contracts until it starts to heat back up. Is there any similarity between this and gravitation/radiation?

    Er, no, there isn’t. Just because you know a small amount about convection doesn’t mean everything else in the universe is really convection in disguise.

    I’m not a scientist. I’m a freaking farmer, for Pan’s sake! I like it simple. Ockham’s razor appeals to me.

    Ockham’s razor doesn’t mean: “Any theory I don’t understand because the mathematics is too difficult must be false, and should be replaced by something I find simpler and more intuitive, despite the fact that all the evidence contradicts the simpler theory.”

    My problem is with the idea that the entire universe is expanding due to one side of this convective cycle being ignored.

    Since there is no “convective cycle”, the problem is yours alone.

    The rest of your comments are full of errors too numerous to address, when the answers will wash over you with no effect.

    I can understand that those who take these ideas seriously think raising questions is bad form, but that is a danger sign in itself. Belief is a very powerful drug.

    Questions are welcome, but you pay no attention to the answers, and you seem to be positively drunk on belief. Why do you take your “convection” ideas at all seriously? Only because you dreamt them up yourself; it’s certainly got nothing to do with either logic or observation.

    For all your attempts to construct some kind of sociological theory for a conspiracy in favour of the status quo, that whole idea is remarkably sociologically naive. There is nothing a cosmologist would love more than to overturn conventional wisdom (and as a non-academic amateur myself, with no stake in the status quo, if I had a chance of fame and glory by collaborating with you and lending mathematical rigour to your stunning revelation, I’d seize the opportunity with both hands.)

    Unfortunately, as dozens of people have no doubt told you already, you are not the bearer of the great Reality Check that cosmology needed to kick it up the arse and wake it from its delusions. You just don’t know what you’re talking about, and you’re too proud and lazy to learn what the thousands of honest, hard-working people who came before you have done.

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    Greg, your patience is impressive. There is a surprisingly clear difference between people who don’t know something and are trying to learn, and people who don’t know something and can’t be bothered learning it and feel strongly that their personal ideas should nevertheless be taken seriously by those people who have bothered to learn. I’m not sure if I’ve ever seen a person in the second camp convert to the first.

    David, it’s not precisely clear to me where we are disagreeing. I was making a purely pedagogical point, not a physics one. Nobody is arguing that only the 00 component of the energy-momentum tensor is important. I was just arguing that the easiest way to explain why dark energy makes the universe accelerate is to look directly at the evolution of the energy density, and not get the pressure involved at all.

    Of course, if the dark energy (or a topological defect or what have you) has spatial gradients, the spacelike terms in the energy-momentum tensor will be important. But this is a great example of where focusing on “w” leads you astray. People begin to think (incorrectly, of course, and the careful people don’t think this way) that p = w ρ is an equation of state, and should have something to do with sounds speeds etc. To get any of that stuff right, you should look at the equations of motion that are derived from the Lagrangian of your underlying theory, not think in terms of p and ρ.

  • http://www.geocities.com/aletawcox/ Sam Cox

    Greg Egans remarks about Einstein reminded me of the famous debate put- down by Bentson in his debate with Dan Quale a while back. Dan was making himself out to be some great guy and compared himself to John F. Kennedy, to which Bentson replied: I’ve known John Kennedy for many years. I have worked with John Kennedy…in fact, John Kennedy was a friend of mine…and you sir are NO Jack Kennedy! (Gales of laughter and applause from the audience) Bentson lost the election, but no one ever questioned the truth of his remark that evening, either. In fact Dan Quale’s bitter rejoinder that Bentson should have known better than talk like that, at once betrayed his lack of a sense of humor and proper modesty in human relations…and showed immediately that Bentsons observation about his character was all too true.

    I thought that Sean had some very interesting thoughts on the issue of dark energy and strongly agree with most of his points. Dark Energy is definately “stuff”. Sean made no real attempt, it seemed to me anyway, to put the subject of Dark Energy to rest once and for all, but he tossed the subject out for ideas and comment…Dark Energy is an important topic in cosmology these days.

    Einstein was a very modest person. I recall his noting once that he had no special talents, but that he was very curious. I’m sure everyone on this thread shares both Einsteins modesty and his curiousity. However Einstein also once observed that if his theories were proved wrong that he would have indeed known that God himself was incorrect! It is a very human characteristic to form opinions and beliefs of any and every kind, and then defend them with a passionate faith in their veracity.

    Hawking concluded some years ago that: “The universe just IS”. That comment, brief it is, can be taken a number of different ways. However when Einstein’s counterintuitive theories were reduced to mathematics and verified to many places, folks slowly came to understand that Einseins counterintuitive ideas were not those of a stubborn crank, but rather of a man of widely unrecognized genius.

    Science still lacks key peices of the cosmic puzzle. However. we have a lot of factual information too…information about the veracity of special and general relativity, of the correctness of the principles of quantum mechanics, the age of the universe, the omega total, the nature of the power spectum etc. Working within the envelope of the information we have at our disposal, we can and should, I believe conceptualize and put our ideas to the test, not only of academic criticism but by equipment designed to confirm and falsify ideas.

    I think, it was in that spirit that Sean started this thread…

  • Belizean

    But this is a great example of where focusing on “w” leads you astray. People begin to think (incorrectly, of course, and the careful people don’t think this way) that p = w ? is an equation of state, and should have something to do with sounds speeds etc.

    There’s nothing wrong with regarding p = w ? as a linearization of the equation of state that is valid for sufficiently low densities. The actual equation of state depends of course on the details of the matter Lagrangian. In certain cases, e.g. a scalar field, the equation of state is precisely given by p = w ? (w = 1 for a massless quadratic scalar field, w = -1 for a static inflaton-like scalar field).

    To get any of that stuff right, you should look at the equations of motion that are derived from the Lagrangian of your underlying theory, not think in terms of p and ?.

    The coupled equations of motion for gravity and matter are often intractable. One therefore has little choice but to proceed by extracting an effective equation of state from the matter Lagrangian. Sometimes this leads to a dilute fluid approximation like p = w ?. Discussions of sound waves are perfectly legitimate, as long that their density variations are within the regime of validity of the approximate equation of state.

    I have to completely agree with David Bennett. Your effort to reduce confusion (which is normally successful) has in this particular case increased it.

  • John Merryman

    Greg, Sean,

    I can understand and respect your professional positions. In my business, horse racing, people who don’t know what they are doing are a major source of income and frequently lose their shirts. Given that, I don’t waste much time raising these issues, except as a hobby.
    That said, my doubts about BBT preceded both the discovery that large scale structure exists to the very edge of our viewing ability and the need to add dark energy, both of which suggest the current finite model of the universe doesn’t effectively contain all the facts and has been stretched to accomodate them, so I have felt vindicated in the past and suspect I will in the future, but since I don’t want to wear out my welcome here, I’ll drop the discussion.

  • John Merryman

    Not to cause too much aggravation, but I would like to put in a plug for convection as a sort of everymans TOE. It does provide a useful model for understanding all sorts of political, social, economic type issues, where fresh energy is constantly rising up and displacing the old order, even as it carries it along, while the old, cold way falls back down, providing sustenance for more fresh growth. It also provides a useful analogy for life itself, as dynamic youth rises up, while crusty age crumbles.

    For us dummies who don’t have the brains or initative to go get a formal education in modern physics, it also provides an interesting analogy for the relationship of Quantum Mechanics to Relativity. QM being the microcosmic indeterminate radiant energy that is constantly expanding out, presumably into new dimensions and universes, while Relativity describes the structured, deterministic, macrocosmic reality that is suffering entropy and gravitational collapse. Obviously this is not for professional consumption, just for those of us unable to grasp the facts and our own inadequacies.

    Anyone wishing to consider the analogy further might consider Complexity Theory, with its modeling of the relationships between bottom up process and top down order.

  • Lawrence Crowell

    To throw a bit of an added complexity to this topic it appears that the anisotropy of the CMB has an anomalous hole. This little hole was first announced last August and there has been some buzz over this. A recent article by Cruz, Turok, Vielva, Martinez-Gonzalez, Hobson in Science, vol 318, 7 Dec 2007 statistically argues that this “hole” is a texture which might be a latent signature of a cosmic string. The paper can be accessed at:

    http://arxiv.org/PS_cache/arxiv/pdf/0710/0710.5737v1.pdf

    It appears that the big bang is the ultimate scattering experiment, and these data are information from which we might understand quantum gravity.

    Lawrence B. Crowell

  • http://www.geocities.com/aletawcox/ Sam Cox

    Ned Wright noted this work on his site, with an implied disclaimer…COBE eliminated the possibility of topological defects in the CMB. However Ned remains open and speculated that perhaps there was one out there somewhere.

    Topological defects have a place, an important place, I would think, but not in the realm of basic cosmological structure, which as Sean pointed out is a matter of stuff and gravity.

    Solitons in a swimming pool are a visual (observed) phenomenon. The stuff in the swimming pool and the effects of wind and gravity are the structure which causes the topological defect…not the other way around.

    The static universe is an interesting concept with a very long and interesting history. Just as the expanding universe, a static or quasi-static universe can be conceptualized in many different ways. If John wants to, he can Google the topic and just enter static or quasi-static universe. He will find enough on the subject to keep him occupied for quite some time.

    Somebody pointed out that when Einstein first conceptualized his static universe, it was widely regarded that the milky Way Galaxy WAS the universe, and he had a peculiar, and not particularly modern way of visulaizing the concept anyway.

    Einstein knew nothing of the true size of the universe, until near the end of his life. He didn’t even regard black holes as more than mathematical artifacts of his relativity theory. He only learned that anti-matter even existed late in his life, and knew nothing of course about acceleration outward.

    Einstein conceived the universe in 4D and after Kalusa offered extra dimensions as a solutions to some of the cosmological problems, proved that particulation only occurs in 4D. For these reasons, and Hubble’s discovery of the expansion of the universe, Einstein disgarded his static universe. However, Einstein knew something was missing…and was searching for the solution of unification when he died in 1955.

    One fact about Einstein which has been widely neglected, is that he was a pretty good engineer, and was very interested in the problem of the existence of information and high complexity in the universe.

    He knew that an expanding universe starts in a low entropy state and proceeds to higher entropy states- and understood the difficulties of finding widespread high complexity in such a universe. He also knew that in any structure, the sum of the moments must be 0 if that stucture is to remain stable…and he tended to view the universe as a structure.

    While the convention of his day was to construct static cosmological models, I suspect that Einstein also had engineering reasons for conceptualizing the universe the way he did. We all remember the famous debate between Einstein and Bohr, and Einsteins remark that “God does not play dice…etc.”

    We may live in a quantum universe, but SR/GR describe the observed universe of information and complexity we live in. Einstein knew that his concepts were deterministic (the “static” universe) in the extreme and felt that QM and SR/GR were as incompatable as oil and water. To Bohrs credit, he saw the outlines of the possible relationship between QM and SR/GR, a relationship which is becoming more clear with the passing decades…

  • John Merryman

    Sam,

    One point to consider with the idea of a convective cycle is the interaction between these opposing and opposite elements of expanding microcosm and collapsing macrocosm, and the complexity it would create.

  • Bren Stockdale

    Hello,

    I am a simple layman that would like very much just to postulate to you all that one of the most coveted laws of physics is the one that states “for every action there must be an equal and opposite reaction”. Why would there not be, at some point in the grand scheme of things, a cosmological reaction to the force that makes automobile-sized rock move 30 million tons of dirt in about 15 milliseconds because of the force of gravity? What would make us so aware of this law (not theory) during high school and once we start being able to write out three page equations, we forget all about the fundamentals that we know to be true, beyond a shadow of a doubt. All I am trying to say is that for every pound (for lack of a better term) of attraction there should be, and Einstein knew it to be true, a force of repulsion to make the cosmos balance. You can call it a cosmological constant or a spaghetti monster or whatever, I will tell you that I am of sound mind and I would be willing to bet even money that we will soon discover that the force of gravity will be offset with a repulsive force at presicely the ratio of 1 to 1. Just because we call it dark matter, does not necessarily mean it is either dark nor matter, the we’ll call it the repulsive force that MUST be present in the universe to acheive balance.

    Thanks for your time.

    Bren

  • Lawrence Crowell

    Sam Cox on Dec 16th, 2007 at 8:45 pm

    Ned Wright noted this work on his site, with an implied disclaimer…COBE eliminated the possibility of topological defects in the CMB. However Ned remains open and speculated that perhaps there was one out there somewhere.

    ——————

    This depends upon what you mean by topological defect. There is no clear indication that the universe is multiply connected. Though that idea has popped up, with some saying the cosmos was a dodecahedron a few years back. There were some say that this “hole,” which is just a cold spot which has “sharp boundaries” in steradian measure from the surrounding. There is a kurtosis measure, a fourth moment as standard deviation is a second moment, for this variation. So there appears to be some sort of physics here, which might be a texture or the result of cosmic strings.

    As a general comment to some of the posters here, I think that in order to understand these matters some familiarity with relativity and general relativity (gravitation) is in order. Some of the ideas expressed here are a bit on the odd side, and frankly just wrong. The resources are out there, in books or on the web.

    Lawrence B. Crowell

  • http://tyrannogenius.blogspot.com Neil B.

    Well, somehow sensing a great need and market niche, I have an idea to promote (not that it seems to need promotion, heh) amateur efforts to weigh in on the deepest questions of cosmology: How about us CPEs (cocktail-party Einstein’s or wannabees) collaborate on a how-to book, I am Einstein (and so can you!) It will of course be a “coffee table book” with plenty of neat diagrams and pictures of curved space and black holes, and just enough equations to give a sophomoric sense that the reader understands these topics even if he or she really doesn’t. It would make a great Xmas gift, so many we can quickly throw together our posts and edit them into a workable approximation thereof; just need some graphics and layout editing.
    ;-)

  • http://tyrannogenius.blogspot.com Neil B.

    PS you won’t *need* weed to use or enjoy this proposed tome, but it will certainly help you enjoy it. Then please watch “What the Bleep do we Know?”, filled with ridiculous fancies I suppose like multiple worlds and the idea that the waves never really collapse. (I haven’t seen it yet, or I suppose I did – since one of my ostensible and unproven, “celestial teapot”-like other selves must have done so out there somewhere. BTW, just where *are* those other universes? “Just asking.”)

  • http://magicdragon.com Jonathan Vos Post

    Re: “One fact about Einstein which has been widely neglected, is that he was a pretty good engineer…”

    The “Einstein Refrigerator” is a type of refrigerator co-invented in 1926 by Albert Einstein and former student Leó Szilárd, who were awarded U.S. Patent 1,781,541 on November 11, 1930. The machine is a single-pressure absorption refrigerator, similar in design to the gas absorption refrigerator. The refrigeration cycle uses ammonia (pressure-equalizing fluid), butane (refrigerant), and water (absorbing fluid). It has been claimed that the Einstein refrigerator is portable, made of inexpensive, nonmoving parts, operates silently, and is very reliable. However, ammonia leaks caused problems among the earlier models, and whether it can cool things adequately is unknown.

    Einstein undertook this invention as a way of helping along his former student. He used the knowledge he had acquired during his years at the Swiss Patent Office to get valid patents for the invention in several countries. The refrigerator was not immediately put into commercial production, but rights to use the patents were sold to companies such as Electrolux of Sweden, and the funds obtained supported Szilárd for several years….

    There’s more on this at Wikipedia, from which I excerpted the above.

    One may be assured that Einstein thus had a very practical (as well as theoretical) grasp of Thermodynamics. It is also clear that he was interested in the connections between Thermodynamics and Information Theory.

    Whether he related that to Cosmology, I do not know. I would ask my teacher, Feynman, to whom Einstein and Oppenheimer and Wheeler were mentors, but, alas, all these men (excepting John Wheeler) are on the other side of a horizon from which, as Shakespeare noted: “No traveller returns.”

  • John Merryman

    Bren,

    I’m also of the opinion it went off the track aways back, but they are the bank and they are printing their own money, so it will take some time for this bubble to reach the popping point.

    Neil,

    Interesting idea, but for my part, I actually do this to decompress. That I feel I’m making some sense, but that no one is listening serves its own purpose. Out in the real world, there are plenty of situations where questioning the powers that be just gets you squashed like a bug. I think that when the history books record this epoch, future psychologists will find it far more interesting then future physicists. Of course, much useful geometry came out of epi-cycles, so we always learn from our mistakes, even those we try to forget. Life is one step back for every two forward and the trick is to make sure as few of them land on you as possible.

  • John Merryman

    “Out in the real world, there are plenty of situations where questioning the powers that be just gets you squashed like a bug.”

    That may be a little too melodramatic. Let’s just say I’ve learned to shut up and do what I’m told.

  • John Merryman

    “That may be a little too melodramatic. Let’s just say I’ve learned to shut up and do what I’m told.”

    That would be the macrocosmic contraction, as opposed to my microcosmic expressions.

  • Jason Dick

    Bren,

    The problem with your analysis is that a single force in Newton’s terms is a force of one object upon another. The force of object A on object B, by newton’s third law, will always be equal to and opposite in direction of the force of object B on object A. This does, in no way, indicate that an attractive force between objects A and B should be offset by a repulsive force (if this were the case, then nothing could ever move with respect to anything else). An attractive force merely means that the force of object A on object B is towards object A, which means that the force of B on A will be towards B. A repulsive force will have the arrows pointing the other way. The forces are balanced by Newton’s third law, and there is no reason a priori to expect there to be any additional forces in there.

  • John Merryman
  • http://www.geocities.com/aletawcox/ Sam Cox

    LC:
    “This depends upon what you mean by topological defect. There is no clear indication that the universe is multiply connected.”

    I agree…the universe seems, from the field evidence so far, simply connected, which is not evidence consistent with an infinite universe or a possibly infinite series of universes.

    Every indication from Ned’s reaction on his site is that he is skeptical, and he gives the circumstances under which he thinks this idea could be taken more seriously by the scientific community.

    Simply connected…completely entangled with no “holes” to anywhere else…

    The widely accepted notion that space in the universe is Euclidean, flat, even globally flat is, I think, a cause for wonderment. Every scientist who speaks about space is careful to use words like almost, or locally flat. The Omega total of 1.02 has been determined to such high precision that no objective person can reasonably assert that space in the universe is globally flat…it is almost flat and certainly marginally closed.

    Ned suggests that the “cosmological constant” if taken with the Omega total might yield globally flat space, but he and everyone else I have questioned on this doubt that figuring a “cosmological constant” into the Omega really changes the inherent geometry of the universe. Neds question comes to mind: “Is space really flat?”.

    The Standard Model requires that the universe had a very specific density at the big bang in order for the cosmos to have developed as it has. The density formula does not accept infinities; for that matter, neither does the grand proportion. Photons are observed to do work. Massless photons would not be expected to do work…as waves-or particles.

    Space in GR is cosmologically curved and closed, Einstein himself visualized it that way. I realize hyperspherical space can be closed and understand that if space is assumed to be hypersperical, proof that space is multiply connected could be considered proof that space is either closed or open- but hyperspherical.

    If space is shown conclusively to be simply connected, it is most likely also spheroid- globally marginally closed, as we already are led to conclude. Overall, space certainly is almost flat…I put emphasis on the word “almost” and remember at the same time the high precision of the experimentally determined Omega total, 1.02.

    It will be interesting to watch and see how things develop! Crazier discoveries have been made in the history of science than (the possibility) that the universe might be multiply connected! Special and General Relativity themselves are so counterintuitive many still refuse to accept them.

    Even folks who use SR and GR every day in their work usually spend little time following the functions and postulates logically. Those who do discover that SR/GR are not really counterintuitive at all. The functions, proportions and geometry explain particulation, space, time and existence in the most precise manner imaginable.

    However, just when we feel the scientific community has a pretty good picture of what is going on, the world can be expected to be broadsided by new discoveries.

    I have enjoyed following your posts, and those of the others as well. The scientific community as well as the general public should be forgiven, I think, their brainstorming.

    As a well trained and informed person, you must smile at a lot of the ideas you see. We all have a tendancy to over generalize and come short in our concepts…missing many possibilites, and focusing on untenable ideas. However it is nice that even the general public senses that SR/GR and QM are astounding, and are interested in the subjects.

    I have taught physics at the high school level, and my students could not wait to get to page 75 in our text…the introduction to Special Relativity!

  • http://www.geocities.com/aletawcox/ Sam Cox

    Errata…

    “Space in GR is cosmologically curved and closed, Einstein himself visualized it that way. I realize hyperbolic space can be closed and understand that if space is assumed to be hyperbolic, proof that space is multiply connected could be considered proof that space is either closed or open- but hyperbolic.”

  • Lawrence Crowell

    The hole or texture which has been discovered in the CMB might be the first indication of experimental quantum gravity or quantum cosmology. I suspect this has much to do with the AdS/CFT. The Anti-deSitter spacetime has some quirky features, such as a periodic time for closed timelike curves, and its conformal infinity is a Minkowki spacetime. That means it is not possible to evolve a Cauchy data set (ie. initial conditions) to conformal infinity without additional boundary conditions on a Poincare 1/2-space. I suspect that this hole, and others doubtless exist as well, may be due to string or d-brane charges that give conformal completeness on the AdS space.

    The global topology of the universe is as yet unknown. If it is a flat space, a spatial R^3 times a real line R, then this means in the inflationary process a three sphere is topologically changed and the boundary as seen by all observers was inflated “to infinity.” We might instead see a tiny piece of the universe, maybe one part in 10^{50} of the whole thing, and it inflated into a huge sphere — but not a flat space. Inflation may have pushed a tiny sphere, where our local region was a trillionth the size of a nucleus into a larger sphere where our local region was expaneded to around a meter across.

    To think about these things does require an open mind. I also think people should not become partisan with either string theory or loop space quantum gravity (LQG). I suspect the two hypotheses are different keyhole views of the quantum gravity problem.

    Lawrence B. Crowell

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  • http://inversesquare.wordpress.com Tom Levenson

    I wrote the pingback above. I have exactly zero to add to the discussion of physics above; I just want to reinforce what I read to be Sean’s complaint about why imprecision in popular science writing matters. I don’t want people to get the message that they should not worry about what a given argument or story actually means. I cannot tell you how many times as a cub reporter at the then Time Inc. magazine Discover I argued with my boss over some variation on the phrase “Fusion: the force that powers the sun….”

    See inversesquare.wordpress.com for my longer screed, taking off of Dennis Overbye’s use of the word “weird” to modify quantum mechanics.

  • Lawrence Crowell

    Quantum mechanics involves a set of relationships between particles. These relationships don’t conform to our usual sense of things. That is why we call them “weird.” It has to be mentioned that space and spacetime involves another set of relationships, which in our low energy world at large is what we ordinarily perceive.

    Two metrics at the same point p will have g_{ab}(p) = g’_{ab}(p), but if that point p is extended to another point in the two metrics the result will not be the same. This means that general relativity does not give an absolute definition of points and their distances, but rather can only determine the location of physical bodies with respect to each other. General relativity does not determine the position of bodies with respect to a manifold. This is the fundamental meaning of general covariance. It should be noted that with a bimetric theory the coordinate identification of points between two metrics completely violates this principle. This is a major criticism of string theory, which imposes a metric curvature on top of a background metric. Technically this runs into some trouble with general covariance in relativity theory. This is the triumph Smolin, Rovelli and others state for Loop Quantum Gravity (LQG). This was realized early on and caused Einstein to write, “That this requirement of general covariance, which takes away from space and time the last remnant of physical objectivity, is a natural one, …” Einstein, Albert; H. A. Lorentz, H. Weyl, and H. Minkowski (1916). The Principle of Relativity, 117.)

    Quantum mechanics is another relationship system between particles. Two particles in an entangled state can exhibit nonlocal properties. For instance let two charged spin particles in an entangled state be separated by any distance. Then we let one of the particles enter a region with a magnetic field. This particle will in a certain basis of states exhibit a precession, just as a gyroscope does due to gravity — the wobbling top. Now assume you submit the other spinning charged particle, far removed from the region with a magnetic field, to a radio frequency (FR) detector. You will then find an RF blip indicating the particle is precessing as one would predict from the magnetic field the other particle is subject to. This will happen so long as the entanglement state is preserved — even if the two particles are light years apart! Without the entanglement issue this is how Magnetic Resonance Imaging works. This entanglement of states, violation of Bell’s equalities, and so forth has been tested positive in literally thousands of experimental tests. Most often it involves entangled photon states, such as squeezed states and parametrically amplitified states of photons and so forth. This is the other relationship system which exists in our universe.

    Quantum gravity involves a unification of these two relationship systems. Most theorists are trying to quantize gravity — given the gravity field as described by general relativity most people try to write put the variables in general relativity in a quantum form, or to get quantum forms of gravity from quantization of strings (a sort of third quantization) and so forth. But I think that ultimately quantum gravity is a general system of relationships where quantum mechanics and relativity are specific examples of this.

    As for writing popularization of science, that is very hard to do. To be honest I think Martin Gardner did the best job it, though his writings are not up to date. Aczel does a pretty good job. But I know from personal experience that I read popularizations as a teenager, where I got maybe 70% of it right, but I had to be disabused of the other 30% which were erroneous ideas I got. I also have talked to many people who have gotten bad ideas from popularizations. In particular my brother, who is a molecular biologist, ended up with all sorts of goofy ideas about things after reading Hawking’s “A Brief History of Time.”

    Lawrence B. Crowell

  • http://www.geocities.com/aletawcox/ Sam Cox

    JVP:

    An interesting post!

    “One may be assured that Einstein thus had a very practical (as well as theoretical) grasp of Thermodynamics. It is also clear that he was interested in the connections between Thermodynamics and Information Theory.

    Whether he related that to Cosmology, I do not know. I would ask my teacher, Feynman, to whom Einstein and Oppenheimer and Wheeler were mentors, but, alas, all these men (excepting John Wheeler) are on the other side of a horizon from which, as Shakespeare noted: “No traveller returns.”

    Richard Feynman was an incredible person, and I envy you for having had the opportunity to be his student.

    I like your mentioning “horizons”. I can’t imagine your studying under Feynman without having had that matter fully discussed!

    I’m inclined, given Einstein’s biography, to believe Relativity theory started as a (static) philosophical world-life point of view he first was briefly exposed to in Hebrew School. Much later, he studied the work of Lorentz and realized its implications. He then integated ideas from Mach and others. Einstein intuitively realized even in 1905 that the universe was locally flat. He was also smart enough not to bite off more than he could chew, so he concentrated on his Special Theory first…but immediately continued with the development of General Relativity. I remember when I was a teenager in the 50′s that the General Theory was still very much being questioned.

    Please note that Shakesphere, NOT Richard Feynman, asserted that death was a horizon “from which no traveler returns”!

    LBC:

    Two really interesting summaries! I want to check a few things, and ask a few questions a bit later…

  • http://www.cyndilauper.com Neil B.

    Tom, Lawrence, other readers:

    I suggest not being so hard on popularizers who loosely use words like “force.” Many words have a broader meaning than for example just in the narrow context of the specific physical parameter with units M*L*T^-2. It’s about extended usage by convention in English (and I’d like to hear from users of other languages of similar issues). “Force” can mean, a source of energy in general without being what moves over distance to give energy. Yet I still think using “the energy source” would have been better. BTW, is the “string tension” of string theory really a “tension” exactly? Maybe, I’m just asking. What examples if any can be found from *professional* usage that aren’t really apt or consistent, not just from popular writing?

  • Jason Dick

    John,

    It does appear that Bren is trying to raise a broader issue about gravity then just specific reaction.

    Bren,

    Try these;

    http://www.plasmacosmology.net/

    http://discovermagazine.com/2005/nov/two-against-the-big-bang/article_view?b_start:int=0&-C=

    http://www.sciencedaily.com/releases/2005/01/050111115201.htm

    http://www.astroleague.org/al/obsclubs/arppec/arphalt.html

    http://www.cosmology.info/

    Sorry, I’m not in the mood for stupidity today. Call back when you’ve got something that has the remotest hint of validity to it.

  • Lawrence Crowell

    A few comments here. First about Feynman, I believe he wrote a note to an associate or his wife something to the effect, “Remind me to not go to any more of those gravity conferences.”

    Force is an interesting concept, and it is something that involves categorically different objects or concepts. Newton’s second law is

    F = ma.

    Now acceleration is a geometric object. It is a purely kinematical concept involving must distance and time. It is also something which can only be measured in an inertial frame, which Newton’s first law implicitely tells us. Mass is something which we have a physical sense of, but that usually involves a measurement on a scale. So then we take F = -kx for the scale (Hooke’s law) and let a = g (0ne gravity or 1-gee) and we measure the displacement x of the spring or scale and we get the mass. But wait a minute! We are defining mass according to a force, which Newton’s second law is supposed to define. The “force” is something which exists independently — it has no meaning outside of Newton’s law. Also notice that to define the “mass” we used Hooke’s law to measure a distance which with a constant gave the force.

    Newton’s second law “compresses” categorically different concepts into a single rule. One must also do an Admiral Nelson “blind eye” approach to use this equation. And this equation is used to put robots on Mars, build passenger planes, automobiles and heart=lung machines. It works awfully darn well. But with some thought it is apparent that it is a rather funny rule.

    Lawrence B. Crowell

  • Lawrence Crowell

    I took a brief look at thise websites:

    http://www.plasmacosmology.net/

    http://discovermagazine.com/2005/nov/two-against-the-big-bang/article_view?b_start:int=0&-C=

    http://www.sciencedaily.com/releases/2005/01/050111115201.htm

    http://www.astroleague.org/al/obsclubs/arppec/arphalt.html

    http://www.cosmology.info/

    There do seem to be these strange “cults” in physics, such as people who think Tesla was some visionary of vacuum energy or these websites or threads based on Arp. These things really don’t measure up very well, and frankly are a physics analogue of what biologists have with Creationism. And in fact some biblical creationists have put their cross hairs on big bang and cosmology and I have seen references to these plasma cosmology ideas as “evidence” of God’s recent creation of the universe.

    Even without these agendas it must be pointed out that plasma physics is the most difficult area of physics. At least this is my opinion. It is based on the Navier-Stokes (NS) equation, which has no known formal solution set. There is a million dollar Claymath award to find this set Magnetohydrodynamics (MHD) couples the fluid flow in the NS equation to the electromagnetic field, where of course the fluid is a bi-fluid of light negative charges and heavier positive charges. These give rise to the Boltzmann-Vlasov equations and related differential equations. Outside of a few artificial cases these equations have no general solutions, and make the pure NS equation look trivial by comparison. People then write and run MHD computer programs to solve problems. If the universe operated primarily by plasma physics then we are really faced with an almost unknowable universe.

    It is worth mentioning that David Bohm wrote down a version of the Schrodinger equation split into its real and imaginary parts. The real part is a modified Hamilton-Jacobi equation and the imaginary part is an NS equation. The NS equation describes what Bohmians call the pilot wave. I am not a “Bohm-mystic” type who thinks this overthrows the “weirdness” of quantum mechanics, but there is something to Bohm’s ideas.

    To imagine the universe as governed by plasma physics suffers from another problem. Gravity is very weak, but there is one “charge” or algebraic root to the field, which is its source called mass, or mass-energy. There is no negative mass. I will leave that bit as I just stated, for there are some controversies over this. This means that while gravity is a very weak interaction it can accumulate arbitrarily with mass-energy density. Electromagnetism has its source as + and – charges, which means the electromagnetic field “saturates.” So while the EM field is much stronger than gravity it cancels itself out on larger scales. For instance, while the sun is largely a very complex plasma its electromagnetic force on the world outside its atmsophere or heliosphere is negligable or zero.

    BTW, the latest issue of science has a feature on the Hinode measurements on solar physics

    Lawrence B. Crowell

  • John Merryman

    Jason,

    http://www.technologyreview.com/read_article.aspx?id=13755&ch=infotech&a=f

    “The quantum world is a world of waves, not particles. So we have to think of electron waves and proton waves and so on. Matter is ‘incoherent’ when all its waves have a different wavelength, implying a different momentum. On the other hand, if you take a pure quantum system – the electrons in a superconducting magnet, or the atoms in a laser – they are all in phase with one another, and they demonstrate the wave nature of matter on a large scale. Then you can see quite visibly what matter is down at its heart.” (Carver Mead Interview, American Spectator, Sep/Oct2001, Vol. 34 Issue 7, p68)
    http://en.wikipedia.org/wiki/Carver_Mead

    http://www.amazon.com/Collective-Electrodynamics-Quantum-Foundations-Electromagnetism/dp/0262133784

    Quotes from this book;

    Quoting Feynman in the preface;
    “If there is something slightly wrong in our definition of the theories, then the full mathematical rigor may convert these errors into ridiculous conclusions.”

    “Einstein was a giant. His head was in the clouds, but his feet were on the ground. But those of us who are not that tall have to chose.”

    The first line of the Introduction;

    “It is my firm belief that the last seven decades of the twentieth century will be characterized in history as the dark ages of theoretical physics.”

    Quoting Einstein in the Epilogue;

    “Assuming the success of efforts to accomplish a complete physical description, the statistical quantum theory would, within the framework of future physics, take an approximately analogous position to the statistical mechanics within the framework of classical mechanics. I am rather firmly convinced that the development of theoretical physics will be of this type, but the path will be lenghty and difficult.”

  • John Merryman

    Lawrence,

    Gravity is very weak, but there is one “charge” or algebraic root to the field, which is its source called mass, or mass-energy. There is no negative mass.

    Light/radiation as negative mass? It would seem to be the opposite in many ways. Gravity contracts/light expands. Also when gravity reaches critical density, it ignites and releases energy as light. As Mead describes light as primarily as waves, possibly when it grounds out/detected as a particle/photon, that it is the first stage of it gravitationally collapsing. Resulting in a larger cycle.

    I think the balance to gravity was what Bren was trying to describe.

  • Jason Dick

    John,

    In reply #99, what’s your point?

    Light/radiation as negative mass? It would seem to be the opposite in many ways. Gravity contracts/light expands. Also when gravity reaches critical density, it ignites and releases energy as light. As Mead describes light as primarily as waves, possibly when it grounds out/detected as a particle/photon, that it is the first stage of it gravitationally collapsing. Resulting in a larger cycle.

    Uh, no. Light has zero mass (as near as we can tell: at the very least, the mass of the photon is absurdly small). Furthermore, to say that “gravity contracts/light expands” is just an absurd statement to make. Gravity is a force, while light is an electromagnetic wave. The two are completely different sorts of phenomena. What you’ve done here would be rather like drawing a comparison between the behavior of, say, ice cream and trees: the two are in different categories altogether.

    And no, wave function collapse has nothing to do with gravitational collapse.

  • Lawrence Crowell

    It is strange that Carver would say that quantum mechanics is all about waves and not particles, since he worked with Feynman. St Rich pretty much said that the quantum world was more about particles than waves. I am not a partisan particularly of either viewpoint, though the wave function in quantum mechanics is really not ontologically real, but is more of a functional distribution which defines what is probable under a measurement at different regions of space. It does have to be pointed out that that measurements usually involve a localization of a wave function into a particle-like sense. The waves are not measured generally, but inferred from the statistics of many measurements

    A paper by Akoury, Kriedl , … may represent the first measurement of quantum waves. They bombarded a single H_2 molecule with X-rays. This photo-ionized the molecule and the electrons of course fly away free. However, the two “sluggish” protons act as a most basic two slit system, and in a quantum mechanical version of the Young experiment in classical wave optics results in a interference-entanglement of the two electron wave functions.

    As for photons and mass. The wave equation for the photon is

    p^2Y – &^2Y/&t^2 = 0,

    for Y the wave function. If the photon has a mass then the zero is replaced with an m^2c^4, which is the Proca wave equation. As a quantum result the propagator for this wave equation is 1/(p^2 – m^2), for p^2 the momentum. Now if the photon had mass then sinse the momentum is p = h/L, for L the wavelength and h the Planck constant, then different frequencies of light would propagate differently and light with different wavelengths of light would exhibit a dispersion. Yet light from the most distant galaxies exhibit no such dispersion. The lower bound on the photon mass is less that 10^{-60}electron volts — essentially zero mass.

    As for so called wave function collapse, the best approach to understanding this is with decoherence of Zurek et al IMO. Roger Penrose does think there is an objective reduction of quantum states and that gravity or quantum gravity actually plays a role. I think in spite of his previous stellar career that he has probably gone off into lala land on this.

    Lawrence B. Crowell

  • http://tyrannogenius.blogspot.com Neil B..

    Lawrence, earlier I was too irritable with long-suffering and mostly helpful Greg Egan about attempts to avoid “collapse” problems, like multi-worlds and decoherence, and just generated heat out of it instead of much light – I can’t really blame him, but the issue wasn’t really cleared up. (What bugged me was the use of terms like “illusion” or “appears to collapse” which aren’t really rigorous scientific terms anyway, are they?) As I read about those things in my middle-brow way, it looks like they cheat: they slip the idea of “probability” into the very attempt to explain the collapse, but probabilities involve collapses already being taken for granted to generate the probabilities! Really, if there is no specific “interventionistic” style collapse mechanism (such as objective collapse), waves just *stay waves* forever! That is the nature of the mathematics of “waves”, and their being equivalent to anything about probability is what we are trying to explain to begin with, not something to sneak into the beginning stages of trying to explain the very same thing. Do you think the transactional approach of John Cramer might help either?

    Not only that, I hear that decoherence and maybe even MW can’t really handle other issues like the reallocation of waves occasioned by Renninger-style negative measurements, and I still haven’t heard decent explanations of how unreliable detectors are supposed to affect WFs (really, we can’t base the physics on mere “displays” of results, they can be wrong!)

  • Lawrence Crowell

    Wow, this touches on a number of things. The problem is that I could spend several hours writing on this and generate a huge post here. The matter of wave function state reduction has a bearing upon this matter of cosmology.

    I think that quantum information is preserved, and in fact I think the total quantum information in the universe is very small, or maybe zero. Information we observe in the universe is due to EPR pairs separated by horizons, such as the cosmological horizon or those with black holes. The conditional entropy across horizons can be negative, which in principle nullifies the information we observe — if we can wait around long enough and have a quantum computer record of all EPR pairs which enter a black hole, or in the earliest moments of the universe More ordinary measurement I think involves a diffusion of entanglement phases into every larger environments or reservoirs of states which prevents a Poincare recurrence of states.

    One of my stipulations is that there is really only one “universe.” So called other universes or cosmologies are amplitudes which are einselected out. Different amplitudes in the cosmological path integral correspond to different cosmologies. If there exist other cosmologies this leads to an open question if one were to say that there exist different cosmologies with classical content. For the state or grand path integral

    Psi[g, Y] = int &g&Y exp^{iS[g,Y]}

    a standard rule is that |Psi[g, Y]|^2 = 1 — the whole shebang as a quantum amplitude is unity. The decoherence between different metric configurations or amplitudes between different cosmologies D[g', g" ] ~= delta_{g’,g”} means that the reduced wave function(al) is

    Psi{g, Y] —> Psi[Y] =~ int &Y exp^{iS[g',Y]},

    where the metric “g” here is a classical spacetime. We would still have that |Psi[y]|^2 = 1 and the amplitudes for the other cosmologies are relegated to tiny amplitudes which might manifest themselves on a larger scale in the classical cosmology as metric fluctuations. So to have universes or different cosmologies with classical content this would appear to require relaxing the unitary rule |psi|^2 = 1 when it comes to quantum cosmology.

    So this is in part my take on the einselection of states in quantum cosmology which leads to a classical cosmology. The we might of course ask, “Why this cosmology and not some other?” We might imagine in the Many Words perspective that our observable world is just one “eigen-branch.” Yet I prefer to stay away from quantum interpretations which to my mind have too much metaphysical content.

    I think gravity is an einselector “machine.” The Weyl curvature distorts the spherical spatial distribution of a set of particles into an oblate spheroid as the cloud of particles falls to a gravitating body. This has a distortion effect on something called the Wigner function for quantum systems. This has a physics similar to decoherence, and it suggests that gravity might play a role in einselecting a few quantum states as classical variables. Also with some calculations I have done I have found that his has some frame dependencies to it which I thought indicated a problem with it. Then came along Don Page who wrote very recently

    http://arxiv.org/PS_cache/arxiv/pdf/0712/0712.2240v1.pdf

    where he advances something very similar — an observational dependence to the state selection process.

    Now I suspect that the einselection principle for the universe we observe, and not a whole gemish of other amplitudes for other cosmologies, is a maximal complexity conjecture. In other words the cosmology which has a classical content is one which permits some maximal amount of complexity in local regions, or some large number of information states which are einselected as classical information. This might be a more operative physics for issues such as Polchinski-Busso theory on 7-brane (dual to 4-brane of the universe) cancellations of a bare cosmological constant which has an Anthropic Principle interpretation.

    The matter of wave function collapse has buggered quantum physics ever since Bohr laid down the Copenhagen interpretation. That works very well, and for most of what people do is operative. But it is unsatisfying on a deep level. Now the matter is being taken up in decoherence theory, einselection and what I see as a matter of quantum gravity. This is not to say I think that Penrose’s idea of Planck scale fluctuations or collapses as inducing state reductions, but more that the classical variables which exist in the universe are einselected in quantum gravity/cosmology. If the deoherence and einselection approach are on the right track then the classical world is really a sort of approximate reality, where really there are still quantum waves underlying everything which we don’t see under a coarse graining.

    Lawrence B. Crowell

  • http://kea-monad.blogspot.com Kea

    Now I suspect that the einselection principle for the universe we observe, and not a whole gemish of other amplitudes for other cosmologies, is a maximal complexity conjecture.

    Lawrence, I like your ideas a lot, and was delighted to come across your book (Quantum Fluctuations of Spacetime) recently while thinking about Hamming codes in M theory. What do you think of the Machian holographic principle (category and number theoretic: ie. not written in terms of stringy classical geometry) as a maximal complexity constraint? This avoids the ‘einselection-looks-like-collapse’ semantics (which I think is a problem but you may disagree) by rephrasing quantum causality in terms of a (categorical) pure quantum logic. The maximal complexity results from the need to use the whole n-cat heirarchy to reach the correct emergent classical picture.

  • John Merryman

    Lawrence,

    While Feynman was a colleage and friend, they were in disagreement on this and this book was Mead’s argument. Suffice to say the math is beyond me. His argument is essentially that quantum mechanics is a digital description of an analog reality.

    As to the earlier point about quantum entanglement, it does make sense as a wave. If you and I were twenty miles to either side of a radio station, that we were both tuned to, it wouldn’t be any mystery that we heard the same sounds at the same time.

    Theoretical physics is to applied physics what design is to engineering. If I want to know what can be concieved, I’d ask a designer. If I want to know what works, I’d ask an engineer. Given Mead has been a seminal figure in the computer revolution, I wouldn’t personally dismiss his experience when compared to academics who’ve spent their careers figuring what happens at the edge of a black hole. Remember it is because of applied physics that society funds theorectical physics to the degree it does, so it is ultimately wise not to dismiss everyone whom you may disagree with, without considering the entire picture.

  • Jason Dick

    Neil,

    What bugged me was the use of terms like “illusion” or “appears to collapse” which aren’t really rigorous scientific terms anyway, are they?

    We’ve gone over this. Of course the appearance of collapse is rigorous scientific terminology. In fact, it is only the appearance of collapse that we can ever conceivably measure. Given two theories, one with collapse and one without, the one without must necessarily have the observed appearance of collapse within it to be valid. From there we have to things that need to be done to decide between the theories:

    1. Occam’s Razor tends to be a good guide for deciding which is more likely, and thus useful for guiding future experiments.
    2. The use of experiments to distinguish the two theories.

    The difference between quantum mechanics with collapse and quantum mechanics with only the appearance of collapse is that there is one less axiom in the latter. Thus, by Occam’s Razor, it seems rather likely that the latter is more likely. Furthermore, quantum decoherence is a phenomenon that does not happen suddenly, but instead quite gradually. As a result, it can be (and has been) observed quite directly in the laboratory.

    Thus it turns out that the many worlds interpretation of quantum mechanics is not in any way an attempt to avoid any “collapse problems.” Instead, it’s an explanation of the observation of wave function collapse that requires no additional assumptions. As a result, we can be pretty confident that it’s accurate.

    Lawrence,

    I think gravity is an einselector “machine.”

    This description could just as easily describe the other three forces we know of too, though, as well as any other quantum mechanical interactions.

  • http://www.geocities.com/aletawcox/ Sam Cox

    LC:
    ABSTRACT: Don N. Page; December 13, 2007…last sentence…

    “SQM also suggests the possibility that past steps along our evolutionary ancestry may be so rare, that they have occurred no where else in the past history of the universe that we can observe”.

    It is almost certain that life in the universe is a common phenomenon. It is also almost impossible that beings identical to ourselves exist anywhere else. One does not have to be a quantum theorist to fathom that! However it is interesting that certain quantum theories point to such an obvious conclusion about our uniqueness in the universe.

    For similar reasons, related to genetic inheritance and environmental upbringing, each human individual who has ever lived is also unique. Cloning people doesn’t produce robots, just individuals with identical genetic inheritance- as identical twins. However, no pair of identical twins live exactly identical lives.

    This comment in Don’s abstract has profound implications…

  • John Merryman

    Jason,

    Uh, no. Light has zero mass (as near as we can tell: at the very least, the mass of the photon is absurdly small). Furthermore, to say that “gravity contracts/light expands” is just an absurd statement to make. Gravity is a force, while light is an electromagnetic wave. The two are completely different sorts of phenomena. What you’ve done here would be rather like drawing a comparison between the behavior of, say, ice cream and trees: the two are in different categories altogether.

    Presumably mass can be converted to energy and vice versa. Obviously all the connections are not apparent, but for those of us not tracking down all the details, it is a logical conclusion that some form of cycle exists.

    Thus it turns out that the many worlds interpretation of quantum mechanics is not in any way an attempt to avoid any “collapse problems.” Instead, it’s an explanation of the observation of wave function collapse that requires no additional assumptions. As a result, we can be pretty confident that it’s accurate.

    While it may not be apparent, I am generally the go along to get along type of person. But when presented with comments like the above, especially when I’ve been expected to swallow a series of other incongruities, from the universe being 13.7 billion years old, which happens to be how far light appears to travel, even though an inflation stage blew it up to many times its visible size, then that there is lots of dark matter causing galaxies to spin faster than Newton’s laws account for and, oh wait, 70% of the universe is actually invisible energy because these darn galaxies are flying away from each other much faster then predicted. Of course I should be softened up enough to buy the many worlds, other universes, etc.. After a while though, the average person is going to start scratching their head. At some point it starts looking like cult behavior.

    Would Einstein buy this? Or would he be going back and reviewing past assumptions. Frankly I’m no smarter then I was at twenty, but I’m alot wiser and much of that has come about from having many of the certainties I was taught break down and having to pick up the pieces and start over again.

  • Jason Dick

    Presumably mass can be converted to energy and vice versa. Obviously all the connections are not apparent, but for those of us not tracking down all the details, it is a logical conclusion that some form of cycle exists.

    No. Mass is energy. Now, it is possible to convert between mass energy (the energy in any internal degrees of freedom) and kinetic energy. But conversion between mass and energy is a nonsensical statement.

    And no, there is no logical conclusion to be had until you define your terms properly, which you haven’t done.

    While it may not be apparent, I am generally the go along to get along type of person. But when presented with comments like the above, especially when I’ve been expected to swallow a series of other incongruities, from the universe being 13.7 billion years old, which happens to be how far light appears to travel, even though an inflation stage blew it up to many times its visible size, then that there is lots of dark matter causing galaxies to spin faster than Newton’s laws account for and, oh wait, 70% of the universe is actually invisible energy because these darn galaxies are flying away from each other much faster then predicted. Of course I should be softened up enough to buy the many worlds, other universes, etc.. After a while though, the average person is going to start scratching their head. At some point it starts looking like cult behavior.

    So? When we enter new areas of observation we should expect things to be weird and counter-intuitive. The statement that a theory describes things as being weird is in no way evidence against that theory. Until you have some real, solid evidence that scientists are being misled, your claims of cult behavior are baseless.

    Would Einstein buy this?

    Irrelevant. The progress of science is independent of any one person.

  • Lawrence Crowell

    Machian holographic principle: The holographic principle came about because of the duality between Anti-deSitter spacetime and conformal field theory. This duality was illustrated by Maldecena as a way in which the AdS spacetime has Minkowski spacetime at conformal infinity.

    The AdS spacetime, a five dimensional spacetime with signature [-,-,+,+,+], with effectively two “time variables,” has at conformal infinity a timelike flat spacetime. As such it can’t be determined by a spatial data set without some additional boundary conditions. The deSitter spacetime is related with signature [-,+,+,+,+], where one of the time directions in the AdS is Wick rotated to a spatial variable.

    In an 11-dimensional “bulk” there is a 10-brane of supergravity. There is a topological result called Poincare duality in algebraic topology, which is that in any n dimensional space a p-dimensional “chain” or cocycle (p —-> |out>. BTW, string theory has its origin with Veneziano amplitudes and S-matrix theory.

    Smolin wrote his three paths to quantum gravity, and I should point out that the LQG is probably just a view of quantum gravity through a keyhole on another door. I suspect that string theory and LQG, both approaches have their warts and problems, are just different approximate perspectives on the same problem.

    Lawrence B. Crowell

  • Lawrence Crowell

    Sam Cox on Dec 20th, 2007 at 1:50 am
    LC:
    ABSTRACT: Don N. Page; December 13, 2007…last sentence…

    “SQM also suggests the possibility that past steps along our evolutionary ancestry may be so rare, that they have occurred no where else in the past history of the universe that we can observe”.

    It is almost certain that life in the universe is a common phenomenon. It is also almost impossible that beings identical to ourselves exist anywhere else. One does not have to be a quantum theorist to fathom that! However it is interesting that certain quantum theories point to such an obvious conclusion about our uniqueness in the universe.

    ———————–

    I worked out a chaos problem with the stability of stellar systems. I looked at the range of extrasolar systems identified and estimated the Lyapunov exponent for a planet at 1AU around these G-class stars. The “Jovian” planets for the most part perturb these putative earths in unstable orbits and with some Bayesian statistics I found that our galaxy may only contain a few hundred Earth-like planets which might permit biology. In other words biology might be a process inherent to the universe under the right conditions, but those conditions are comparatively rare. Observership in the universe is maybe far more rare as well. We share this planet with other intelligent life forms, cetacians and cephalopods, such as octopi — which are invertebrates and some have basketball sized brains, but they lack some faculties required (social behavior, or hands or … ) to be a cosmological observer.

    Don Page’s idea here is commensurate with Stephen J. Gould’s comments as well. Evolutionary biology does not have an apriori attractor point or “goal” for some progress. Biological evolution may select for an increased complexity in organisms, as measured by tissue types, or organizational structures, but the range of possibilities seems to literally explode. Of course this is a geo-centric view of biology — who knows what another bio-planet has going on. I just published a book on sending probes to such planets BTW. Yet biological evolution does not appear to operate with some goal of generating cosmological observers.

    This tends to make my cast a suspicious eye on cosmological principles. If you think about it the only thing we human beings really make at the end is garbage. If there is any identifiable long term function our species serves it is to tear up this planet and convert everything into trash. We are doing a bang up job of this!

    Page’s main thesis is that einselection appears to have an observer dependent content. It suggests a sort of frame dependency which might indicate a reason for some confusion we have. It might also be a pathway to a commonality between freme dependencies with geodesics and the rest with general relativity.

    Lawrence B. Crowell

  • http://tyrannogenius.blogspot.com Neil B.

    Jason, yes we’ve been through this in the sense that you nor Greg E. never defined (and certainly haven’t defended same) what you think “appearance of” means in this context. Just what is an “appearance” instead of the “real thing” here anyway? I keep asking because you keep saying nothing in the answer (nothing that satisfies describing what a collapse is, versus what an appearance is, etc.) For example, it is absurd to talk of “appearance of collapse” being “the only thing we can measure” when the measurement is the very definition and probable cause of collapse. (If you and other empiricism end-runners are now meaning some tricky way of talking about appearance and reality, don’t pretend that is just “science” business as usual.) The wave has to really collapse because the detection at some point means it can’t be anywhere else. It isn’t about which description posing as a “theory” is simpler, it’s about which description is what we find happens, and then trying to explain *that*.

    Since we started out with dark energy, here’s another issue and question, about energy conservation and gravitational waves. I asked this at Backreaction (where they are more appreciative of my questions and less into too-clever-by-half metaphysical manipulations),
    at http://backreaction.blogspot.com/2007/12/indirect-detection-of-gravitational.html:


    At 2:19 PM, December 19, 2007, Blogger Neil’ said…

    I was browsing Penrose’s latest big opus, The Road to Reality, and saw discussion about gravitational radiation and energy. I got the impression, there is no way to assign energy to traveling gravity waves like there is in E&M radiation (E and B amplitudes squared leading to energy density.) Well, maybe there’s proper justification, but: how can you get energy conservation if the radiating bodies lose energy, but there’s no energy “out there” to make up the difference?

    And BTW, shouldn’t criticisms or alternative perspectives (like what Al refers to) get some open-minded attention? I wouldn’t know, just asking.

    At 2:30 PM, December 19, 2007, Blogger Bee said…

    Hi Neil’,

    I don’t mind ‘alternatives’ and it’s nice people are looking into various things etc blahblah, but given that GR works pretty damned well I’d like to see really good reason before I consider replacing it with something else.

    Regarding your question, I’m not sure I know what you mean with “out there”, but I will have a try. It is of course correct that there is no well defined stress-energy-tensor of the gravitational field itself, and esp. that of grav. waves vanishes (well, it’s a vacuum solution). One can however very well talk about energy transport towards infinity, e.g. like the energy loss of the source discussed above. That usually requires a gauge-fixing. I think Weinberg discusses this very nicely in his book. Best,

    B.

    OK, but I still want to know *how* and “in what” the lost energy is stored, to comp. for the radiating system having less, if not in gravitational waves per se?

  • Jason Dick

    Neil,

    The appearance is just that: when one performs a measurement under certain conditions, one sees collapse. Of course, this is only the classical limit of the phenomenon. Quantum decoherence predicts a very specific, gradual transition to where the system appears to be fully collapsed dependent upon the interactions that the system undergoes.

    For example, it is absurd to talk of “appearance of collapse” being “the only thing we can measure” when the measurement is the very definition and probable cause of collapse.

    Nope. It’s the interactions that we make use of to perform the measurement that cause the appearance of collapse. That there is a person there to read out the results is irrelevant.

    The wave has to really collapse because the detection at some point means it can’t be anywhere else.

    Not in the least. The problem is that we are not separate from the system we are measuring. The reason that we see collapse is because we are described by the exact same quantum mechanics that describe the system we are measuring, and in order to see a measurement we have to interact, however indirectly, with the system we are measuring. Quantum decoherence is, after all, about components of the wave function losing information (and the ability to interact) with other components of the same wave function. Thus we see the detection at some point (in the example of a spatial detection) not because it really is there, but rather because that is simply the component of the wave function which “we” happen to be (the other components would also be the same persons, of course, just with different outcomes).

    As far as your gravitational wave question, that’s a pretty good question. This paper claims to have the answer:
    http://arxiv.org/abs/gr-qc/0102072

    I’d read through and try to get a basic understanding, but my plane is boarding, so I have to go.

  • John Merryman

    Jason,

    No. Mass is energy. Now, it is possible to convert between mass energy (the energy in any internal degrees of freedom) and kinetic energy. But conversion between mass and energy is a nonsensical statement.

    And no, there is no logical conclusion to be had until you define your terms properly, which you haven’t done.

    The gravitational field of a galaxy extends out several times its visible size, so presumably it’s drawing matter in from that area. Galaxies are visible from 10+ billion lightyears away, so presumably they radiate light out over that area. Are you arguing that the matter being drawn into a galaxy has no causal relationship to the light radiating away from it?

    So? When we enter new areas of observation we should expect things to be weird and counter-intuitive. The statement that a theory describes things as being weird is in no way evidence against that theory. Until you have some real, solid evidence that scientists are being misled, your claims of cult behavior are baseless.

    When I was young, I saw patterns in the clouds. Now that I’m a good bit older and pushed the horizon of reality a few times, I see clouds in the patterns. Few things seem weird to me anymore, just degrees of organization, which modern cosmology has issues with, since its loose ends have been increasing much more rapidly(96% invisible universe?)then they have been decreasing. As for science being misled, how can the increase of the energy density of the universe by such a massive amount not cause anymore soul searching then it did? Can you think of any other field where prediction could be that far off and not have serious repercussions?

    Irrelevant. The progress of science is independent of any one person.

    The progress of science is independent of any group of people as well. BBT can’t paint itself much further into the corner.

    Lawrence,

    And in fact some biblical creationists have put their cross hairs on big bang and cosmology and I have seen references to these plasma cosmology ideas as “evidence” of God’s recent creation of the universe.

    Actually the reverse is true; Hannes Alfven, one of the developers of plasma cosmology; “I was there when Abbe Georges Lemaitre first proposed this theory [Big Bang]. Lemaitre was, at the time, both a member of the Catholic hierarchy and an accomplished scientist. He said in private that this theory was a way to reconcile science with St. Thomas Aquinas’ theological dictum of creatio ex nihilo or creation out of nothing. There is no rational reason to doubt that the universe has existed indefinitely, for an infinite time. It is only myth that attempts to say how the universe came to be, either four thousand or twenty billion years ago.”

    Monsignor Georges Henri Joseph Éduard Lemaître (July 17, 1894 – June 20, 1966) was a Belgian Roman Catholic priest, honorary prelate, professor of physics and astronomer.
    Fr. (later Msgr.) Lemaître proposed what became known as the Big Bang theory of the origin of the Universe, although he called it his ‘hypothesis of the primeval atom’.
    He was a pioneer in applying Einstein’s theory of general relativity to cosmology: suggesting a pre-cursor of Hubble’s law in 1927, and then publishing his primeval atom theory in the pages of Nature in 1931. At the time Einstein believed in an eternal universe and had previously expressed his skepticism about Lemaître’s original 1927 paper. A similar solution to Einstein’s equations, suggesting a changing radius to the size of the universe, had been proposed in 1922 by Alexander Alexandrovich Friedman, as Einstein informed Lemaître when he approached him with the theory at the 1927 Solvay Conference (Friedman had also been criticized by Einstein), but it is Lemaître, with his proposed mechanism, that made the theory famous for several reasons according to historians. First, Friedman was a mathematician who was not working with astronomical data or concerned with the math as a description of physical reality. Secondly, Friedman died young and could not further work on his ideas. Thirdly, Lemaître worked with astronomers and made his theory in accord with observations and had consequences which could be tested. Fourth, Arthur Eddington made sure that Lemaître got a hearing in the scientific community.
    Lemaître also proposed the theory at an opportune time since Edwin Hubble would soon release his velocity-distance relation that strongly supported an expanding universe and, consequently, the Big Bang theory. In fact, Lemaître derived what became known as Hubble’s Law in his 1927 paper, two years before Hubble. However, since Lemaître spent his entire productive life in Europe rather than emigrating to America, American publicity machines have preferred to stress the contributions of scientists such as Hubble or Einstein who can be claimed to have a US connection.(from wikipedia)

  • Lawrence Crowell

    State reduction is an open problem in physics, and we should not be to quick to make hasty assumptions. A complete reduction of a state is within the Copenhagen viewpoint. A wave function psi = sum_n C_n phi_n that gives a measurement O_i of the observable O reduces the state to phi_i, for some i in the summation index over the state space. In Bohr’s Copenhagen interpretation the classical world imposes a projector operator P_i on the wave function to project out that state. Projector operators are not unitary, and are idempotent, which puts them outside standard quantum formalism. But Bohr tells us not to worry because the imposition of a classical world or the detector necessitates this. So here a measurement is thought to reduce a wave function to a “point,” or some spectific eigenstate corresponding to our measurement.

    The Copenhagen interpretation has gotten a lot of criticism by some folks, but it first has to be pointed out that it works very well. The main problem with it is that we all know that the classical world is built up from quantum systems, atoms, electrons, nuclei etc. And so this dichotomy is something artificial. The decoherence approach says that a quantum system with its entanglement phase looses that phase to a reservoir of states corresponding to the environment. This is not too different from the Fermi golden rule for spontaneous emission. There excited states emit photons in a vast number of possible occupation states (vacuum states) and a grand sum over these leads to a spontaneous irreversible emission of photons. Similarly a quantum system with some density matrix is reduced to a diagonal matrix and the off-diagonal terms of the form C_m^*C_n|n>

  • Lawrence Crowell

    My last post on state reduction was cut off. So before I talk about Lemaitre here is the rest of them:

    (state overlaps or entanglements) are lost to the reservoir of states. The entanglement is preserved but just scrambled up in the reservoir of states. The now diagonal density matrix then just gives a classical-like set of probabilities for the outcome. Decoherence does not tell us which state obtains, but it does tell us how under a measurement the observed outcome is reduced first to a classical probability problem. We still have to look at the dice to see the outcome.

    Einselection is a bit more on decoherence, for it attempts to indicate how a wave function is “squashed” into a sharp peak, or a near delta function. If this is completely reduced to a delta function corresponding a measured outcome this recovers the Copenhagen ad hoc state reduction (collapse). Yet to be true to QM we can’t completely reduce it that far. We might come very close, but maybe not completely.

    So we might find that the classical world is something which exists FAPP, or as itself a good approximation. In the same light a measurement of a quantum system is an approximation. And of course realistically measurements are never exact: first we have the uncertainty principle, then we have instrumentation tolerances, shot noise in electronics and so forth. So the prospect that we don’t completely reduce a quantum state might not be so horrid. We are giving up a security blanket more than anything.

    As for Many Worlds and other interpretations my main problem with these ideas is that they are fundamentally untestable IMO. There does not appear any way around the Bell inequality result to peek behind the curtain to tell which of these, MWI, Bohm etc, are really operative. This is a problem I think exists with the Meade idea with QED.

    As yet the problem is still open. Some progress has been made on this, but the problem has yet to be satisfactorily solved and produce results which can be tested and not rely upon “things” behind the quantum curtain.

    ——————-

    I was referring to more recent times. I have seen some Creationist stuff in recent times which reference “plasma cosmology” as evidence for a recent origin of the universe — recent as in 6000 years ago.

    Lemaitre also admonished the Pope that this should not be taken as evidence of God’s creation. He did say that the universe came about from the “radioactive decay” of a primeval atom. In a way inflationary cosmology of Guth is a more precise statement of this: An unstable vacuum with a Higgs particle that adjusts the vacuum state to a physical vacuum and inflates a spacetime from a near Planck scale to the large.

    As for light emitted by galaxies influencing gravity, or visa versa, I suspect that you are not quite on track there. Gravity provides the pressure inside a star to maintain nuclear fusion, which is the energy source for light emitted by stars. But there is no causal relationship between light and stars as you might be thinking. Black holes are the epitome of a non-emitting object and they have a gravity field — one hell of one close up.

    Lawrence B. Crowell

  • http://www.geocities.com/aletawcox/ Sam Cox

    LC:

    1.) “Yet biological evolution does not appear to operate with some goal of generating cosmological observers.”

    GOOD point, in my opinion…and I appreciate the second interjectory paragraph too, but then in the third paragraph below, you correctly return to discuss frame dependency as a possible reason and explanation for this conundrum….

    2.) “This tends to make my cast a suspicious eye on cosmological principles. If you think about it the only thing we human beings really make at the end is garbage. If there is any identifiable long term function our species serves it is to tear up this planet and convert everything into trash. We are doing a bang up job of this!”

    3.) “Page’s main thesis is that einselection appears to have an observer dependent content. It suggests a sort of frame dependency which might indicate a reason for some confusion we have. It might also be a pathway to a commonality between freme dependencies with geodesics and the rest with general relativity.”

    When the universe is observed from a particulate 4D frame of reference, and because what we observe is the result of accelerations, gravitational and relativisitic effects, we are not seeing the universe the way it actually cosmologically exists.

    Yes, our existence is tied in the reality we observe- to evolutionary developments which could not be exactly duplicated anywhere else in the universe. Yes, the world we live in is so real, technologies can be developed on the basis of careful observation and measurement of the cosmic processes and universe we observe.

    Yet, in a phylogenically developing quantum quasi-static universe, the requirement for its very existence, observation in ever higher levels of complexity, may in a sense, be like a few diamonds processed from huge amounts of cosmic “ore”.

    It is important, I think, to remember that inorganic and most likely, organic complexity in the universe are actually very widespread. The proportions and behavior of specific sets of similar particles and atoms are global phenomena. For observational complexity to exist in the universe, particles must not only be particles and atoms, atoms, but the behavior of all this inorganic matter, resonances at stellar temperatures, valence relationships and the like are and must be strictly constrained.

    All of this is tied to the nature of gravity itself, the very specific density necessary at the big bang and the nature of the grand proportion…the way energy becomes energy densities…matter…and the behavior of energy as scale in the universe varies.

    I keep coming back to Hawkings observation that the universe “just is”. From our frame, we place value judgments on what we observe and try to ascertain “purpose”, “worth” or “worthlessness”. However, however low our opinon of the quality of existence, existence…the observation, measurement and appraisal of our 4D reality is all we have…it is all there IS. I should stress that the universe emphasizes diversity…human culture, conformity. The reason for this difference is the reality of existence VS the way we collectively observe from limited frames.

    A relative of mine passed on recently, and the day before she died of congestive heart failure resulting from cancer, some of us visited her. She was quite lucid. One of the relatives expounded on the religious viewpoint regarding death…very passionately!

    When he finished, she turned to me and said: “Sam, what do YOU think? I told her that if death was non-existence, there wasn’t much she- or we- could do about it, so worry under that circumstance was unnecessary.

    However, I also told her we live in a universe which exists only as it is observed and measured, so while I felt non-existence was possible, it was the least likely answer to her question. I told her that reincarnation from my point of view is untenable because we exist as individuals ONLY because of our unique genetic and environmental experiences.

    I told her, that from her frame, and the frame of any and all living, I felt there were only two really viable possibilities. 1. Exeriencing existence in geometric inversion and decreasing entropy, followed by reemergence into the same life she already experienced, or 2. A gradual re-awakening after death, as a child into her same existence…she would be chasing her kid sister around the house some day, and suddenly stop and look in a mirror with surprise…wondering why she was young…then continuing to chase her sister around the house- and into eternity.

    If life ended at death, it is virtually impossible we would be existing “now”.

    I might add that I do not regard existential problems as philosophical issues. To my mind, such things are at their heart matters for scientific inquiry and ultimately factual solution and understanding.

  • John Merryman

    Lawrence,

    As for light emitted by galaxies influencing gravity, or visa versa, I suspect that you are not quite on track there.

    As for the vice versa, assuming that’s gravity influencing light, I thought that was what provided the original proof of Relativity, the experiments in 1919 showing the light from stars being bent by the gravity of the sun, during a solar eclipse!

    It’s not that light influences gravity, obviously the gravity has the local advantage, but if gravity affects light, it would seem the symmetry would imply that there is some very minor counter-effect? “For every action, there is an equal and opposite reaction.”

    Gravity provides the pressure inside a star to maintain nuclear fusion, which is the energy source for light emitted by stars. But there is no causal relationship between light and stars as you might be thinking. Black holes are the epitome of a non-emitting object and they have a gravity field — one hell of one close up.

    There has been much discussion recently of jets from galaxy cores;

    http://www.space.com/scienceastronomy/071217-death-star-galaxy.html

    http://news.xinhuanet.com/english/2007-12/18/content_7272144.htm

    Here is a clear picture of a jet from a galaxy core;

    http://apod.nasa.gov/apod/ap000706.html

    Just like the radiation from the stars surrounding the black hole, this is another form of energy escaping from galaxies. According to the first link above, it may well provide the source for future galaxies;

    Turns out that the “death ray” may not be all bad news for the victimized galaxy, at least theoretically, as such a massive influx of energy and radiation could help form new stars and solar systems by compressing gases.

    “In the end [3C321] may be the source of new life in that distant galaxy,” said Martin Hardcastle, an astronomer at the University of Hertfordshire, in the United Kingdom. Hardcastle explained that the jet will continue to pour out of its parent supermassive black hole for about 10 to 100 million longer — plenty of time to squeeze otherwise inert gas together into new star systems.

    “Jets can be highly disruptive … but [create] stellar nurseries,” Tyson said. “It’s a fascinating sort of duality about how these high-energy phenomena influence the environments in which they’re embedded.”

    If you are willing to consider that the mass falling into the galaxy is the original source of this energy, then here is a version of the cycle.

    As I recall, at the center of a normal gravitational body, such as the earth, the gravitational effect balances out, so that while the pressure is enormous, the gravity is neutral. If this was applied to galaxies, it might explain why they shoot these jets out from the poles.

  • Lawrence Crowell

    This posts answers multiple posts above:

    In Sam Cox’s response he quotes me in, “This tends to make my cast a suspicious eye on cosmological principles. ” I meant to say anthropic cosmological principles.

    My point in mentioning this is two fold. The weak anthropic principle (WAP) is really a sort of question. Bethe challenged a WAP statement that the laws of physics had to conform to an ancient Earth, but gravity compression models of solar energy predicted a sun lasting only a few 10′s of thousands of years. So Bethe figured out a nuclear fusion model of solar energy, and viola the WAP problem was removed. I think something similar is afoot here. The WAP implication of D4-brane and D7-brane duality and the cancellation of the bare cosmological constant by Polchinski-Busso suggests strongly that there is some other “non-anthropic” physics, or quantum gravity, or cosmological principle waiting in the wings.

    The second objection is that we humans have a prejudice to see the universe as existing around us, or that it was created with us as its purpose. Religion is largely fashioned around this idea. Yet to be honest I find these things as intellecually vacuous, though maybe I am somewhat disposed to the Flying Spaghetti Monster :-) But you do indicate that the universe does permit a vast array of diversity, which is in line with my hypothesis that the cosmology einselected from the grand path integral (analogous to a grand partition function of “everything” in a Euclidean measure) is somewhat in line with this. Yet I think that we humans are just some flash in the pan, even if we appear to be cosmological observers.

    This is not exactly the forum to write about it, but I can offer some pretty strong reasons to see us humans as really dysfunctional life forms, or as some sort of terminator species that is hopelessly out of balance. At no point in the natural history of this planet do I think there was ever a species of animal our size and dietary requirements that numbered at one time 6.6 billion. Then consider we drive cars and run machines and use far more energy. We are just billions of ground apes exponentially rampaging out of control. We also tend to put some of the most insane or lunatic of our kind in positions of great power — my country elected GW Bush twice! And GWB IMO is a dim-witted loony.

    As for J Merryman, I also saw the astrophysics of the galactic jet spraying a second galaxy. This involves lots of complicated astrophysics of accretion disks around black holes, in this case a galatic black hole of 10^6 or larger solar masses. The gravity pulls in surrounding matter and heats it up. This enormous heating up of material is what generates these spectacular processes. It involves lots of plasmas heated up by gravity accretion, magnetic fields getting wound up in the plasma which ejects ionized high energy material into these jets. I am not particularly that learned in these astrophysical complexities, where you get the geniuses who run complex differential equations on computers to simulate or predict these things.

    Gravity waves and energy — Gravity waves are type N solutions in the Petrov classification. This classification involves Killing eigenvectors of the Weyl curvature. The easiest way to understand gravity waves is with weak gravity waves, so called pp-waves. These obey a differential equation of the form

    &_c&^c h^{ab} = k T^{ab}

    where h^{ab} = g^{ab} – 1/2 h_{ab} tr(g) and h_{ab} the flat Minkowskian metric. Here & = 4-dim partial, k = 8piG/c^4. The momentum energy term on the right is the source of the gravity wave. This is a wave equation similar to that for a Maxwellian electromagnetic wave with a source. In this weak case matters of energy conservation don’t appear. Weak gravity waves are all we are likely to ever detect from distant astrophysical sources, such as colliding black holes and other violent events.

    This apparent energy conservation appears because this is a bimetric theory, which departs in subtle ways from the general covariance of general relativity. In a way we are imposing an implicit energy conservation onto the problem, which works sell enough in this weak field domain. For strong gravity fields we are not quite so fortunate in being able to pin down energy conservation — the time variation in the field prevents a global timelike Killing field.

    However, as Feynman pointed out if you have two beads on a stick a gravity wave will cause them to move. If these rub the stick they generate heat, or if we were to put magnets on the beads and fix solonoids around them we will get a current. So from some basic physical arguments it can be seen that gravity waves carry energy or impart it on systems they interact with.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    So from some basic physical arguments it can be seen that gravity waves carry energy or impart it on systems they interact with.

    That is essentially a description of my understanding of gravity as a collapsing spacetime geometry. Not that it is energy, but that the release of energy results in a collapse of the system. This may not be entirely correct, as there may be a gravitational attractor, but that if it is part of a larger cycle, there is a siphoning effect, where systems that are radiating energy also draw in material. What might propel this system is the existence of more energy then the space can hold in solution, so that it keeps clumping and precipitating out, until it heats up to the point of breaking down and radiating away. Since this released energy is hotter then the existing background radiation, it displaces it, so that the cooler radiation starts to clump and precipitate out and so on. Necessarily this cycle means that the universe is infinite space already occupied by energy and therefore cannot expand, as this would result in the loss of energy and eventual dissolution to the level of cold radiation, which the space can hold in solution, below 2.7K.

    But you do indicate that the universe does permit a vast array of diversity, which is in line with my hypothesis that the cosmology einselected from the grand path integral (analogous to a grand partition function of “everything” in a Euclidean measure) is somewhat in line with this. Yet I think that we humans are just some flash in the pan, even if we appear to be cosmological observers.

    Here is an interesting biological hypothosis from this plasma site; http://www.holoscience.com/synopsis.php?page=10

    It seems that when a dwarf star or gas giant planet “gives birth” to a rocky satellite, parent and child usually remain closely bound. Our solar system, with its widely spaced orbits and chaotic features, appears to be the result of a recent cosmic “traffic accident”. This seemingly wild conjecture is supported by the global stories of prehistoric planetary encounters. So to use our situation as a measure of a normal planetary system will give wildly misleading ideas of how life begins and estimates of the likelihood of life elsewhere in the universe. The most benign situation for life in an Electric Universe is inside the electrical cocoon of a brown dwarf star. Radiant energy is then evenly distributed over the entire surface of any planet orbiting within the chromosphere of such a star, regardless of axial rotation, tilt, or orbital eccentricity.

    The exceedingly thin atmosphere of such stars has the essential water and carbon compounds to mist down onto planetary surfaces. The reddish light is ideal for photosynthesis. Such a model provides one reason why the Search for Extra-Terrestrial Intelligence (SETI) project is unlikely to succeed. Any advanced civilization on such a planet will be unaware that the universe exists outside its own stellar environment, and radio communication through the glow discharge of the star is impossible!

  • Jason Dick

    Well, now that I’m back online, I’ll go ahead and respond to this.

    John,

    The gravitational field of a galaxy extends out several times its visible size, so presumably it’s drawing matter in from that area. Galaxies are visible from 10+ billion lightyears away, so presumably they radiate light out over that area. Are you arguing that the matter being drawn into a galaxy has no causal relationship to the light radiating away from it?

    The gravitational field is infinite, actually. But that doesn’t mean it draws in matter from that far away.

    However, there is some interesting physics to be had here. Within the galaxy, much of the matter (most, I think) is not yet collapsed into stars, but is instead in a diffuse gas that permeates the galaxy. As these gas atoms zip around the galaxy, they radiate, due to the acceleration due to gravity, and due to interacting with other gas atoms (note that the gas is more than hot enough to be ionized, so the particles that make up the gas are charged, and the acceleration of charged particles induces radiation). This thermal radiation causes them to lose energy: as they radiate, they cool. This loss of energy is seen in that the cloud as a whole, as it radiates, slowly collapses inward.

    So the collection of matter really doesn’t do anything to the radiation. But once the matter has been collected, it will radiate and its orbit will decay as a result.

    As I recall, at the center of a normal gravitational body, such as the earth, the gravitational effect balances out, so that while the pressure is enormous, the gravity is neutral. If this was applied to galaxies, it might explain why they shoot these jets out from the poles.

    The physics is the same. It’s just that the Earth is neutrally charged (to an extreme degree), so its orbit doesn’t decay as a result of its acceleration due to gravity. The solar system has also largely been cleared out, so its orbit doesn’t decay significantly due to interactions with other matter in the solar system. If either was the case, then the Earth would lose energy (largely through radiation, though in the case of interactions, some of the energy would also be transfered to the interacting particles), and its orbit would decay as a result.

  • Lawrence Crowell

    Gravity waves are analogous to electromagnetic waves. With electromagnetic waves the oscillation of charges on a dipole, or higher moment, will result in changing electric and magnetic fields which propagate out in waves. Gravity waves are similar, but they are quadrupole or higher. The reason for that is a dipole moment is mx, m = mass, x = displacement and a time variation of that would be m dx/dt, which is zero by momentum conservation. Also gravity waves have to directions of polarization, instead of one for EM waves, which is tied to something called helicity which is 2. For this reason the putative quantum particle of a gravity wave, called the graviton, is said to have an intrinsic spin of two.

    A static gravity field, say one around a star produces no gravity waves. It requires the orbit of one body around another. Further, the orbit has to be elliptical, or rather it can’t be circular. A noncircular orbit has a quadrupole moment which can produce gravity waves — distrubances in spacetime which radiate out as waves. I can’t recall the man’s name at the moment, but a Nobel prize was given to him for finding two neutron stars in a mutual orbit that decayed, or the pulsar frequency measure of the orbit increased, as the two neutron stars spiralled in and lost energy to weak gravity wave production.

    As for extrasolar systems, most of them have so called torch Jovians, or large gas planets that orbit tightly around the parent star. Even those which don’t most often have a Jovian (the identifiable planet by Doppler wobbling of the star) in an orbit 1 or 2 astronomical units from the star. A terrestrial planet in such a system would not exist in a stable orbit that kept conditions proper for the evolution of life.

    I do finally have to point out that gravity is cancelled out in general relativity. A freely falling body experiences nothing strange if the frame is small enough. The conditions are equivalent to being in distant space with little or no gravitating bodies nearby. This is the Einstein equivalence principle. There are some other aspects to this, but I will leave it at this. A solid body resists the inward drop of gravity through material forces, mostly electromagnetic in the buld properties of cool matter, and anything at rest on the surface of this body experiences an upward force from this geodesic deviation from free fall. In this way one measures a gravity force. As it is said, it is not the fall that kills you, but the sudden stop and the end.

    Lawrence B. Crowell

  • Lawrence Crowell

    I need to give a bit more on extrasolar planets. A gas giant around a star in an orbit comparable to Jupiter, with a distance ~ 5 AU and orbital frequency 11.8 years, would be hard to detect. The Doppler wobbling is smaller and the frequency of this is very low. So the statistics against extra-solar systems comparable to our solar system may well be skewed by this.

    On a more general note, it has been my experience with elementary students that teaching physics involves “unteaching” in many cases. Sometimes students have all sorts of strange ideas about physics, and teaching physics can often mean stripping away these mistaken ideas.

    The internet is to my mind a mixed blessing. When it comes to physics and astronomy there are many sites out there with bogus notions. I am an amateur astronomer and in Sky & Tel or Astronomy there was a full page advert for a so called theory and a book on this. I went to the website for this and quickly deduced this was nonsense. Just a few days ago I got an email spam for some relativity site. I looked at it and found it to be completely ridiculous. The internet has a democratic aspect to it, which I fully support and disagree with schemes against so called equal access, but Science is not really a democracy, and wrong ideas are simply discarded, no matter how much the upholders might scream unfair. At the end of the day the final arbiter is nature or the universe, and no amount of wanting things to be a certain way can change that verdict.

    Lawrence B. Crowell

  • http://tyrannogenius.blogspot.com Neil B.

    Pardon me if already answered (there’s so much here), but I still am not clear how energy is conserved if gravity waves can’t actually “hold” energy as Penrose, Bee, and some of you here tell me. As the energy of the rotating system decreases, energy has to increase “somewhere”, right? But how?

  • http://www.gregegan.net/ Greg Egan

    In GR, it’s not possible to assign energy and momentum to spacetime curvature with a stress-energy tensor that gives meaning to ideas like “the local energy density due to the gravitational field”.

    However, you can still define a “gravitational stress-energy pseudotensor”, which although meaningless at a single point nonetheless gives sensible results when integrated, yielding the total energy and momentum in a region surrounded by flat spacetime, and the fluxes of energy and momentum in or out of such a region.

    So energy doesn’t “disappear” when it turns into gravitational radiation, it’s just that the bookkeeping scheme becomes a lot more subtle. In Newtonian physics and SR, you can pick a reference frame and then talk unambiguously about the energy density at any single spacetime event. In GR, you can’t do that, but you can, for example, integrate this pseudotensor over several wavelengths of a gravitational wave to get a meaningful result for the energy and momentum that it’s carrying — a result that will tell you how much energy the wave will deposit in various kinds of gravity wave detectors.

    See Misner, Thorne and Wheeler Chapter 20 for details. Here’s a quote from pp 467-468:

    At issue is not the existence of gravitational energy, but the localizability of gravitational energy. It is not localizable. The equivalence principle forbids.

    Look at an old-fashioned potato, replete with warts and bumps. With an orange marking pen, mark on it a “North Pole” and an “equator”. The length of the equator is very far from being equal to 2pi times the distance from the North Pole to the equator. The explanation, “curvature”, is simple, just as the explanation, “gravitation”, for the deficit in mass of the earth-moon system (or deficit for the neutron star, or surplus for the region of space occupied by the gravitational waves) is simple. Yet it is not possible to ascribe the deficit in the length of the equator in the one case, or in mass in the other case, in any uniquely right way to elements of the manifold. Look at a small region on the surface of the potato. The geometry there is locally flat. Look at any small region of space in any of the three gravitating systems. In an appropriate coordinate system it is free of gravitational field. The overall effect one is looking at is a global effect, not a local effect. That is what the mathematics cries out. That is the lesson of the nonuniqueness of [the gravitational stress-energy pseudotensor].

  • http://tyrannogenius.blogspot.com Neil B.

    Greg – thanks for the explanation. It seems that at least my question was worth asking. I was exasperating to you sometimes, so I appreciate your efforts even more. I have seen some of the best writing in this thread explaining gravitational issues from you, Lawrence Crowell, et al, and you guys aren’t even being paid for it (I suppose!)

    Happy Holidays. I suppose the summertime Christmas season comes across a little odd to traditionalists in Australia. It hardly ever snows here in SE Virginia anymore, so machts nichts for me.

    PS – In the spirit of good will toward all men and women, the following is cute. Time grows short!

    Synchronized Global Orgasm for Peace

  • John Merryman

    Jason,

    The gravitational field is infinite, actually. But that doesn’t mean it draws in matter from that far away.

    Einstein proposed the cosmological constant because he calculated gravity would cause space and thus the universe to eventually collapse to a point. Doesn’t this presume the universe is finite in the first place? It would seem that if the universe is infinite, all this gravitational tugging would create a gravitational equilibrium, as everything would be pulled in all directions equally.

    However, there is some interesting physics to be had here. Within the galaxy, much of the matter (most, I think) is not yet collapsed into stars, but is instead in a diffuse gas that permeates the galaxy. As these gas atoms zip around the galaxy, they radiate, due to the acceleration due to gravity, and due to interacting with other gas atoms (note that the gas is more than hot enough to be ionized, so the particles that make up the gas are charged, and the acceleration of charged particles induces radiation). This thermal radiation causes them to lose energy: as they radiate, they cool. This loss of energy is seen in that the cloud as a whole, as it radiates, slowly collapses inward.

    Obviously I’m drawing a very simplistic picture, but this seems in general agreement, that radiation is the heating/expansion and gravity is the cooling/contraction. Yes the various interactions are complex, yielding much detail to be sorted out. Obviously radiation also carries away some of these complex gases and the collapsing gases also trap energy that is contracted. It still seems to me that the larger picture is still a cycle. Whatever complex structure does eventually collapse creates its own energy and the pressure and eventual radiation process breaks the complex structure down and radiates it away. What is radiated would seem to lose energy the further it radiates, for various reasons; 1) It runs into obstacles and passes energy to them. 2) The further it travels, the greater the area it must expand to cover. 3) To the extent light is affected by gravity, it must also have some counter-effect, thus has some extremely minute mass. Therefore light as particles might have gravitational effects on each other. Since evry point in open space has radiation crossing it from all directions, it would not be a pure vacuum, but it also may not interfere with the precise path of a photon, while serving to slow it. The combination of all these factors causes radiation to cool and eventually start to clump. Possibly there is a phase transition level that this clumping starts to become obvious, such as 2.7K. A dew point, so to speak.

    So the collection of matter really doesn’t do anything to the radiation. But once the matter has been collected, it will radiate and its orbit will decay as a result.

    Thus my earlier point that the reason space within the galaxy isn’t blueshifted. It’s the mass that’s collapsing, not the radiation.

    The physics is the same. It’s just that the Earth is neutrally charged (to an extreme degree), so its orbit doesn’t decay as a result of its acceleration due to gravity. The solar system has also largely been cleared out, so its orbit doesn’t decay significantly due to interactions with other matter in the solar system. If either was the case, then the Earth would lose energy (largely through radiation, though in the case of interactions, some of the energy would also be transfered to the interacting particles), and its orbit would decay as a result.

    As a satellite, it is in a fairly stable orbit, but presumably the sun will eventually expand and incinerate it anyway and its energy will radiate away, whether it falls in the fire, or the fire comes to it.

    Lawrence,

    The internet has a democratic aspect to it, which I fully support and disagree with schemes against so called equal access, but Science is not really a democracy, and wrong ideas are simply discarded, no matter how much the upholders might scream unfair. At the end of the day the final arbiter is nature or the universe, and no amount of wanting things to be a certain way can change that verdict.

    Democracy isn’t about unlimited rights for everyone, but about the balance of rights and responsibilities. Eventually the laws judge everyone, high and low. Often this creates a convective cycle, where the deserving rise, as those who don’t maintain their balance of rights to responsibilities, fall.
    ‘The law grinds slowly, but it grinds exceedingly fine.’

  • John Merryman

    That last paragraph was a response, not a quote.

  • http://tyrannogenius.blogspot.com Neil B.

    Einstein proposed the cosmological constant because he calculated gravity would cause space and thus the universe to eventually collapse to a point. Doesn’t this presume the universe is finite in the first place? It would seem that if the universe is infinite, all this gravitational tugging would create a gravitational equilibrium, as everything would be pulled in all directions equally.

    John, you can’t think of things as if Newton’s concepts applied, like asking what the net force is on an object. An infinite universe can exist in GR, and still has a tendency to “contract” in the sense of separations everywhere getting smaller with time. Maybe you could imagine it as being like tension in an elastic skin, but I don’t want to start misapplying analogies. Indeed, a finite but closed space would have no edge (and thus no preferred center), meaning that any given bit of mass would naively be expected to have no “net force” on it (from symmetry.) Then, you would expect everything to just sit as it was, or continue at the same relative velocity.

    However, in old-fashioned GR such a space will actually suffer net contraction of separations imposed relative to the progression that would apply at constant relative recessions (IOW, the “velocity” of a given galaxy relative to us would decrease over time.) Of course, dark energy has complicated all of that, so now we find instead that the distant galaxy will be going even faster from us in the future. In any case, just intuitively working out apparent framings and implications doesn’t do justice to the way the universe actually works. That way is often very counterintuitive, and often (despite platitudes) only really describable in terms of advanced mathematical concepts.

  • http://tyrannogenius.blogspot.com Neil B.

    “An infinite universe can exist in GR, and still has a tendency to “contract” in the sense of separations everywhere getting smaller with time.” – actually, getting bigger and bigger, but not as high a rate as if things continued with constant rate of recession. That’s similar in the finite but bounded universes (cycloid), but they could contract again later.

  • John Merryman

    Neil,

    I’m just not convinced the math transcends the logic. This isn’t a matter of wanting to hold on to my own beliefs, because I’ve certainly dropped more then enough beliefs over the years that a few more would mean very little, but the fact is that I’ve grown up around a bunch of first rate salesmen(horsetrading doesn’t get its rep for nothing) and what’s is going on has all the hallmarks of a conjuror’s trick, ie. get everyone so focused on one bright spot that they ignore everything else. The simple fact is that the equations are WAY off course. You don’t suddenly say, “Oh, wait, 70% of the universe much be dark energy to keep the theory on track.”, when your whole shtick is that the equations are the only way to go.
    They also try to say that since time is a dimension, change is an illusion! Reality might be an illusion, but change is not, as we are all about to shortly find out, when the credit cards are all finally maxed out and lots of our little illusionary bubbles get popped. Including quite a few of those who thought they could make a living scribbling equations.

  • http://www.gregegan.net/ Greg Egan

    You don’t suddenly say, “Oh, wait, 70% of the universe [must] be dark energy to keep the theory on track.”

    What you imagine is some radical new hypothesis is actually “Oh wait, the vacuum energy density that we thought was very low, and might even be exactly zero, is … very low, but isn’t exactly zero: it’s about 6 * 10^-30 the energy density of liquid water.” The only reason this tiny non-zero value comprises 70% of the energy density of the universe at large is because there is a lot of vacuum. And the reason it has taken 90 years to shift the estimate (tentatively) away from zero is because the effect it has on the things we can easily observe are very small. Stop blaming people in 1970 (or 1917) for not knowing what modern instruments would measure.

    From the very start of GR, there were three different terms that could appear in the equation linking matter to spacetime geometry:

    (1) The stress-energy tensor of matter and radiation
    (2) The Einstein tensor, derived from the curvature of spacetime
    (3) The metric tensor itself

    These terms all share the property that they are “divergence-free tensors”; in the case of (1), the stress-energy tensor, the fact that it is divergence-free is what guarantees local conservation of energy and momentum. So Einstein knew that the most general form his equation could take would be to equate (1) with a sum of constant multiples of (2) and (3).

    Assuming the universe was static, he first believed that he would have to fine-tune the “cosmological constant” multiplying (3) to achieve a static outcome. When Hubble’s observations made it clear that the universe was expanding, Einstein realised that he could get a perfectly sensible result by assuming that the cosmological constant was very small, and the simplest small value — zero — could not be ruled out by the observational data at the time.

    So the fact is, we’re using the same equations for GR that we’ve been using for 90 years, and in the light of observational evidence, we’ve just (tentatively) refined the value of the cosmological constant from “very small, maybe zero” to “very small, but on the evidence to date about 6 * 10^-30 g/cm^3″. This is no different from using improved observations to refine estimates of the density of baryons — or any other empirical input into the theory that can’t be known from first principles.

    No doubt some cosmologists in the past assumed prematurely that the cosmological constant was exactly zero. If the evidence continues to favour a non-zero value, they will — very sensibly — change their minds.

  • http://tyrannogenius.blogspot.com Neil B..

    Good rundown of the issues, Greg. Now, the really interesting question – is it possible to get started on “why” the Cosmo constant is not zero, and is about what it is? (Also, how much cred to the idea that lambda is getting stronger with time?) And about that notion that some theory of vacuum energy gave a massive energy density to empty space (was it maybe about one planck mass per cuble one planck-length on a side?) Remember, “10^120 order wrong” etc. So, why “should” it have been that much, why isn’t it, etc., and can we use ZPE somehow etc in principle, even though very small? (Note to any reader, that Casimir force is required by basic QM and is calculated independently of the DE or lambda value.)

    Since someone mentioned Arp above in the alternate community, well – red shifts must be real in general I suppose, but isn’t there some support for the peculiar “quantization” of the red shift measurements? Could it be, when the universe was small, standing matter waves set up various harmonics which collected around certain recession rates? (Yeah, the universe supposedly wasn’t a hypersphere anyway, but just curious.)
    A lot on anyone’s plate to deal with, whatever you have time for, tx yet again.

  • John Merryman

    Greg,

    Thank you for making the effort to explain that to me. I’m not going to pretend I get all the terms, so let me put it in concepts gleaned from popular explanations; That the rate the universe is expanding doesn’t match what has been calculated from gravitational slowing of the expansion, therefore there must be some basic energy content to space itself, which is maintaining this expansion.
    Since the further away a source is, the faster it appears to recede, the expansion must have been greater in the past and has been slowing since. Dark energy is that some of this expansion is due to the nature of space itself, not just the initial singularity. More recent measurements show there wasn’t a specific time, originally proposed about 7 billion years ago, when this basic energy of space took over, but that it is a even curve back as far as can be measured, which is currently about 9.5 billion years ago. This later, more accurate measure showed it in line with a potential cosmological constant.

    Now my point has been that it all is a cosmological constant and that the further light travels through space, the more this effect affects the rate of wave propagation, thus compounding the effect, so that the further the light travels, the greater the rate of redshift, such that the source appears to be receding at an increasing rate. If the source is far enough away, it will appear to recede at the speed of light and any source beyond that distance will effectively be over the horizon line.

    Since gravity curves space and we detect this by the fact that the path of light is bent, this must mean gravity affects light and presumably then, light would have some mass content for gravity to affect. Otherwise gravity would not bend light.
    So what would the effect of light on light be, given that light waves continually cross each other in open space? The reason tired light was dismissed was because the path of light was not disturbed by whatever caused it to redshift. but gravity only causes the path of light to bend, it doesn’t otherwise distort or scatter it. Therefore if there is some very minor effect of light on other light, it wouldn’t distort its path, other then to slow it somewhat. That would explain why quasars have a much higher redshift then associated galaxies, since the local radiation is so intense.

    As Omega is very close to one, the contraction of space by gravity balances its cosmic expansion, so it seems less complex to consider that expanding radiation and collapsing mass are two sides of a cycle, of which the redshift is as much a component of the radiation, as gravity is of mass.

    As for my perspective on the philosophy of modern physics, consider this analogy; Say you have a factory and accounting says there are 8,000 widgets in stock, but the stockroom says it only has 3,000. Most likely the paperwork is ahead of or behind the distribution and you just have to give it time to straighten out. If that doesn’t solve the problem then either the accountants screwed up or the stockroom people misplaced 5,000 widgets. So to solve the issue, you examine both sides of the question. For modern physics, this doesn’t seem to be the case anymore, because the math no longer is simply a model of reality, it is the reality. It has gone from being a tool to being a God and God is never wrong. You can’t say it’s just due to discrepencies between the model and reality, because the model is reality and you can’t say the math is screwed up, cause it’s the word of God. Therefore there must be 5,000 missing widgets and if you want a Nobel on your resume, you look for the widgets, you don’t question the math.

    Admittedly I’m more of a stockroom type than an accounts department type, but my model only supposes that light affects other light to an extremely minor degree, but measurable over intergalactic distances, not that the universe began in a faster then light flash and is 96% invisible to everything but the theory.

  • http://tyrannogenius.blogspot.com Neil B.

    John, one thing to avoid confusion: You said, “Since the further away a source is, the faster it appears to recede, the expansion must have been greater in the past and has been slowing since.” – The Hubble rule means that right now, or any observer in the past or future, is going to find a galaxy twice as far away moving away at twice the “velocity” (I put in quotation marks since it isn’t a simple matter of things just moving in space, but some analogies apply.) (Or, is even that not so simple anymore?)

    That is not to be confused with the change in rates of acceleration (“deceleration” if want to refer to inward accel. vector that way) with time. That in turn is not to be confused with the change in rates of acceleration that would occur even if there wasn’t any dark energy (just from a galaxy being subject to a lower density of matter over time – you can “pretend” that the galaxy is being pulled toward us by the mass in the enclosing figural sphere made by a radius between us and it, to get the right rate in the absence of DE, IIRC. So, both the velocity away from us and the acceleration toward us of a given galaxy were higher in the past, but the devil is in the details.

    The important thing to remember is, mass density of the universe changes with time. But if the DE is an intrinsic property of space, it likely stays the same (same value of acceleration/r) which means it will predominate as time goes on. But I hear that Lambda (the factor showing influence of DE) may change, such as increasing with time, which has even more effect in the future. It could literally tear atoms and even particles apart someday by making every point in space like a sort of reverse black hole.

  • John Merryman

    Producing high energy/low entropy?

    Milky Way’s black hole seen as particle smasher

    Feb. 27, 2007
    Courtesy University of Arizona
    and World Science staff

    Scientists were startled to find in 2004 that the center of our galaxy is emitting gamma rays, the highest-energy form of light. Now astrophysicists say they’ve discovered what might produce these.

    A black hole believed to lurk in that place, they propose, could be a cosmic form of particle accelerator—a machine built to smash subatomic particles together in order to understand their components.

    The black hole, according to this view, would rev up particles known as protons, parts of the cores of ordinary atoms, and smash them at near-light speeds in to lower energy protons. The collisions would produce gamma rays.

    The Large Hadron Collider is expected to be able to accelerate protons to seven trillion electron volts, a measure of energy. Our galaxy’s blackhole whips protons to up to 100 trillion electron volts, according to the new study. That’s all the more impressive because “Our blackhole is pretty inactive compared to massive black holes sitting in other galaxies,” Ballantyne said.

    A blackhole is an object so tightly compressed that its own weight creates gravity that sucks in anything within a certain range, including light. Most galaxies are thought to harbor central, huge blackholes dubbed supermassive blackholes.

    Powerful, chaotic magnetic fields accelerate protons and other particles near our blackhole to extremely high energies, Ballantyne’s team argued.

    The Milky Way blackhole “is one of the most energetic particle accelerators in the galaxy, but it does this by proxy,” Melia said. It cajoles a magnetized plasma, or electrically charged gas that’s “haplessly trapped within its clutches, into slinging protons to unearthly speeds.”

    http://www.world-science.net/othernews/070227_blackhole.htm

  • http://www.gregegan.net/ Greg Egan

    Neil,

    I have absolutely no idea why the cosmological constant has the value it has. There are lots of proposals, most of which involve new and untested particle physics, and which I am not qualified to assess.

    John,

    Light has two effects on other light. The first is that light, like everything else, is both a source for spacetime curvature, and is affected by spacetime curvature. The second is that there is a tiny probability for two photons to interact and produce particle-antiparticle pairs. Both of these effects are quantified by well-tested, and well-understood theories, and do not explain the cosmological red shift. There is no room for you to insert some new process into the mix, because (a) that would contradict existing observational evidence about the behaviour of light, and (b) contrary to what you assert, it would suffer from all the side-effects of other “tired light” theories, i.e. any effect strong enough to account for the red shift would degrade distant images, which is not what is observed.

    BTW, light does not have “mass content” (though it has energy). The fact that the path of light is “bent” does not imply that it has mass, it is a consequence of the fact that there are no straight lines in curved spacetime that anything could follow. If you live on the surface of a sphere, are any of the great circles going to obey Euclidean geometry?

    Contrary to your beliefs, people have spent a considerable amount of effort questioning GR, proposing new interactions, etc. The reason these efforts don’t get much press is because they have yielded no results. If you want a Nobel on your resume, you overturn all of existing cosmology. This is, however, easier said than done.

    You seem to think it’s some kind of massive con trick to propose that there are forms of matter in the universe that we’re having trouble detecting by anything other than their gravitational effects, but since there is no fundamental reason why everything in the universe should interact with us by any other means, it’s actually not surprising that this is the stuff we’re getting around to finding at this point in history — after all the other easier invisible things, like the non-visible 99% of the electromagnetic spectrum, have been identified. Whether dark matter and energy were 0.1% or 96% of the energy density of the universe is completely beside the point; as I’ve already explained, dark energy is 30 orders of magnitude less dense than the matter around us, so complaining that we would have noticed it earlier if it was real is as silly as complaining that if neutrinos were real, and trillions of them were streaming through our bodies every second, then the Ancient Greeks would have known all about them and calculated their mass to six decimal places.

  • http://www.gregegan.net/ Greg Egan

    #137. So what? If you imagine this supports any of your gibberish about cosmic convection, I’m afraid you’re mistaken. Lawrence has already summarised the whole jets thing once, but you paid no attention to him, so there’s no reason for anyone else to waste their time re-explaining it to you.

  • John Merryman

    Neil,

    If space expands(due to increasing energy from light radiation), but then falls into gravity wells, it would appear that every galaxy is flying away from each other and the further away, the more space light has to cross, so the more the effect is multiplied and the faster the source appears to recede. This is what we see and we don’t need a singularity, Inflation, or dark energy to explain it.

  • http://tyrannogenius.blogspot.com Neil B.

    Well, if we are going to talking about weird notions, try this one:

    Time is running out – literally, says scientist

    By Tom Chivers and Roger Highfield, Science Editor
    Last Updated: 6:01am GMT 18/12/2007

    [pieces]

    The idea that time itself could cease to be in billions of years – and everything will grind to a halt – has been set out by Professor José Senovilla, Marc Mars and Raül Vera of the University of the Basque Country, Bilbao, and University of Salamanca, Spain.

    The motivation for this radical end to time itself is to provide an alternative explanation for “dark energy” – the mysterious antigravitational force that has been suggested to explain a cosmic phenomenon that has baffled scientists.

    The problem is that no-one has any idea what dark energy is or where it comes from, and theoreticians around the world have been scrambling to find out what it is, or get rid of it.

    The team’s proposal, which will be published in the journal Physical Review D, does away altogether with dark energy. Instead, Prof Senovilla says, the appearance of acceleration is caused by time itself gradually slowing down, like a clock that needs winding.
    advertisement

    “We do not say that the expansion of the universe itself is an illusion,” he explains. “What we say it may be an illusion is the acceleration of this expansion – that is, the possibility that the expansion is, and has been, increasing its rate.”

    Instead, if time gradually slows “but we naively kept using our equations to derive the changes of the expansion with respect of ‘a standard flow of time’, then the simple models that we have constructed in our paper show that an “effective accelerated rate of the expansion” takes place.”

    http://www.telegraph.co.uk/earth/main.jhtml?xml=/earth/2007/12/18/scitime118.xml

  • http://tyrannogenius.blogspot.com Neil B.

    PS – I don’t think that is any worse than the idea that collapses are an illusion, that there are multiple worlds, etc.

  • http://www.gregegan.net/ Greg Egan

    If space expands(due to increasing energy from light radiation)

    Electromagnetic radiation does not cause anything to expand. If the universe is initially expanding, radiation acts to slow down the rate of expansion.

    As far as I can tell, you claim to believe in GR. So start paying attention to what it actually implies, not what you wish it did. The scenario you describe is not a solution of the equations of general relativity, nor is it compatible with what we observe, and there is no change you can make to the properties of light that would make these problems go away.

    Every now and then you admit that you don’t have any real knowledge of this subject, but you never follow through with the consequences of that admission: you are no more competent to devise and test a cosmological model, or to assess the existing models, than I am to do brain surgery. I happen to believe that anyone on the planet who isn’t intellectually disabled could learn general relativity if they really wanted to, but you’re suffering from a fantasy where your intuition provides a reliable short cut that lets you make judgements about cosmology without ever learning any of the details of the subject.

  • http://www.gregegan.net/ Greg Egan

    PS – I don’t think that is any worse than the idea that collapses are an illusion, that there are multiple worlds, etc.

    Until you know how to calculate the effective density matrix of a quantum subsystem correlated to inaccessible degrees of freedom, what you think about collapse is about as relevant as Paris Hilton’s thoughts on the Middle East peace process.

  • John Merryman

    Greg,

    I realize I’m proposing ideas that have been considered from every possible angle, but;

    The fact that the path of light is “bent” does not imply that it has mass, it is a consequence of the fact that there are no straight lines in curved spacetime that anything could follow.

    contrary to what you assert, it would suffer from all the side-effects of other “tired light” theories, i.e. any effect strong enough to account for the red shift would degrade distant images, which is not what is observed.

    If what I’m trying to describe amounts to an opposite effect of gravitational curvature, ie. expanding hills between those collapsing gravity wells, why would it degrade the image, since curvature doesn’t?
    Gravity lensing also magnifies the light that it bends and thus allows us to see further; http://www.space.com/scienceastronomy/050503_grav_lensing.html

    “When a galaxy sits near the line of sight to distant quasars, two things happen (see accompanying figure). The quasars are magnified to look brighter, and their apparent positions in the sky are shifted.”

    No one argues that gravitational lensing distorts the image, just shifts its position and magnifies it, so the opposite effect, spead across the volume of space between galaxies, would mostly just make the source appear moving further away, since there is no gravitational vortex to curve it around.

    I may seem thick-headed, but then I am thick-headed.

  • John Merryman

    Greg,

    If the universe is initially expanding, radiation acts to slow down the rate of expansion.

    So it can slow the expansion, but it can’t slow light?

  • http://tyrannogenius.blogspot.com Neil B.

    John, think of the universe as like a balloon with spots on it, being inflated. The separations between spots increases all the time, but there is also the issue of change in the rate of the inflation of the balloon (BTW, I mean “inflation” of the balloon, not the theory of Cosmic Inflation, where the universe expands very much at a very early period of its existence.) Light tries to catch up with receding spots, and covers each little piece of rubber at the same local rate we are familiar with (crosses a set of adjacent spots at “c”.) IIUC, the light radiation in the universe does increase the overall average mass-energy density, which increases the mutual pull of things on each other – but I don’t think there’s any special odd trick about it, is there?

    And, well, even Paris Hilton can appreciate that it’s better if they get along with each other over there than not, eh? ;-)
    I doubt that Paris knows at least that a density matrix is about the statistical properties of the system, and there wouldn’t even be a “statistics” (meaning, patterns of counts or “hits” of some type, right?) if the waves didn’t already have something to collapse them (into places, like scintillations on a screen) in the first place. (IOW, they would just stay waves forever.) Well, that’s just a rough general argument, whither I know not, but I won’t say the alternative represents evil, lunacy, etc, as I would in my wilder days.

  • http://www.gregegan.net/ Greg Egan

    John

    Firstly, gravitational lensing itself does not produce any frequency shift, either red or blue. If I am observing two stars in the same galaxy a few million light years away, and the view of one of them is subject to gravitational lensing by some compact object in the line of sight, those two stars will still have identical red shifts.

    Secondly, the question of image degradation depends on the detailed geometry and magnitude of the effect: a tiny amount of gravitational lensing by a single compact object causes very little distortion of the image, but your proposed “anti-lensing” due to light spread out across intergalactic space (a) is simply not what light does to other light via gravity, and (b) if there was such an effect, it would degrade the image, because it would involve billions of small interactions. That light and gravity are involved doesn’t magically make the image as clean as one lensing event by one galaxy; billions of small interactions will always give a result that is essentially the same as positing that the red shift is due to something like intergalactic dust.

    I may seem thick-headed, but then I am thick-headed.

    Then either go and study brain surgery and make yourself less thick, or stop hanging around hospitals ranting at the surgeons that they’re conspiring to defraud the world with their self-serving fantasies about “glial cells” and “astrocytes”.

  • http://www.gregegan.net/ Greg Egan

    So it can slow the expansion, but it can’t slow light?

    No, it can’t slow light. Nothing can slow light.

    Stop positing ad hoc nonsense, and make up your mind what your theory is supposed to be. Half the time you claim to believe in GR, and insist that cosmologists have just neglected what GR itself predicts, but the other half of the time you feel free to assert any magical effect of light and matter on each other that takes your fancy.

    Either come up with a coherent theory to replace GR (and which reproduces all its successes), or accept what GR predicts, which is that the radiation in intergalactic space has no chance whatsoever of explaining the cosmological redshift.

  • http://www.gregegan.net/ Greg Egan

    there wouldn’t even be a “statistics” (meaning, patterns of counts or “hits” of some type, right?) if the waves didn’t already have something to collapse them (into places, like scintillations on a screen) in the first place.

    I suppose you think it’s meaningless to talk about the statistical properties of the frequency components of a complex electromagnetic waveform, unless the waveform can be literally, physically rendered monochromatic. Just because individual radio receivers couple to narrow frequency bands doesn’t require the whole electromagnetic field across a city to “collapse” into just one of those bands.

    Quantum mechanics is a linear theory, and in every situation where we can test that hypothesis, it is validated. If a photon striking point A is a valid solution in a particular setup, and a photon striking point B is also a valid solution, then so is any linear combination of both A and B. Complaining that you’ve never personally witnessed A and B together has no force as an objection once you analyse what’s involved when you observe something; you can’t just magically sense what a quantum mechanical state vector is, there has to be a process by which you become correlated with the system in question. When you end up with distinct perceptions and memories correlated with the outcomes A and B — but no access to the billions of other microscopic degrees of freedom that are also correlated with those outcomes — then your perceptions will contain nothing that identifies the continued coexistence of the two outcomes. You will perceive a collapse, when there has been no collapse.

    Now this might or might not be what actually happens, but it is certainly what linear quantum mechanics predicts.

  • John Merryman

    Neil,

    think of the universe as like a balloon with spots on it, being inflated.

    The problem is that these spots amount to holes in the balloon that are letting the air out at the same rate it’s being pumped in. It was Einstein who originally proposed gravity would cause space(the balloon) to collapse to a point and it seems generally agreed that the rate of expansion and the force of gravity are in inverse proportion. I’m really not trying to say anything that isn’t being said, just pointing out that if these two points are true, it appears to be a stable cycle of some sort.

    Greg,

    Re the above point. I’m just making guesses as to how this might be. Obviously I don’t know squat, just pointing out the above situation. Gravity presumably causes space to contract, while inbetween gravitational vortexes it appears to expand. These two effects are supposedly equal. I just don’t see how this adds up to an expanding universe!

    Then either go and study brain surgery and make yourself less thick, or stop hanging around hospitals ranting at the surgeons that they’re conspiring to defraud the world with their self-serving fantasies about “glial cells” and “astrocytes”.

    I live just outside of Baltimore, which has an active and world reknown medical community. On the local PBS radio station the other day, they were interviewing a neurologist on the ralationship between the brain and the mind. I called up and made my point that ‘if two atoms collide, it produces an event. While the atoms go from past events to future events, these events go from being in the future to being in the past.’ I pointed out that this is the difference between the brain, which is material and goes from past events to future ones, while the mind records these events and so sees time as narrative falling away into the past. His first response was that it was very deep, then he recovered his composure and start to explain how physics describes time as a dimension which we just happen to be at some point on. At which point the moderator cut to the next question.

  • http://www.gregegan.net/ Greg Egan

    John

    Gravity presumably causes space to contract, while inbetween gravitational vortexes it appears to expand. These two effects are supposedly equal.

    “Supposedly equal”? Who ever said anything about the two effects being equal? Einstein once contemplated picking a value for the cosmological constant by hand, purely to balance gravitational contraction and ensure a static universe. But there was no reason whatsoever from first principles to compel the cosmological constant to take on such a value. Logically (at least as far as GR is concerned), it can have any value whatsoever. Empirically, it appears to have a value which is definitely not exactly balancing gravitational contraction. It is not open to you to say “hey, maybe it is exactly balancing gravity”, because what we observe is not what we would observe if that were the case.

    the mind records these events and so sees time as narrative falling away into the past

    If you want to think of time like that, go ahead; it’s a perfectly sensible account of people’s experience (and indeed is a predictable consequence of conventional physics). I’m not going to jump up and down and tell you that change is an illusion; if you’ve ever been away from Baltimore, then that was a change, not an illusion.

    But don’t kid yourself that this perspective implies that there’s something wrong with relativity’s concept of time. Relativity and thermodynamics (with a little help from basic evolutionary biology) have no trouble at all explaining (in general terms) what you’re able to perceive and remember at different times in your life; you’ll find that physicists are entirely unsurprised that you fail to remember the future, or to get confused between now and 20 years ago. It is of course physically possible for an organism to pay so much attention to its memories of 20 years ago that it confuses that time with the present, but that’s where evolutionary biology comes in; a creature like that would get eaten very quickly.

  • John Merryman

    Greg,

    “Supposedly equal”? Who ever said anything about the two effects being equal? Einstein once contemplated picking a value for the cosmological constant by hand, purely to balance gravitational contraction and ensure a static universe. But there was no reason whatsoever from first principles to compel the cosmological constant to take on such a value. Logically (at least as far as GR is concerned), it can have any value whatsoever. Empirically, it appears to have a value which is definitely not exactly balancing gravitational contraction. It is not open to you to say “hey, maybe it is exactly balancing gravity”, because what we observe is not what we would observe if that were the case.

    Specifically I first came across the idea is Hawking’s, A Brief History of Time, where he went into the concept that Omega has to be very close to 1 for the universe to be as stable as it is. Later studies of the CMBR by Cobe and WMAP seemed to confirm that the various pertubations of space seemed to balance out to a basically flat or Euclidian space. Even if it isn’t exactly 1, a very close relationship would seem to cancel out expansion as a sinificant effect on the overall universe.
    What is the Singularity other then a type of universal macro vacuum fluctuation. It would seem that dark energy is also a form of micro vacuum fluctuation, pushing the galaxies apart. It would seem that with sufficient dark energy, there would be no need for the singularity,other then as the point where it all started. But if X(expansion)+(-X)(gravity)=0, rather then X, there is no need for a beginning. This was how I first started organizing it in my head, if was only later that someone who described himself as a physicist in the Chicago area pointed out that light made a possible medium for the transfer of this energy from galaxies back out across the universe.

    If you want to think of time like that, go ahead; it’s a perfectly sensible account of people’s experience (and indeed is a predictable consequence of conventional physics). I’m not going to jump up and down and tell you that change is an illusion; if you’ve ever been away from Baltimore, then that was a change, not an illusion.

    I did, among other escapades, hitch hike across the country at 17. It involved a lot of change for me, but probably not as much as the birth of my daughter.

    But don’t kid yourself that this perspective implies that there’s something wrong with relativity’s concept of time. Relativity and thermodynamics (with a little help from basic evolutionary biology) have no trouble at all explaining (in general terms) what you’re able to perceive and remember at different times in your life; you’ll find that physicists are entirely unsurprised that you fail to remember the future, or to get confused between now and 20 years ago. It is of course physically possible for an organism to pay so much attention to its memories of 20 years ago that it confuses that time with the present, but that’s where evolutionary biology comes in; a creature like that would get eaten very quickly.

    I’m trying to make some sense of this, but it doesn’t really tie into my very simple observation that material change creates events, not the other way around.

  • John Merryman

    P.S.

    If you want to think of time like that, go ahead; it’s a perfectly sensible account of people’s experience (and indeed is a predictable consequence of conventional physics).

    Thinking of time as a dimension is also “a perfectly sensible account of people’s experience.” It’s called narrative. History, if you prefer.

  • http://www.gregegan.net/ Greg Egan

    But if X(expansion)+(-X)(gravity)=0, rather then X, there is no need for a beginning.

    Well I’m afraid it’s not zero, so bad luck.

    someone who described himself as a physicist in the Chicago area

    Perhaps this should attract the same penalty as describing yourself as a policeman or a doctor.

    material change creates events, not the other way around

    Nobody at this point in history has the last word on whether physical processes occur “because time passes”, or whether there’s no more content to the passage of time than the occurrence of such processes. Hopefully quantum gravity will eventually clarify this.

    But you need to be aware that there are already highly successful ways for physics to deal with time in theories like general relativity, and though these are unlikely to be the last word on the subject, trying to insert a new concept of time into those theories when you don’t have a firm grasp of the existing one is not going to be productive.

  • Lawrence Crowell

    Wow, go away for a day and lots of stuff happens

    When it comes to gravity waves Egan points out the nonlocalizability of energy. To IMO give a bit of a picture of this imagine that you are trying to quantify some complicated gravitational system with gravity waves. You identify some region, analogous to a Gaussian volume, you want to measure things in. You find that this volume will change, and even in a source free region it may have the same volume but its boundary area will change. The nonlocalizability of energy is the ultimate problem of shooting at a moving target, where not only does the target move but the definition of range and space changes as well. The geometric construction you try to impose to define or measure physical quanitites is effectively a dynamical aspect of general relativity.

    When it comes to:

    The team’s proposal, which will be published in the journal Physical Review D, does away altogether with dark energy. Instead, Prof Senovilla says, the appearance of acceleration is caused by time itself gradually slowing down, like a clock that needs winding.

    “We do not say that the expansion of the universe itself is an illusion,” he explains. “What we say it may be an illusion is the acceleration of this expansion – that is, the possibility that the expansion is, and has been, increasing its rate.”

    —————-

    The problem with this idea is similar to the old phrase about time being a river that keeps flowing on. By saying this one is referring to a rate of time by another form of time. This really is a sort of category error in my opinion.

    When it comes to black holes and cosmic rays, and increasingly cosmic rays are thought to be due to these types of astrophysics, I have certain ideas in the works about aiming spacebased lasers at these sources. The purpose is to then have particle detectors down stream from the lasers. These very high energy protons, which can get up to 10^6 TeV, will scatter with these photons which in its frame are high energy gamma rays. Then with some fancy triggering we can measure the scattering products. In these way we might be able to do some high energy physics with cosmic rays and measure the physics of SU(3)xSU(2)xU(1) standard model at energies far above its symmetry breaking energy. Maybe if there is a framed Higgs field we can detect that as well at symmetry “recovery.”

    The gravitational effect in producing these jets and high energy processes is in a way secondary. Imagine that I might have some giant machine which I can squash a planet with. Now this planet might have a 1 Gauss magnetic field similar to Earth, but if I could squash it down to the size of a tennis ball the lines of magnetic field would be pressed together so the magnetization near this squashed planet is huge. The galactic sized black hole does something similar. A moderate or diffuse plasma with a weak magnetic field is gravitationally in an orbit around the black hole. A bit of friction due to interatomic or ionic collisions drains the energy from the plasma. This draws the plasma closer to the black hole with a faster orbit or orbital frequency (Kepler law). This then increases the heating of the plasma and tightens it closer to the black hole. This process accelerates until the plasma is intensely hot and the magnetic field lines of flux are compressed to huge magnetizations. So as this plasma goes deeper into the gravity well the energy E = 1/2mv^2 + GMm/r says constant and the kinetic part becomes very large. I use the classical term because curiously most of this is modelled using Newtonian mechanics. Extreme relativistic effects occur only very close to the black hole.

    It might sound a bit strange, but it is actually rather hard to fall into a black hole. You have to pretty much aim right for it, or drop precisely in. The Earth orbits the sun at 29.5 km/sec. If we were to dump garbage into the sun (a slightly silly idea), the mass would have to be sent to a velocity v = 29.5km/sec so it comes to a dead stop in the heliocentric coordinate system. Then the stuff would just drop into the sun. Anything appreciably different will send the mass into an elliptical (Keplerian) orbit that avoids the sun. Also for this reason Earth is not constantly pummelled by the thousands of near Earth astroids that can come very close to Earth. Similarly for a black hole it takes a “dead-eye Dick” aim to actually hit the thing. So the plasma around the sun spirals in by losing energy and the above process occurs in a fairly adiabatic manner. This is why black holes, even collosal ones, can be fairly quiet and are not the star eating monster machines we sometimes think they are. The 10 million solar mass black hole at the Milky way center is actually rather quiet right now.

    Lawrence B. Crowell

  • http://tyrannogenius.blogspot.com Neil B.

    Lawrence, I am OK with the general concept of non-localizability (to whatever extent, I presume not “all over the universe”) of gravitational energy in various contexts. It does make me wonder, what then about the effective gravitational mass-energy of the radiating system? I presume that as time goes on, I would detect a little less attraction toward a radiating system. In that sense, the energy has been “carried off”, but I wonder about the details of how g would evolve at various r from a radiating system.

    Also, isn’t there an issue with conservation of angular momentum in curved space? Make arbitrary Earth-style coordinates for a hypersphere. I can move an equator-parallel spin vector along a longitude to the arbitrary “pole”, then move it parallel to itself down the longitude 90 degrees away, then move it along (but now perp. to) the “equator” back to its original location – rotated 90 degrees with no torque put in. Would that really violate CoAM in the sense there really isn’t a trade-off somewhere, or is total AM thus ill-defined in principle?

    (Uh, John, I guess you are waxing poetic up there about those “holes” in the balloon…? Or, do you mean sophisticated newish ideas that gravitons are leaking into other dimensions, etc? If the latter, that is a deep concept that really can’t be done justice to with intuitive models, IIUC.)

  • Lawrence Crowell

    Galactic Einstein Lensing:

    One of the things which many people do not realize is that this does not stand out as a clear test of general relativity. It can largely be understood with Newtonian gravity, and for a light ray that passes near an elliptical galaxy the dominant gravitational effect is essentially Newtonian — well sort of as I will show below.

    So let us just consider this in the light of Newton. A photon which leaves the surface of a body of mass M will start out with a wavelength L. The frequency of this light is then f = c/L. The energy of a photon at the surface of the body is E = hf. Yet if we are to include the gravity field we then have to include that into the picture, and so the total energy is

    E = hf – GM(hf/c^2)/r.

    We are thinking of the photon as a ballistic object with mass m = hf/c^2 (by the infamous E = mc^2 formula). Now this photon leaves the body and reaches “infinity” or r —> infinity. We have by energy conservation that the total energy must be preserved, and so the photon has a different frequency, we will call f’, and E = hf’. So equate these and we find that

    f’ = f(1 – GM/rc^2)

    Now clearly f’

  • Lawrence Crowell

    (for some reason this cuts these off sometimes)

    Now clearly f’

  • Lawrence Crowell

    It cut off again, but I will try once more. The prime frequency less than the unprimed and there is an inverse for the wavelengths.

    Now for a light ray that comes close to a gravitating body the calculations are a bit complicated, but we can understand something of the net redshifting and blue shifting of light. If the photon starts out with a frequency f and falls into a gravity “well” it will be blue shifted as measured by an observer there. This would be the f in the above formula and by switching the definition of primed and unprimed we have that with binomial theorem (used for GM/rc^2

  • Lawrence Crowell

    Well I got a little further, so let me see if the rest will go. It ended with my stipulation on the use of the binomial theorem. Anyway we get the blue shift

    f’ = f(1 + GM/rc^2).

    Then if that photon travels through the well and then out of the well it is redshifted by the first formula. It should not be hard to see that the blue shift is then completely taken away by the redshift as the photon goes of to “infinity.”

    In this Newtonian perspective what we see is that the gravity field is conservative. It does no net work on a body that it interacts with, but simply transfers kinetic energy to potential in a periodic manner in the case of an orbit, or in a transient manner for a body that comes in, is then deflected by the field and goes off on its merry way.

    In a full general relativistic setting this situation is complicated somewhat, but the ultimate outcome is not significantly changed. The gravity field does nothing to change the energy of the photon as detected far away. Similarly for a cosmology, say a large spherical S^3 space that evolves with “time,” what ever “higgly piggly” gravitational bumps (hills or valleys etc) due to galaxies or gravity waves or … , that might exist do not change the energy of the photon as measured “far away.”

    Finally, what might be noticed by anyone familar with the Schwarzschild metric is that the redshift formula above looks about right, but that it really should read

    f’ = f(1 – 2GM/rc^2),

    with the “2GM” instead of just “GM.” This reflects a significant departure from an expected Newtonian effect, and was found in 1919 in the famous Eddington expedition to measure the abberation of light around the limb of the sun in an eclipse.

    Lawrence B. Crowell

  • Lawrence Crowell

    The parallel transport of a vector in a spacetime differs from there being a “force.” Remember, general relativity removes the gravity force. So any vector that is changed by parallel transport along a path does so without there being a force applied. It is the whole coordinate frame which is being rotated. This means that any local observer on that frame will conclude that angular momentum is perfectly conserved.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    You’re right, it does take some digesting.

    Then if that photon travels through the well and then out of the well it is redshifted by the first formula. It should not be hard to see that the blue shift is then completely taken away by the redshift as the photon goes of to “infinity.”

    So a photon coming out of that well would be redshifted to an observer on the outside by this same effect? Since the gravity field presumably extends to infinity, would it continue to be redshifted to infinity? Decreasing proportional to distance of course.

    Neil,

    The balloon analogy is imperfect, since the space in question is just the surface of that balloon, not its volume. So to clarify, yes the surface does expand, but since it is relative and not absolute, it’s essentially as fluid as the matter and energy defining it, which is falling into these wells and radiating out of them. Of course gravity isn’t just the galactic vortex, but any mass. So we only measure the light crossing the space that is only occupied by (expanding) radiation. Not that occupied by (contracting) mass.

    Greg,

    Well I’m afraid it’s not zero, so bad luck.

    Yes, but even close and it still cancels out most of the expansion effect.

  • John Merryman

    Those quotes didn’t come out quite right. Been a long day.

    Lawrence,

    That would be a photon originating from that well.

  • Lawrence Crowell

    A photon leaving the surface of a gravitating body would be redshifted. This has been of course detected in the spectra of radiation leaving the surface of the sun.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    I guess my theory has been something along the lines that light is redshifted by climbing over the hills between gravitational wells, as opposed to the Big Bang model, which says it is because these wells are flying away from each other.
    You are saying significant redshift is due to climbing out of these wells.
    Since the lines between where the well ends and where the hill begins is a matter of perspective, especially since Newton says the wells extend to infinity, can you see why I think the Big Bang model may be overlooking some factors?

  • Lawrence Crowell

    John M: Again you need to read what I wrote. If you drop a ball down an elevator shaft it will accelerate, or equivalently its kinetic energy increases. Also its potential energy decreases. Now assume it hits the bottom without loss of energy. We assume a perfect loss-less impact and it bounces back up to the top. It will then reach its point of origin with zero velocity. A similar thing happens to light which traverse local gravity wells. The photons will blue shift locally, but then in climbing back out of the well will then redshift so that the local gravity field results in no change in the energy (equivalently the wavelength) of the photon.

    A static gravity field with force F = GMm/r^2 becomes very small as r becomes very large. Its influence is negligable. The potential energy for this force is U = -GMm/r, and if you think about it with a bit of calculus

    F = -dU/dr.

    The total energy of a mass is the kinetic plus the potential

    E = 1/2mv^2 + U.

    If this total energy E > 0 then the mass will then leave the gravitating mass and go off to “infinity.” If you set E = 0 you can easily calculate the minimal velocity where this happens, called the escape velocity.

    It is best to review some basic Newtonian physics IMO. While Newtonian mechanics has been surpassed by relativity and quantum physics classical mechanics is in many ways very deep and profound. It will also help to clarify some of these issues. Also it really should come as no surprise that people looking at cosmology tend to be pretty bright and are not likely to be tripped up by the issue you appear to be citing.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    I understand that you are saying whatever blueshift created by a photon falling into a gravity well is compensated for by the redshift of it coming back out of that well.

    My point is that if the photon originates from within that well in the first place, it is redshifted by exiting it, according to your description. Whether this would explain all of the redshift is another matter, but it would seem to explain redshift as having other possible causes then only recession. If we are detecting redshift of light coming from the sun, it doesn’t mean it is moving away from us.

    Astronomers have only been able to seriously examine these effects for what amounts to a moment in time and from one rather small point in space. That limits our perspective. These are effects that have happened over hundreds of millions and billions of years and barely imaginable distances. As Greg said of dark energy, it wouldn’t take much, given the volume of space and lengths of time involved, to add up to serious effects.

  • Lawrence Crowell

    The problem with assigning gravitational redshift to stars in galaxies is this is less parsiminous. We might identify a galaxy moving away at 10% the speed of light as interpreted by Doppler shift. This is not too extreme and is a common result for galaxies in the multi-100 mP range. We would also identify the stars in this galaxy, at least by some statistics of light spectra as similar to stars in our galaxy. If we were to interpret the red shift as due to a change in gravity this leads to two difficulties.

    The first is that it would mean that any sun-like star in such galaxies is similar to our sun with a larger gravity. Yet a larger gravity would mean a larger pressure in the stellar interior, which would change the internal physics of nuclear energy production. Yet these stars on some average appear no different from star in our galaxy — just redshifted.

    The second problem is that the Hubble relationship was derived by looking at Cepheid variables. These are stars with a pretty strict empirically known luminosity-periodicity relationship. We can identify these in galaxies that are reasonably close and we infer their distances with this “meterstick.” If we were to interpret the redshift as due to the gravity of these stars we would conclude that gravity is stronger the further out you look. This would mean that we exist in a very special region of the universe. Yet a crucial aspect of physics is that things are Point Of View Independent (POVI). This interpretation is not POVI, but a model with has galaxies receeding away from each other is POVI.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    The theory I’ve been suggesting is that redshift is a function of the space, a genuine cosmological constant. Say that space really is expanding. Possibly something like a positive vacuum fluctuation that is more field effect then particle production. The redshift of the original space it crosses is further magnified by all the subsequent space and so on, so the further away it is, the faster it appears to recede. Since relative space is essentially as fluid as what is defining it, this field condenses out as particles, which eventually gravitationally clump.

    This model would be point of view independent because every galaxy would appear to be flying away from each other, with speed proportional to distance, since we can only measure the light which has actually traveled the distance, not all that which has been intercepted, deflected, absorbed, etc. We only see what has been the most redshifted, not everything blueshifted as it fell into gravitational vortexes and didn’t manage to come back out the other side. Which is most of the energy and which released the pressure, keeping the universe from actually expanding. Consider the effect attributed to dark matter, the spin of the outer bands of galaxies that cannot be attributed to gravity. An external pressure on these gravitational systems and the gases that are their initial stages might solve the problem as well as adding additional internal attractive forces. On the stellar level, it may explain the Pioneer effect.

    Obviously I’m proposing a field/wave/particle relationship that is beyond my ability to explain at the microcosmic level, so its basis is on how it explains the macrocosmic phenomena. I realize I’m not going to get any support on it either, but it certainly isn’t any more fantastical then many of the other theories, both establishment, quack and many of those somewhere inbetween.

    Do we really undertstand the relationship of light and electricity as particles, as waves and as fields to say that radiation doesn’t interact at levels we are unable to measure with current techniques? It does seem to me that we have become convinced that reality at the quantum level is discontinuous digits more then analog fields, but maybe it’s only that particles are easier to detect then what holds them together.

  • http://www.geocities.com/aletawcox/ Sam Cox

    This is a most interesting thread. Seans initial assertion that “dark energy” is “stuff”, and has a gravitational moment is, I believe very correct.

    Dark energy is singular massed space…observed as a quantum Planck Realm at differing scales directly related to local energy density…it is completely non-particulate, but has a cumulative mass equal to 74% that of the universe…perhaps as much as 96% if we assume “dark matter” to be the combined mass of all macroscopically (from our frame of reference in scale) identifiable singular objects…10 solar masses up.

    I’m not the only person who seriously doubts that the cosmological red shift is doppler related…even though we all know that motion DOES cause a doppler redshift in light. Some galaxies nearby actually have their light blue shifted.

    From our frame, today, we observe space to be almost flat (Omega total 1.02).

    However as we observe outward, we observe a universe where by General Relativity (and Big Bang concept) space time was more curved than today; the universe was smaller in terms of its present size and more gravitationally dense. The farther out we look with our telescopes, the greater this observational effect becomes.

    At 2 million light years “distant”, the Andremeda glaaxy fills about 30 minutes of arc in the sky. At 10 billion light years “out”, that same 30 minutes of arc contains millions of galaxies. The combined mass of the space between us and these galaxies and to a much lesser extent, the baryonic mass of the galaxies themselves cause the light we observe to be gravitationally red shifted.

    From our frame of reference, we feel that the universe is more vast with distance. It is not. Rather the universe becomes progessively younger and smaller, space becomes more curved and dense, and we observe the same gravitational redshift with the universe itself which we can identify with single astronomical objects of extreme density…quasars for example.

    Since quasars are distant, we observe them to be gravitationally redshifted in much the same way as the distant galaxies which surround them.

  • http://www.geocities.com/aletawcox/ Sam Cox

    LC,

    In following this thread, I gather that you have a strongly temporal interpretation and concept of the universe.

    No quick and general definition is very much good, but for JM’s benefit, and as “temporal” relates to this discussion, the temporal approach regards the universe as an object which is evaluated by a separate, objective observer- and this is very important- has an identity of its own…it essentially exists as it is whether I (we) are here to observe it or not.

    I get this impression from the way you (LC) have discussed biological existence, and its role in the universal order on this thread.

    I believe reconciling General Relativity and Quantum Mechanics can only be achieved by disgarding the “temporal” view and adopting an “atemporal” approach, in which the universe ONLY exists in tandem with observation and in which the observer is an integral part of the cosmic system.

    From what I have studied about what modern physics has learned over the last 75 years or so, I believe a temporal view of the universe is not justified by the field evidence..the facts…presently at our disposal.

    Best Wishes…Sam Cox

  • Lawrence Crowell

    A gravitational blue shift is only observed if you are at the “bottom” of the gravitational well.

    The dark energy, a moniker we give it, may well be due to a Higgs-like particle that in four dimensions gives an action

    S = int d^4x sqrt{-g} (k + H^2)(R – A*H^2),

    where k is or related to the gravitational constant and A is another constant. The Higgs field evaluated on the physical vacuum (after the Goldstone has been absorbed) and so H^2 —> . Th value of H^2 on the vacuum expectation defines what we call the cosmological constant. How this action is arrived at, which is a rather canonical form, has to do with the nature of quantum gravity and unification. There are a number of ways to look at this, such as string theory, Loop Quantum Gravity, or maybe some other approach.

    Again to say that dark energy is a “stuff” is problematic. It is similar to the temptation to consider space and time as a physical “something” in general relativity. If we have a point “x” and define this in two metrics for spatial surfaces (two different frames) g_{ij}(x) amd g’_{ij}(x), then by “pushing” the spatial metric forward in time this will give two different points. That this is the case it indicates that spatial quantities are frame dependent and not physically real. This is an aspect of general covariance. General relativity is really about the relationship between particles, not between abstract geometric objects such as points in space or spacetime. In the case of dark energy it is likely a manifestation of the physical vacuum expectation of the Higgs particle H, and is then something which gives a relationship between physical particles.

    An atemporal approach to quantum gravity is probably somewhat on the mark. Time is a curious quantity. In quantum mechanics it is regarded as conjugate or complementary to energy. Yet for those who understand classicl physics and Hamiltonian formalism there are not Poisson brackets between time and energy. Quantum mechanics exploits a Fourier relationship between frequency (or energy by E = h*freq) and time, but quantum mechanics does not define an energy operator. Time exists in a manner not entirely equivalent to spatial quantities which have a strict dual to momentum in classical mechanics.

    Consider a quantum wave equation i&Y/&t = iHY, for the wave function defined for the metric as the configuration variable Y = Y[g]. Then for two states Y[g] and Y[g'], we might expect that a superposition of these two states is possible

    Y” = AY[g] + BY[g']

    for A and B amplitudes with 1 = sqrt{A^2 + B^2}. But this really is not possible in a completely covariant manner. To form such a superposition is to define a coordinate map between two metrics g’ = g + &g. Yet this is really a “bimetric” abuse.

    The Einstein field equation R_{ab} – 1/2Rg_{ab} = – k T_{ab} in the trace reversed form is R_{ab} = k(T_{ab} – 1/2Tg_{ab}). For a source free spacetime, T_{ab} = 0 the Ricci curvature is zero. In a source free region R_{ab} = 1/2Rg_{ab}, but under the assignment of two metric in &g assume a small violation of the Einstein field equations means a nonzero Ricci curvature is determined by a “potential,”

    R_{ab} = nabla_a nabla_bV =/= 0

    where the potential is a metric difference V = (g’ – g)_{ab}g^{ab}. The perturbed vacuum Einstein field equation may then be written as

    nabla_a nabla_bV = 1/2 nabla^2V &g_{ab}

    or according to the difference in the metric

    nabla_a nabla_b& delta g = 1/2&g_{ab}nabla^2 &g.

    When contracted on indices and integrated over a region volume in M^4 we find that using the Greens theorem

    int_{vol} dv &g nabla^2 &g = -int_{vol}dv nabla &g nabla &g = -int_{vol} dv (nabla g’ – nabla g)^2,

    which is the source of the energy error functional &E_g = |nabla g’ – nabla g|^2.

    The energy error functional may be written according to a variation in the Ricci curvature, where the contributing term will be R_{44} = -nabla^2 Phi/c^2, for Phi the newtonian gravitational potential

    int_{vol} dv &g nabla^2 &Phi/c^2 = -int_{vol} dv (nabla Phi’ – nabla Phi)^2/c^2

    Hence the relevant quantity is a fluctuation in the Newtonian force. The variation in the Newtonian force will then manifest itself as the variation in the angle of swing for the torsional balance. The energy error functional is &E_g = hbar/&T. This error functional is a measure of our “ignorance” in assigning a coordinate map between the two metrics. It also indicates a potential relationship between the uncertainty principle and spacetime physics.

    This appears to be an indication of how one relationship system, gravity and a geometric relationship between particles, and another system of relationships, quantum mechanics and entanglements etc, are related to each other in a general relationship system. This appears to require that time be regarded as “derivative.” the energy error functional for zero energy uncertainty (a fine grained description) has the time uncertainty &T —> infinity. In other words time is so uncertain that it effectively does not exist.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    If you drop a ball down an elevator shaft it will accelerate, or equivalently its kinetic energy increases. Also its potential energy decreases. Now assume it hits the bottom without loss of energy. We assume a perfect loss-less impact and it bounces back up to the top. It will then reach its point of origin with zero velocity. A similar thing happens to light which traverse local gravity wells. The photons will blue shift locally, but then in climbing back out of the well will then redshift so that the local gravity field results in no change in the energy (equivalently the wavelength) of the photon.

    Why is there no loss? Some of the light falling into the well doesn’t re-emerge at all, so why wouldn’t that which does loose some energy?

    General relativity is really about the relationship between particles, not between abstract geometric objects such as points in space or spacetime. In the case of dark energy it is likely a manifestation of the physical vacuum expectation of the Higgs particle H, and is then something which gives a relationship between physical particles.

    Are particles the reality, or are they the equivalent of the crests of waves that cannot otherwise be measured? They would still be another layer of abstraction in that case.

    This appears to require that time be regarded as “derivative.” the energy error functional for zero energy uncertainty (a fine grained description) has the time uncertainty &T —> infinity. In other words time is so uncertain that it effectively does not exist.

    Temperature is a derivative of energy, but that doesn’t mean it doesn’t exist. It seems that relativity recognizes the subjective nature of time, but still assumes there must be one absolute dimension of it along which everything ultimately travels. If time is a consequence of motion, like temperature, rather then a basis for it, then the only absolute time would be the complete absence of it, like temperature.

    Sam,

    Dark energy is singular massed space…observed as a quantum Planck Realm at differing scales directly related to local energy density…it is completely non-particulate, but has a cumulative mass equal to 74% that of the universe…perhaps as much as 96% if we assume “dark matter” to be the combined mass of all macroscopically (from our frame of reference in scale) identifiable singular objects…10 solar masses up.

    I’m not the only person who seriously doubts that the cosmological red shift is doppler related…even though we all know that motion DOES cause a doppler redshift in light. Some galaxies nearby actually have their light blue shifted.

    From our frame, today, we observe space to be almost flat (Omega total 1.02).

    However as we observe outward, we observe a universe where by General Relativity (and Big Bang concept) space time was more curved than today; the universe was smaller in terms of its present size and more gravitationally dense. The farther out we look with our telescopes, the greater this observational effect becomes.

    At 2 million light years “distant”, the Andremeda glaaxy fills about 30 minutes of arc in the sky. At 10 billion light years “out”, that same 30 minutes of arc contains millions of galaxies. The combined mass of the space between us and these galaxies and to a much lesser extent, the baryonic mass of the galaxies themselves cause the light we observe to be gravitationally red shifted.

    It seems from the above that you are describing a non-expanding universe, where redshift is due to crossing non-particulate energy of space, while the following seems to describe an expanding universe?

    From our frame of reference, we feel that the universe is more vast with distance. It is not. Rather the universe becomes progessively younger and smaller, space becomes more curved and dense, and we observe the same gravitational redshift with the universe itself which we can identify with single astronomical objects of extreme density…quasars for example.

  • Lawrence Crowell

    QUESTION: Why is there no loss? Some of the light falling into the well doesn’t re-emerge at all, so why wouldn’t that which does loose some energy?

    The set up is artificial with loss-less impact of a ball at the bottom of a shaft, and of course assuming it bounces right back up vertically. But it is a matter for illustration. Gravity is a conservative for F = -GMm/r^2, assumed in the radial direction — I’d prefer not getting into vector notation. Kinetic energy is defined by the displacement of a mass projected on the force T = int F*dx, or for a linear (eg eacy) displacement FX. So consider the change in the kinetic energy from going between the radial point R and R’

    T = -GMm in_R^R’ dr/r^2 = GMm(1/R’ – 1/R).

    Now consider the displacement of the mass upward back to R

    T’ = -GMm in_R’^R dr/r^2 = GMm(1/R – 1/R’).

    Now clearly T’ = -T and so the change in energy of the particle falling down the shaft, bouncing at the bottom and returning is zero. Similarly this is why two gravitating bodies can remain in orbit “eternally.”

    QUESTION: Are particles the reality, or are they the equivalent of the crests of waves that cannot otherwise be measured? They would still be another layer of abstraction in that case. Quantum waves are complex valued, which means they are not real valued in mathematics. Physically the quantum wave is not regarded as real either, but more as an abstraction which contains all possible information about a quantum system in a measurement. Now a quantum wave Y defines a probability amplitude dP = Y^*Y dV, where dV is an infinitesimal unit of volume of space. This leads to

    P = int dP = int_V’ Y^*Y dV = 1

    over all space. A sufficiently peaked wave function or a probability weighted heavily around a point appears similar to a particle. In fact classical mechanics is similarly probability wave mechanics, but where the position is weighted by xY^*Y and if Y^*Y = delta(x-x’) then under integration gives x’ and the classical dynamics of a particle x’ = x’(t).

    As for temperature, that also has relationships to energy as well. The euclideanization of a wave function with t —-> it (i = sqrt{-1}) converts exp(i*freq*t) to exp(freq*t) so that freq*t appears formally equivalent to E/kT, k = Boltzmann constant, T = temperature.

    At the Planck scale unification there is an absolute upper temperature, given by the equipartition theorem E = kT and for E = sqrt{hbar c^3/G} = Planck energy, then T = E/k. This Planck temperature is about 10^{37}K — huge and appears to represent an upper temperature limit. In string theory there is the Hagedorn temperature, related to this, where all string modes contribute. This extreme temperature is tied to the origin of time in some way, and it is the temperature of the earliest part of the big bang, or a temperature associated with the singularities of black holes. Hot Stuff!!!

    As for the curvature of the early universe, if it is a sphere then at earlier epochs it has a higher radius of curvature. So as we look further out, since light travels at its locally finite speed we see earlier into time. So far the universe looks very flat, so if the universe is a sphere we see only a tiny portion of it. The inflationary period converted a region of the universe a billionth the radius of a nucleus into a meter or so in size. The curvature of the universe was drastically reduced.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    Now clearly T’ = -T and so the change in energy of the particle falling down the shaft, bouncing at the bottom and returning is zero.

    But light can’t go faster then the speed of light, so light falling into a gravitational well can’t go any faster, so how can its energy be increased? On the other hand, it can go slower then C, so it can be decreased.

    Quantum waves are complex valued, which means they are not real valued in mathematics. Physically the quantum wave is not regarded as real either, but more as an abstraction which contains all possible information about a quantum system in a measurement. Now a quantum wave Y defines a probability amplitude dP = Y^*Y dV, where dV is an infinitesimal unit of volume of space. This leads to

    P = int dP = int_V’ Y^*Y dV = 1

    over all space. A sufficiently peaked wave function or a probability weighted heavily around a point appears similar to a particle. In fact classical mechanics is similarly probability wave mechanics,

    So it seems waves and particles are both abstractions. A duality defining the deeper reality. Waves being the expanded potential and particles being the contracted focus. Both meaningless without the other.

    So as we look further out, since light travels at its locally finite speed we see earlier into time. So far the universe looks very flat, so if the universe is a sphere we see only a tiny portion of it.

    It would seem that curvature is only detected in redshift being relative to distance. It’s curved in time, but not in space. And our ability to measure ‘time is so uncertain that it effectively does not exist.’

  • Lawrence Crowell

    How can the energy of light be increased? By Doppler blue shifting of course. The energy of a photon is E = h*frequency. A higher frequency then the higher the energy.

    Well, I am not going to belabor the issue of particles vs waves too much. There are some experiments which have gotten direct measurements of the modulus squared of waves. Most experiments detect a particle. Generally a particle is real valued, and is regarded as “real.” OTOH waves are complex valued and not regarded as directly real. There are all sorts of quantum interpretations, one in particular by Bohm that has a real particle “guided” by a so called pilot wave. I am not a partisan of so called interpretations.

    The redshift is given by v = Hd, for H the Hubble constant, v a velocity and d a distance.

    Lawrence B. Crowell

  • http://www.geocities.com/aletawcox/ Sam Cox

    LC,

    “An atemporal approach to quantum gravity is probably somewhat on the mark. Time is a curious quantity. In quantum mechanics it is regarded as conjugate or complementary to energy. Yet for those who understand classicl physics and Hamiltonian formalism there are not Poisson brackets between time and energy. Quantum mechanics exploits a Fourier relationship between frequency (or energy by E = h*freq) and time, but quantum mechanics does not define an energy operator. Time exists in a manner not entirely equivalent to spatial quantities which have a strict dual to momentum in classical mechanics.”

    “Hence the relevant quantity is a fluctuation in the Newtonian force. The variation in the Newtonian force will then manifest itself as the variation in the angle of swing for the torsional balance. The energy error functional is &E_g = hbar/&T. This error functional is a measure of our “ignorance” in assigning a coordinate map between the two metrics. It also indicates a potential relationship between the uncertainty principle and spacetime physics.”

    “This appears to be an indication of how one relationship system, gravity and a geometric relationship between particles, and another system of relationships, quantum mechanics and entanglements etc, are related to each other in a general relationship system. This appears to require that time be regarded as “derivative.” the energy error functional for zero energy uncertainty (a fine grained description) has the time uncertainty &T —> infinity. In other words time is so uncertain that it effectively does not exist.”

    NOTE: You summarize your conceptual viewpoint on the possible relationship between GR and QM very briefly and very well. I can see that our points of view on this are much closer than I first assumed.

    “As for the curvature of the early universe, if it is a sphere then at earlier epochs it has a higher radius of curvature. So as we look further out, since light travels at its locally finite speed we see earlier into time. So far the universe looks very flat, so if the universe is a sphere we see only a tiny portion of it. The inflationary period converted a region of the universe a billionth the radius of a nucleus into a meter or so in size. The curvature of the universe was drastically reduced.”

    NOTE: Conceptually many people have difficulty with a universe which is eternally everywhere, and is based on invariant frames, yet potentially varies widely in spatial extent. I liked your appropriate comments about space as only existing as it relates energy densities. Understanding this fact makes it easier to conceptually internalize the axiom that nothing exists outside of a GR universe! In fact, that space is defined as a relationship between particles also must be understood as foundational to understanding the concept of space/time curvature, inertial and non-inertial motion.

    Global space time in GR is spherical, however space as observed from our particulate 4D frame of reference is anything but spherical…almost flat, in fact. As energy densities have become more widely separated, and space itself more diluted to the level of the present submicroscopic Planck Realm, a CMB, space at our coordinates seems almost flat at 360 degrees.

    However, a universe with both black holes and white holes can immediately be seen to complete the picture of an everywhere, eternal universe, with space varying from non-existent to spherical and then becomming almost flat…then becomming spherical and non-existing anywhere, while the universe as a whole yet continues to exist, from other frames, in reversed polarity, everywhere.

    We know black holes attract energy and continue to grow in gravitational influence. That the universe emerged in a “bang” from a massive singular entity is evidence enough that white holes are a reality as well, but the overall evidence for the existence of white holes is almost as varied and rich as the evidence for black holes…photons do work; what else can they be interpereted to be? Big bang/ white hole is but a matter of scale, and observational frame.

    As singular cosmological objects, entangled with the Planck Realm, continue to grow in mass and the entangled Planck Realm everywhere rises in scale, there comes an instant, after eons of “almost flat space” where and when the universe becomes, at one half of its coordinates, spherical in shape…then briefly non-existent…and re-emergent as a white hole in opposite baryonic polarity.

    If we observe this process in the sub-microscopic, we can observe a rapid proper time pulse…continuous baryonic polarity reversal, which when mathematically evaluated in terms of the gravitational time dilation formula produces “space” and the sensation of the passage of “time” at our observing frame.

    SR, GR and QM tie the universe together. All the formulae when taken together, provide us with a jigsaw puzzle-like description of the universe which when carefully pieced together, matches what we observe in an uncanny and incredible manner.

    It just amazes me that these concepts are not really esoteric at all. We live in a continuously accelerated frame of reference on the surface of the Earth which in some key ways is much like that of an astronaut leaving the Earth in an equally continuously accelerating spaceship. What we observe as ourselves, the Earth..in fact space and time themselves are the products of relativistic and quantum relationships. From the GR perspective, our baryonic informational existence is tied to the relationships of particles and the resulting geometry of space-time.

    Appreciated your remarks very much…

  • John Merryman

    Lawrence,

    How can the energy of light be increased? By Doppler blue shifting of course. The energy of a photon is E = h*frequency. A higher frequency then the higher the energy.

    Yes, but what is being described isn’t Doppler Effect, because the source of the light isn’t actually getting closer.

    Generally a particle is real valued, and is regarded as “real.” OTOH waves are complex valued and not regarded as directly real.

    So if the particle is real and the wave is statistical, how do you impart more energy/higher frequency into the particle, other then to make it travel faster?

    Sam,

    I liked your appropriate comments about space as only existing as it relates energy densities. Understanding this fact makes it easier to conceptually internalize the axiom that nothing exists outside of a GR universe! In fact, that space is defined as a relationship between particles also must be understood as foundational to understanding the concept of space/time curvature, inertial and non-inertial motion.

    So if you add more energy between points of reference, they are effectively being pushed apart and vice versa. So presumably dark energy is causing galaxies to fly away from each other. On the other hand, this expansion presumably results in increasing distance, as measured by lightspeed, so it would seem the metric of light traveling in a vacuum measures a stable dimension.

    Does the fact that this energy is falling into gravitational wells balance the expansion effect?

  • Lawrence Crowell

    First: When it comes to gravitational Doppler effect, as illustrated by J.M.’s question, it appears that I am having to answer the same questions over and over. I would advise looking up sources on this issue. I am sure Wikipedia might provide a first look at this.

    The orgin of the universe is of course an open question in physics, and general relativity indicates a singularity as time —> 0. Of course general relativity is a classical physical theory, which has singularities and divergences which might be ameliortated by quantum mechanics. A similar situation exists with electrodynamics, and quantization removes these problems.

    Feynman first proposed a path integral as a way of describing the motion of particles as traversing all possible paths. These paths were thought to “go anywhere,” such as an electron which traverses a band gap in a solid has some probable path (amplitude) for travelling to the Jurassic period, then to the M82 galaxy and then across the band gap. Feynman’s vision was not entirely fulfilled since such a general path integral involves inequivalent vacua. So the path integral had to be “tamed” with time ordering procedures and other tools, and divergences still required regularization schemes.

    Quantum fields in curved spacetime exist with non-unitarily equivalent vacua. These different vacua are related to each other by Bogoliubov transformations which emerge from relativistic transformations. As a result the radiation which an accelerated observer measures and that which comes from a black hole has a thermal distribution. Again due to limitations the Rindler wedge of spacetime on an accelerated from is a Poincare half plane, which is conformally mapped to the Poincare disk. The Poincare disk is seen in the Escher prints of tilings that “pile up” near the edge of the disk. This is similar to the deSitter spacetime, or more the Anti-deSitter spacetime, which appears similar to the universe we observe and in the AdS case has a duality with quantum (conformal) fields in the spacetime.

    The early universe was likely a configuration of a huge number of inequivalent vacua that were unstable. There is a framed Higgs field (the inflaton etc) which is a measure of this instability in that it will evolve to the lowest energy physical vacuum configuration locally. This is likely how the universe emerged from the vacuum (or a set of inequivalent vacua) and the increasing entropy of the universe may be a measure of a coarse graining over these inequivalent vacua.

    The AdS spacetime has as its conformal infinity a Minkowski spacetime. There are subtle issues of how this can be described by the evolution of a spatial surface, which involves the matter of conformal completeness. Yet the universe does appear to be evolving to a Minkowski flat spacetime completely devoid of matter fields. The grand path integral (similar to a grand canonical partition function in stat mech) takes as its initial point in superspace a maximal configuration of inequivalent vacua and low entropy and as its final point (at infinity) as one with a singly unitary vacuum but maximal entropy.

    So quantum gravity likely involves fullfilling Saint Richard’s vision of a grand path integral over all possible configuration of fields, vacua, paths and so forth in order to describe how cosmology emerges from an unstable “nothing” and approahes at conformal infinity a stable “nothing.”

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    Sorry to have tested your patience. I thought I had a handle on how gravity redshifts light, such as that coming from the sun. Something of a drag on the frame, so to speak. It just didn’t seem to translate that the opposite effect would cause a blueshift, since the light would already be traveling at C and couldn’t be speeded up, but it doesn’t appear that the answer lays in anything resembling classical or basic relativistic physics, so I guess I better just paddle back to shore and leave it at that.

  • Lawrence Crowell

    Red shift and blue shift are the same as the high pitch of an approaching sound source and the lower pitch once it receeds. If you are at the bottom of a gravity well the frequency of light will increase (wavelength decrease) before you detect it. It does not speed up. Similarly if you are looking down into a gravity well where photons are being emitted there is a redshift, the frequency decreases and the wavelength increases. Again the light does not slow down as measured in any local frame. It is important to recognize this is for local frames. So a photon that leaves the sun will be gravitationally redshifted, but if you measure its speed it is the same.

    Lawrence B. Crowell

  • Lawrence Crowell

    PS — I notice in the start of this with regards to sound pitch I had the high and low reversed for comparison. I should have started out with “Blue shift and red shift ….”

  • John Merryman

    Lawrence,

    If you are at the bottom of a gravity well the frequency of light will increase (wavelength decrease) before you detect it. It does not speed up.

    Is the blueshift a compression factor?

  • Lawrence Crowell

    You can think of it as a compression factor, though that term is not usually used. The wavelength of a photon expands or contracts in response to climbing out of a gravity field or falling into one. Similarly if the space is expanding, or points of the space are being shifted apart, the wavelength of a photon expands proportionately. The inverse is the case if the space is contracting, say if the universe were recollapsing, and photons would be blue shifted. However, that is not what is observed.

    Lawrence B. Crowell

  • http://www.geocities.com/aletawcox/ Sam Cox

    LC,

    “The AdS spacetime has as its conformal infinity a Minkowski spacetime. There are subtle issues of how this can be described by the evolution of a spatial surface, which involves the matter of conformal completeness. Yet the universe does appear to be evolving to a Minkowski flat spacetime completely devoid of matter fields. The grand path integral (similar to a grand canonical partition function in stat mech) takes as its initial point in superspace a maximal configuration of inequivalent vacua and low entropy and as its final point (at infinity) as one with a singly unitary vacuum but maximal entropy.

    So quantum gravity likely involves fullfilling Saint Richard’s vision of a grand path integral over all possible configuration of fields, vacua, paths and so forth in order to describe how cosmology emerges from an unstable “nothing” and approahes at conformal infinity a stable “nothing”.”

    A good concise description of the evolution of the 4D model!

    The discovery of black holes, acceleration “outward” and other astronomical and sub-microscopic phenomena lay the foundation for a continuing extention of this obviously incomplete conceptual paradyme. I think the first item on the agenda, even before we look at related but extended geometries and topological relationships, is to recognize that the mathematical dualism (as you mention) of both relativity and Quantum Mechanics is not vestigial…a mathematical artifact of no cosmological significance, but rather is an essential part of a viable and verifiable concept which explains not only the part of the universe we observe, but also that part, the existence is which is inferred by the field work of the past 75 years.

    In my opinion, understanding the significance of quantum entanglement as a singular and photonic universal phenomenon, and establishing the connection of this “quantum reality” with the relativistic scale of time and space, are essential conceptually to a more complete understanding the atemporal nature of the cosmos and the link between the quantum/relativistic universe and its observation in space/time at an almost infinite number (variety) of interdependent levels of biological complexity and organization.

    A related, and important task (as in the study of terrestrial organic evolution) is to trace the phylogenic development of the universe itself back to an archaic condition in which the inorganic complexity and behavior which underlie today’s biological complexity was much simpler than presently- and understand how the system gained in informational complexity toward the conditions we observe in this epoch.

  • John Merryman

    Lawrence,

    By compression, I don’t exlusively mean between waves. I mean that if space is being compressed by gravity, that this causes the distance between waves being compressed? Sort of like does the compression of longitude also compress latitude? On the other hand, it is radiation that DOES escape gravity!

    Since gravity fields effectively extend halfway to the next equivalent source of gravity and most of what is affected is mass, while light radiates to the extent it is visible, which, for a galaxy is 10+billion lightyears, light is gravitationally blueshifted over a much smaller diameter, though far more intensely, than it is radiated…

    My argument has been that radiation is the opposite effect of mass/gravity. That light, in all its forms, is the ‘white hole.’ That by putting energy back out into space, it effectively causes it to expand, just as gravity causes it to contract. As Sam said;

    “space is defined as a relationship between particles also must be understood as foundational to understanding the concept of space/time curvature, inertial and non-inertial motion.” (substitute energy fields for particles)

    …since much of what’s contracted is mass, while most of which is expanded is radiation, the redshift of light predominates over what’s blueshifted.

    I know you’re probably sick of this, but from my perspective, way out here in the moon, where all the math runs together, it keeps coming around in a cycle of collapsing mass and expanding radiation. Sorry if this gets old, its just one of those simple patterns for simple minds.

  • Lawrence Crowell

    Think of Doppler shifting like this. If you have a unit cube of volume then on average for every photon that leave it one comes in. So we can think of the cube as a resonance cavity for electromagnetic radiation, such as with a microwave oven. Now if the space evolves so that the volume changes in a homegenous manner (not like a Kasner spacetime) then the standing waves of electromagnetic radiation are stretched or shrunk with expansion or contraction of the volume.

    A spherical shell of dust that falls to a gravitating body will become distended into a prolate ellipsoid. This is because the part of the shell closest to the gravitating body is under a larger gravity force. This is a way to think about tides. So as the spherical shell gets distended into a cigar shape along the radial direction of fall, we can think also of this as being an electromagnetic reonance cavity. If you are in this volume, freely falling with this reference frame, you would then witness a redshifting of light from other falling sources along the radial direction. Yet, just as the spherical shell is constricting into a cigar shape you would see radiation on a plane perpendicular to the radius a blue shifting of light from objects coming towards you.

    There are a number of configurations one can consider.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    So it would seem that from the perspective of being in the falling volume, the longitudal lines are blueshifted, but the latitudal lines are redshifted?

    The question then, for an observer at the bottom of the gravity well, it would seem these waves would be distended and redshifted, since the earlier waves get pulled in at an accelerated rate? It seems that from this explanation, of an elongated volume, it would be redshifted, since the distance between latitudal waves is stretched?

    Also I’m still having problems with C constraining this, since the light is presumably traveling at C. If the “objects coming towards you,” is light itself, how can the ‘light’ from it be blueshifted?

  • Lawrence Crowell

    Again think of the spherical cloud of particles or “dust” falling radially inward towards a gravitating body. Since the spherical cloud has a spatial extent it may not be a pure local inertial frame. The local inertial frame is an infintesimal ideal, which is physically approximate for reference frames defined on a small enough of a scale. The particles in this spherical cloud will then fall along slightly different geodesics. From a Newtonian perspective the particles closest to the body along a radial direction have a slightly larger gravitating force than particles furthest away. As such these particles will separate with a relative acceleration. Particles along an “equator” defined by these two points as the “poles” will have accelerations that are along slightly different radial directions. These particles

    Think of youself are at the center of the spherical cloud of particles. You along with this cloud are falling towards a gravitating body. The particles along the radial direction of fall will in your frame be seen to accelerate in opposite directions away from you. Conversely particles on a plane prependicular to the radial direction of fall will in your frame be seen to accelerate towards you.

    Now suppose these particles emit some known wavelength of radiation. The particles on the antipodal points along the radial direction will emit photons you measure as redshifted, while the particles on the perpedicular plane will emit photons you measure as blue shifted. Further since these particles are accelerating away or towards you this red and blue shifting will increase. If the gravitating body is a black hole this Doppler shifting will diverge.

    If the universe were a black hole we would observe this sort of anisotropic distribution in Doppler shifts. Of course we don’t observe this, which is why the universe is different from a black hole.

    Lawrence B. Crowell

  • Lawrence Crowell

    erratum: I ended the first paragraph with : These particles

    I meant to write:

    These particles will accelerate towards each other and towards the observer.

    I got distracted and forgot to conclude the paragraph.

  • http://www.geocities.com/aletawcox/ Sam Cox

    “Now suppose these particles emit some known wavelength of radiation. The particles on the antipodal points along the radial direction will emit photons you measure as redshifted, while the particles on the perpedicular plane will emit photons you measure as blue shifted. Further since these particles are accelerating away or towards you this red and blue shifting will increase. If the gravitating body is a black hole this Doppler shifting will diverge.

    If the universe were a black hole we would observe this sort of anisotropic distribution in Doppler shifts. Of course we don’t observe this, which is why the universe is different from a black hole.”

    Excellent point. Some on the fringe have attempted to conceptualize the universe as a black hole and have even insisted we live inside a blsck hole…completely bizzare- and not supported by field observations either. It is one thing to assert that by definition the universe everywhere is (and must be) singular below a certain level of scale. It is quite another to assert we live inside a black hole!

    The nature of the Hubble function, the uniformity of the cosmological redshift with observed distance, the acceleration of the universe outward, a measured Omega total of 1.02…all these observations and many others including the existence and behavior of black holes, imply a geometry for the cosmos which is at least based on Einsteins original local Euclidean SR and global GR spherical concept.

    It is highly unlikely the universe we live in originated as the technology of a pre-existing outside intelligence. First, there is nothing outside this kind of universe anyway. Second, the way informational complexity is organized and interacts implies that the development of informational complexity in the universe is a continuing and (in some ways) quite irregular process which occurs within a set of implicit cosmic constraints, for example, mass and spatial extent.

    The question: “Where did the cosmic constraints and orginal energy come from?” is not valid. A preqequisite for the continuing evolution of this kind of universe…finite in mass and spatial extent is that it must be eternal…infinite along the time dimension. If it has always existed, it “just is”. This axiom of existence can be further understood as we note the atemporal connection between existence and observation.

    Of course, all this does not preclude a developing, profound, relating process within the universe itself which in fact, is somewhat implied by entanglement at singular and photonic scales. We definitely live in a universe where there is a place for everything and everything is in its place. Rather than saying time is an illusion, perhaps it should be said that time make the universe observable- and is the way it is possible to physically experience existence in this kind of reality. Subtract time, spacelike or time like and we bo longer have a cosmological concept, nor can we exist as we are.

  • John Merryman

    Lawrence,

    Think of youself are at the center of the spherical cloud of particles. You along with this cloud are falling towards a gravitating body. The particles along the radial direction of fall will in your frame be seen to accelerate in opposite directions away from you. Conversely particles on a plane prependicular to the radial direction of fall will in your frame be seen to accelerate towards you.

    Now suppose these particles emit some known wavelength of radiation. The particles on the antipodal points along the radial direction will emit photons you measure as redshifted, while the particles on the perpedicular plane will emit photons you measure as blue shifted. Further since these particles are accelerating away or towards you this red and blue shifting will increase. If the gravitating body is a black hole this Doppler shifting will diverge.

    I get what you are saying here, but it still raises the two issues I mentioned; From the perspective of an observer on the surface of that gravitational body, the approaching light isn’t blueshifted because it is traveling at the speed of light in the first place. In terms of Doppler Effect, it would be as if the train were traveling at the speed of sound. The whistle wouldn’t be pitched higher, because you wouldn’t be able to hear it until the train passed and all the waves hit at once, creating a sonic boom.

    Now as you described it, since the gravity is stronger for the preceding wave/particles, then for the succeeding ones, it actually stretches the frequency out on the radial, as it compresses their energy perpendicular to the radial. So it would seem to actually redshift them as they pass this observer on the surface of the gravitational body.

    Since gravitational lensing magnifies light, it would seem logical that this would be caused by the perpendicular compression.

  • Lawrence Crowell

    The description of redshift from comoving particles surrounding an infalling observer was given as way of demonstration. As for JM, the redshift as observed by an infalling observer obtains for that observer’s inertial frame. An observer on the surface of the gravitating body is on a different frame. Thus to compare directly the redshift/blueshift results of the infalling observer with what this observer would measure is wrong. Also, this has nothing to do with any speeding up of light or photons moving faster or slower, at least as measured in any local frame.

    A comparison with Doppler shift of sound is only approximate for slow velocities. For large velocities there are Lorentz factors which enter into the picture. In the case of cosmology there are then also metric/curvature terms to consider as well. In the case of light the speed of light locally is an absolute invariant.

    The redshift of galaxies in the universe is pretty isotropic, as is the cosmic microwave background, and so we can pretty safely conclude the whole universe is not a spacetime containing a black hole.

    As to how particle masses and the strength of gauge fields are obtained has a bit to do with inflationary cosmology. One of the curious results of this is that the universe we observe may only be about one part in about 10^{50} of the whole thing. Without inflation everything in the universe would be causally connected more tightly. The inflaton, or Higgs-like particle that induced inflation, expanded rapidly across the cosmological horizon to determine the curvature of the universe and the nature of gauge fields and their fermionic sources on a spatial surface not causally connected to the same initial conditions. This opens a lot of questions on how the cosmos was determined with a single structure. Some such as Linde and Vilenkin have proposed bubbles of different vacua that determine different particle masses. This is given by Yukawa lagraingian terms L_y = psi-bar H psi, and if the Higgs or inflaton field H settles into different configurations on the degenerate physical vacua then H —> will differ.

    An interesting note is that the Relativistic High-energy Ion Collider at Brookhaven has found the large “blobs” of excited particles can be modelled as a sort of black hole. This machine slams heavy ions together which generates high energy “plasmas” of quarks, gluons, leptons and a gemish of other gauge particles. This then energetically fly apart and the decay products measured by hadron calorimeters and other detectors. It turns out this has a black hole-like behavior. I have been working on similar physics with what I call gauge-holes (which is what I call these) in Anti-deSitter spacetimes. This gets into the AdS/CFT Maldecana duality, but there should have existed black hole-like field configurations in the early universe that result in conformal completeness of the AdS. This gets into some rather subtle issues with AdS spacetimes and cosmology. Yet it turns out that the cosmic microwave background has some “textures” which appear to be defects that might be due to cosmic strings. I think these are the result of gauge-holes which were inflated into a large scale.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    My little mind can only take in small parts of the picture at a time. I’m still just trying to figure out how light is blueshifted by falling into a gravity well, as it is redshifted by climbing out of it. As you have described it, it would seem to be reshifted by the gravity pulling it in and stretching the “volume.” Am I correct in assuming this volume is the trough between waves?

    That it does this by compressing them perpendicular to the line of radiation would seem to explain the magnification/focusing of gravitational lensing.

    This is over-reach, but it would explain this point raised by Sam;

    At 2 million light years “distant”, the Andremeda galaxy fills about 30 minutes of arc in the sky. At 10 billion light years “out”, that same 30 minutes of arc contains millions of galaxies. The combined mass of the space between us and these galaxies and to a much lesser extent, the baryonic mass of the galaxies themselves cause the light we observe to be gravitationally red shifted.

    Since the further light travels, the more residual gravity fields it passes through. If they both magnify and redshift light, then the more distant galaxies might be much further then we assume, but their light is being magnified and focused, so they appear closer and clearer then they would over the same distance of completely empty space, but redshifted, so they appear to be moving away at an accelerated rate.

    Don’t include me with those who think the universe is in a black hole. Black holes are a projection of gravitational effects to infinity. As I see it, gravity is one side of a cycle, where mass/gravity is constantly curving back out as radiating energy, not collapsing into infinity.

  • http://www.geocities.com/aletawcox/ Sam Cox

    LC,

    “The redshift of galaxies in the universe is pretty isotropic, as is the cosmic microwave background, and so we can pretty safely conclude the whole universe is not a spacetime containing a black hole.”

    This thread is quite amazing! Usually before a thread goes 50 posts, people are discussing everything except the original topic and its implications!

    1. The universe contains not one black hole but n…don’t ask me how many!
    2. The “empty” universe model has be shown to be “flat” (a little play on words) incorrrect to a high degree of certainty, anyway.
    3. Particulate matter exists on 4D event horizon surfaces in the sub-microscopic…that is where baryonic matter forms and exists according to the general mathematical parameters of SR, QM and GR.
    4. There IS “extra mass” in the space of the solar system. Technological explanations for the anomolous acceleration of the Pioneer spacecraft have been pretty much eliminated.
    5. Remember, according to the standard model, the mass of the universe is constrained by a certain, very particular density. So long as we theoretically accept the concept of a universe which is finite in mass, we can make it as massive as we wish, and still be within the parameters of the standard model, however, a universe which is 10 to the n (th) power greater than what is observable is a bit out of line with a universe which exists only as it is observed and measured. The geometry gets a bit out of line with spherical space in GR. Hyperbolic space can of course be closed, and would be expected to exist locally in a GR universe, however to assume space in the entire universe is hyperbolic is not consistent with an omega total of 1.02 either!

    Best Wishes!…it has been very interesting following the development of this thread…..

  • http://www.geocities.com/aletawcox/ Sam Cox

    Another very important point or two…

    The age of the universe has been determined to a high degree of precision…about 13.7 billion years. Everywhere we observe outward, astronomically, the universe cumulatively becomes singular at 13.7 billion light years distant…space and time cease to exist anywhere and everywhere at that distance…there IS no universe as we understand it…only energy.

    Although this fact by itself does not put a “lid” on the mass of the universe, it serves as a reminder and important parameter in determining the necessary limits of the universe. The most recent work I have seen is pretty consistent in deriving a universal mass of about 10 to the 60th Kg.

    All the professional speculation about parallel universes, multi-verses, an infinity of universes…etc is fascinating but remains speculation.

    Some of these ideas at least, are principally intended to explain the existence of universal information and complexity using infinities and probablilities, and since only one infinity (eternity) and certain fundamental universal parameters can also explain complexity in a vast universe of finite mass and limited spatial extent, it is hard to see how such radical speculation is really necessary. Most of those who propose these ideas readily admit they are probably not falsifiable- or provable. Max Tegmark for one is very open about this, and freely discusses the important “caveat’s” involved in the multi-verse idea.

  • John Merryman

    Sam,

    The line between knowledge and speculation is always a little fuzzy, but when it gets as fuzzy as current physics and cosmology would have it, it’s possibly due to some earlier speculation being incorporated as knowledge and throwing subsequent investigation off course.

    I’m currently reading a Christmas gift called Aristotle’s Children, by Richard Rubenstein. It’s about the reintroduction of the works of Aristotle and other Greek philosophers, as well as centuries of Jewish and Muslim commentary, with the reconquest of Spain in the early part of the last millenium. Because they took these early explorations as fact, rather then speculation, much chaos eventually worked its way into the established assumptions. Epi-cycles being the most obvious. I think we may also be at a late stage of the current cycle, where the speculation becomes increasingly fantastical, before it finally breaks down.

  • Lawrence Crowell

    The entire universe might actually be a grand nothingness. If one considers gravity wells as having negative potential energy and one then does an approximate sum over all energy and mass equivalent it may be be grand zero, as with Tolman’s thesis. Of course there are subtle issues of there being no time like Killing vector that projects onto the portion of a spacetime momentum 4-vector to give a constant energy. Yet this may also be telling us that globally energy is not defined, and that on a grand cosmological scale to say that the universe has a mass-energy is meaningless.

    If one things about it there is no way one can step out of the universe and place it on a scale. Weight is a measure of a force that resists geodesic motion in spacetime, but “outside of the universe,” if such has any meaning, there is no spacetime, thus no geodesic motion, curvatures, gravity or — anything.

    As for black holes, an early idea was that the universe was a spacetime with a giant black hole or a Schwarzschild spacetime. This black hole would have been a thundering thing weighting in at a mass greater than all observed galaxies. The entire universe is not such a thing. The vacuum solution for the black hole, before it was even called a black hole, had a symmetrical part that connected a cosmological patch’s conformal past infinity to a singuarity for a white hole. The white hole gives way to a black hole that connects up to the spacetime’s conformal future infinity. Some early ideas had the white hole part as some sort of creation field and the black hole as the recollapsing destruction field. The idea has passed into non-physics as the white hole portion is seen as a mathematical fiction of sorts.

    Clear the universe contains black holes, and an average galaxy probably harbors many thousands or millions of them. They often have a very large one at their centers. The CMB of the universe contains anisotropies which were the seeds for matter clumping that lead to the formation of proto-galaxies and the earliest stars. These then may have lead to the formation of black holes early on. I think that the “texture,” in the CMB recently discovered are the result of a black hole-like object formed by gauge charges. This is called black hole-like, for in pure spacetime it is not a black hole, but in extended dimensions (eg 5-dim for AdS or 10-11 in supergravity) it has a guage charged induced horizon. This horizon forms IMO a conformal completeness on the AdS, which is tied to AdS/CFT duality. This object during inflation is stretched into a cosmic string, possibly tied to a black hole. There may have been a number of these objects in the early universe. A finer observation of the CMB might reveal 4-th order deviations (beyond second order standard deviations) in the CMB which point to a distribution of these strange objects.

    The RHIC has found that heavy ions in high energy collisions have a black hole-like physics. It may well be that what is a black hole and what is not has a “fuzzy” quantum mechanical distinction. These RHIC objects, blobs at high energy for a 10^{-20}sec or so, might have some tiny quantum amplitude for being black holes, or gauge holes.

    Lawrence B. Crowell

  • John Merryman

    Here is an interesting article in today’s NYTimes, business section, that makes the basic psychological point I think physics and cosmology will have to eventually face; http://www.nytimes.com/2007/12/30/business/30know.html

    IT’S a pickle of a paradox: As our knowledge and expertise increase, our creativity and ability to innovate tend to taper off. Why? Because the walls of the proverbial box in which we think are thickening along with our experience.

    Andrew S. Grove, the co-founder of Intel, put it well in 2005 when he told an interviewer from Fortune, “When everybody knows that something is so, it means that nobody knows nothin’.” In other words, it becomes nearly impossible to look beyond what you know and think outside the box you’ve built around yourself.

    This so-called curse of knowledge, a phrase used in a 1989 paper in The Journal of Political Economy, means that once you’ve become an expert in a particular subject, it’s hard to imagine not knowing what you do. Your conversations with others in the field are peppered with catch phrases and jargon that are foreign to the uninitiated. When it’s time to accomplish a task — open a store, build a house, buy new cash registers, sell insurance — those in the know get it done the way it has always been done, stifling innovation as they barrel along the well-worn path.
    ———-
    When experts have to slow down and go back to basics to bring an outsider up to speed, she says, “it forces them to look at their world differently and, as a result, they come up with new solutions to old problems.”
    ———————–
    “I would ask my very, very basic questions,” she said, noting that it frustrated some of the people who didn’t know her. Once they got past that point, however, “it always turned out that we could come up with some terrific ideas,” she said.
    —————–
    “Look for people with renaissance-thinker tendencies, who’ve done work in a related area but not in your specific field,” she says. “Make it possible for someone who doesn’t report directly to that area to come in and say the emperor has no clothes.”

  • Lawrence Crowell

    Some of these criticisms might be applicable to physics. Often what happens is that radically different physics amounts to appealing to completely different modes of thought. In my small way I at least attempt to think this way by seeing general relativity and quantum mechanics as relationship systems between particles.

    Maybe our whole society needs that sort of boot, that is unless we are to tread a sorry road laid out by Bush/Cheney — a road that will lead us to some sort of totalitarianism. Yet a precursor for such changes are usually seen in the artistic and intellectual fields. Usually such changes are preceeded by new forms of art and music or new intellectual ideas. Unfortunately music and art are pretty much in the nadir right now as I see it.

    Lawrence B. Crowell

  • http://www.geocities.com/aletawcox/ Sam Cox

    LC,

    I have been reading your research and am really impressed! Best wishes in your continuing responsibilities both re field work and in the classroom. I’ll continue to follow your work…you have many interesting ideas in a subject area, an understanding of which is, I believe, critical to a proper understanding of cosmology.

    The wacky, quirky, and sometimes revolting nature of existence, is powerful evidence, I believe, that the development of information, order and intelligence in the universe, as basically awesome as it is, originated internally within the archaic universe an eternity ago, according to some process resembling the natural selection of organic evolution we observe here on Earth over the eras and epochs of the development of existing life terrestrially.

    You really are interested in that process! It is tempting to speak about “origins” in a universe where such a word is cosmologically meaningless…as meaningless as asking where the original energy “came from”. As finite humans we simply cannot conceive of eternity…even in our imagination! I think it is best, for scientific purposes, to regard eternity as a kind of (very gradually changing) horizon.

    However, just as on the lifeless early Earth, we can justifiably assume there was a time in the eternal past when quantum randomness was everywhere and information was nowhere. Because of a universal atemporal nature, frame invariance and a very specific energy density, however, it was possible for different quantum conditions to develop at different frames- and remain that way- conserved.

    As the quantum conditions at different frames interacted, certain types of information became dominant and pervasive in the universe, to the exclusion of other types of quantum states. Initially this process resulted in sets of classical particles, then baryonic matter in certain proportions…and eventually eternal “knots” of complexity related to each other in their origin and existence and continuing development of diverse observational capacity. These gradually evolved to the level of complexity we observe today.

    JM,

    It is funny how the passage of time usually results in great advances in knowledge, but the old ideas keep re-surfacing- with important modifications.
    Relativity is, in many ways Platonic and likewise reflects in some crude ways the observer centered universe of Ptolomy. Yet Platonism while based on periodicity, is completely static in concept, and we can be sure that change DOES occur in the universe, even if we do not observe change in the way it actually occurs cosmologically. The fact that time and change exist at all is a hint as to the finitude of universal mass and spatial extent. I don’t agree with Mach on everything, but he made many, I believe irrefutable cosmological points.

    LC,

    I have a biology background but have taught HS physics, physical science, geometry, trigonometry. I posted some conceptual material on the internet 10 years ago and was contacted by UNC Chapel Hill and asked to continue my conceptualizing of their website for a while. I have studied relativity since 1967. While overseas, with no TV or other distractions around, I ordered materials and focused on the subject. The site is archived material and some of the earliest is not particularly accurate, however it has been a work in progress. Some professors have had their undergraduate physics students read it, and I have been contacted by a number of researchers and theorists.

    Ned Wright expressed inital friendly support for the project as did RM Kiehn from the University of Houston. Dr. Kiehn took the time to read extensively on the site and graciously commented that it was “off in a few details”. From what I have continued to learn, I realize now how gracious the good Doctor was! However, both Ned and Dr. Kiehn are just fabulous teachers and they, as good teachers, know the importance of encouraging their students. I myself have spent 24 very rewarding years in the classroom…rewarding partly as a result of benefiting myself from that kind of mentoring!

    This is really a great blog! You all are to be commended!

    Sam Cox

  • John Merryman

    Lawrence,

    To the extent it is a cycle, there is ascent and descent. Economically, politically and religiously, we seem to be at the top and headed down. Sometimes it’s prelude to crashing at the bottom and sometimes it’s creating energy for the next climb.
    With expanding energy and collapsing mass, the secret is to have enough energy to keep the structure expanding. The problem is that the larger the structure gets, the more energy it takes to keep growing. Eventually the weight exceeds the input and it starts collapsing. Call it the physics of institutions. The bigger they get, the harder they fall.

    Sam,

    It’s good to feel you have something to give.

    This is the only writing I’ve had published anywhere that got some amount of feedback;

    http://www.exterminatingangel.com/index.php?option=com_content&task=view&id=203&Itemid=118

  • Lawrence Crowell

    I met R. Kiehn at a conferece some time ago, maybe 8 years go or so.
    He’s the guy with the nonlinear soliton stuff as I recall.

    Some sort of change is likely to occur with quantum gravity. I think that gravitation and quantum mechanics are systems of relationships between particles. I have indicated some on how I think that works, but it goes into considerable depth on lie algebraic systems and quantum codes, lattices and the like. I intend to get a web site up in a few months on this, and have actually written most of the web pages already. I call one group of them climbing up heterotopia to AdS/CFT. Another chunk involves a lot of work on the preservation of quantum information and how certain quantum codes, Golay codes on the sporadic M_{24} and Leech lattices. This stuff actually gets infernally mathematical, but in order to express a unification of these “relationships” there appears to be no escape from this.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    The problem isn’t with the math. The problem is the assumption that the math is the reality, rather then a model of reality.

    If you want some outside perspective on this, look at what the financial markets have become, relative to the economy they are based on and supposed to be a tool for.

  • Lawrence Crowell

    This is diverging from cosmology and physics, but honestly I don’t have too many cares about anything which involves “institutional physics.” If I had to sum it all up, the human species is some sort of terminator species that is turning everything it can consume into garbage. It is just that we also happen to be at least locally cosmological observers. Our future tenure is likely to be rather brief, certainly on cosmological or geological time scales. So we are faced with the question of whether we can figure out the nature of the universe within an unknown, but likely very short, time we have left.

    I think it is a problem with all intelligent life, at least as defined by the ability to abstract concepts, to communicate them in some linguistic system and finally to have the physical attributes required to configure their world according to such concepts. In other words in the case of human beings this involves brains, tongues and hands. Once that gets going, and I suspect that with Homo erectus this crossed the rubicon to intelligent beingness with learning to manipulate fire — the gift of Promethius.

    Once that happens an intelligent life form of this type is no longer constrained by its environment. Given any such constraint imposed on intelligent beings they are able to figure a way around it. This then means that a cardinal rule of biological communities or ecosystems is broken: Species of life are regulated by their interactions with the broader community of life. As a result we humans number 6.6 billion currently, and at no time in the history of life on this planet has there numbered this many animals of our size and dietary requirements at once. Then compound this by our 100 fold increase in energy and resource demands, and not to mention our entropy impact in the form of pollution and environmental degradation. Step outside, or drive around and look at it all — it’s exceedingly extraordinary. Some of our fabricated stuff is in space, even some on the moon with booted footprints — astounding!

    I suspect this is a problem with all intelligent life, though we humans have some additional properties that hot-wire us, such as we do not have sexual seasons as with other animals — we “do it” all the time and have babies like large rabbits. The SETI conjecture is that we are not alone, and in the universe in total this is probably correct. Yet I suspect that intelligent life is very rare and may prove impossible to detect in the universe, for it needs to be close enough for us to detect.

    The role of intelligent life in the universe is then an interesting one. I suspect in most if not all cases it is transient. Intelligent life might then observe the universe and if they persist long enough, maybe they are not so wreckless with their nuclear firecrackers or they are sufficiently limited in their appetites for consumption, they understand the universe up to some limit (what ever that is) of knowability. Maybe there is some ensemble of possible intelligent life forms, and we humans are just one of the experimental cases in the sample space. On the other hand, maybe we are indeed the only ones in the whole thing — and we are a two legged locust swarm tearing down the life support system on our planet or “spaceship.”

    I am not a fan of so called Anthropic Cosmological Principles (ACP), though I think the weak ACP does raise questions. Clearly the universe is configured as “such as such” in order for us to exist. However, I think that there is some comsological einselection process, some system of decoherent processes that reduce the overlap between possible cosmological states D(Psi, Psi’) —> 0 which selects for an extremization of local complexity. Intelligent life might then just be a specific example of this, and maybe ultimately some sort of fluke in this outcome. This has a sort of Leibniz-esque element to it, for it echos his “best of all possible worlds” thesis. So maybe the grand path integral for all possible quantum cosmological amplitudes self-decoheres by inflationary processes so that locally classical (like) structures come about by an extremization of possible local complexity.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    Consider it from a biological perspective.

    For one thing, consciousness, as bottom up emergent phenomena, is cause, while intelligence is top down effect. Life creates organisms in order to consume them, so what will emerge from the ashes of the monetary wildfire that is about to burn down our current abode?

    To the extent life on this planet is capable of functioning as one super-organism, we might be at the embryo stage, consuming all the proteins and other nutrients within the egg before hatching. We have definitely reached the limits of what our environment can support with humanity at top predator, but after this paper bubble bursts, the only way I can see to re-constitute it is to formulate money as a public utility. Similar to a public road system. This would tie rights to responsibilities in a very coherant fashion. This would place the very basis of public wealth as a public utility. Private wealth would have to be largely a function of maintaining a healthy community and environment, because the reliance on wealth would be initially constrained and only expand as people developed faith in the public process. I went into the foundation of this situation somewhat in the link on post#203, but not the structure that might emerge from it.
    Possibly humanity can be reformulated as the central nervous system of the planetary organism, not just its primary exploiter.

    You’re right, this is somewhat off topic, but I’m in this discussion in the first place because I do feel that in a very fundamental way, a lot of the general confusion with life and reality goes to the very core of our philosophic assumptions. The issue of whether the absolute is an ideal from which we fell(Plato), or the essence out of which we rise(Aristotle) is still playing out, bubbling under the surface of everything from monotheism to mathematics.

  • http://www.geocities.com/aletawcox/ Sam Cox

    LC,

    “I met R. Kiehn at a conferece some time ago, maybe 8 years go or so.
    He’s the guy with the nonlinear soliton stuff as I recall.”

    NOTE: Outside of the concept description on the homepage of my site, the rest of the material is archival…some as much as ten years old, so some of the links do not work. However the link to Dr. Kiehn’s site, “Cartans Corner” is still live and there is some interesting recent material posted there.

    Dr. Kiehn is “emeritus” and retired now, but the last I heard he is still active. He has done a lot of work with non-linear solitons as you note, and time process. He was on the team which developed thermonuclear weapons during the 50′s and spent a lot of time at Bikini and Eniwitok.

    “Some sort of change is likely to occur with quantum gravity. I think that gravitation and quantum mechanics are systems of relationships between particles.”

    NOTE: You are working in a very challenging area, at the lower levels of scale where GR established relationships between particles meld with the world of quantum fluctuations. GR as a description of gravity is of course, precise to very small scales. When you speak of quantum gravity, you are inferring a kind of Newtonian gravity in which universal entaglement becomes an important principle.

    Just from a very rough conceptual perspective, I would think that such problems as wave/particle duaity would complicate your work. Conducting an investigation as to how information originates, is embedded (rooted), and is conserved in the sub-microscopic region between the Planck realm and particulate reality is essential to a proper understanding of what the universe is, where it came from and where it- and we- are going.

    ” I have indicated some on how I think that works, but it goes into considerable depth on lie algebraic systems and quantum codes, lattices and the like. I intend to get a web site up in a few months on this, and have actually written most of the web pages already. I call one group of them climbing up heterotopia to AdS/CFT. Another chunk involves a lot of work on the preservation of quantum information and how certain quantum codes, Golay codes on the sporadic M_{24} and Leech lattices. This stuff actually gets infernally mathematical, but in order to express a unification of these “relationships” there appears to be no escape from this.”

    NOTE: I’ll be looking for your web site. It is one thing to roughly conceptualize this and quite another to formally reduce what we know must be true to a mathematical model which has excellent descriptive and predictive value. We know gravity has to be Newtonian- and thus quantum. We also know that because GR is scale related and is so accurate, it is probably not wrong. What we learn will only serve to enrich and extend our present knowledge.

    By its very nature of course, GR is a scale related (geometric) concept and we know that quantum effects, while measurable at macroscopic scales, diminish as scale in the universe increases. We know that CPT symmetry seems ludicrous at macroscopic scales where time process becomes “obvious”, and that the reason for this must be related to the existence of scale related observational horizons of one sort or another.

    We also know that once we get our complete concept of the universe as described in SR/GR/QM properly combined and mathematically formalized we will not only understand the universe better, but will lay the foundation for an unbelievable expansion of technology.

    Just one final remark. Newtonian quantum gravity is really a pretty simple idea, and we know gravity has to both quantum and roughly newtonian to prevent the universe from coming unglued. I’ve taught basic probability theory, binomial expansion and related concepts in Genetics and Physics and I would think that any mathematical formalism relating to the emergence of information from the quantum realm- or, in the reverse, its appearence on 4D event horizons would be related to an involved study SR/GR relationships, set theory and lattices as you mention. I’m sure you won’t forget the time element…that different locations in the universe are not only distance, but time and observer related.

    The fact that the universe is what the observer observes, and the universe can be observed in an almost infinite variety of ways, will make your job more difficult.

  • Jason Dick

    Sam Cox,

    You mention that we can’t conceive of the origins of the universe. Well, that’s the case with a lot of science which we can describe very accurately mathematically, such as quantum mechanics or extra dimensions. The inability to intuitively understand something does not indicate an inability to describe that something. Science has basically been nothing but a long process of moving past our own limitations in understanding to better describe the world around us. There is no reason yet to suspect that we won’t be able to go all the way back and say something definitive about the beginnings (if there were any), or the ultimate nature of the universe. The best we can say now is that we don’t yet know how much we will be able to discover.

  • Lawrence Crowell

    If we can look further into the distant unvierse we should be able to understand the big bang. Already the anisotropy of the cosmic microwave background is revealing much. With gravity wave detectors and neutrino astronomy we might be able to observe much further back to near the earliest moments of the universe. Depending upon how science policy plays out in this nation or other nations it is possible that in the next 50 years we may actually be getting data from the ultimate scattering experiment — the big bang. With that we might be able to support quantum gravity/cosmology theories with real data.

    An important aspect of physics is triality. An example would be with the family structure of elementary particles. The weak interactions is likely an su(2) + su(2) theory for left and right fields. Due to CP violations our low energy universe is just the left handed part. Now this is so(4), if you are familiar with group theory stuff. Gravity is so(3,1) and this with the weak interactions is so(7,1) = so(3,1) + so(4). This may be extended to the exceptional group f_4 if we add in the short roots 8 + 8′ + 8″

    f_4 = so(7,1) + 8 + 8′ + 8″,

    and these additional roots are the particles (e,nu_e), (mu, nu_mu), (tau,nu_tau) for the leptons. This is a triality structure, and what this exceptional group does is to put the Grassmannian (Fermionic) fields on the same frame bundle with the gauge fields.

    This can be carried to the exceptional group E_8 with QCD as,

    e_8 = f_4 + g_2 + 26×7,

    where the “26″ is the Jordan algebra J^3(O) over the octonions. The “26″ is the bosonic string. In a more general setting there are three of these E_8′s: one the chiral dual to the first E_8 and the third an exceptional group required to define homeomorphisms over all four-manifolds that are configuration variables for quantum gravity states. This gets into some very abstract mathematics, but from these three is the Mathieu sporadic group m_{24} which is the quantum code I am working towards.

    Lawrence B. Crowell

  • Lawrence Crowell

    I was going to write a further ending to this. The e_8 group contains string theoretic information. Yet the requirement for there being three E_8′s, an additional one to the E_8xE_8 of the heterotic string theory, is due to a quantum constraint problem, how wave function(al)s over metric configuration variables correspond to classical spacetimes, and a matter of general covariance. This portion ties heavily to the Loop Quantum Gravity (LQG) approach. String theory appears to be a vast theory of many possibilities, while LQG is more of a constraint theory. Indeed LQG is a theory of constraint conditions on the action.

    String theory and LQG appear to be different views of quantum gravity, as if one were looking into the same room through different keyholes in separate doors. Of course there are certain “battle lines” between these two approaches to quantum gravity, and unfortunately there seems to be a bit of pride on both sides which appears to be drawing up a growing wall between them.

    Lawrence B. Crowell

  • http://www.geocities.com/aletawcox/ Sam Cox

    LC,

    “This portion ties heavily to the Loop Quantum Gravity (LQG) approach. String theory appears to be a vast theory of many possibilities, while LQG is more of a constraint theory. Indeed LQG is a theory of constraint conditions on the action.”

    NOTE: I’ve read up on string theory, but in a general kind of way have come to regard “strings” as pretty much of a 4D frame of reference way of describing the quantum realm, not well enough constrained…not enough anyway to logically lead to a universe filled with informational complexity. I’m still open…thats just a general reaction.

    LQG is something else again. I mentioned elsewhere on the blog the recent work at Fermi, an actual discovery, that certain types of mesons occillate between matter and antimatter at a regular and predictable rate…2.8 trillion cycles per second. Although Fermi is not dogmatic about it, since this occillation actually occurs at the quark level, there may be a similar, general occillation of the baryonic universe as a whole at the quark level, expalining “where the antimatter has gone”- by implication, nowhere. At our level of scale we observe one side only- there is a horizon involved. This has implications about the very nature of black holes and white holes, the nature of time as this “pulse” relates to the gravitational time dilation relationship and so on.

    LQG seems to me at first glance to fit better with a concept of gravity-and the quantum (Planck) realm in general- which is better organized foundationally and less inherently random…more in line with Fermi’s recent discoveries of matter-antimatter occillations at the quark level.

    LQG also seems to me to fit nicely with the GR invariant frame concept…which provides a logical mechanism for the development, preservation, and possible inter-relating of information…inorganic and organic evolution.

    I don’t personally understand why battle lines need to be drawn, but I guess when people devote a lot of time to their work they have a certain (I believe) unnecessary emotional investment in the outcome. We forget that the universe just “is”…it does not “care” what Sam Cox- or anybody else, for that matter, thinks. Anyway, as the songwriter said; “Fame if you win it, comes and goes in a minute”!

    One thing about the universe I really like is that it has this “feral” quality about it. On the one hand it is “domesticated” in the sense that it seems to operate according to a well coordinated set of principles and should I say, by LQG “constraints”? On the other hand, the universe can, in a way that sends chills down my spine, be a wild and very demanding place in which to exist.

    I don’t think that being too “sheltered” is really the way to live, yet mankind and all mammals must give a measure of protection to their young- or they wouldn’t survive to adulthood!

    However, being exposed to almost constant danger and challenge has really “made” my life. I grew up in a tough neighborhood and became “street-wise” in a hurry. I attended camps where we cooked over fires and showered in cold water. Later, I matured in a thatched roofed South Pacific mens house, fought off sharks as we netted fish, was exposed to just about every disease known to man, and survived a rogue wave which crashed over us guys as we slept on the hold of a ship. That’s just for starters!…but that is the universe I know, and have been very close to since I was a kid. Yet it is not just the danger and challenge of the universe which makes it what it “is”. I have known the power of the love, loyalty and devotion of family and friends…foxhole friendship too!

    The link between observation, experience and existence truly makes us what we are!

    JD,

    I think your comments were very appropriate. In the end, just as in the case of the human exploration of the planet, theoretical horizons like “eternity” may turn out to be completely- and easily- inderstandable. In fact, these “horizons” may not really turn out to be horizons at all…we may recognize eternity for example, to really be a part of ourselves!

    Sam Cox

  • http://www.geocities.com/aletawcox/ Sam Cox

    An additional thought…

    a rather obvious additional thought. There are important constraints built into probability theory, as binomial expansion for example. We usually use repeating, periodic events and or sets of events in our evaluation, as heads/tails, boy/girl. When we evaluate quantum behaviour some analogous periodic phenomena of restricted character are being evaluated. To my mind, this kind of mathematical structure foundational to QM, also implies duality, periodicity and implicit structural constraints…structure, lattices, scale, certain kinds of invariance etc and is therefore most consistent with LQG….

  • http://www.geocities.com/aletawcox/ Sam Cox

    LC,

    …I also illustrated for my students in classroom experiments, how dimensionality is implicit in many probablility studies- and if that dimensionality varies even slightly, the results of our experiments are drastically altered. For example, if we use nickels instead of pennies in a coin toss, the nickel may actually land on its third side, and the wider the coin, the greater the chance of this additional event occuring.

    You are working in an area where dimensionality is just appearing as a characteristic of the universe, and that would seem to me to be a complicating factor in your work. Fortunately, in terms of orders of magnitude, the region between 10 to the minus 36th Cm and 10 to the minus 12th Cm. or so is vast, but relativistic effects will make your task more challenging…and relativistic effects dominate in that part of the universe!

    Relativisitic effects which are seemingly so easy to describe as “reality” when remotely observed from our frame, can be expected to become a horse of a different color when the scale of observation is reduced.

  • John Merryman

    Sam,

    Periodicity, duality, etc. is one side of a larger duality, in which the two sides define a larger whole and the cycle is part of a larger process. It takes many forms and relationships. Walking along involves many discrete steps, but it also involves a constant motion. Order and chaos describe complexity. Inside and outside define a set. To the extent physics is largely premised on making measurements, it’s focused on the particles and not the space inbetween, which seems to be dismissed as completely defined and dependent in these perimeters, but what if it is the other way around; the field creates the particles, even though it’s the particles which define the field.
    Think of it in terms of the eco-system and the organisms inhabiting it. Generally we accept that form follows function, but it seems that in physics, we can only measure form, so it’s assumed function is the consequence, not the cause.

  • John Merryman

    Sam,

    Your last post seems to cover the point I was making.

  • Lawrence Crowell

    Loop Quantum Gravity is more honest with general relativity. It is a “space plus time” spinor theory of relativity which quantizes certain connection coefficients. There are a lot of details, but it essentially is a theory with the action

    S = NH + N_iH^i + B*Q + ….,

    where N is the lagrange multiplier for the Hamiltonian N_i the shift or momentum lagrange multiplier and so forth. This action enters into a path integral

    Z = int &g exp(iS),

    which determines the field amplitudes. These are all constraints which define the dynamics on a contact manifold. It has no background dependencies and so forth.

    String theory is a bit more problematic with gravitation in some ways. In particular a string on the spacetime metric has “vibrations” which on a scale larger than the string give curvature corrections on a background metric. This runs into trouble with general covariance and coordinate independence. However, there are some nuggets of gold due to this as well, particularly this indicates something about the nature of four manifolds as configuration variables of quantum states.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    Since most of what you say goes way over my head, I can’t figure out if you addressed my query in #195(unless it was the first paragraph of #199).

    It was that you describe light being stretched out as it falls into a gravity well. This would seem to mean that it is redshifted falling in, as well as climbing out. I’m repeating the question because the conclusion I drew from it seemed a bit too simple and obvious that I must be missing something;

    That it does this by compressing them perpendicular to the line of radiation would seem to explain the magnification/focusing of gravitational lensing.

    This is over-reach, but it would explain this point raised by Sam;

    “At 2 million light years “distant”, the Andremeda galaxy fills about 30 minutes of arc in the sky. At 10 billion light years “out”, that same 30 minutes of arc contains millions of galaxies. The combined mass of the space between us and these galaxies and to a much lesser extent, the baryonic mass of the galaxies themselves cause the light we observe to be gravitationally red shifted.”

    Since the further light travels, the more residual gravity fields it passes through. If they both magnify and redshift light, then the more distant galaxies might be much further then we assume, but their light is being magnified and focused, so they appear closer and clearer then they would over the same distance of completely empty space, but redshifted, so they appear to be moving away at an accelerated rate.

    It would seem easy to disprove this by observation, since light passing close to the sun or some other star would be neutralized if it is blueshifted falling and redshifted by an equal amount climbing out, but if the light is being stretched out as it fell in and stretched as it climbed out, there would be an overall redshift from this passage. What am I missing?

  • Lawrence Crowell

    Light as measured by an observer on the surface of a gravitating body would be blueshifted (compressed), while it is redshifted as measured by an observer watchiing photons emitted from the surface of a gravitating body.

    A gravity field acts a bit like a lens to photons. A regions with spacetime curvature can be modelled as if it had a spatial variation in the index of refraction. Just as light passes through an ideal lens with no loss and with the same wavelength the same happens to photons which pass through a region of spacetime curvature. Large elliptical galaxies act as “Einstein lenses” which give a distorted image of more distant galaxies.

    Lawrence B. Crowell

  • Jason Dick

    It would seem easy to disprove this by observation, since light passing close to the sun or some other star would be neutralized if it is blueshifted falling and redshifted by an equal amount climbing out, but if the light is being stretched out as it fell in and stretched as it climbed out, there would be an overall redshift from this passage. What am I missing?

    It’s blueshifted as it falls in, and redshifted as it comes out. Now, there’s a slight change due to the expansion of the universe from non-matter components (e.g. dark energy), dubbed the Integrated Sachs-Wolfe effect (ISW effect), as the expansion of the universe over the time the light traverses the potential, if that expansion is driven by more than just normal matter, causes the potential to change during the traversal. With a cosmological constant, for instance, the potential becomes shallower as the light traverses it, so the blueshifting as it goes in outpaces the redshifting as it comes out, making for a small blueshifting of the light as it passes through overdense regions, and a small redshifting as it passes through underdense regions.

    This, however, is quite a small effect, and the overall redshift that we see in far-away galaxies is predominantly due to the expansion of the universe, which also stretches the wavelength of the light as it travels. So, for example, if a light beam was emitted when the scale factor of the universe was 1/100th its current value, then the wavelength will now be 100 times longer than when it was emitted (neglecting the small ISW effect above).

  • Lawrence Crowell

    Right, and the largest effect is that the light path can be bent or deflected to distort the image behind the gravitating body. Yet the wave length of the photon at “-infinity” is equal to that at “infinity,” where these are defined as asymptotic regions. This of course ignores comsological expansion and other matters, so the “infinity” is a bit more local — but it is good enough FAPP.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    Light as measured by an observer on the surface of a gravitating body would be blueshifted (compressed), while it is redshifted as measured by an observer watchiing photons emitted from the surface of a gravitating body.

    I suppose it would be essentially whiteshifted(?), since the light is traveling at the speed of light, so there would be no signal preceding it, that would be blueshifted by its approach. I guess the stretching out you described would be meaningless to an observer on the surface, as all the lightwaves hit at once. Sort of like a sonic boom is caused by all the sound waves being compressed. together.

    A gravity field acts a bit like a lens to photons. A regions with spacetime curvature can be modelled as if it had a spatial variation in the index of refraction. Just as light passes through an ideal lens with no loss and with the same wavelength the same happens to photons which pass through a region of spacetime curvature. Large elliptical galaxies act as “Einstein lenses” which give a distorted image of more distant galaxies.

    Not only do gravitational lenses distort the path of the light, but they apparently magnify it as well. Does this have any side effect on the wave length? I ask because of your point that from the perspective of the light, gravity squeezes it, as it stretches it. Does this squeezing intensify the light and thus magnify it? For example; Shining a light through a magnifying glass intensifies it, as it compresses it to a point. Does it affect the frequency of the light waves by stretching them, as it compresses the area of focus?

    Jason,

    the overall redshift that we see in far-away galaxies is predominantly due to the expansion of the universe, which also stretches the wavelength of the light as it travels. So, for example, if a light beam was emitted when the scale factor of the universe was 1/100th its current value, then the wavelength will now be 100 times longer than when it was emitted

    If it is stretching the wavelength “as it travels,” this would seem to be a local effect. So why does the speed of light remain the same? As you describe it, the very fabric of space is being stretched, yet the speed of light remains constant to a dimension of space that does not stretch.?

  • Jason Dick

    I suppose it would be essentially whiteshifted(?), since the light is traveling at the speed of light, so there would be no signal preceding it, that would be blueshifted by its approach.

    Whiteshifted makes no sense. Just like any other particle, as a photon enters a potential well, it gains energy. For a photon this means that its frequency increases/wavelength decreases, hence it is blueshifted (the speed doesn’t change, for obvious reasons).

  • Jason Dick

    If it is stretching the wavelength “as it travels,” this would seem to be a local effect. So why does the speed of light remain the same? As you describe it, the very fabric of space is being stretched, yet the speed of light remains constant to a dimension of space that does not stretch.?

    Yup, it’s a local effect. No, the speed doesn’t change. The important thing to note here is that speed itself is only well-defined locally. The expansion of the universe greatly affects how long it takes for a light beam to get from point A to point B (if A and B are far enough apart for the expansion to make a difference), but at every step along the way it’s only ever traveling at the speed of light.

  • Lawrence Crowell

    A lens diverts the path of light by definition. It may magnify an image, and gravitaitonal lenses has a magnification effect, though with a high degree of distortion.

    A gravitational lens has no effect on wavelength. I went to a hotspring yesterday, one you have to hike into a ways. On the bottom of the pool the light illuminated with the usual caustics randomly wiggling around. Around these caustics were little “fringes” of red and blue. Most optical media have an index of refraction that depends on the frequency of light

    eps = eps(freq)

    which causes this chromatic abberation. This is a problem for the lens designer and optician. The gravitational lens has no chromatic abberation! If it did then it would mean geodesic motion depended upon inertial mass in a way which violated the equivalence principle and the equivalence of inertial and graviational mass.

    On a flat background the overall change in wave length is zero. If the background is expanding so there is a gravitational physics comoving frames apart (points on the space are sliding away from each other) there will then be an added redshift of light. This is of course what is observed, and further this comoving of frames away from each other is accelerating.

    Lawrence B. Crowell

  • John Merryman

    Jason,

    Whiteshifted makes no sense.

    I was trying to understand this description of light by Lawrence of light falling into a gravity well, from the perspective of an observer on the surface of the gravitational mass;

    #190, Think of youself are at the center of the spherical cloud of particles. You along with this cloud are falling towards a gravitating body. The particles along the radial direction of fall will in your frame be seen to accelerate in opposite directions away from you. Conversely particles on a plane prependicular to the radial direction of fall will in your frame be seen to accelerate towards you.
    Now suppose these particles emit some known wavelength of radiation. The particles on the antipodal points along the radial direction will emit photons you measure as redshifted, while the particles on the perpedicular plane will emit photons you measure as blue shifted. Further since these particles are accelerating away or towards you this red and blue shifting will increase.

    Using the model of a sonic boom, since light travels at the speed of light, it can’t emit photons that would precede it and be blueshifted by the light’s approach, all the waves across the spectrum would all arrive at once, hence white light, not blue or red.

    Yup, it’s a local effect. No, the speed doesn’t change. The important thing to note here is that speed itself is only well-defined locally. The expansion of the universe greatly affects how long it takes for a light beam to get from point A to point B (if A and B are far enough apart for the expansion to make a difference), but at every step along the way it’s only ever traveling at the speed of light.

    I understand that redshift is proportional to distance, so that the further away a lightsource is, the faster it appears to recede. According to Big Bang Theory, the universe was expanding at a faster rate to begin with and has slowed, so the further away the source, the earlier in time the light was radiated and the faster the universe was expanding. Since the basic geometry of a conventional expansion would mean we are at the center of the universe, it was amended to space itself expanding. Yet from all I’ve read, it seems space is also, according to the equivalence principle, falling into gravitational wells.
    So if space IS expanding, it doesn’t have to have been expanding at a greater rate in the past, since the further light travels, the more the effect is multipled, ie. light that is redshifted by crossing the initial space, has this effect further multiplied as the redshifted light is further redshifted by crossing more space. Eventually it crosses enough space that the source effectively appears to be receding at the speed of light and this creates a horizon line. I say “appears” because if space is effectively dynamically fluid, as it must be to expand and collapse, then the quantity of expansion is largely compensated for by the collapse of gravity. Since we only measure that light which has crossed space and not fallen into gravitational wells, or covered so much distance that it has been completely redshifted off the scale, we see what is flying away from us, not the compensating factors, ie. collapsing mass.

    I realize I’ve been over this before, but I don’t think I’m really proposing anything which hasn’t been already accepted(expanding space/collapsing gravity), just putting them together in a larger cycle. In Sean’s last post, on the recent Edge question, he refers to a Paul Steinhardt (http://www.edge.org/q2008/q08_4.html#Steinhardt), who raises serious issues with making Inflation Theory work. So it’s not as though fundamental issues with BBT are resolved to the point of saying we are not missing anything.
    What might actually cause space to expand, as opposed to reference points simply moving away from each other in stable space, is an open question. Is it some form of non-neutral vacuum fluctuation? Does light have some field effect we cannot yet measure? It appears to be some form of cosmological constant.
    The fact is that these theories have only been developed over the last hundred years, so the astronomy on which it is based amounts to a moment in time, from one rather small spot in space. It wouldn’t be the first time in history a promising model had to be dropped because it simply didn’t answer the questions as well as other models that eventually replaced it.

  • John Merryman

    Specialists are like gravity. Reality bends around their point of focus.

    Generalists are like radiation. Weightless, but everywhere.

  • Lawrence Crowell

    The sphere of dust particles around a central falling observer is not presumed to be moving faster than light. The distortion of this sphere is due to the Weyl tensor components of curvature and in a weak field limit is the source of tides here on Earth. The doppler shifting of light simply is anisotropic: It is blue shifted around an equator and redshifted for light emitted by particles at the antipodal points. Try to draw a picture.

    The cosmological constant is thought to be due to the quantum vacuum of the universe. The momentum-energy tensor is

    T^{ab} = (e + p)U^aU^b + pg^{ab}

    e = energy density and p = pressure of the vacuum. If we equate this to a cosmological constant we get

    / = Trace(T) = (e + 3p).

    This goes into the Einstein field equation

    R_{ab} – 1/2Rg_{ab} = -(8piG/c^4)/g_{ab}.

    This is a part of the canonical model here. There are some funny elements to this. In particular a Ricci curvature with R_{ab} = Kg_{ab} (K = constant) defines an Einstein space with some nonzero Ricci curvature in source free case. Yet here we have defined a momentum-energy tensor according to a source, the vacuum, and then turned this into an Einstein spacetime.

    Steinhardt is the author of the quintessence theory and a cosmological idea called ekpyrotic (if I remember the spelling). The quintessence idea I think is a certain state of the vacuum, maybe related to dark matter, which is a space and time variation in the inflaton (Higgs-like) field in the universe. The dark energy vacuum I think is the dominant phase, and there is the final phase called phantom energy. These are I think related to each other in a way analogous to the onset of the “heavy destruction” of a Landau electron fluid phase in solid state physics. But that gets into some technical issues.

    Lawrence B. Crowell

  • Jason Dick

    I understand that redshift is proportional to distance, so that the further away a lightsource is, the faster it appears to recede. According to Big Bang Theory, the universe was expanding at a faster rate to begin with and has slowed, so the further away the source, the earlier in time the light was radiated and the faster the universe was expanding. Since the basic geometry of a conventional expansion would mean we are at the center of the universe, it was amended to space itself expanding.

    Okay, first of all, the change in the rate of expansion is really irrelevant to this point. The expansion rate could be completely constant in time, and we’d still observe objects further away having larger redshifts (this is, in fact, a very good approximation for the nearby universe).

    Yet from all I’ve read, it seems space is also, according to the equivalence principle, falling into gravitational wells.
    So if space IS expanding, it doesn’t have to have been expanding at a greater rate in the past, since the further light travels, the more the effect is multipled, ie. light that is redshifted by crossing the initial space, has this effect further multiplied as the redshifted light is further redshifted by crossing more space.

    Okay, I think I see what you’re saying now. Yes, there will probably be some biasing of measured redshifts due to the local environment of the source. However, there are two points to make:

    1. Since matter falls into potential wells, looking far away, into the past, the universe was more uniform, thus the effect is more important locally, and less important far away (meaning it should cause a slight underestimation of the expansion rate).
    2. This is, however, a minuscule effect. If we travel just 10,000 light years from the center of a 10^13 solar mass object (this is far more dense than any galaxy, I believe), then our gravitational redshift will only be around 10^-5, a value that is so small as to be negligible for the systems in question.

  • John Merryman

    Lawrence,

    The sphere of dust particles around a central falling observer is not presumed to be moving faster than light. The distortion of this sphere is due to the Weyl tensor components of curvature and in a weak field limit is the source of tides here on Earth. The doppler shifting of light simply is anisotropic: It is blue shifted around an equator and redshifted for light emitted by particles at the antipodal points.

    The question is what are the effects on light falling into a gravitational well? Is it stretched antipodally and squeezed equatorially? What would be the effects of it climbing out of this well? Does it squeeze antipodally and stretch equatorially? Is there some residual effect that would explain whatever magnification results?

    Jason,

    Think in terms of the description of gravity as a bowling ball on a rubber sheet. The ball creates a gravity well. What determines whether the sheet is actually flat where there is no ball? Think in terms of hills and valleys. Where does the valley end and the hill begin? This is my feeling of expanding space, that it is the hills around these gravity wells and if you could bulldoze the hills of expanding space into the wells of collapsing space, the result would be flat (Euclidian) space.

    This is, however, a minuscule effect. If we travel just 10,000 light years from the center of a 10^13 solar mass object (this is far more dense than any galaxy, I believe), then our gravitational redshift will only be around 10^-5, a value that is so small as to be negligible for the systems in question.

    As I’m proposing it, it’s not simply that gravity bends space one way, but that radiation bends it the other way. Gravity doesn’t scatter light, mostly it bends its path around the source of gravity. So if radiation, which emanates from gravitational objects in the first place, has the opposite effect, so that it expands space, rather then collapsing it, it wouldn’t scatter light either, nor would it even bend it around, because there isn’t the gravitational point of attraction. It would simply cause space to effectively expand, thus redshifting light crossing it, as a local, but extremely minute effect that would only be apparent at great distances. In this way, gravity and radiation would be opposite sides of a cycle of expanding energy and collapsing mass.

  • Lawrence Crowell

    The weakness of the gravitational bending of light is realized when you consider that the Abel galaxy cluster is about 1 billion light years out and it lenses a quasar billions of light years behind it, and the angle of view and lensing is subtended by a few second of arc. Gravity is a very weak interaction.

    The energy of light is Planck’s constant of action times the frequency E = hf. If it proceeds radially into or out of a Schwarzschild gravity well (a static spacetime solution) then the energy of the photon is

    E = hf(1 – sgn*2GM/rc^2),

    where sgn = + for the photon climbiing out and sgn = – for it falling in. For sgn = + the detector is at r —> infinity and the photon leaves a surface of radius r, and for sgn = – the photon comes in from infinity and is detected at the surface of the gravitating body at radius r.

    I don’t know really what else to say about this. Don’t confuse this with the statements about an infalling shell of material and the antipodal expansion and equitorial contraction, which results in the observer at the center of the shell seeing an anisotropy of Doppler shift. To explicitely show this requires some analysis with the Weyl curvature or a general form of the geodesic deviation equation. I think I will avoid going there for that will involve some detailed mathematics.

    Lawrence B. Crowell

  • Lawrence Crowell

    I figured I’d illuminate a little more on this subject of light rays in curved spacetime. If you have a set of light rays then at an time they define a wave front. A spacetime with curvatures or gravity wave or what ever will distort this wave front the red or blue shift the light in the wave front. There are a set of equations which describe this called the Raychadhuri and Sach’s equations. I am not going to write in any depth on these for they are fairly complicated objects, yet one can look them up. They are pretty standard stuff in general relativity from the 1950s. They also apply to distributions of matter on timelike curves as well.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    Gravity’s effect on light does seem to be minor, except at the extreme. The nature of gravity is contraction and the nature of light is expansion. Of course, as a source of thermal energy, light can also cause mass to expand, to an extremely minor degree.

  • Jason Dick

    John,

    Think in terms of the description of gravity as a bowling ball on a rubber sheet. The ball creates a gravity well. What determines whether the sheet is actually flat where there is no ball? Think in terms of hills and valleys. Where does the valley end and the hill begin? This is my feeling of expanding space, that it is the hills around these gravity wells and if you could bulldoze the hills of expanding space into the wells of collapsing space, the result would be flat (Euclidian) space.

    Well, it doesn’t work that way. On average, the universe is expanding. Thus, though on average space appears to be flat, space-time is most definitely not flat.

    As I’m proposing it, it’s not simply that gravity bends space one way, but that radiation bends it the other way.

    Nope. First of all, gravity doesn’t bend space: gravity is the bending of space. It is energy and pressure caused by various forms of matter that bend space-time.

    And, during the current epoch, the bending of space-time by radiation is completely negligible: the density is just far too low to have any significant effect.

    Gravity doesn’t scatter light, mostly it bends its path around the source of gravity. So if radiation, which emanates from gravitational objects in the first place, has the opposite effect, so that it expands space, rather then collapsing it, it wouldn’t scatter light either, nor would it even bend it around, because there isn’t the gravitational point of attraction. It would simply cause space to effectively expand, thus redshifting light crossing it, as a local, but extremely minute effect that would only be apparent at great distances. In this way, gravity and radiation would be opposite sides of a cycle of expanding energy and collapsing mass.

    Not in the least. The effect of normal matter and radiation is far from symmetric. Radiation has vastly lower energy density, for one, which means it doesn’t have anywhere close to the same effect on gravity. Furthermore, even if they did have the same energy density, their effects still wouldn’t be symmetric, because the behavior of radiation is categorically different (radiation has pressure, while normal matter, on large scales, does not).

  • Lawrence Crowell

    The bending (curving is a preferrable term) of spacetime by gravity does exist. The Lagrangian for a Yang-Mills field theory is L = (-1/4)F^{ab}F_{ab} for F^{ab} a covariant tensor with field components. The momentum-energy tensor is

    T^{ab} = &L/g_{ab} – g^{ab}L,

    and it is not hard to get the momentum-energy tensor which feeds into the Einstein field equation

    R^{ab} – 1/2Rg^{ab} = -8piG/c^4 T^{ab}.

    Yet if you know or look it up the gravitational constant G is small, and c is fairly large and you are dividing by c^4 in the coupling constant 8piG/c^4. So it takes HUGE electromagnetic field densities (or some other Yang-Mills gauge field such as QCD) to induce spacetime curvatures.

    A star might pump out what appears to be lots of photon energy, but this is nowhere near what is needed to induce spacetime curvatures. In fact such spacetime curvatures induced by EM radiation or other gauge fields likely only plays a major astrophysical role in the very early universe, or maybe in high energy interactions between elementary particles in tiny regions, such as an exceedingly high energy (near GKZ limit) cosmic rays impacting an oxygen atom in the upper atmosphere, or maybe with the gold heavy ion collisions performed at RHIC — at least maybe there are some signatures of spacetime physics (black hole-like structures) in the context of string theory or other quantum gravity theories.

    Lawrence B. Crowell

  • Jason Dick

    High energy cosmic rays are themselves so small in number, though, that they don’t gravitate appreciably.

  • John Merryman

    Jason,

    Well, it doesn’t work that way. On average, the universe is expanding. Thus, though on average space appears to be flat, space-time is most definitely not flat.

    Remember I’m not even on board when it comes to describing time as basis for motion, as opposed to consequence of it. If every clock is its own dimension of time and the only temporal absolute is the absence of all motion, then the question is whether the positive of expanding energy is balanced by the negative of contracting mass. Where does the energy for radiation come from, if not from the mass accreted to gravitational bodies in the first place? Does all energy above the level of the CMBR eventually coalesce back into mass? I realize that from your perspective, I’m just stupid and misguided, but for me, it is a basic pattern that does at least as effective a job of organizing the facts(redshift of galaxies, gravitational attraction) as the device of trying to describe how the universe originated from a point. An idea originally proposed by a theologian intent on justifying Genesis.

    Nope. First of all, gravity doesn’t bend space: gravity is the bending of space. It is energy and pressure caused by various forms of matter that bend space-time.

    Radiation is also energy and pressure.

    And, during the current epoch, the bending of space-time by radiation is completely negligible: the density is just far too low to have any significant effect.

    So it would only be over intergalactic distances that the effect might even be noticeable. Especially since there is even less gravitational counteraction.

    Not in the least. The effect of normal matter and radiation is far from symmetric. Radiation has vastly lower energy density, for one, which means it doesn’t have anywhere close to the same effect on gravity.

    Wouldn’t the fact that gravitational bodies occupy a vastly smaller area then irradiated space be a countervailing factor?

    Furthermore, even if they did have the same energy density, their effects still wouldn’t be symmetric, because the behavior of radiation is categorically different (radiation has pressure, while normal matter, on large scales, does not).

    So if this pressure is causing space to expand, but the entire volume of the universe doesn’t, possibly because it is infinite to begin with, then this pressure would exert itself on already collapsing gravitational fields, causing a greater inward force then can be explained only by gravity, thus removing the need for dark matter, as well as explaining the Pioneer effect.

    Lawrence,

    A star might pump out what appears to be lots of photon energy, but this is nowhere near what is needed to induce spacetime curvatures.

    The gravitational field for a star only extends out a few lightyears, yet the photons radiated travel for ten+ billion lightyears. When you consider the differences in not only distance but volume covered, plus the fact that every point in space is washed by light from nearly every star within that 10 billion lightyear radius, while the gravitational effect of any star is essentially local to its own area, that gravity would be a much, much stronger factor in its given field, is understandable. It would seem that radiation, as expanding factor, predominates in volume, while gravity, as contracting factor, prevails in density. They play to their strengths.

  • Jason Dick

    Remember I’m not even on board when it comes to describing time as basis for motion, as opposed to consequence of it.

    I know. And you’re wrong. The description of space and time as space-time indicates a particular symmetry: that transformations between reference frames of different velocities can be mathematically described as a sort of rotation. This is an accurate description whether you like it or not.

    then the question is whether the positive of expanding energy is balanced by the negative of contracting mass.

    That’s not really a question. It’s just energy conservation. This in no way means that matter and radiation have symmetric behavior under gravity: they don’t.

    Does all energy above the level of the CMBR eventually coalesce back into mass?

    What do you mean “above the level of the CMBR?” But I am aware of no mechanism that could cause the radiation that exists in the current universe to be turned into massive particles (the energy is too low).

    but for me, it is a basic pattern that does at least as effective a job of organizing the facts(redshift of galaxies, gravitational attraction) as the device of trying to describe how the universe originated from a point.

    It didn’t originate from a point. Singularities of that sort almost certainly cannot exist, as they are mathematical nonsense.

    Radiation is also energy and pressure.

    No, radiation has energy and pressure. Big difference.

    So it would only be over intergalactic distances that the effect might even be noticeable. Especially since there is even less gravitational counteraction.

    No. Other effects completely dominate the curvature due to radiation, specifically the gravitation due to normal matter, dark matter, and whatever dark energy is.

    Wouldn’t the fact that gravitational bodies occupy a vastly smaller area then irradiated space be a countervailing factor?

    The average density of the normal matter and dark matter is still vastly larger today than the average density of radiation, so it’s not enough.

    So if this pressure is causing space to expand, but the entire volume of the universe doesn’t, possibly because it is infinite to begin with, then this pressure would exert itself on already collapsing gravitational fields, causing a greater inward force then can be explained only by gravity, thus removing the need for dark matter, as well as explaining the Pioneer effect.

    No, it wouldn’t. First of all, you have to do a hell of a lot better than just wave your hands and say, “this is the effect.” Secondly, the pressure doesn’t “cause space to expand.” It actually slows the expansion down (during the radiation dominated era, the expansion rate slowed more rapidly than during the matter-dominated era, and this was due to the pressure that radiation has that normal and dark matter lack).

    The only significant effect that radiation has on the collapse of gravitating bodies is to act as sort of an accountant: it carries off the energy that is lost when gravitating bodies interact and move to lower orbits. The effect of radiation pressure is well understood, and does not grow in strength with distance compared to gravity.

    The gravitational field for a star only extends out a few lightyears,

    The gravitational field of any body extends to infinity. It has the exact same falloff as the radiation emitted.

  • John Merryman

    Jason,

    I know. And you’re wrong. The description of space and time as space-time indicates a particular symmetry: that transformations between reference frames of different velocities can be mathematically described as a sort of rotation. This is an accurate description whether you like it or not.

    That it can be mathematically modeled to a high degree of accuracy doesn’t mean that model is reality. History is a model of time as a particular dimension and it is very effective, but the fact is that the material energy doesn’t manifest all of time for all time. It is a process of flux that creates time, not one based on it. Time is a measure, like temperature. Temperature can also be measured to a high degree and it can affect our ability to measure other dimensions in very precise ways, but no one claims temperature is the basis of motion, rather then a measure of it.(Not to start the argument over again, just giving Lawrence a heads up on this particular point of discussion.)

    That’s not really a question. It’s just energy conservation. This in no way means that matter and radiation have symmetric behavior under gravity: they don’t.

    Obviously. Radiation expands. It’s matter that contracts.

    What do you mean “above the level of the CMBR?” But I am aware of no mechanism that could cause the radiation that exists in the current universe to be turned into massive particles (the energy is too low).

    It’s a long way from radiation to massive particles and we don’t really know what does occupy that space. If anything, photons would be the initial condension out of a energy field. How about quantum fluctuations out of a quantum field? Be interesting to see what the LHC comes up with.

    It didn’t originate from a point. Singularities of that sort almost certainly cannot exist, as they are mathematical nonsense.

    Agreed there.

    No, radiation has energy and pressure. Big difference.

    Hmm.. I don’t suppose radiation without energy and pressure would make any sense?

    No. Other effects completely dominate the curvature due to radiation, specifically the gravitation due to normal matter, dark matter, and whatever dark energy is.

    And dark energy is? It doesn’t take much dark energy to add up to 70% of everything, given the spaces involved. Okay, let’s say it isn’t regular radiation. Let’s say that it’s a positive vacuum fluctuation. It would still be falling into gravity wells, as well as increasing pressure on them. Expanding space between galaxies that is then falling into them.

    The average density of the normal matter and dark matter is still vastly larger today than the average density of radiation, so it’s not enough.

    A big chunk of that is the dark energy and if some part of the spin rate of galaxies attributed to this gravitational attraction were due to external pressure, the balance would be more equal.

    No, it wouldn’t. First of all, you have to do a hell of a lot better than just wave your hands and say, “this is the effect.” Secondly, the pressure doesn’t “cause space to expand.” It actually slows the expansion down (during the radiation dominated era, the expansion rate slowed more rapidly than during the matter-dominated era, and this was due to the pressure that radiation has that normal and dark matter lack).

    Is that pressure, or friction? My impression is that this earlier era would presumably be more dense, whereas matter has condensed out of this radiation. You are saying that matter can no longer condense out of radiation? Is that faith or knowledge?

    The only significant effect that radiation has on the collapse of gravitating bodies is to act as sort of an accountant: it carries off the energy that is lost when gravitating bodies interact and move to lower orbits.

    Yep. Expands as gravity contracts.

    The effect of radiation pressure is well understood, and does not grow in strength with distance compared to gravity.

    No, that’s why it’s pervasive, while gravity is focal. Even expansion.

    The gravitational field of any body extends to infinity. It has the exact same falloff as the radiation emitted.

    Since gravity mostly affects mass, it’s a matter of proximity, size and density that determines real effects. So the effect is overwhelmed as soon as another field is stronger. While radiation really does travel pretty damn far.

  • http://blogs.discovermagazine.com/cosmicvariance/mark/ Mark

    Jason – you’re a hero. John Merryman – have you ever spent time learning General Relativity? Your every comment screams that you have not, but I thought I’d ask. If not, then you need to take an introductory course (or carefully read through an introductory book) if your preparation is sufficient. You cannot just try to make these “arguments” without understanding why people have come to this understanding of nature.

    Your comments about gravity “mostly affecting mass” and many others indicate you have an elementary misunderstanding of GR.

    Jason is being too patient. I do not wish to insult you, but you need an introductory graduate student understanding of GR to buy into a discussion like this and it truly does not seem like you have one.

  • Jason Dick

    Thanks, Mark.

    John,

    Obviously. Radiation expands. It’s matter that contracts.

    You keep saying this, but it really isn’t an accurate description of what is going on. Rather, as matter collapses, radiation escapes. It’s a rather different idea.

    To (maybe) better understand this, consider what would happen if we had an interacting, self-gravitating cloud of gas and dust that did not emit any photons (i.e. no Bremsstrahlung radiation, nothing but elastic collisions). What would happen is that as the particles in the cloud interact, and transfer momentum between one another, some of the particles will achieve a momentum that gives that particle escape velocity: the particle will escape the potential well. Depending upon a particle’s mass, it will need some specific amount of momentum to reach this escape velocity, so lighter particles will escape more easily. Due to energy conservation, every time such a particle escapes, the average action of the cloud will be to collapse inward on itself ever so slightly.

    The only difference with photons is that they always have enough momentum to reach escape velocity, because they always travel at the speed of light (no black holes in this thought experiment…they’re negligible in this sort of situation anyway).

    This is the physical picture of what’s going on. And it’s just not accurately described by your exceedingly simplistic “matter contracts while radiation expands.”

    Since gravity mostly affects mass, it’s a matter of proximity, size and density that determines real effects. So the effect is overwhelmed as soon as another field is stronger. While radiation really does travel pretty damn far.

    The same is the case with radiation. Both follow 1/r^2 laws. This is just down to the fact that we live in 3+1 dimensional space-time. Unless there’s something weird going on with gravity at large distances that we don’t yet know about, gravity falls off at exactly the same rate as radiation, all the way out to infinity.

    Is that pressure, or friction? My impression is that this earlier era would presumably be more dense, whereas matter has condensed out of this radiation. You are saying that matter can no longer condense out of radiation? Is that faith or knowledge?

    It’s an energy question. When the average energy of the particles in your system are greater than the rest mass of the lightest particles, then matter/anti-matter pairs of those particles will make up part of the “radiation” energy density. For example, when the energy of individual photons is above the rest mass of the electron (~0.5MeV), you could have two photons collide and produce an electron/positron pair. Once the temperature drops below a certain point, however, the number of collisions producing new electron/positron pairs is outnumbered by the number of annihilations of electron/positron pairs, and in a relatively short time all of the electron/positron pairs disappear, leaving behind only the few that don’t have a pair (it’s another interesting question as to why the early universe had a slight overabundance of normal matter).

    So, sure, it can happen today whenever you have a situation where you have a plasma that is hot enough to produce, at the very least, electron/positron pairs (the matter/anti-matter pair that requires the lowest temperature to be produced in large numbers). And so you might well get this sort of thing happening in, say, neutron star collisions or in supernovae. But most of the time the temperatures are just far too low for electron/positron pairs to be produced, so there is no possibility of cooling so that normal electrons can condense out of the mass (note: the production of the imbalance in matter and antimatter can only happen at still higher temperatures, higher than we’ve yet pushed in our most powerful particle accelerators, so any electrons that condense out of such a state today would have existed before that region got hot enough for them to condense in the first place).

  • John Merryman

    Mark,

    I’m reasonably aware of my own ignorance and I commend Jason for his patience. My simple minded point is that much of the processes in the world I live in can be understood in terms of a convection cycle of expanding heat and condensing particles/order. Not just the climate and the geology, but many aspects of psychology, physiology, politics, economics, sociology, etc. So given the extent to which physics is dominated by energies that expand and ordered systems that contract, I think it reasonable to assume there is some grand cycle that we can only perceive bits and pieces of.

    Jason,

    Got to work, return to argue this evening…

  • Jason Dick

    My simple minded point is that much of the processes in the world I live in can be understood in terms of a convection cycle of expanding heat and condensing particles/order. Not just the climate and the geology, but many aspects of psychology, physiology, politics, economics, sociology, etc. So given the extent to which physics is dominated by energies that expand and ordered systems that contract, I think it reasonable to assume there is some grand cycle that we can only perceive bits and pieces of.

    Uh, what you appear to be describing sounds rather like thermodynamics, which is quite well-understood in these situations. But it’s not a “cycle” by any reasonable meaning of the word.

  • Lawrence Crowell

    My mention of cosmic rays was to indicate that maybe these generate “blobs” that have some small amplitude for a black hole. This idea is not original completely to me, but is a part of some physics out there by Nimi and Randall. This would be a quantum system with some black hole amplitude on the scale of a nucleon. So obviously this is nothing large or that has a gravity field of any extent. But if you shove enough mass-energy into a small enough of a region, such as with a high energy scattering, you might get some probability for a black hole. In this case there is a possiblity for a tiny quantum black hole amplitude to exist in small region for some very brief period of time. The RHIC experiements might in fact be detecting these.

    Of course some think that these black holes will gobble up the Earth, but of course we are talking about a small amplitude for a quantum black hole that decays very quickly. So such a scenario is not possible. It is similar to concerns early on that a nuclear chain reaction might cause the Earth to become engulfed in a nuclear cauldron and burn like a star.

    Electromagnetic radiation and gravity force fall off as 1/r^2 for a similar reason. In the case of EM radiation if we have some number, call it N, of photons that are emitted at one time from a point then N is conserved. Now think of an imaginary sphere (Gaussian surface) enclosing this point at a distance r. This sphere has an area 4pi r^2. No matter how one changes the radius there will always be N photons which cross this sphere. So for p = energy per unit area we then have that the total energy E = N*e, e = energy of each photon, is equal to p times the area it crosses:

    E = int dA p = 4pi r^2 p.

    Now we agree that N is conserved as well as e, and of course we are assuming that the photons all have the same energy. It is then apparent that for E to be a constant that p = k/r^2, for k = a constant.

    In the case of gravity it is similar in that if the force is determined by lines of force which are preserved in much the same way the number of photons are above then the force of gravity must also vary as ~ 1/r^2. Newton actually equated the centripetal force F = mr(omega^2) to some force F = kr^n and arrived at n = -2 as the case which obeyed Kepler’s second law.

    The reason for the 1/r^2 fall off for radiation and gravity as analogous, but are not physically identical. The electric field falls off as 1/r^2, which is a reason for the fall off with radiation, and is associated ultimately with the masslessness of the photon. This gets into some other details, and H. Yukawa propsed a force that varied as

    F = -k e^{-ar}/r^2,

    for k and a constants. This was a potential for the nuclear interaction mediated by a massive particle, the meson.

    I always find it amusing to see people take flash pictures at night of distant objects. The 1/r^2 makes pretty short work of that.

    I do advise that people study the physics they don’t understand, and in the case of JM it is a bit clear that he not only does not understand relativity, but a lot of basic physics as well. Even just basic Halliday & Resnik level physics can tell you a whole lot about how the world works and clear up some of the confusion that is apparent.

    Lawrence B. Crowell

  • John Merryman

    Jason,

    It can be countervailing forces, but convection is a thermodynamic cycle, as specific material absorbs heat, whether from radiation, pressure, etc. causing it to expand and as Lawrence points out, spead this energy over an expanded area, causing it to cool and contract.Call it whatever you want. Agood example is the current political revolution bubbling to the surface, as the structure of the old guard looses is sources of energy that are expanding out the cracks in the system.

    Lawrence,

    When we are young, we can choose what we want to study. When we get old, the lessons are what get shoved in our face. You might say I’ve had enough personal experience to know how and why structures crumble and what amount of energy it takes to keep them moving in a forward direction. Maybe it didn’t come from text books, but the fact is that reality is the territory and the math is just one more map. I’ve seen enough come and go to know only children think it’s all a straight line from start to finish. Wisdom is having been around enough to know those cycles are not just issues to overcome, they are the reality.

    Not meaning to get snippy, but it has been a long day. Thank you both for your efforts and attempts to lift my brain up a few steps.

  • Jason Dick

    John,

    Thermodynamics is not a cycle. Overall, it describes a one-way, irreversible process: the increase of entropy. Of course, there are cycles that exist in nature, but they’re never completely adiabatic: there is always some increase in entropy.

  • John Merryman

    Jason,

    Entropy applies to a closed system and closed systems loose energy, but where does the energy go? While I realize cosmology describes the entire universe as one singular unit, going from start to finish and even if I agree with that description, it still begs the question of where the energy of the universe came from, prior to the singularity and where does it go, after the fadeout.

    Gravity sucks. Eventually something gets spit back out. Even if it’s another closed set, going from beginning to end, physics just hasn’t tied up all the loose end to say there isn’t some attractive element that pulled it all together to begin with.

    Unless you propose some supernatural, one off event, nature requires explanations, as well as descriptions.

  • Jason Dick

    Entropy applies to a closed system and closed systems loose energy, but where does the energy go?

    By definition, closed systems do not lose energy. Increase in entropy isn’t about loss of energy. It’s about systems tending towards more probable states.

    And yes, you can still talk about the entropy of open systems. That’s not a problem in the least. It’s just that the “entropy always increases” 2nd law of thermodynamics doesn’t always apply (granted, it doesn’t always apply in closed systems either, as it’s only a probabilistic law, as we now know from its derivation from statistical mechanics).

    The 2nd law does, however, appear to apply to an expanding universe, as there is no ordered inflow our outflow of energy that is required for entropy to decrease in an open system.

    While I realize cosmology describes the entire universe as one singular unit, going from start to finish and even if I agree with that description, it still begs the question of where the energy of the universe came from, prior to the singularity and where does it go, after the fadeout.

    No, cosmology approximates our region of the universe by assuming that it extends infinitely in all directions. There’s no reason to believe this is actually the case, but there are good reasons to believe that it doesn’t matter for any inferences we make from the theory. We typically don’t try to describe all of existence as one unit, and often don’t even try to describe all of existence in the first place, just the region of the universe that we can observe, either directly or indirectly.

    As for where the energy came from, that’s not really an interesting question: energy in matter fields isn’t conserved in an expanding universe anyway. Educate yourself a bit here:
    http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

    What’s interesting, rather, is where the very low entropy state from which our region of the universe evolved came from. I can’t believe you’ve been on Sean’s blog this long and are still ignorant of what he’s said on this topic.

    Gravity sucks. Eventually something gets spit back out. Even if it’s another closed set, going from beginning to end, physics just hasn’t tied up all the loose end to say there isn’t some attractive element that pulled it all together to begin with.

    What are you babbling about?

    Unless you propose some supernatural, one off event, nature requires explanations, as well as descriptions.

    Duh. But it’s also important that those explanations/descriptions be correct, and yours clearly are not.

  • Lawrence Crowell

    A few comments:

    Some mention was made of the Pioneer anamoly. This is not likely anything due to gravitation of some unknown physics. At least it can’t be due to the cosmological constant, for that is too small. Further given there are three other such spacecraft crawling away from the solar system one might expect a similar effect with them as well. One might suggest that a clump of dark matter is gravitationally tugging at the Pioneer. Maybe, but this would suggest there is a fair amount of it out there and this would perturb the Oort cloud of small planetoids (Pluto has been demoted from being a planet) and would likely have made this unstable. Yet clearly the Oort cloud is as old as the 5 billion years of the solar system. So there is not likely much dark matter haunting the outer reaches of the solar system. Then again, though unlikely, we just got very lucky and sent the craft near a clump that just happened by.

    The most likely explanation is that there is some sort of outgassing from the craft. A leaky tank or something of that sort might be shooting of a bit of reaction mass with some velocity that is nudging it off the expected course.

    Thermodynamics plays a role in astrophysics, such as the area of a black hole is proportional to its entropy, or the collapse of matter in a gravitationally imploding star is thermodynamically similar to the compression of a gas with a “gas law” or some equation of state. Yet most of what we have been talking about here does not involve a temperature (thermodynamics = heat-motion) and so appealing to thermodynamics here is not on the mark.

    Lawrence B. Crowell

  • John Merryman

    Jason,

    By definition, closed systems do not lose energy. Increase in entropy isn’t about loss of energy. It’s about systems tending towards more probable states.

    Possibly then that falls under the category of Sephen Jay Gould’s ‘Punctuated Equilibrium,’ a rewording of the old catastrophism. Which is that systems don’t so much evolve, as they settle into an equilibrium, until such time as something disrupts or destroys that stable state, at which time different forms develop to take advantage of the changed circumstances and eventually settle into a new equilibrium, until the process repeats itself. Evolution vs. revolution.

    The 2nd law does, however, appear to apply to an expanding universe, as there is no ordered inflow our outflow of energy that is required for entropy to decrease in an open system.

    No, cosmology approximates our region of the universe by assuming that it extends infinitely in all directions.

    So we know the age of the universe is finite, because redshift assures us it is expanding, but other then that other factors say that space is flat as far as we can tell? What about redshift? Isn’t that evidence of curvature? Why would we need models that assume a flat space, if redshift is incontrovertible proof? It alway seemed to me that Inflation theory was an attempt to shoehorn a spatially infinite universe into a finite cosmological model. If space is expanding, but the universe isn’t,our location may be radiating infinitely in all directions, but it is also absorbing energy from the same infinite sources.

    I realize you don’t accept my ideas, but from my perspective, I have followed the evolution of Big Bang theory for several decades now and just don’t buy into it anymore, so from my perspective it’s like trying to explain epi-cycles to me and insisting I’m just too stupid to understand all the complexities involved. Honestly, I would make more effort if I felt it was on the right track, but I see it that science settled on a model several decades ago and has put every effort possible into fitting all information into that model. Thus we have a finite universe that is curved according to redshift, but flat according to measurements of CMBR. One that is expanding space, but stable speed of light. As well as having begun as an expansion of space that was faster then the speed of light, but not really, because it carried light along with it. Although it appears bigger because it takes light more time to cross this expanded space, that was supposedly carrying the light along with it. Did I also mention that the energy content of the universe is 96% invisible, because observations and theory don’t quite match, so since theory must be right, there is just lots of stuff we don’t see. I’m truly sorry that not only does the emperor appear naked to me, but fat, old and ugly as well.
    To the people whom I live around, I tend to be a mediator. Of course that does require me to figure out who is full of it and who is being rational.

    What are you babbling about?

    Old sixties joke/bumpersticker; “There is no gravity. The earth sucks.”

    Duh. But it’s also important that those explanations/descriptions be correct, and yours clearly are not.

    Yours are? Isn’t that faith? The question isn’t, “What is correct?” The question is, “What is logical?”

  • Lawrence Crowell

    I generally concur with Jason’s statements here. The first law of thermodynamics is a statement about the conservation of energy. The total energy E is equal to the energy taken out in “work” W plus energy acuumulated in entropy time temperature

    dE = -dW + TdS

    and for certain systems one integrates the change of these quantities. One result for a closed system, which involves the exact differential employed is that the entropy increases in time dS/dt >= 0. When dS/dt = 0 the system has reached equilibrium.

    In a statistical mechanical setting a system is partitioned into sets of macrostates, where a reshuffling of the microstates that compose it do not change it. If you define a system as existing in a macrostate, or equivalently a phase space volume V in a total volume V’ > = V, the entropy of the system is defined as

    S = -k*log(V/V’ ) > 0 since V/V’ = infinity.

    Lawrence B. Crowell

  • Lawrence Crowell

    [this cut off again, so here is the rest (I hope)]

    where k is the Boltzmann constant. There are a couple of things which are apparent. How one defines this volume is subjective, and there is no clear procedure for doing this. However, the logarithm comes into save our tails, for any “slop” in defining V results in a small entropy change. How this is constructed is given by the H-theorem and has some connections with Bayesian statistics. If entropy increases it is clear that V increases in size. The system evolves through larger macrostates or phase space volumes. This means that the state of the system approaches the most probable, which occurs when the system reaches equilibrium.

    The entropy of the universe is a complicated subject. If we consider it to be a quantum wave function(al) then on a fine grained scale there is no entropy. Similarly a macroscopic system is considered to be built from molecules that obey dynamical principles, but since there are so many of them we parition the system into course grained states. In the same way the universe, which is a closed system will on a coarse grained descriptive level evolve to ever greater entropy. There is a further complicating matter that spacetime has a negative effective heat capacity. In a model universe with a black hole who’s horizon temperature equals the background (eg CMB) temperature, if that black hole absorbs a photon or emits one by quantum radiance its thermodynamic state is removed from equal temperature with the background. So there is no stable equilibrium state for the universe, at least not locally or probably not in a finite time. The entire path integral of the universe may end up as a flat Minkowski space, similar to how the anti-deSitter spacetime has Minkowski spacetime at conformal infinity. This will then be the final state of the universe, as it appears recollapse does not happen, which occurs as time —> infinity.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    You’re like an atomic clock to my sundial.

  • Lawrence Crowell

    I will try to make some sort of statement here about attempting to theorize about physics or cosmology.

    It is common for people to say that modern physics is an “epicycle on epicycle” endevour and that maybe somebody from the outside can come in and throw the whole thing in a cocked hat. The often made statement about “scientific authority” and so forth is made to draw analogues with the pre-Copernicus state of affairs, or with what Galileo faced. Biblical creationists make similar gripes against the predominance of evolutionary theory in biology.

    The conditions then in no way match conditions today. We live in a very different world from that of the late middle ages or the renaissance. The Church codified Aristotle’s physics and Ptolemy’s astronomy, or what might be called proto-physics, into their theology. It was in some sense a model building process. Yet the purpose of this was very different. The Aristotlean-Ptolemaic physical and astronomical systems were incorporated into theological canon in order to bolster a faith system. This faith system was beyond question, and is still so in some circles, and the extensions of this were also put beyond question. The whole system was founded on philosophical methods without empirical input, and was ultimately completely wrong. In effect science was starting from the ground floor.

    This is very different from the revolution in physics at the turn of the 20th century. Classical mechanics was not found to be completely wrong, but more incomplete or inadequate outside some domain of observation or experimentation. In the education of a physicist Newtonian mechanics and its extension with Lagrangian and Hamiltonian mechanics are ground work. At the same time physics degrees do not involve first a study of Aristotle or Ptolemy. This is carried on today. In order to understand contemporary physics and cosmology some familiarity with established physics is needed. In order to do research and publish papers a strong grounding in these is necessary. The conditions are very different from 400 years ago.

    This is not to say there are not entrenched schools of thought, particularly in frontier research areas. You have communities of people determined to pursue a line of thought and investigation, and to out argue competing schools of thought. The string theory vs loop quantum gravity debate suggest this sort of thing. People are people after all. Yet as the process continues eventually a single “picture” emerges as the new theory, particularly if it is upheld by observational or experimental results. As time goes on that theory becomes a canon of sorts in the field of physics.

    So as things stand nobody who is completely outside of physics, who has never darkened the door of a physics classroom, or has never solved a Lagrangian problem or a wave equation or … , is going to suddenly jump on the scene with the brilliant answers to contemporary problems in physics.

    Lawrence B. Crowell

  • John Merryman

    Of course, I think every clock is it’s own dimension of time, that being why time is relative and not absolute.

  • Jason Dick

    Possibly then that falls under the category of Sephen Jay Gould’s ‘Punctuated Equilibrium,’ a rewording of the old catastrophism. Which is that systems don’t so much evolve, as they settle into an equilibrium, until such time as something disrupts or destroys that stable state, at which time different forms develop to take advantage of the changed circumstances and eventually settle into a new equilibrium, until the process repeats itself. Evolution vs. revolution.

    Uh, no. First of all, “Punctuated Equilibrium” is very poor terminology. Equilibrium, by definition, is the final state to which a system eventually evolves. Without changing the system, it will never get out of it.

    This is not the case at all with the ecological systems which Stephen Jay Gould was describing, which can undergo massive changes without any external change to the system. These systems aren’t in equilibrium at all between these revolutions: they are in metastable states. If they were in equilibrium, then even after an external forcing of the system (e.g. a meteor impact), they’d go right back to the previous state in some finite time: you’d have to make a permanent change to the system for the state which the system approaches to be changed, such as by adding a new constant energy source or some such.

    Biological systems are, in fact, massively out of equilibrium. But, regardless, this is rather off topic. I’m wasn’t discussing anything at all like that. What I was talking about is that systems tend towards higher-entropy states, and there’s no going back. If you lower the entropy of one isolated system (e.g. by heating or cooling your home), you have to raise the entropy somewhere else even more than you lower the entropy of your system. So, overall, the entropy increases. Eventually, our universe will (as near as we can tell) approach a state where there is nothing but empty space (and vacuum fluctuations): there won’t be any more entropy increase that living organisms like ourselves can exploit. Every fusion reaction in a star, every fission reaction here on Earth, every new star that is born, every old star that dies, every galaxy that forms, every two galaxies that merge, all of these bring us one step closer to this eventual fate of nothing left but empty space. Granted, it will take an astronomically long time to get there, but it is moving in that direction nonetheless:
    http://en.wikipedia.org/wiki/Heat_death

    So we know the age of the universe is finite, because redshift assures us it is expanding,

    No, we don’t know that the age of the universe is finite. We know that the age of our region of the universe is finite, but our region of the universe could easily have been born from some other region, which could have been born from some other region in perpetuity.

    I realize you don’t accept my ideas, but from my perspective, I have followed the evolution of Big Bang theory for several decades now and just don’t buy into it anymore, so from my perspective it’s like trying to explain epi-cycles to me and insisting I’m just too stupid to understand all the complexities involved.

    It seems to me, John, that you’re entire reasons for thinking that there’s something wrong with the Big Bang theory are based upon misconceptions brought about by confusing or inaccurate language used to attempt to describe the science to lay people. Really, now, you have no good reason to suspect that many thousands of highly intelligent people who have dedicated their lives to understanding this are all wrong just because we have a hard time communicating the concepts without a great deal of mathematics to describe what we’re talking about.

    Honestly, you simply do not have the tools at your disposal to properly evaluate any of the current theories on the nature of the universe. Above all, you need to learn what scientists are talking about in the first place before saying it’s all wrong, and you aren’t even close to understanding that. Every single one of the “problems” you brought up in your above post is nothing more than a misunderstanding of what the physics are actually describing. It’s not necessarily that you’re too stupid (though that certainly is a possibility), it’s that you aren’t even going by the true description of the physics, which is mathematical. Any description of a physical law or process can only be accurate if it is a mathematical description: this is the language of the universe, and if you don’t understand that language, then you simply aren’t going to be capable of understanding the physics we’re talking about.

    That said, I might as well try to clear up a few of your misconceptions.

    but other then that other factors say that space is flat as far as we can tell? What about redshift? Isn’t that evidence of curvature?

    The expansion is evidence of curvature of space-time. Space can be flat while space-time is curved. If space is flat but space-time curved, it just means that the only non-zero elements of the Ricci tensor are the time-time and time-space elements, with all the space-space elements zero.

    This basically means that when describing a spatially-flat universe we often end up using Cartesian coordinates for our spatial coordinates that are dependent upon time but independent of space (note: there are an infinite number of possible coordinate choices, time-dependent Cartesian coordinates are just one). If there is spatial curvature, our Cartesian-like coordinates also become dependent upon space as well as time.

    One way of visualizing this is that a spatially-flat universe with space-time curvature might potentially be visualized as a rubber sheet that is being stretched with time, or as a raisin cake that is rising: at any given time Cartesian coordinates are perfectly good, but those coordinates change with time. That change can be described as the curvature.

    An expanding universe with both curvature in space and in space-time might be visualized as a balloon that is being blown up: spatially, it’s the surface of a sphere, which is spatially curved, and the points are also moving away from one another, which is space-time curvature.

    One that is expanding space, but stable speed of light.

    The two have nothing to do with one another, so I’m really not sure what your issue with this is. The expansion of space doesn’t change the laws of physics as space expands, so I don’t see why it’d change something that appears to be part of the fundamental laws of physics.

    As well as having begun as an expansion of space that was faster then the speed of light, but not really, because it carried light along with it.

    Well, it’s just incorrect to say that the expansion was ever faster than the speed of light (or slower for that matter). The units of expansion are inverse time. The units of speed are distance over time. So saying that the expansion was ever greater than the speed of light would be rather like saying that two miles is greater than three kilograms: it’s a nonsensical statement. When physicists talk about a superluminal expansion, they’re not really talking about an expansion that is faster than the speed of light. They’re using incorrect, misleading language to describe a rapid acceleration of the rate of expansion. This is just one among many ways where you really need to understand the math to understand what’s going on, and it isn’t an expansion faster than light.

    Did I also mention that the energy content of the universe is 96% invisible, because observations and theory don’t quite match, so since theory must be right, there is just lots of stuff we don’t see.

    So? First of all, this is only because of the particular time that we are observing the universe. If we were observing it a few billion years ago, or a few billion years in the future, we would see quite different ratios. Secondly, there’s no reason to expect that we should be able to use electromagnetic radiation to observe most of the universe. Some particles just don’t have electric charge.

    Yours are? Isn’t that faith? The question isn’t, “What is correct?” The question is, “What is logical?”

    I didn’t say that. I don’t know what the right answers to some of these questions are. Nobody does. But just because we don’t yet know the right answers to all of these questions doesn’t mean that we can’t point out answers that are wrong. And yours are wrong. There are things that I’m pretty certain about (e.g. the existence of dark matter), due to the weight of the evidence, and many others which I have no idea about (e.g. the nature of dark energy), because the evidence just isn’t yet in. But some ideas are just nonsense, because they either are in direct contradiction to what we do know, or are in direct contradiction to themselves. Your ideas are in direct contradiction to what we do know (they aren’t well-formed enough to be self-contradicting, as near as I can tell).

  • John Merryman

    Jason,

    You are to be commended on your patience. Since part of my problem seems to be the disconnect between the math and the analogies being used, here is one I keep bringing up that might be clarified;

    One way of visualizing this is that a spatially-flat universe with space-time curvature might potentially be visualized as a rubber sheet that is being stretched with time, or as a raisin cake that is rising: at any given time Cartesian coordinates are perfectly good, but those coordinates change with time. That change can be described as the curvature.

    As I keep mentioning, my problem is relating this to the speed of light. Let’s say there are two sheets parallel to each other. One is being stretched out and the points are moving away from each other. The other remains stable. The redshifted light is the expanding sheet, while the stable sheet is the speed of light. So when the redshifted sheet is twice the original size, it takes light twice as long to cross between any two points as it did originally. Yes, the speed of light is a local effect, but it would seem that the stretching of the other sheet is a local effect as well, given that every place on it is being stretched. It would seem that if space is a fundamental dimension, logically we would use the most stable method of measuring it to determine its size, just as we use the most stable measures of atomic activity to measure time. So saying two points are twice as far apart, as measured by the speed of light, would seem to be increasing distance in stable space, not expanding space?????

    I realize I’m probably not going to understand whatever math formulae you think is necessary to properly explain this and I admit that my scepticism towards the math being the reality, as opposed to modeling the reality, is deep, so I suppose this will be a difficult issue to resolve, but the effort does stretch the mind and that is healthy for everyone.

  • Lawrence Crowell

    I will second that so called superluminal expansion, such as in inflationary cosmology, does not mean things travelling faster than light. Locally the speed of light is still c = 299,980 km/sec. This only means that there are distinct frames on different regions where the so called frame bundle differs by a large curvature on the spacetime.

    Punctuated equilibrium is a misnomer. Equilibrium in biology is equal to death. If there is no Krebs cycle, no metabolism and no more ATP to phosphorylate peptides in kinase activity etc, then that organism is simply dead — and it is in equilibrium, or is on a monotonic course to equilibrium as it decays or is consumed by other organisms. Homestasis is a more operative word in biology and it is a sort of analogue of the limit cycle or strange attractor in nonHamiltonian physics. An ecosystem can be in homeostasis, evolutionarily stable and it can be punctuated by some chaotic even — volcanos, asteroid impacts, etc.

    A part of JM’s confusion is that general relativity is built up from local “patches” that are glued together in a chart system. The whole space is built up this way, but certain things such as the speed of light are measured on a local patch which is small enough to be flat, or approximately so. There is considerable Riemannian geometry behind this, in fact it really is Riemannian geometry.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    Doesn’t the space between galaxies consist of innumerable “local patches,” that might appear on a small enough scale to be flat, yet wouldn’t these have to expand/curve to some small degree for the galaxies to be moving away from each other? Why wouldn’t this expansion also be “superluminal?”

    At what point did the superluminal expansion of inflation become the non-superluminal expansion of the current expanding universe? Is there a theory for why this expansion ceased to carry the light along with it and could be measured against a stable speed of light?

  • Lawrence Crowell

    If the patches can be made small enough the curvature becomes vanishingly small. You don’t notice any expansion or acceleration of objects away from you due to cosmological expansion right around you. It only become apparent when we look far out.

    I must confess I don’t quite understand what you are asking in the second paragraph.

    Lawrence B. Crowell

  • Jason Dick

    As I keep mentioning, my problem is relating this to the speed of light. Let’s say there are two sheets parallel to each other. One is being stretched out and the points are moving away from each other. The other remains stable. The redshifted light is the expanding sheet, while the stable sheet is the speed of light.

    This analogy just makes no sense whatsoever. The speed of light can’t be thought of as a static sheet. The units are wrong.

    So saying two points are twice as far apart, as measured by the speed of light, would seem to be increasing distance in stable space, not expanding space?????

    What do you mean by stable space vs. expanding space? If space is expanding, then it’s not stable.

  • Marty Tysanner

    Lawrence,

    Regarding the Pioneer anomaly…

    You speculated that

    The most likely explanation is that there is some sort of outgassing from the craft.

    A few years ago I attended an informal talk by John Anderson, a NASA scientist who first noticed the possible anomalous acceleration of the Pioneer spacecraft toward the sun when he analyzed their radio Doppler and ranging data. He and others have done an extensive analysis that take into account the particular characteristics of the spacecraft, along with all known plausible sources of the apparent acceleration. What they have found is that after adding up all these sources, they are insufficient to account for the anomaly.

    Wikipedia has a short article about the subject, including some references like one of Anderson’s papers (also available on the arXiv). It mentions some of the problems with trying to observe the anomaly with later spacecraft (design issues, etc.).

    What is puzzling is that both Pioneer spacecraft observed the same anomaly, and they both saw it begin at similar distances from the sun. It would be surprising to some people if by coincidence both spacecraft had malfunctions that conspired to produce the anomaly at similar radii, but such a coincidence is certainly possible. They used the same design, so an independent mission is needed to eliminate that source of systematic error.

    You may be right. We’ll have to wait to find out…

  • Jason Dick

    Given that the Voyager spacecraft have now traveled farther, we should have independent confirmation of the Pioneer anomaly, if it’s real.

  • John Merryman

    Lawrence,

    If the patches can be made small enough the curvature becomes vanishingly small. You don’t notice any expansion or acceleration of objects away from you due to cosmological expansion right around you. It only become apparent when we look far out.

    Large distances are still made up of lots of small distances, so while the effect may be too small to detect at these short distances, it still must exist in them to become apparent at large distances, re; curvature. The speed of light isn’t “curved” because it doesn’t change over time.

    I must confess I don’t quite understand what you are asking in the second paragraph.

    If Inflation is superluminal expansion, then it is presumably carrying the light along with it, so it would seem that during the inflation stage, the speed of light did increase as the universe expanded. So at some point, the speed of light stablized, while the universe continued to increase in size.

    Jason,

    This analogy just makes no sense whatsoever. The speed of light can’t be thought of as a static sheet. The units are wrong.

    If the distance between two objects is x lightyears and 10000 years from now, it is still x lightyears, that would imply a stable unit of distance. Currently metric distances are defined in terms of lightspeed, so it is certainly considered as defining a stable unit of distance.

    What do you mean by stable space vs. expanding space? If space is expanding, then it’s not stable.

    That’s the point. We consider it as expanding because we measure it in terms of lightyears and assume the distance between objects is increasing in terms of lightyears. So that as the universe expands, it takes light longer to cross the space between them. If lightspeed is stable then this expansion isn’t expanding space, rather it is increasing distance in stable space.

    Of course we have no other point in time to measure from. If we were actually able to compare measurements taken thousands of years apart, would these other sources appear further away, due to actual recession, or would they still seem to be at the same distances, but still redshifted? If the second, then redshift would be due to something other then recession, but we have no way of making these measurements.

  • Jason Dick

    John,

    If Inflation is superluminal expansion, then it is presumably carrying the light along with it, so it would seem that during the inflation stage, the speed of light did increase as the universe expanded. So at some point, the speed of light stablized, while the universe continued to increase in size.

    Superluminal expansion, as I have repeatedly explained, is a misnomer. Furthermore, velocity as a quantity only makes sense locally, and locally the speed of light never changes. Think about it for a second: does the far away expansion of space really have any effect on how we think of the behavior of light here on Earth?

    This has always been true: at any point in space and time, you could (as a thought experiment) set up a little experimental apparatus to measure the speed of light at that location. Provided the experimental apparatus was small enough compared to the local curvature that it could be approximated as flat space-time, that apparatus would always measure the same value for the speed of light, no matter where or when the apparatus was set up, whether it was during inflation, or here on Earth, or inside the event horizon of a black hole. This is the real meaning of the constant speed of light in General Relativity: it’s constant with respect to measurement by any observer measuring it at their current location in space-time.

    That’s the point. We consider it as expanding because we measure it in terms of lightyears and assume the distance between objects is increasing in terms of lightyears. So that as the universe expands, it takes light longer to cross the space between them. If lightspeed is stable then this expansion isn’t expanding space, rather it is increasing distance in stable space.

    Nope. Describe a universe where all of the objects are moving away from one another at constant speed, use the Einstein equations to solve for the curvature, and you’ll find curvature that indicates that space is expanding. The curvature of space-time and the matter content of the universe are coupled, and cannot be separated from one another.

  • Lawrence Crowell

    That the anomalous acceleration is occurring with the Pioneer craft and not the Voyagers indicates a device dependent process. This is most often a sign of an instrumentation problem. I can’t say why the Pioneers are experiencing this. Differential scattering of light from its surface, outgassing, or … ? A part of the problem is that it is an uncontrolled experiment, the craft were not designed specifically for this purpose.

    To be honest if there were some physics involved with this the same decelleration should be observed in the motion of planets. This should produce a small deviation from Kepler’s laws of planetary motion as dictated by Newtonian mechanics. A planet is big enough so that photon pressure can’t nudge the body, there is no outgassing and so forth. If this is due to a cosmological constant / ~ 10^{-56}cm^{-2} and if the acceleration is

    a = (2//3)rc^2,

    for r the relative separation between two bodies, then there should be some orbital ephermis deviation for the outerplanets.

    The term superluminal is unfortunate, and to be honest I cringe a bit when ever I hear the word. I can only say that with curved spacetime the usual notions of distance, velocity and the rest is “deformed.” The universe has some four dimensional curvature, even if the spatial surface (or coordinate choice or spatial “slice”) is flat. As a result our usual ideas about space and velocity are changed. This is why we exist in a universe that is 70 billion light years out to the deinoization limit or the CMB, but the universe is 13.7 billion years in age. Particles on different frames have been comoved with their frames to give rise to this.

    Lawrence B. Crowell

  • John Merryman

    Jason,

    The curvature of space-time and the matter content of the universe are coupled, and cannot be separated from one another.

    So we know gravity bends space, because it distorts the path of light and we know space is expanding because light from distant sources is redshifted.

    The speed of light? That’s just a local effect. If a galaxy that appears 100,000 lightyears away now should appear 200,000 lightyears away in 20,000,000 years, that’s not increasing distance, no, that’s expanding space. Oh yes, I get it now! Not.

    The speed of light is the most stable measure of space, in fact;

    Speed of light set by definition
    In 1983, the 17th Conférence Générale des Poids et Mesures adopted a standard value, 299,792,458 m/s for the speed of light. This in turn defines the length of a metre in terms of the speed of light, so that further refinements in the current experimental value of the speed of light would only refine the definition of a metre. (http://en.wikipedia.org/wiki/Speed_of_light)

    It is considered the most basic measure of distance, so if something is further way then it was, according to how long it takes light to travel from there, that is increasing distance, not expanding space.

  • Jason Dick

    It is considered the most basic measure of distance, so if something is further way then it was, according to how long it takes light to travel from there, that is increasing distance, not expanding space.

    That’s like saying, “That’s not a car, that’s a hatchback!” Why can’t it be both?

  • John Merryman

    Jason,

    Because if it is increasing distance in stable space, that would mean the space pre-exists the expansion. Sort of like the train moving away isn’t stretching the tracks, but moving along pre-existing tracks.
    This poses serious problems for Big Bang theory, in that if space isn’t curved/expanded, then we would seem to be at the center of the universe, since other galaxies are all redshifted directly away from us, proportional to distance. It also poses serious problems for Inflation theory, because if space pre-exists, it’s subject to quantum fluctuation, if not other material and energy and the superluminal expansion would result in a shockwave that would burn everything to a crisp.
    If redshift is somehow a function of light crossing distance, then that we appear at the center isn’t a problem, as every point would appear to be the center. The math is the same, it’s just that gravity wells cancel out the effect, rather then the entire universe expanding.

  • Jason Dick

    No, John, it doesn’t work that way. The geometry of space-time is intimately connected to the matter that inhabits it. The Einstein equations describe the relationship between space-time and matter, and if we have matter that is moving apart, then space is necessarily expanding.

  • John Merryman

    Jason,

    But some ideas are just nonsense, because they either are in direct contradiction to what we do know, or are in direct contradiction to themselves.

    Space, as I pointed out, is defined in terms of light speed. So if something is moving away, as measured in lightyears, that is not expanding space. That is increasing distance.
    The difference is that if the markers on your stretching sheet are stretched as well, that would be expanding space. If it takes more markers to cover the stretched area, that is increasing distance.

  • Lawrence Crowell

    Space and time (or spacetime) are the fields in gravitation, just as the electric and magnetic fields act on charged particles. There is a whole lot I could write about this, but I am not sure how far to go and I have limited time. In the ADM form of gravitation the metric of a spatial surface g_{ij} and its conjugate momentum variable pi^{ij} obey a commutator relationship similar to that of the electric and magnetic fields. The conjugate momentum is defined according to Gauss’ second fundamental form, or the extrinsic curvature of a manifold (space) embedded in a manifold of higher dimension. This is the bedrock for the loop quantum gravity theoretic approach.

    There is no preexisting space, nor is there a background space or spacetime upon which general relativistic spacetime exists. This type of construction has problems with the general covariant basis of general relativity. This bi-metric approach only works approximately if the metric with curvatures has small deviations from the background.

    I would recommend to JM that he do some reading of popularizations on this subject, and be sure you understand what the author is writing and not what you previously thought. This forum appears to be caught to a degree in the confusion you appear to have, and nobody can write the thousands of word required to enlighten you on this subject. General relativity is an old subject by this time, first written down 93 years ago. Of course the subject is rich and offers research problems, but when it comes to some of these basic questions there are really no mysteries. Some of these matters are well understood and have been for many decades.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    There is no preexisting space, nor is there a background space or spacetime upon which general relativistic spacetime exists.

    I understand this. My point is that space is defined by the speed of light, so if you say the result of expansion means it takes light longer to cross between two points of reference, then that is an increased distance, as measured by lightspeed as the standard measure of space. If this expansion resulted in an increase in the speed of light, so that it took the same amount of time to cross that space, then that would be expanding space, as measured by lightspeed.

  • Lawrence Crowell

    Well were are back to square one. The speed of light is defined locally. Look at an Eddington-Finkelstein diagram for a black hole. Outgoing light rays asymptotically peel away from near the cyclindrical horizon and the curve out. So you might be tempted to say that the speed of light is slow near a black hole. But this is just a particular coordinate representation. There are others which appear different. The same is the case for light which traverses large distances in the universe. It is tempting to say that since the manifold they are moving on is spreading apart ever faster that light must be coing faster. But this really is an abuse of language, or relativity. If you were in a laboratory falling towards a black hole you would measure the speed of light to be the same, even within the fraction of a second before crossing the event horizon. Indeed, you would measure the same light speed inside the black hole. So there is no real slowing down of light, and by the same token there is no real speeding up of light due to the eternal inflationary expansion of the universe.

    Yeah, it’s kind of strange. It is a good idea we are not discussion Bell inequalities in quantum mechanics, for there things get really strange. Physics is that way. The deeper we probe into its foundations the further it departs from our ordinary experience and intuition of things based on that.

    Lawrence B. Crowell

  • Jason Dick

    John,

    There is no ruler out in space. None. The numbers we place on space-time are entirely arbitrary, human constructions. Now, placing numbers out there is a useful tool for human understanding of what nature is doing, but when we do it we understand that we are making one of many possible choices of labels to place upon space-time, and our interpretation of what’s going on necessarily depends upon those labels in some regards.

    When we say that space is expanding, or that space is flat while space-time is curved, we are taking the most simple, straight-forward labeling of space-time that can be used for our observable universe as a whole: FLRW coordinates. In the context of FLRW coordinates, these statements make perfect sense, and are a good physical description of what is going on: as time goes on, space expands (or, in general, contracts, though not in our region).

  • Lawrence Crowell

    Right, its like doing a survey. One can platt out the land in any way possible, but how you do this does nothing to the hill, valley or dale. The land is what it is. Now given a certain lay of the land there might be more convenient ways to do the survey. In the case of cosmology the FRW coordinate system is convenient, though we have found departures and the universe appears to be asymptotically approaching a deSitter spacetime.

    Ah yes, to the chosen few, that band of brothers who know general relativity! Even if it can be an infernal pain in the ass at times.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    It is back to square one, but that just means I have to go around it again to explain why I see it as a cycle, not a line.

    I understand that spacetime is defined locally, by its contents. That’s why I originally asked you if expanding space meant the speed of light is affected. I know it can be a matter of relative effects, but the simple point here isn’t complicated. It’s like 2+2=4. If we measure space as a function of lightspeed and two points are moving apart, as measured by the time it takes light to pass inbetween them, then there is more space/distance between them, not that the space is stretched, if the space is still being measured by lightspeed. Otherwise we need to say that lightspeed is not the basis of measuring space.

    As you point out, the speed of light is apparently slowed emerging from the vicinity of a black hole, thus we say space is contracted, because the space is curved/contracted, but we don’t say the black hole is shrinking and will vanish in the near future. Why not?

    BUT we do say the opposite; That since light crossing space between these gravitational wells is redshifted, then they must actually be flying away from each other and will eventually vanish from the view of each other.

    As you say,

    There is no preexisting space, nor is there a background space or spacetime upon which general relativistic spacetime exists.

    And Jason further qualifies,

    The geometry of space-time is intimately connected to the matter that inhabits it. The Einstein equations describe the relationship between space-time and matter, and if we have matter that is moving apart, then space is necessarily expanding.

    The reason gravity wells don’t vanish is because they are constantly drawing in fresh energy and matter that defines space. (Being gravity, mostly matter.)

    Now the radiation escaping from all these wells goes back out to fill all that nearly empty space. Is it a surprise then that it appears to expand?

    So gravity doesn’t cause the space around it to vanish, because there is always more material being drawn in. Space between these galaxies is expanding, as it is continually filled with more radiation. but the distance between these galaxies doesn’t actually grow, because the material defining this space eventually falls into these wells.

    Now I know you say the physics of how energy turns into matter doesn’t fit this model, but is our knowledge of this complete, or are we drawing conclusions from what we can measure in our particular environment, when this would have to be something happening at nearly the level of absolute zero, over very large volumes of space?

    The alternative involves saying that space expands, but our most basic measure of space is stable. As well as superluminal expansion and a number of other highly speculative features.

    Jason,

    There is no ruler out in space. None. The numbers we place on space-time are entirely arbitrary, human constructions.

    Yes, but we can’t start contradicting what we said previously, or it really does get Kafkaesque. If we say that lightspeed is our fundamental ruler of space, then if we wish to say that space expands, it must be because this measure is curved/expanded, not that this measure is the stable ruler we use to show that space is expanding. That isn’t even a self-referential argument. That is a self-contradictory argument.

  • John Merryman

    Lawrence,

    Those last five paragraphs prior to the reply to Jason were not supposed to be in quotations.

  • Jason Dick

    John,

    The expansion of space has nothing whatsoever to do with the gravity wells that inhabit space.

  • John Merryman

    Jason,

    No, they are the contraction of space. Einstein was originally concerned that gravity would cause the entire universe to collapse. So he added a cosmological constant to maintain a stable universe.

    Redshift was evidence the space between these gravity wells is expanding.

    If Omega=1, or appears even close to it, then presumably gravity and expansion are in inverse proportion, or nearly so.

    Could it be that redshift is actually evidence of a cosmological constant? Measurements of the Dark Energy effect indicate the expansion is comparable to a c.c.

  • Lawrence Crowell

    Gravitating bodies in the universe tend to counter the expansion. A popular model of the FRW cosmology was a recollapse model, which is similar to ballistic flight. It appears this is ruled out, and as the universe expands in an eternal inflationary acceleration it will asymptotically approach a deSitter spacetime. There matter in the cosmology will dilute into an ever smaller density and asymptotically approach being a vacuum spacetime.

    The Omega = 1 appears to be the case. Yet this factor has three parts

    Omega = Omega_m + Omega_{dm} + Omega_{de}

    form m = matter, e = energy and d = dark. As this blog-o-page is based around the dark misleading force, we can look at dark energy in a misleading way as due to a “vacuum field” with the equation of state w = -1 so the pressure is negative. So this “flip” in how gravity operates means that this cosmological gravitational field is repulsive. Dark energy constitutes about 70% of the Omega, dark matter about 27% and ordinary matter only 3%. These are the percentages I recall at the moment without looking them up.

    This contributes to the cosmological constant, in the dark misleading form, if we consider the vacuum as a momentum-energy tensor and trace over that to obtain the cosmological constant /.

    Lawrence B. Crowell

  • Jason Dick

    If Omega=1, or appears even close to it, then presumably gravity and expansion are in inverse proportion, or nearly so.

    No. Firstly, “gravity and expansion” is a false dichotomy. Gravity drives the expansion, and, depending upon the matter content, can either slow it down or speed it up.

    Secondly, it wholly depends upon the sort matter content with Omega=1 what’s happening with the universe. Omega=1 does not remotely indicate a balance between expansion and contraction. What it does mean is that space is, on average, flat. If there is only normal/dark matter, then any such universe, were it to start in an expanding state, would end up with eternal expansion asymptotically approaching no expansion. If there was a negative cosmological constant, then the universe would recollapse in on itself. If there is a positive cosmological constant, then it expands (accelerating in the future). There is simply no balance to be had in expansion/contraction.

    And yes, it is certainly possible that the dark energy is a cosmological constant. We can’t yet say it is, because we haven’t ruled out other possibilities. But, suffice it to say, we haven’t yet found any better idea than it’s just a cosmological constant: as bad as the cosmological constant idea is theoretically, the other ideas are even more ad-hoc and contrived.

  • Jason Dick

    Lawrence,

    Minuscule quibble, but I’d like to mention that there’s also photons and neutrinos that make up the fractional energy density of the universe. Of course, their density is much smaller, and diluting more rapidly, than matter, so they don’t matter a whole lot. But I thought it might be a point of interest.

  • Lawrence Crowell

    These are factored into the Omega_m. The PMN matrix for neutrino oscillations predicted masses for neutrinos, which were found by the super Kamiokande detector in 1997 or so, with m = 10-100ev. People had thought that neutrinos would close the universe up. But the masses are too small and dark energy came on the scene, which overwhelms any gravitational influence from neutrinos. There is also the axion particle issue, putative small mass particles which “protect” QCD from CP violations. So that is an open question at this time, but they are expected to have very small masses.

    The original cosmological constant was put into the Einstein field equation

    R_{ab} + 1/2Rg_{ab} + /g_{ab} = -8piG/c^4 T_{ab}

    to counter the gravtational collapse of the universe. Without the momentum-energy tensor the / in the field equations predicts that the universe is an Einstein space where the Ricci curvature is proportional to its metric. If we just look at / this way then dark energy is a pure gravitational effect, or due to the structure of spacetime in the absence of any source. On the other hand if we say that dark energy is due to the ZPE of the vacuum (I have a lot to say about this and how much of this is frankly B.S.) then it is a source that defines a T_{ab}, which when traced over gives the /. So there is a dichotomy of sorts in how to interpret this dark energy, which is a part of the issue of how this is a misleading force.

    Lawrence B. Crowell

  • Jason Dick

    These are factored into the Omega_m. The PMN matrix for neutrino oscillations predicted masses for neutrinos, which were found by the super Kamiokande detector in 1997 or so, with m = 10-100ev.

    Actually, the detectors so far have only detected the differences in the masses between neutrino flavors, but the mass differences are in meV, not eV. We actually don’t know their absolute masses at all, though from experience we might suspect that it’s of the same order of magnitude as the mass differences.

    But I thought I’d like to point out something that you didn’t make clear:

    It only makes sense to factor in the neutrino mass density with Omega_m, and then only after the neutrinos have sufficiently cooled that they are no longer relativistic. Radiation will always have to be handled as a separate sort of matter density.

    The problem, however, is that due to the uncertainty in the absolute neutrino masses, we can’t actually say that we can adequately factor them into Omega_m. But, fortunately it’s really a non-issue as the energy density is so small that it’s pretty irrelevant anyway. I just thought it was of mild interest.

  • Lawrence Crowell

    The neutrino mass differences are

    Delta_{12} =~ 0.009

    Delta_{13} ~ Delta_{23} =~ 0.05

    For 1, 2, 3 = e, mu, tau. When I wrote that I got the tenths and hundredths mixed with 10′s and 100′s. The delta mass squared enter into the neutrino phase

    e^{-i Delta m_{ij}L/2E},

    for L the oscillation length.

    The usual neutrino has ~1-10 MeV energy, so that is a bigger factor in the end for an y contribution to Omega

    In this latter matter dominated phase the contribution of radiation is pretty small. I can’t quote right off what it contributes to Omega_m, but it is a small percentate of it and Omega_m ~ .03*Omega. That is not much to worry about.

    Lawrence B. Crowell

  • Jason Dick

    Er, Omega_m is ~0.23. Omega_r is around 10^-5 currently (this is measured from the thermal spectrum of the CMB).

  • John Merryman

    Lawrence, Jason,

    Gravitating bodies in the universe tend to counter the expansion.

    This is the basic relationship. Observations suggest expansion exceeds contraction, though. I could ask whether the incredible amounts of energy bound up in mass might be a mitigating factor, but that might be too technical a question for me to follow the math.(Given how much of it is “dark,” are we positive there are no more surprises out there that might balance the two columns?)

    Right, its like doing a survey. One can platt out the land in any way possible, but how you do this does nothing to the hill, valley or dale. The land is what it is.

    Omega=1 does not remotely indicate a balance between expansion and contraction. What it does mean is that space is, on average, flat.

    Given the analogies involved, is it any wonder I might assume “flat” means all the hills and valleys cancel out?

    This still doesn’t explain which of the two metrics of space based on different quantities of light, a stable one described by lightspeed, or an expanding one based on redshift of distant sources, is the real measure of space.

  • Lawrence Crowell

    To Jason:

    Omega_m = .23 if you include dark matter, though I though it was a bit higher than this, but I’d have to look it up. I was thinking of luminous matter or “ordinary stuff.” That is only about omega = .05. Agreed the radiation stuff is pretty small, it is way down on the list.

    As for John,

    The surveyor analogue can’t be taken quite the way you think. Maybe navigating on the Earth is a better way to think about it. You are sailing in some ocean and you have your local chart or map. Somebody else is sailing elsewhere far away, and they each have their respective maps. Yet globally we know that one captain is upside down, or nearly so, relative to the other. Yet both captains are using maps which has them standing horizontally. This is what confused people in centuries past about a spherical Earth’s surface. In effect, whether you know it or not, your insistence on using your “local map” and imposing it on another coordinate region globally removed is a GR fallacy similar to what had people confused about living on a round Earth.

    The speed of light is measured on a local frame that is small enough to be considered flat spacetime, just as some local region you see looks like a flat Earth. But globally your chart is different from that of someone elses, which in their local frame is also flat. If you come up with a curved geometric system that patches these maps together you find a more general rule for geometry. This is loosely how general relativity works.

    Lawrence B. Crowell

  • Jason Dick

    This is the basic relationship. Observations suggest expansion exceeds contraction, though. I could ask whether the incredible amounts of energy bound up in mass might be a mitigating factor, but that might be too technical a question for me to follow the math.(Given how much of it is “dark,” are we positive there are no more surprises out there that might balance the two columns?)

    No. The energy bound up in mass is what makes it gravitate in the first place. It’s the relationship between the matter and pressure that determines how it gravitates, and normal matter has zero pressure on large scales. The dark energy, whatever it is, has pressure less than -1/3 its energy density. This negative pressure property is what causes its gravitational effect to be an acceleration of the expansion rate (note: this is assuming the “dark energy” isn’t actually a misunderstanding of gravity, that GR is actually accurate on very large scales…but that’s another whole can of worms).

    Given the analogies involved, is it any wonder I might assume “flat” means all the hills and valleys cancel out?

    No. The universe could still be quite spatially curved on a whole and still have all the “hills and valleys” cancel out (by some measure). It’s more of a question of initial conditions or our region of the universe.

    And no, space isn’t “stable” as described by light. Light is redshifted in passage, and can take a very long time to reach what was originally a rather short distance. That’s not an indication of stable space at all. For example, the light that we see in the CMB was emitted about 13.7 billion years ago, a few hundred thousand years after the classical big bang singularity. The surface that emitted those photons was then only a few hundred thousand light years from our present location. The only explanation or why it’s taken so long to reach us is that as space expanded, it had more and more distance to travel.

  • Jason Dick

    Slight clarification:

    It’s not the relationship between matter and pressure, but rather between matter’s energy and matter’s pressure that determines how it gravitates. This relationship determines how it collapses, whether it collapses, and how it affects the expansion of the universe as a whole.

  • John Merryman

    Lawrence,

    Even though curvature may be imperceptible at the local level, it still must exist for it be manifest at larger scales. Truly flat space would be a plane held against the surface of the ball.

    The earth is quite literally curved because it is way over on one side of the equation, ie. it is shaped by the contraction effect of gravity. By “flat” space, I take it to mean that the sum total of all universal contraction and expansion effects cancel out. If you want to argue that actually the universe is expanding more the it is contracting and that eventually everything will disappear from sight, no problem, but that means the universe is curved out, not flat.

    I’m not arguing that the speed of light represents flat spacetime, or not. I’m simply saying that we define distances in space using lightspeed as the metric, so if two locations are further apart then they were, as measured by lightspeed, that would be increased distance, if you are still using lightspeed as the metric, not expanded space. So far as we know, the speed of light could be variable, as measured against some unknown dimension, but we don’t know that because at these distances, lightspeed seems the most stable parameter. For example, the speed of light is slowed passing through some mediums, but we don’t say the medium is expanded because it takes light longer to pass through it. We say the medium is stable and lightspeed is slowed.

    Jason,

    And no, space isn’t “stable” as described by light. Light is redshifted in passage, and can take a very long time to reach what was originally a rather short distance. That’s not an indication of stable space at all. For example, the light that we see in the CMB was emitted about 13.7 billion years ago, a few hundred thousand years after the classical big bang singularity. The surface that emitted those photons was then only a few hundred thousand light years from our present location. The only explanation or why it’s taken so long to reach us is that as space expanded, it had more and more distance to travel.

    So you are saying space, as measured by the emitting objects, is expanding faster then the speed of light? Of course, that is classic Inflation theory. Or maybe lightspeed was much slower then and it has been increasing and finally caught up with us.

    It’s the same problem I pointed out to Lawrence; Curvature may be imperceptible at the local level, but it still must exist in order to manifest at larger scales and if spacetime is curved enough at the local level to become apparent at intergalactic scales, then it should be carrying light along with it, as well as the emitting objects, such that while objects might appear to be flying apart, the measured distance doesn’t change over time. A topological analogy might be having two towns on either side of a lake and you don’t have a boat, so while they look only as far apart as the diameter of the lake, to get there means you have to walk around the lake and it takes longer, so you think they must be moving apart, but that’s not how it works.

  • Jason Dick

    So you are saying space, as measured by the emitting objects, is expanding faster then the speed of light? Of course, that is classic Inflation theory.

    No. The units are different. The expansion rate of space has units of inverse time. The speed of light has units of distance over time. It’s like saying that a car is faster than a stopwatch: the claim is nonsensical.

    Or maybe lightspeed was much slower then and it has been increasing and finally caught up with us.

    Impossible. The speed of light is intimately tied to the properties of the electromagnetic force. As a result, a changing speed of light results in a change in electromagnetic interactions, which we can be pretty confident were at least nearly identical to the way they are today all the way back to the emission of the surface of last scattering.

    Interestingly enough, some work has been done to attempt to discover if a faster speed of light in the distant past might actually be an explanation for inflation (i.e. what we view as “inflation” was actually a faster speed of light at that time, instead of an accelerated expansion). But it looks like this work just wasn’t promising, and it appears that the scientists working on it have largely abandoned it.

    It’s the same problem I pointed out to Lawrence; Curvature may be imperceptible at the local level, but it still must exist in order to manifest at larger scales and if spacetime is curved enough at the local level to become apparent at intergalactic scales, then it should be carrying light along with it, as well as the emitting objects, such that while objects might appear to be flying apart, the measured distance doesn’t change over time. A topological analogy might be having two towns on either side of a lake and you don’t have a boat, so while they look only as far apart as the diameter of the lake, to get there means you have to walk around the lake and it takes longer, so you think they must be moving apart, but that’s not how it works.

    Okay. But if the universe was static then the CMB wouldn’t exist.

  • Lawrence Crowell

    John Merryman on Jan 11th, 2008 at 12:33 pm
    Lawrence,

    Even though curvature may be imperceptible at the local level, it still must exist for it be manifest at larger scales. Truly flat space would be a plane held against the surface of the ball.

    —————–

    We might be making progress. A flat plane held against the ball, or its spherical boundary is a tangent plane. Now think of putting postage stamp sized flat planar elements at many points, or every point, on the sphere. How these little planes deviate from each other from point to point tells you how a vector field on the sphere will change. Each local plane has its (x,y) coordinate system, but they are unique to each of these little planar segments. So if you have a vector V at a point with coordinates (x,y) and another vector V’ with coordinates (x’,y’) nearby then there difference between these two vectors V’ – V is

    (V’ – V)^i = nabla_jV^i (x’^j – x^j)

    where x^1 = vector in the x direction and y^2 = y directed vector, and “i” is an index over the coordinate labels. nabla_j is a derivative the vector in the jth direction. In some books this is called a directional derivative. The stuff on the right hand side is telling us what has to change to get V to match up to V’.

    BTW, I hope you have had calculus and know what a derivative is.

    Now this idea gets generalized some, for there are rotational symmetries for these coordinate systems. In the case of an (x,y) coordinate system this is given by a matrix with cosines and sines (easily looked up) of an angle. This structure is then written according to these local transformations (unique on each “postage stamp” tangent to the sphere. This assembly of tangent planes is then given by a tangent bundle, where we think of there being a unique set of local symmetries at every point (or small coordinate chart) on the sphere.

    This gets generalized to higher dimensions with larger local groups. In the case of spacetime this is the Lorentz group (three ordinary rotations plus three hyperbolic transformations called boosts. This can also be extended to the Poincare boosts for translations included as well. The Lorentz group is the structure of special relativity, which is also applied to any small local flat frame. The hyperbolic transformations or boosts have asymptotes, which correspond to the fundamental invariant of special relativity — the speed of light. Each local flat frame has its own Lorentz group, and how these “mesh together” in a tangent bundle describes the curvature of spacetime.

    This is a 101-introduction to the topic of Riemannian geometry, but this is basically how general relativity is mathematically structured.

    The space sometimes called the Hubble frame is either a very large sphere, or it could be flat. Yet the spacetime it is embedded in is not flat, which is why it is being stretched out in this eternal inflation. It is worth pointing out that how one puts this spatial frame into the spacetime is a matter of one;s coordinate choice. It is analogous to a gauge in electromagnetism. We observe galaxies not on this frame, but from light rays on a past light cone. This is a projective space in spacetime — with lots of interesting properties. But I’d better not delve in that direction right now.

    Lawrence B. Crowell

  • John Merryman

    Jason,

    The expansion rate of space has units of inverse time.

    This means the further we look, the faster it recedes?

    The speed of light is intimately tied to the properties of the electromagnetic force. As a result, a changing speed of light results in a change in electromagnetic interactions, which we can be pretty confident were at least nearly identical to the way they are today all the way back to the emission of the surface of last scattering.

    So you agree that lightspeed provides the most stable metric of space and if a source of light were actually receding, in terms of lightyears, this would be increasing distance in stable space, not expanding space?

    Okay. But if the universe was static then the CMB wouldn’t exist.

    Static and stable are not the same. If you have an infinite universe of collapsing gravity wells, balanced by expanding radiation, then there is a definite curvature of space and the further light manages to travel, the more it is curved, so that eventually it is redshifted to the point that the source appears to be receding faster then the speed of light, which creates a horizon line of visibility, but not necessarily of radiant energy, so the spectrum of this energy begins where visible light ends, out about 13.7 billion lightyears. Since it is lower then red, it is black body.

    Lawrence,

    BTW, I hope you have had calculus and know what a derivative is.

    Are you joking? I ran off to join the circus at 16. Actually I changed my mind. Some drifter told me Florida cops were mean, so I ended up working in a polo club in Santa Barbara CA. I did eventually graduate from school, but mostly it’s just self motivated curiosity and my math abilities ran out around trig.

    My appreciation for relativity is due to it helping make sense of my world, as opposed to all the litttle postage stamp sized absolutes.

  • Lawrence Crowell

    Well don’t laugh too much at the postage stamp idea. Think of the glitterball in the karioke or dico dance floor that is made of may little flat reflecting elements. It is a sphere approximated by lots of little flat areas pasted together. In calculus there is the limit idea, and if you take the limit that each of these elements becomes very small or infinitesimal and the number of them increase to cover the sphere you recover the sphere. Each of these little flat areas are similiar to a local inertial frame in spacetime.

    Lawrence B. Crowell

  • Jason Dick

    This means the further we look, the faster it recedes?

    Effectively, yes.

    So you agree that lightspeed provides the most stable metric of space and if a source of light were actually receding, in terms of lightyears, this would be increasing distance in stable space, not expanding space?

    I’ve already explained with this is nonsense.

    Static and stable are not the same. If you have an infinite universe of collapsing gravity wells, balanced by expanding radiation, then there is a definite curvature of space and the further light manages to travel, the more it is curved, so that eventually it is redshifted to the point that the source appears to be receding faster then the speed of light, which creates a horizon line of visibility, but not necessarily of radiant energy, so the spectrum of this energy begins where visible light ends, out about 13.7 billion lightyears. Since it is lower then red, it is black body.

    Then this wouldn’t explain the temperature of the CMB, it wouldn’t explain the anisotropies we see in the CMB or how those anisotropies are correlated with the distribution of matter in the nearby universe, it wouldn’t explain why we see significant evolution of galaxies (that is, galaxies that are at a redshift of 2 are very different from galaxies at a redshift of 1), it wouldn’t explain the primordial (before stellar processing) abundances of hydrogen and helium, and finally it describes a universe where the energy in every region of space is decreasing with time, a situation that is not stable at all (redshift is a decrease in energy).

  • John Merryman

    Lawrence,

    I wasn’t making fun of it. It is similar to my observation that three dimensions are simply a coordinate system, not space itself and that any number of such frames can be used to define the same space, just like any number of planes can be used to define the surface of this planet. The point about postage stamp absolutes is because people tend to view others from their own set of references and try to fit everything into the same set of coordinates. This goes a long way towards explaining political/relgious conflict. You might say the Arabs and the Israelis used diffferent coordinates to describe the same space.

    In fact, Jason and I have been over this before. His position is that since three dimensions are the most efficient description of space, that they are the ideal form of space and presumably all the messy irregularities are just clutter. My position is the opposite, that three dimensions are just a reductionist model and that the reality is far more multifaceted, so three dimensions are just a mapping device, not the basis of the reality.

    Jason,

    Effectively, yes.

    Could that be due to space being curved, so that redshift is compounded by crossing ever more space, rather then that the universe was simply expanding faster, earlier in time?

    I’ve already explained with this is nonsense.

    Just because you keep pushing your mental reset button hasn’t given me sufficient reason to erase it off my hard drive.

    Then this wouldn’t explain the temperature of the CMB, it wouldn’t explain the anisotropies we see in the CMB or how those anisotropies are correlated with the distribution of matter in the nearby universe, it wouldn’t explain why we see significant evolution of galaxies (that is, galaxies that are at a redshift of 2 are very different from galaxies at a redshift of 1), it wouldn’t explain the primordial (before stellar processing) abundances of hydrogen and helium, and finally it describes a universe where the energy in every region of space is decreasing with time, a situation that is not stable at all (redshift is a decrease in energy).

    It would explain large scale structure as far as we can detect, since it removes any age limit on it. It would explain why redshift is isotropic in all directions without having to describe space as expanding, when electromagnetic properties would seem to maintain a fairly static dimension of space, as measured by lightspeed. It wouldn’t need Inflation Theory and all the issues involved, to explain why space appears flat. It wouldn’t need dark energy to explain why redshift appears as a curvature/cosmological constant, rather then the cooling remnant of a singularity. I certainly don’t have all the answers, but I suspect that you are young enough not to really appreciate how concepts that seem so all encompassing can suddenly pop and everyone(still alive) just walks away. It happens in politics over the course of decades. It can happen in religion over the course of centuries. It can happen alot of ways, even in science. Solid ground is always temporary, but it’s all we have to stand on.

  • Jason Dick

    It would explain large scale structure as far as we can detect, since it removes any age limit on it. It would explain why redshift is isotropic in all directions without having to describe space as expanding, when electromagnetic properties would seem to maintain a fairly static dimension of space, as measured by lightspeed. It wouldn’t need Inflation Theory and all the issues involved, to explain why space appears flat. It wouldn’t need dark energy to explain why redshift appears as a curvature/cosmological constant, rather then the cooling remnant of a singularity. I certainly don’t have all the answers, but I suspect that you are young enough not to really appreciate how concepts that seem so all encompassing can suddenly pop and everyone(still alive) just walks away. It happens in politics over the course of decades. It can happen in religion over the course of centuries. It can happen alot of ways, even in science. Solid ground is always temporary, but it’s all we have to stand on.

    Oh, I’m sorry. By “wouldn’t explain” I meant “is completely incompatible with our observations of”. Oh, and by the way, you don’t get redshift from purely spatial curvature. It doesn’t work that way.

    And, by the way, I have changed my mind a great number of times, occasionally resulting in a complete transformation of the way I view the world.

  • John Merryman

    Jason,

    I think I’ve presented my thoughts to the best of my ability and it’s certainly reasonable for you to disagree with what isn’t the standard model. You have done an admirable job of arguing for the established position and I thank you for the time. That said, I have certainly changed my view of things before, but you haven’t closed the case for the current model being on the right track, in my mind, so I suppose we will have to wait for more evidence to come in, one way or another.

  • Lawrence Crowell

    To JM I would recommend trying to read some literature out there. A part of the problem is that as you admitted your mathematics education stopped at trigonometry. I picked up a masters in math while doing my doctoral work in physics. There is a huge gap here, and without trying to sound patronizing I can only say that there simply is no way that you have a particularly sound understanding of these things. I say this based on some of the things you have been writing here.

    A cardinal rule of physics and cosmology is that things are point of view independent (POVI). In the expanding universe all observers will see the universe expanding away from them. With what you are trying so say it appears that our galaxy is on a perferred coordinate system. What we observe of the universe is a “cooling remnant” of a singularity, but it is a spacelike singularity. As we look back in time we see events further back in time. This singularity contains all the “data” for the structure of the universe. In what you are saying if there were no correlation between z and the observation back in time is that the singularity is timelike. This singularity would have no event horizon around it, or a chronology protection of an initial spacelike singularity. This would mean our universe is subject to all sorts of horrible pathologies, including closed timelike loops or past time travel. In other words you are removing the conceptual problems you have with comoving frames and expansion by introducing something into the universe that would make it logically contradictory.

    I could go on with this, in particular the Hawking-Penrose energy conditions and other matters. Yet I think that would not go far. So I can only state this as a matter “fact.” Science proceeds a bit like a medical diagnosis. You check the most likely diagnosis, if that fails certain tests you eliminate that and go onto the next most likely and so forth. The current theoretical model of the universe has been arrived at in just this way. In its general outline the expanding eternal inflationary cosmology appears to be what we exist within.

    Lawrence B. Crowell

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    I’m certainly not saying that our galaxy is a preferred coordinate system. If space is curved out, by expanding radiation, as it is curved in by collapsing mass, then every point is the center of its own coordinate system and every other source of light is going to appear to be receding, ie. redshifted directly away from it by this effect. Although other factors, such as gravity and velocity are going to distort it.

    The problem with the essentially top down, noun, form oriented view of reality is that it is a linear search for ultimate form, yet everything that can be grasped, whether it’s mass collapsing into a black hole, or energy radiating away to nothingness, is that it is a linear unit of time, going from beginning to end. Safe to say the people locked in this view will go to their death, convinced by their own end, that all of reality is on the same path, from start to finish.

    There are two sides of the coin, but when these people turn the coin over, it vanishes into motion and all they can see are many coins, all moving around, so they see it as one one vs. many, rather then form vs. function. Consider string theory; Everyone is obsessed with finding out what the strings are, yet they turn into a labyrinth of dimensions. What they ingore is the vibrations, the motion/verb. So just like the search for the Higgs particle, it will alway be this quest for the ultimate form, yet reality isn’t just turtles all the way down, it’s layers of an onion and as one is peeling away, others are growing up under it. Time is not a static dimension. It is not noun. It is verb. It is process. Matter is not traveling along it from past events to future ones, it is moving about, in motion, verb, function. This creates form, which once created, is replaced by the next and fades into the past. Form goes from future to past. That’s why we see only the end coming.
    This stagnation of form is a natural part of the process and when it gets too old to contain the energy within, it peels away, just as any concept that can no longer explain the information will be eventually replaced by the next stage/layer, as its proponents grow old and cannot answer the questions that keep coming up.
    You are born into one world and spend your life watching it die off and another grow up in its place.

  • Jason Dick

    Consider string theory; Everyone is obsessed with finding out what the strings are, yet they turn into a labyrinth of dimensions. What they ingore is the vibrations, the motion/verb.

    Uh, the vibrations on the strings in string theory are a fundamental aspect of the theory. You’ve heard of the different types of string theory, I presume? See the Wikipedia article on string theory for a cursory description if you haven’t:
    http://en.wikipedia.org/wiki/String_theory#Dualities

    The differences between these different types of string theory are the types of vibrations that exist.

    And, by the way, if you don’t think there’s any expansion, how, pray tell, do you explain the finite age of our region of the universe?

  • John Merryman

    Jason,

    I’m certainly not accusing physics of not recognizing motion, just of trying to explain it away. Such as describing time as a dimension, where all events exist equally and the present is as subjective as a point in space.

    The relationship between strings and vibrations does provide another example of my observation that there are two directions of time, in that while these strings go from past vibrations to future ones, the vibrations go from being in the future to being in the past.

  • John Merryman

    Also; I didn’t say there is no expansion. I said it’s balanced by contraction, so light, that is not otherwise interrupted, travels about 13.7 billion lightyears before it’s so redshifted that the source appears to be receding at the speed of light. Since visible light can’t travel any further, it creates a horizon line. That’s why, in all directions we look, it appears that everything is emerging from an explosion of light.

    I also made the observation that the radiation does still expand/move, just not at a visible wavelength and it’s coming from all directions, providing a black body CMBR.

  • Lawrence Crowell

    I don’t know how to say this, but radiation leaving galaxies don’t contribute much in the way of gravitation. In other words you are just plain wrong on this. I and others have given a number of developed arguments for why this is so, but we seem to keep coming around to the same thing.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    Is that gravitation as all forms of curvature, or only that curving into gravitational objects, because my point is that radiation would cause the opposite effect, not an inward, but an outward, expanding curvature and at a very imperceptible level, given the amount of distance required for it to become measurable.

    As mass collapses, radiation expands. While collapse prevails in density, expansion prevails in volume.

  • John Merryman

    Keeping in mind that radiation is the one aspect of fundamental reality that does escape gravitational attraction. As Jason pointed out, space is inseparable from the material and energy in it, so since gravity is defined by mass falling into it, what does that say about the energy escaping from gravitational fields?

  • Lawrence Crowell

    The radial expansion of radiation is not a causal agent for the expansion of the universe. You need to get this erroneous “barnacle” removed from you mind. It is just plain wrong. I wrote a couple of weeks ago on how the electromagnetic field couples to spacetime. Photons radiating from a source, such as a star, have far too small a mass-energy density to contribute to spacetime curvature in any significant way.

    Black holes can in principle form without the emission of electromagnetic radiation. A whole gaggle of masses, say black dwarf stars, in a gravitationally bound cluster could by a statistically improbable evolution have their trajectories bring them at one time into a small region r

  • Lawrence Crowell

    For some reason this did not all get sent:

    small region r

  • Lawrence Crowell

    a small region r less than 2GM/c^2. This would collapse the cloud of masses into a black hole without the radiation of many photons. Black holes can collide and form larger black holes and so forth.

    It is also worth noting that a source of radiation which emits a pulse inside a black hole will not emit them into the distant universe. The null geodesics of the photons will be inward to the singularity. Remember, a black hole is defined in an elementary way as a gravity field from which light can’t escape.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    The point of my argument is that the universe isn’t expanding, so no, the expansion of radiation would be far too minor a force to cause all the galaxies and matter etc. to be flying away from each other at the rates proposed. What I’m arguing is that it effectively expands the space crossed by radiation, since it is only radiation that crosses the immense spaces involved. Sort of like climbing the down escalator doesn’t cause the floors to move further apart, even though it might seem that way, because the extra steps are falling into the gravity wells scattered around space.

    Weight is a function of gravitational attraction, so is it theoretically possible that light is not only weightless, but “anti-weight,” ie. gravitationally repulsive?Obviously in a strong gravity field, this effect would be overwhelmed, so light is pulled in by gravity, but not to the extent massive particles are.

    As for black holes and their effect on radiation, there are a lot of speculative theories and certainly gravity can accumulate mass and build up a store of energy, without losing it at an equivalent rate, but for practical purposes this energy is stored, not lost to some other dimension. I’ve read the primary black holes, those at the center of galaxies, don’t actually consume much matter when they are stable, so it would seem they function much like the eye of a storm, so most of the real activity is the donut around the center.

    Safe to say, the variety of interactions across space is every bit as complex, if not far more so, then the variety of effects we see on earth. They will keep us guessing as long as humanity exists.

  • Jason Dick

    The point of my argument is that the universe isn’t expanding,

    And yet you haven’t explained how the implied infinite age of a non-expanding universe would allow us to exist at all. So, why don’t you do that? Why does anything exist if the universe isn’t expanding?

  • Lawrence Crowell

    I am aware that you have this idea of expansion vs contraction and that the universe is static or stationary. Look it is simply wrong. A problem is that this is starting to have similarities with arguing with creationists. In such arguments no matter what you present or argue to support evolution the creationist almost never changes their mind. Debates over global warming are taking on a similar characteristic, and anti-global warming advocates and creationists have big dollars behind them, which makes it particularly hard to argue with them in a final or convincing manner. In the case of cosmology there does not exist the big dollar organizations promoting alt-science stuff, though there are some small nascent groups with a small religious backing, such as geocenterists. In your case you are just an individual who has a quirky idea about things, but you appear unable to admit your error.

    I understand that what you think has some internal logic in your mind, but the problem is that it is just wrong. What you think is not how the universe actually works. A whole lot of theories written by the most educated people and at top universities have been falisified as well. In most of these cases people admit they are wrong and go to work on other problems.

    The following might be worth bearing in mind:

    “The hardest part about gaining any new idea is sweeping out the false idea occupying that niche. As long as that niche is occupied, evidence and proof and logical demonstration get nowhere. But once the niche is emptied of the wrong idea that has been filling it — once you can honestly say, “I don’t know”, then it becomes possible to get at the truth.” R.A. Heinlein

    Lawrence B. Crowell

  • John Merryman

    Jason,

    Why does life require a finite universe? Currently physics and cosmology try getting around various inconsistancies by proposing multiple universes. Why is an infinite universe less reasonable then that?

    Lawrence,

    I’m trying to figure how you have managed to lump me in with monotheistic fundamentalists. I’m not even a Platoist. As I recall, Big Bang Theory was originally proposed by a Catholic priest, Georges Lemaitre, trying to provide cosmological support for Genesis.

    I realize I probably keep these ideas around out of stupidity, but not hardheadness. If someone could explain, in terms that make sense to me, why I’m wrong, I would certainly follow the more sensible route. As it is, physics currently prides itself that it’s “not intuitive,” ie. doesn’t make sense.

    Don’t worry about me, though. I’m not trying to climb up the Ivory Tower. Just offering some commentary. The real weak link isn’t that current theories are about to be overthrown, but that the imminent implosion of the monetary bubble will likely strangle funding for research that doesn’t promise immediate realworld returns.
    Sorry to test your patience. It has been an interesting discussion, at least for me.

  • Jason Dick

    Why does life require a finite universe? Currently physics and cosmology try getting around various inconsistancies by proposing multiple universes. Why is an infinite universe less reasonable then that?

    The problem is entropy. I don’t really need to explain the second law of thermodynamics to you, do I?

  • John Merryman

    Jason,

    So this low entropy state just sprang into existance with the singularity and we are not supposed to look behind that curtain. That would be like questioning, uh…God!

    I have no fear that Big Bang Theory is going anywhere anytime soon, because the basic premises on which it is based go back to the roots of western civilization. We would literally have to throw out the Bible, go back to before the time the Greeks were seduced by monotheism and reopen the debate between Plato and Aristotle. The absolute isn’t one, it’s zero. It’s not an ideal from which we fell, but the essence out of which we rise. It’s not the singularity, but the vacuum. Not the dimensionless point, but empty space. That an incredibly complex mathematics has been developed to support it, isn’t proof it’s right. Remember epi-cycles?

    Time is not a linear dimension from start to finish, Genesis to Armageddon, birth to death, prologue to epilogue. It’s a cycle. Expansion, contraction. Mass/order collapses. Energy expands. Order falls away into the past, as energy moves into the future.

  • Lawrence B. Crowell

    The origin of entropy in the universe I think comes from the self-squeezing of the vacuum state for gravitation. This is where the uncertainty in one quantum observable is reduced to near zero while the uncertainty in the other is expanded to near infinity. This is a trick common in quantum optics with the parametric amplification of a photon into two entangled photons. Sapphire has this effect on photons, which is used in various quantum experiments. There is an entropy measure associated with this in a coarse grained sense. The quantum gravity vacuum may well have this property.

    Lemaitre did not propose the big bang as a support for Genesis. In fact he admonished Pope Pius XII not to encorporate this into an infallibility doctrine supporting the Church’s theology on creation. Lemaitre was working as an honest theoretical physicist, and said the origin of the big bang was something similar to the radioactive decay of an atom. Replace atom with an unstable vacuum configuration and this statement was not too far off the mark.

    Back to the origin of entropy. The conformal group su(4) ~ so(4,2) contains the deSitter (dS) and Anti-deSitter (AdS) group. The AdS exists in a five dimensional space with two timelike directions, and as a result it has cyclic timelike solutions. So one selects out a patch with a pi cycle on the timelike directions. The conformal infinity of this is a Minkowski spacetime. The rub with this is that no amount of data on a spatial surface in AdS can uniquely give this conformal infinity. So additional data or boundary conditions are needed. I think this additional data is given by black holes and their brane dual as condensates of gauge fields, similar to the quark-gluon plasmas being probed at RHIC. This determines the cosmological constant / = /_0 + k*F^{ab}F_{ab}, where phi is the dilaton field with a quartic potential, k = constant, and F^{ab} a Yang-Mills field tensor. This data then provides the conformal completeness of the S subset AdS, or S = pi-cycle patch.

    The initial state of the universe consisted of some set of unitarily inequivalent vacua, which under a coarse graining define an entropy to spacetime. This initial entropy was low, where by initial I mean during the inflationary period. The entropy increases until the cosmos expands as time “goes to” infinity to a deSitter space with the cosmological constant / and horizon radius r = sqrt{3/ /}. Hawking-Gibbon radiation will cause this to decay, similar to the emission of radiation from black holes, so that / approaches zero value and the spacetime is a flat Minkowski spacetime with nothing. This matches the dS with the AdS at conformal infinity, is a state with a single vacuum, but at maximal entropy. I think that how the universe started out with minimal entropy and with the structure of elementary particles we observe is in order to give this conformal completeness on AdS, and further to define the conformal group su(4) with a single vacuum states “at infinity.”

    In spite of the 13.7 billion year age of the universe it is an infant compared to the time left in the future, which is infinite or “nearly so.” Things are going to get cold and dark and eventually everything will fade into nothingness and a complete void defined by a Minkowski spacetime. This is the endpoint of the Feynman path integral of the universe, while the initial state with a set of inequivalent set of vacua is the initial point. The path integral has a finite meaning when the conformal infinity is “mapped” to a finite value.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    Lemaitre was working as an honest theoretical physicist, and said the origin of the big bang was something similar to the radioactive decay of an atom. Replace atom with an unstable vacuum configuration and this statement was not too far off the mark.

    Pardon my conceptual immaturity, but I see the difference between a primordial atom and unstable vacuum, as that between a dimensionless point and unstable, but otherwise featureless, space. In other words, is the initial state bound up in a single point, from which everything grew/expanded, or does it rise from an infinite, unstable vacuum?

    The origin of entropy in the universe I think comes from the self-squeezing of the vacuum state for gravitation.

    Since this unstable vacuum would have to expand, otherwise it wouldn’t be unstable, the reaction is that at a certain level, it collapses and this effect builds on itself, creating ever larger regions of collapse. They then reach a state of density caused by this collapse not efficiently neutralizing the instability and bouncing back out as radiation. This radiation further destablizes the vacuum, causing it to continue expanding and so on….

  • Lawrence B. Crowell

    I am using a different notion of the vacuum. It is the “no particle state” for a quantum field usually expanded in harmonic oscillator modes. There are operators a^* and a, where the ^* means complex conjugate and transpose the matrix. These act on states with n particles as

    a|n) = sqrt{n}|n-1) —> reduces the number of particles

    and

    a^*|n) = sqrt{n+1}|n+1).

    The Hamiltonian or energy operator turns out to be

    H = hbar-freq(a^*a + 1/2).

    These operators are derived from the form of the classical Hamitlonian for the harmonic oscillator, such as a spring of a pendulum with small oscillations. This Hamiltonian operator then acts on a state |n) as

    H|n> = hbar-freq(n + 1/2)|n),

    and there is this energy for the vacuum state |0). This is sometimes called the zero point energy (ZPE), which is an artifact of quantization. It can be removed by various techniques.

    There is a lot of nonsense about the ZPE, such as people who think it is a source of free energy. But anyway this is what I was meaning by the vacuum state. In the case I wrote this morning I am referring to a vacuum state associated with a quantum wave function(al) for a metric spacetime configuration variable. A vacuum for this state means the spacetime in a sense does not exist.

    BTW, normally the state vector is written with the horizontal carrot instead of a paranthesis, but this system seems to not like them.

    Lawrence B. Crowell

  • John Merryman

    So it’s only particles and oscillations?
    If there is no ZPE, what is “dark energy” in the context of an expanding universe?

  • Lawrence B. Crowell

    I can only describe this right now. The Hamiltonian for the Harmonic oscillator is

    H = 1/2(p^2 + f^2q^2)

    where p is the momentum, q the position, f the frequency, and the mass term has been absorbed in these. Now if I add a term i(qp – pq) [i = sqrt{-1}] classically by commutivity this is zero. Yet if I write the momentum and position variables in quantum operator form this commutator is not zero. The hamiltonian for the Harmonic osciilator is

    H = hbar-f/2(a^*a + aa^*) = hbar-f(a^*a + 1/2)

    where I have added a^*a – a^*a = 0 and this gives a commutator

    [a, a^*] = aa^* – a^*a = 1.

    Now if I do this quantization on the classical level with the zero commutator added in with the classical variables

    [p, q] = pq- qp = 0

    and then quantized I can eliminate the ZPE term hbar-f/2. Classical mechanics has commutivity of variables, but when quantized that commutivity is lost, such as [q, p] = i hbar.

    A common way of doing this is something called normal ordering. This is somewhat justified by the fact there is no classical content to the ZPE. This is what I have just argued for. The traditional approach to the cosmological constant is to take a ZPE vacuum energy and construct the cosmological constant from a momentum-energy tensor constructed from ZPE terms. This causes all sorts of problems. A straight ZPE constructed this way predicts a cosmological constant 123 orders of magnitude larger than what is observed. Other horrors rear their head, and in a way they are related to this problem of the “dark misleading force.”

    The cosmological constant is due to an inherent curvature to spacetime. It is not due to a source, such as a “dark misleading force.” Yet if we pause for a minute we might think of a ZPE energy as having a mass-energy content and that this is something which could couple to a spacetime manifold. So is this inherent curvature induced by the cosmological constant related in some way to a quantum ZPE? Probably, but not quite in the naive way we do this. To work on this involves walking through a minefield. Huge amounts of confusion lies here, such as ideas that virtual loops and the like are some real aspect of the vacuum and so forth. Yet this does indicate some subtle connection between general relativity and quantum field theory. Yet I think this connection is far more subtle than what is thought by most.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    The cosmological constant is due to an inherent curvature to spacetime.

    Presumably an opposite curvature then that commonly associated with gravity. Sort of like a hill is the opposite of a valley?

    p is the momentum, q the position, f the frequency, and the mass term has been absorbed in these.

    So you don’t think there is any possibility that radiation can have the effect of curving space, as recorded by light, such as redshifting it, without having equal effect on the position of emitting objects? I should point out that light passing through a gravity field is curved, but that doesn’t mean the source is moved by this effect. At least there would be no need for ZPE, or dark energy, to explain why space appears to expand, if this is a possibility.

    The recent posting by Sean, on the article by Dennis Overbye about Boltzmann brains, is a pretty graphic example of the problems cosmology is having in trying to fit together all the current concepts that are considered resolved. Do you think the answers will suddenly become clear, or is cosmology headed down the path of becoming a scientific laughingstock?

  • Lawrence B. Crowell

    Please, you have to abandon this idea about a competing expansion of space due to radiation balancing a contraction by gravity. It is just wrong. A number of posters here have indicated by various means why this is the case.

    I think in the next couple of decades some work with deep space astronomy and some new particle physics experiments is going to lead to data supporting an emergent theory of quantum gravity and cosmology. What does emerge might be different from what is now thought. We will just have to see how things develop.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    Thanks for the time and effort.

    Regards,

    JBMjr.

  • Pingback: Dark Energy. Coming soon to web browsers near you. « Morning Coffee Physics

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Cosmic Variance

Random samplings from a universe of ideas.

About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] cosmicvariance.com .

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