Does Space Expand?

By Sean Carroll | October 6, 2008 12:35 pm

There seems to be something in the air these days that is making people speak out against the idea that space is expanding. For evidence, check out these two recent papers:

The kinematic origin of the cosmological redshift
Emory F. Bunn, David W. Hogg

A diatribe on expanding space
J.A. Peacock

Expanding Space: the Root of all Evil?
Matthew J. Francis, Luke A. Barnes, J. Berian James, Geraint F. Lewis

Admittedly, my first sentence is grossly unfair. The correct thing way to paraphrase the underlying argument here is to say that “space is expanding” is not the right way to think about certain observable properties of particles in general-relativistic cosmologies. These aren’t crackpots arguing against the Big Bang; these are real scientists attacking the Does the Earth move around the Sun? problem. I.e., they are asking whether these are the right words to be attaching to certain indisputable features of a particular theory.

Respectable scientific theories are phrased as formal systems, usually in terms of equations. But most of us don’t think in equations, we think in words and/or pictures. This is true not only for non-specialists interested in science, but for scientists themselves; we’re not happy to just write down the equations, we want sensible ways to think about them. Inevitably, we “translate” the equations into natural-language words. But these translations aren’t the original theory; they are more like an analogy. And analogies tend to break under pressure.

So the respectable cosmologists above are calling into question the invocation of expanding space in certain situations. Bunn and Hogg want to argue against a favorite cosmological talking point, that the cosmological redshift is not an old-fashioned Doppler shift, but a novel feature of general relativity due to the expansion of space. Peacock argues against the notion of expanding space more generally, admitting that while it is occasionally well-defined, it often can be exchanged for ordinary Newtonian kinematics by an appropriate choice of coordinates.

They each have a point. And there are equally valid points for the other side. But it’s not anything to get worked up about. These are not arguments about the theory — everyone agrees on what GR predicts for observables in cosmology. These are only arguments about an analogy, i.e. the translation into English words. For example, the motivation of B&H is to do away with confusions in students caused by the “rubber sheet” analogy for expanding space. Taken too seriously, thinking of space as an expanding rubber sheet convinces students that the galaxy should be expanding, or that Brooklyn should be expanding — and that’s not a prediction of GR, it’s just wrong. In fact, they argue, it is perfectly possible to think of the cosmological redshift as a Doppler shift, and that’s what we should do.

Well, maybe. On the other hand, there is another pernicious mistake that people tend to make: the tendency, quite understandable in Newtonian mechanics, to talk about the relative speed between two far-away objects. Subtracting vectors at distinct points, if you like. In general relativity, you just can’t do that. And realizing that you just can’t do that helps avoid confusions along the lines of “Don’t sufficiently distant galaxies travel faster than light?” And reifying a distinction between the Doppler shift and the cosmological redshift is a good first step toward appreciating that you can’t compare the velocities of two objects that are far away from each other.

The point is, arguments about analogies (and, by extension, the proper words in which to translate some well-accepted scientific phenomenon) are not “right” or “wrong.” The analogies are simply “useful” or “useless,” “helpful” or “misleading.” And which of these categories they fall into may depend on the context. Personally, I think “expanding space” is an extremely useful concept. My universe will keep expanding.

CATEGORIZED UNDER: Science, Words
  • Aaron

    So can you explain *why* the GR space expansion point-of-view doesn’t apply to solar-system scale objects or galaxies? Every explanation I’ve heard throws around terms like “gravitationally bound”, but doesn’t say why that effects anything. So what if they’re gravitationally bound?

    Is it just so long as the metric closely approximates, say, the Schwarzschild metric, that the deviations due to the large scale changes are small enough that they don’t matter, or are they even in principle not there? If the first, okay, but what’s so special about these cases that they should be called out that way, rather than any other case where the effects just happen to be too small? If the second, how does that come about that the local perturbation completely suppresses the large scale structure?

  • http://www.freakangels.com Paul

    @aaron
    If I’m not totally muddled, I think it’s because gravity and the other forces hold closely grouped objects such as the stars in galaxies (and of course anything smaller) together in clumps that don’t expand, even though the ‘fabric’ in which they exist is technically expanding. It would be like having some stones suspended in a gel that expands, carrying them further apart. Obviously the stones wouldn’t expand with the gel.

    I understand all of this from a perspective that consists of nothing but analogy though, not knowing much of the underlying maths.

  • Aaron

    Paul: but what’s holding together the solar system, or a galaxy is just gravity — warped space-time — which is the gel in your analogy.

  • http://morningcoffeephysics.wordpress.com Jasper Palfree

    @Paul
    I think that the point the physicists Sean has mentioned above are trying to get across is that such an analogy does not hold for localized clusters of matter. Unfortunately, I’m as muddled as you are. I don’t quite see why the analogy doesn’t hold locally. The only answer that has ever been offered to me by my teachers is that “gravity holds them together”, which never made sense to me.

    I’m with Aaron. It would be absolutely great if someone could explain this better.

  • http://letterstonature.wordpress.com Berian

    @(Aaron, Paul); There is an attempt at addressing this in Secs. 2.3-4 of the third paper to which Sean links. Section 2.3 is an extended mathematical argument using results from an earlier work, but it culminates in: “[o]bjects will not expand with the universe when there are su?cient internal forces to maintain the dimensions of the object;” while Section 2.4 is all prose and addresses the question of gravitationally-bound systems directly.

  • http://letterstonature.wordpress.com Berian

    The section numbering in comment 5 is incorrect: I mean 2.6.2 and 2.6.3; please forgive my not double-checking! The reason an explanation such as “gravity holds them together” might be confusing is that it isn’t clear what is meant by ‘gravity': the Newtonian picture of forces or the GR picture of an expanding space-time—it seems like these two must be competing for primacy. But there is only one gravity!

    The gravitational motions here are the governed by solutions to the Einstein field equations, given a particular choice of ‘metric’ (a measure of distance between points). In the solution used for cosmology, the metric is changing with time (the distance between points is getting larger), and this is what is generally meant by ‘expanding space.’ But this says nothing of the galaxies themselves, which are usually put on the other side of the field equations to the metric. The Friedman equations, which are the stock and trade of theoretical cosmology, are a reduction of the field equations under the assumption of this expanding metric and a particular description of matter, both agreed not to be accurate on the scales of galaxy clusters or the Solar system. Instead, the metric on these scales must be some kind of strange admixture of the very-large scale cosmology form (expanding space) with the small-scale metric for isolated clumps of matter (like the Schwarzschild metric). But working that out has so far proved too difficult!

    I hope that is some help; additionally, the passage I had in mind is: “Unsurprisingly then, the resulting picture the student comes away with is is somewhat murky and incoherent, with the expansion of the Universe having mystical properties. A clearer explanation is simply that on the scales of galaxies the cosmological principle does not hold, even approximately, and the FRW metric is not valid. The metric of space-time in the region of a galaxy (if it could be calculated) would look much more Schwarzchildian than FRW like, though the true metric would be some kind of chimera of both.”

    Sorry again about the numbering; I feel like a dunce.

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  • http://www.peacefalls.net/me John

    I think it is very very important for Scientists to be concerned about producing useful analogies. They need to to do this to an even greater extent so that it reaches the general public. This needed communication of ideas and concepts to the general public is so very important, otherwise all this good science and information stays locked away in ivory towers and those of us in the unwashed and unlearned masses are left with nothing but the traditional analogies; myths and religions.

    It would be great if everyone was able to think in terms of higher mathematics but that is not the reality. Today the entrenched ancient analogies are still influencing political debate with the potential to curb funding in some areas of study.

    Albert Einstein made the effort to publish a book for the general population, “Relativity: The Special and the General Theory”.

    Perhaps I have not searched hard enough but now that I am retired I am searching for reading that will bring me up to date on all the current research in Physics.

  • JJ

    Great post as always Sean. Way off topic: As we all know tomorrow the Nobel prize in physics will be announced and there is not a single post in CV about predicting the winner. Come on people, what´s wrong with you? :D

  • Aaron

    Berian: thanks. Of course I should have thought to *gasp* actually read the papers, and that they might discuss these points.

    This description of the local metric as a mixture of FRW and Schwarzschild is exactly how I was trying to think of things.

    Thanks.

  • neophyte

    Isn’t is true that for a wide range of cosmological models the total volume of space is finite and increasing with time, no matter how you slice it, right?

    So how could anyone deny that space is expanding in this scenario?

  • ST

    To a first approximation, matter is uniformaly distributed in the universe. Precisely at that level of approximation, “space is expanding”. The “expansion” of the universe is really a statement about homogeneity, isotropy, etc. (of coarse-grained distributions of matter in the universe.)

    Glaxies are test particles moving in the ambient spacetime curved by everything else in the Universe. When we look at local structure at the level of galaxies, we are already far from the regime of the original approximation.

  • Dylan Dog

    There are two distinct issues here, and it’s very confusing to mix them.

    Issue 1: The “rubber sheet” story is definitely an *analogy*. As Sean says, there is no right or wrong here, only misleading and not misleading. And this particular analogy really IS misleading, particularly when people are discussing Inflation. When you stretch a rubber sheet, you really do flatten out the inhomogeneities. Inflation is not like that: it just makes everything bigger, it doesn’t flatten anything out. Of course, to “small” beings like ourselves, making everything big makes it difficult for us to detect the inhomogeneities, but they are still there.

    Issue 2: Is the universe “really” expanding? Is this too a matter of opinion, as some of the authors of these papers state or imply? Well, to say that the universe is expanding means that you have modified Pythagoras’s theorem to include an increasing function of time. Technically, the extrinsic curvature of the relevant spacetime foliation is non-zero. This is a question of fact, not opinion or convenience. So I think I have to part company with Sean here: several of these papers are either *wrong* or so close to it that it makes no difference. Certainly any idea that GR can be understood in terms of Newtonian mechanics is quite nonsensical. The essence of FRW cosmology is isotropy, and a vector cannot be isotropic unless it vanishes. So you will never understand cosmology if you insist on thinking in Newtonian terms. [In particular, thinking of cosmic acceleration in terms of “gravitational repulsion” is a terrible mistake — vacuum energy cannot point in any direction, it is intrinsically isotropic.] Similarly, thinking of cosmological redshift in terms of Doppler effects…..well, if you *really* want to get your students badly confused about proper motions etc, go ahead, and if you *really* want to complete their utter confusion you will talk about that stupid Milne cosmology; but those of us who prefer clarity will avoid this idea like the plague.

    What I find strange about this Doppler business is this. The “correct” explanation of cosmic redshift, in terms of the extrinsic curvature, is really beautiful and, as students say, “cool”. You are directly observing the curvature of spacetime every time you measure a redshift. The alternative “explanation” in terms of the Doppler effect is contrived, clunky, and boring. Why do these people prefer boring to cool?

  • Geraint

    > Why do these people prefer boring to cool?

    We don’t – we prefer accurate to cool. Breaking redshifts into three “different” kinds actually confuses the beautiful E=-p.u underpinning all redshifts, and as we know, we can play around with the metric to do the dot product and so your “interpretation” will be different.

  • Geraint

    >Similarly, thinking of cosmological redshift in terms of Doppler effects…..well, if you *really* want to get your students badly confused about proper motions etc, go ahead, and if you *really* want to complete their utter confusion you will talk about that stupid Milne cosmology; but those of us who prefer clarity will avoid this idea like the plague.

    Hmm – it seems we do disagree – are you arguing that the standard FRW metric is the “correct” metric for the universe? If so, then I disagree and point you towards discussions in

    Coordinate Confusion in Conformal Cosmology
    Geraint F. Lewis, Matthew J. Francis, Luke A. Barnes, J. Berian James
    http://arxiv.org/abs/0707.2106

    and

    Cosmological Radar Ranging in an Expanding Universe
    Geraint F. Lewis, Matthew J. Francis, Luke A. Barnes, Juliana Kwan, J. Berian James
    http://arxiv.org/abs/0805.2197

    There is more than one way to skin a cat (luckily).

  • Speedy Gonzale

    Thanks Sean! This is my absolute favorite question! And I crave for answers! ;)

    On Science Saturday: Cosmic Bull Session, John Horgan asks you to explain how the universe can expand faster than the speed of light, and you answer: There is no such thing as expanding faster than the speed of light.

    http://bloggingheads.tv/diavlogs/9433?in=11:09&out=12:43

    At my very basic non-mathematical-amateur-level we seem to have a “problem” here, or maybe two:

    1) The universe is about 14 billion years old, and we observer objects that is 27 billion light years away. How on earth can that ever be possible?

    2) If you are right Sean (and Mr Einstein of course!), what will happen with the expansion speed in the future? We know today at that the expansion of the universe is actually accelerating (measuring quasars)? Will the “mass” of the universe increase due to acceleration, and slowing down the speed, or what? Otherwise, we will eventually expand at the speed of light (or more!), right?

    Okay, I trust you Sean as a serious scientist. I also trust this guy, Michael S. Turner and you are on a sort of “supernova collision course”, as far as I can see.

    Michael S. Turner writes; How Can an object we see today be 27 billion light years away if the universe is only 14 billion years old? And the answer is:

    According to Einstein’s general theory of relativity, the expansion of the universe is actually an expansion of space itself, and galaxies are moving away from each other because they are “being carried along by space.” The theory does NOT limit the speed at which space expands, only the motion through space. Thus, the distance to this quasar can be greater than 13 billion light years. In fact, if we ask the question, “How fast is the distance between us and this quasar increasing?” we get the seemingly amazing answer of 540,000 km/sec or about 1.8 times the velocity of light. This number is ultimately not very interesting, both because this is not the best way to think about distant objects, and because there are objects farther away whose distance is growing even faster. To quote Fermilab’s Judy Jackson, “There is no speed limit on the universe.”

    So what is actually going on here, what is the right way to tackle this question?

  • Lawrence B. Crowell

    Points of space and spacetime slide around. J. A Wheeler called general relativity geometrodynamics to bring this point out. The FRW metric

    ds^2 = -dt^2 + R(t)(dr^2 + r^2 d(Omega)^2)

    has the radius R(t) changing with time and curvatures determined by derivatives of it. We all know or have seen these. As way of analogy it is the old picture of points on a balloon being blown up.

    However, how points move is given by a gauge condition. How one shoves points on a spatial manifold is entirely given by the coordinate gauge-like choice one imposes on the problem. For a given point p one can define one spatial surface (a surface where one has set all clocks to synchronicity) and how this point along with others are lapsed into the future. Similarly one can chose another surface and push the same point into a completely different point by this change of coordinate condition on the second spatial surface of choice. So the points on a “rubber sheet” moving apart really only makes sense when one is talking about the relative deviation between two points — the geodesic deviation equation.

    We can well enough say that space expands in a cosmology, or that galaxies are on comoving frames with this expansion and the rest. However, I do think this is in some ways a model construction. General relativity as a theory of general covariance only makes reference to moving points or coordinate systems when one imposes a gauge-like coordinate condition on a problem. Of course this condition is freely chosen by the analyst.

    Lawrence B. Crowell

  • http://orbum.net/mark Mark R

    I think analogies are very useful. More useful than simply a means of communication with non-scientists. Analogies also can lead to the construction of actual experiments that can tie mathematics to the physical.

    Unless I’m wildly mistaken, being directly tied to the physical is still something important to physics.

    This was a wonderful post. I’m very happy seeing things that shine a light upon orthodoxy. It needs to be lit up.

  • Jason Dick

    Well, the nice thing about the “expansion of space” description, for physics students at least, is that it translates extremely well to the mathematics.

    As for why the local universe isn’t expanding, another way to look at it is this. First, remember that the force that is driving this expansion is gravity. The universe as a whole is expanding on average because the initial conditions combine with gravity to make this occur. But the action of gravity depends upon the distribution of matter, and this expansion depends upon an approximately homogeneous distribution of matter.

    Here near the Earth, we don’t have anywhere close to a homogeneous distribution of matter. So gravity acts differently, and doesn’t drive any expansion. On the contrary, gravity supports a nearly steady state set up due to the fact that matter near us isn’t distributed uniformly.

    As is alluded to above, one could examine this explicitly by embedding a Schwarzschild metric as a perturbation on top of an expanding space-time, and see how orbits behave.

  • Haelfix

    I don’t like encouraging people not to think of the possibility that space can expand between say atoms. Strictly speaking you can only make a manifold flat around some epsilon.

    The point is a general manifold (not necessarily FRW) can and does feel this expansion, via tiny tidal forces, which are suppressed by many orders of magnitude.

    The reason I insist on making that point, is that this can be important in understanding the role of the cosmological constant. If its too big, gravitationally bound systems will find it difficult to form. Theres a bit of a word game here with what we mean by expansion (a FRW concept) vs negative pressure density, but thats semantics.

    The point is, this sort of game is what allowed people to put anthropic bounds on the size of the CC, and its a very real effect.

  • Garth A Barber

    You have to first solve the appropriate gravitational equation, i.e. the appropriate GR field equation and then comment on it using an analogy to communicate what this means with ‘joe public’, your students and yourself.

    For example, Peacock in his “A Diatribe on Expanding Space” uses the Schwarzschild solution to show that ‘expanding space’ is an inappropriate analogy for the cosmological solution and that space therefore does not expand.

    However as the Schwarzschild solution is that of a static spherical mass embedded in Minkowski space-time, i.e. non-expanding space, I find this criticism unconvincing.

    What happens if the Schwarzschild solution, such as that describing the gravitational field of the Sun, is embedded in expanding cosmological space? Would not the solar system, and by extension the galaxy, not expand with it?

    Garth

  • ObsessiveMathsFreak

    Perhaps it is time for a general audit of some of the outstanding interpretations in theoretical physics.

  • Speedy Gonzalez

    Off-topic: The 2008 Nobel Prize in Physics goes to Yoichiro Nambu, “for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics” and to Makoto Kobayashi and Toshihide Maskawa “for the discovery of the origin of the broken symmetry which predicts the existence of at least three families of quarks in nature”.

    Congratulations!

  • Reginald Selkirk

    Expanding Space: the Root of all Evil?

    No, no, no, that’s all wrong. It is Love of expanding space that is the root of all evil.

  • Count Iblis
  • Speedy Gonzalez

    With all due respect to all very intelligent theoretical physicists and mathematicians, it seems that we have a slight Blind Men and an Elephant problem here.

    I hope we all can agree that we are living is this real physical world, and not in an equation on a piece of paper, right? I can use my physical eyes to look at this fantastic and beautiful Hubble Ultra Deep Field Image, right? In this picture I can see about 100 small red galaxies, existing when the universe was just 800 million years old. The larger, brighter and well-defined galaxies thrived about 1 billion years ago, when the cosmos was 13 billion years old.

    Theoretical physicists have calculated (redshift) that some of these small red galaxies are at the mind-boggling distance of 27 billion light years away from the lens of the Hubble Space Telescope. Yes yes, I know the red galaxies aren’t in “this moment” 27 billion light years away, we only see the light that was emitted… wait!? 27 billion years ago!? That’s impossible!? The universe is only 14 billion years old!? Help!?

    And now there’s an academic discussion on highest level on which proper words should be used to get around this “problem”.

    Sean claims that this is a “well-accepted scientific phenomenon” and that “you can’t compare the velocities of two objects that are far away from each other”. Okay, it would be more than bold to question this, but I still can NOT get this in to my simple little hillbilly brain, and I still have simple unanswered questions that wouldn’t be that hard to answer if what you are saying is correct:

    1) Exactly at what precise distance are the normal human thoughts about measuring velocities breaking down; on one tenth of a light year, or 800 million light years, or 13 billion light years, or what?

    2) Are Michael S. Turner/Judy Jackson right when claiming; “There is no speed limit on the universe.“, or is Sean right when claiming; “There is no such thing as expanding faster than the speed of light.“?

    (I sure hope that everybody agrees that No. 2 is perfectly contradictory?)

    Please, can anybody explain this in plain English!?

  • jpd

    you make approximations like that all the time.
    the distance from me to the door is a strait line
    measuring about 3 meters. (i can neglect the
    curvature of the earth)
    the distance from me to a door in the southern hemisphere
    would need to take the curvature of the earth into account.

    things measured on large scales have to take cosmological
    curvature into account

  • John Peacock

    I wrote my “diatribe” on expanding space to address many of the confusions and disagreements aired in these comments – which are arguments I’ve heard so often. I encourage people who still think expanding space is trying to rip the Earth away from the Sun to read my note.

    The only other thing I would add is that the virtue of GR is that you can calculate things from any point of view and still explain what you see. So there is no unique right viewpoint – but if a viewpoint leads you to get the wrong answers unless you are very very careful, then its use should be discouraged. I’d say it’s clear that the idea of *locally* expanding space falls into this category. Experts can use it correctly, but we should certainly ban it from public talks, since it so easily leads people to incorrect conclusions.

  • Chris W.

    Doctor in Brooklyn: Why are you depressed, Alvy?

    Alvy’s Mom: Tell Dr. Flicker.
    [Young Alvy sits, his head down – his mother answers for him]

    Alvy’s Mom: It’s something he read.
    Doctor in Brooklyn: Something he read, huh?

    Alvy at 9: [his head still down] The universe is expanding.
    Doctor in Brooklyn: The universe is expanding?

    Alvy at 9: Well, the universe is everything, and if it’s expanding, someday it will break apart and that would be the end of everything!

    Alvy’s Mom: What is that your business?
    [She turns back to the doctor.]
    Alvy’s Mom: He stopped doing his homework!

    Alvy at 9: What’s the point?

    Alvy’s Mom: What has the universe got to do with it? You’re here in Brooklyn! Brooklyn is not expanding!

    Doctor in Brooklyn: It won’t be expanding for billions of years yet, Alvy. And we’ve gotta try to enjoy ourselves while we’re here!

    (— from Annie Hall)

  • Speedy Gonzalez

    jpd, even I can use elementary math to calculate the circumference for a trip to the southern hemisphere (c=pi*d) but it doesn’t change the speed of my car anyhow.

    There seems to be some mix-up in using plain English.

    My (stupid) understanding of physicists saying “well guys here is a supernova 27 billion light years away” was that this is not where the object is “now”, but how far the light has traveled. But after reading this Understanding the expansion of space, this seems to be totally wrong!?

    Oh man! Take me back to earth. This picture of embedded Lambda-CDM geometry explains it all. It’s not complicated and you don’t have to grasp miles of mathematical hieroglyphs to understand what’s going on. It’s just a woolly use of plain English that lead to this confusion.

    The red line is the path of a light beam emitted by the quasar about 13 billion years ago and reaching the Earth in the present day. The orange line shows the present-day distance between the quasar and the Earth, about 28 billion light years.

    It’s perfectly clear and as easy as taking your car to the southern hemisphere. Sure, the supernova is 28 billion light years away. But we are never going to see any emitting light at this point in worldline! It’s forever beyond our reach and Einstein can rest in peace, as always.

    Why are physicists creating this kind of “pseudo confusion”? Or is it me?

    Yea yea, I know you all Gurus out there is laughing you pants of right now! :)

  • jpd

    i wasn’t saying anything about your abilities, i was
    addressing your comment:
    “Exactly at what precise distance are the normal human thoughts about measuring velocities breaking down; on one tenth of a light year, or 800 million light years, or 13 billion light years, or what?”

    we (you and me) make adjustments depending on scale all the time,
    my example was distance on the earths surface.

  • Geraint

    One minor point – Sean says

    > For evidence, check out these two recent papers:

    but lists three. Should we read anything into this (considering ours is number 3)?

  • Speedy Gonzalez

    jpd, it’s all okay and forgot to say, thanks man!

    My “exasperation” falls back on my own stupidity and fixation with the fact that there was something weird going on with the speed of light. Your thoughts about curvature, took me back to earth for some “reconciliation”.

    And I must apologize to both Sean and Michael S. Turner, it was all perfectly correct, if I just had examined all text carefully. My only excuse is that this is not my native language and I’m a complete “Swedish Chef” in physics. :)

    Well, nice to be back on track again with the universe and the speed of light. It took me four (light) years, but it was worth every second! ;)

    Oh, and by the way, I have no problems what so ever that Brooklyn Is Not Expanding, i.e. Steady State Brooklyn. :)

  • JP

    Hi John,

    Your analysis seems a bit fishy. You say Birkhoff’s theorem implies that a test particle at distance r0 from us at time t0 in an isotropic universe should fall towards us. If the universe is isotropic, why does it choose to fall towards us?

    I don’t intuitively understand the idea that local stuff doesn’t respond to the expansion. If it’s purely kinematic and driven by initial conditions, why do peculiar velocities of galaxies damp out over time? Why wouldn’t the same damping of peculiar velocities occur on the small scale, does the analysis leading to that damping formula depend on scale?

  • JP

    [ Of course I understand the effect on the scale of the solar system is totally negligible/unmeasurable and swamped by local gravitational fields, but still finite ]

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

    My understanding of “space expanding” is, that in such a case particles have rates of separation based on successive distances in a way that resembles classical kinematics. IOW, it’s not like special relativity, and we can actually assign rates of recession to extremely distant objects in principle, and those rates of recession can be indeed greater than c. Space could be huge, even infinite, and if the galaxy at distance X goes 0.1c then the one at 10X goes c, and the one at 100X goes 10c.

    Here is how it could be rightly defined: increase in “distance” means what it intuitively suggests, defined in terms of successive adjacent increments. So, I see a galaxy 100 MLY from me, critters there see another one 100 MLY from them, opposite me; and so on and so on. This works because those distances can be all defined and calibrated in terms of “cosmic time” – how long since your own proper clock ticked from the big bang, the time when things started receding. Everyone notes local distances at such and such moment of CT. No, it doesn’t matter whether they can get together to compare notes since we consider an objectively realist view of the universe. The very large distances are simply what the increments all add up to at successive moments of CT whether anyone is around to understand or deal with it or not. Isn’t this the basic concept you can tease out of the Robertson-Walker metric? The only problem I see is, space is not perfectly uniform and things are moving a bit to and fro, ruining the perfection of cosmic time and the regimentation of the progression of increments and local relative recessions.

    As for red shift, this is usually put as: the ratio of wavelength equals the ratio of the “size of space” (benchmarks like two galaxies each “at rest” relative to CMB) between reception and emission.

    One issue though, is that apparently one can pretend that SRT still applies. Imagine that the receding material is ever-more Lorentz contracted with distance and speed, relative to any self-appointed “central observer.” Supposedly the results are the same as “expanding space” only if the rate of recession stays the same, and there’s no way to slow things down and run them back together. This is what Milne tried in his off-beat cosmology. It’s fun to play with, and imagine what happens if one properly “infinite” but limit-Lorentz-contracted edge bashes into another …

    Since the properties of “space” depend on material relations and the existence of gravity, I can get the idea of “space expanding” because there is a difference in effect as I said (the unbound extent possible for collections of mutually receding or approaching vantage points.) However, what bothers me instead is how to demarcate a given “space” from another “space” in which it supposedly can be embedded, like a soap bubble in the air – but what keeps it constrained as a separate thing? See my comment, at Backreaction thread “100 Years of Space-Time” at https://www.blogger.com/comment.g?blogID=22973357&postID=5978898531609158226. No one gave me an answer. Better luck here?

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

    In case it wasn’t clear, we concatenate successive separations and relative velocities all together, calibrated under “cosmic time” (I didn’t make up that term, it’s out there.) Then we can get a “cosmic” definition of both separations and recession velocities over boundless extents of space. So add up the little distances to get the big distances, and add up the little relative velocities to get the big velocities at big distances (and other derivatives by extension – so for example, acceleration should be a = -(4/3)pi*rho*R relative to a given observer. It doesn’t make direct physical sense anymore as the gravity from the sphere “under” the shell of matter beyond the point you’re looking at, but it has to be consistent with the kinematics all the way out (well, not counting overall curvature.))

    BTW this is an over-simplification since it only makes good sense over the region space is reasonably flat, but if expansion is about the right rate then that is the case – well, dark energy has made this all a mess, so I’m not sure anymore.

  • http://www.nutcase.org H.M. Amir al-Mumenin al-Mutawakkil ‘Ala Allah Rab ul-Alamin Imam Yahya bin al-Mansur Bi’llah Muhammad Hamidaddin, Imam and Commander of the Faithful, and King of the Yemen.

    Geraint said “Hmm – it seems we do disagree – are you arguing that the standard FRW metric is the “correct” metric for the universe? If so, then I disagree”

    Surely not? Perhaps you really meant to say that you don’t believe that the usual coordinates used to *describe* the FRW metric are “correct”.

    If that’s what you meant, consider the following. An FRW spacetime has the property that it can be sliced up into spacelike pieces which are isotropic about each point. This statement has nothing to do with any choice of coordinates. Now it turns out that in GR a set of timelike geodesics perpendicular to these distinguished slices necessarily have non-zero geodesic deviation if the stress tensor is not zero. [I’m including the cosmological constant in the stress tensor.] This geodesic deviation is what we call, very naturally [look at any textbook picture of geodesic deviation] “the expansion of the universe”. Again, no coordinates. So yes, space is expanding. An observation of cosmic redshift is a direct observation of geodesic deviation. Nothing to do with Doppler effects of course, though the random motions of galaxies does give rise to an ordinary Doppler effect which is superimposed on and should not be confused with geodesic deviation.

  • Geraint

    > Surely not? Perhaps you really meant to say that you don’t believe that the usual coordinates used to *describe* the FRW metric are “correct”.

    No – I don’t think that the FRW coordinates are the unique way to cover the underlying geometry, and that any other slicing is equally valid way of doing so. If this means homogeneity is lost, then so be it, homoegenity was special to the FRW slicing anyway.

    The point is that the observable, the observed redshifts at a particular time for a particular observer are the same, irrespective of how we chose to slice and dice spacetime in terms of coordinates.

    I note that several posts in this thread are on the verge of declaring space as a “thing” that can bend and expand. This is where the problems begin!

  • neophyte

    Geraint: “I note that several posts in this thread are on the verge of declaring space as a “thing” that can bend and expand. This is where the problems begin!”

    What?! Are you saying space is not some thing?

    In fact, I emphatically declare that space is some thing! I would go further to state that space is essentially every thing! (at least in our observable patch of reality)

    So, what are you saying space is, if it is not some thing?

  • Geraint

    > So, what are you saying space is, if it is not some thing?

    Nothing

  • http://www.nutcase.org H.M. Amir al-Mumenin al-Mutawakkil ‘Ala Allah Rab ul-Alamin Imam Yahya bin al-Mansur Bi’llah Muhammad Hamidaddin, Imam and Commander of the Faithful, and King of the Yemen.

    “No – I don’t think that the FRW coordinates are the unique way to cover the underlying geometry, and that any other slicing is equally valid way of doing so. If this means homogeneity is lost, then so be it, homoegenity was special to the FRW slicing anyway. ”

    But you do believe in the approximate validity of the FRW *metric*, right? The point being that the metric doesn’t care about coordinates.

    I think you are missing the point, which is that FRW spacetimes have a very special property which corresponds precisely to [the rate of] “the expansion of space”, AND this property has nothing to do with how you choose your coordinates, or indeed whether you choose any particular coordinates at all. Again, whether one thinks of space as a “thing” [whatever that is] is completely beside the point, though I agree with an earlier commenter that the rubber sheet business is really horribly misleading. Still, it is not a good idea to replace one horribly misleading statement [“galaxies are like bumps on a rubber sheet”] with another [“the universe is not *really* expanding — it depends on how you look at it.”]

    Again: the key point here is geodesic deviation of geodesics corresponding to galaxies. Maybe you can twist words in some ingenious way so that geodesic deviation is not describable in terms of “expansion” [which by the way has a technical definition], but what you hope to gain from such a strange exercise escapes me. Whatever it is, “clarity” is in a different world.

    The problem with all of these papers seems to be an obsession with the freedom to choose different coordinates. It would be better to just ignore coordinates altogether, neither they nor the freedom to choose them are of any importance fundamentally.

  • Geraint

    > But you do believe in the approximate validity of the FRW *metric*, right? The point being that the metric doesn’t care about coordinates.

    I am not talking about any approximations anywhere – when you say “metric” do you mean geometry? the FRW “metric” is a coordinate system on the underlying geometry. But it is not special in anyway and there are may ways you can cover the same geometry with different “metrics” (same geometry). The important thing is the observables are the same.

    I do understand the FRW metric – have a read of the papers above.

  • http://www.sonic.net/~rknop/blog/ Rob Knop

    Heh… I just came down strongly on the side of expanding space here:

    http://www.sonic.net/~rknop/blog/?p=66

    Hogg once took me to task for using the “space expanding” picture, even warning me that he was afraid people were going to think me ill-informed for speaking out against the “galaxies flying apart” picture…. But, to my mind, the “galaxies flying apart” picture introduces *more* confusions and problems and misconceptions than the “space expanding” picture. That’s part of what my blog post is all about.

    Another important point about the “space expanding” picture… if you live in a Universe that has vacuum energy… and, there is some reason to suspect that just perhaps our Universe is like that… saying that there is “more space” between galaxies, as opposed to thinking about the galaxies as moving apart from each other, conceptually fits closer to the mathematics of what’s going on in GR when you have something whose density is constant. Dark Energy is becoming an ever more important dynamical contributor all the time. Really, there is something *physical* between the galaxies that there is more and more of as the Universe expands. Saying there is more “space itself” is perhaps a nebulous concept… but there is most definitely more Dark Energy between the galaxies as the Universe expands.

  • http://www.sonic.net/~rknop/blog/ Rob Knop

    There’s an incorrect statement in the Burns & Hogg paper:

    that “hydrogen atoms, the solar system, and the Milky Way Galaxy must all constantly “ressit the temptation” to expand along with the Unvierse. … is an erroneous consequence of the reaification of the rubber sheet: there is no such temptation, because there is no expanding rubber sheet.

    First, to be fair to them, there is no such temptation for a matter dominated Univesre; there, the expansion is the left over coasting from the Big Bang, and there’s no ongoing “force” driving the expansion any more than a golf ball flying through the air continues to feel the force of “the hit”.

    However, in our Unvierse, there is a temptation, and that is Dark Energy. I don’t want to comment on the scale of the hydrogen atom, since that would probably involve quantum gravity, but on the scale of the Solar System and the Galaxy, without the gravitational forces that hold those systems together, test particles placed initially at rest with respect to each other on those spatial scales would begin to move apart from each other due to the negative gravity effects of Dark Energy. Those effects are tiny compared to the gravitational binding of the systems, but the temptation exists.

    My problem with viewing cosmological redshifts as an infinite number of infinitesimal Doppler shifts is that it’s *more* confusing than the other picture. You have to implicitly consider the infinite (or at least one over epsilon) of reference frames between source and observer in that picture… whereas the “space itself has expanded” picture doesn’t require implicit consideration of all of that. E=-p.u at the beginning and the end does it– yes, for Doppler and Gravitational redshifts. But in each case you need consider only the event of emission and the event of detection. If you only consider those two events, then it becomes very tempting to take u as a relative velocity between the source and observer… but, as even Burns and Hogg agree, that relative “velocity” is ill defined if there’s no single special relativistic frame that is valid at both events.

  • http://letterstonature.wordpress.com/ Luke Barnes

    Mentioned in CV – that’s probably as close to immortality as I’ll ever get …

    One of the main points of our paper was that even though the “expanding space” analogy is open to misinterpretation and can be pushed too far, it is still the most useful way of thinking about the RW metric. John Peacock is right to point out its flaws, especially in the local universe, but I don’t think a “global vs. local” dichotomy is perfect either, even though it is rigorous (the RW metric can be approximated locally by Minkowski spacetime).

    To JP: John’s analysis is correct. From the standpoint of “space is not expanding locally”, the particle falls toward us because a particle that is not moving away with the exansion will be pulled back toward the origin by gravity – what’s not going up will start coming down. From an exanding space perspective the expanation is slightly more subtle. We have to analyse the situation from the perspective of Bob, who is in the hubble flow, but wayy out there next to the particle. From Bob’s perspective, the particle is being shot out into the universe, in our direction. It will approach us because, even though the particle’s peculiar velocity and our expansion velocity are initially equal, the expansion of the universe is decelerating in this scenario, and so the particle starts to catch up with us as we both race away from Bob.

    Also, the issue of dampening peculiar velocities and joining the hubble flow isn’t as straightforward as you might think. I’ll refer you to one of our earlier papers:

    Joining the Hubble Flow: Implications for Expanding Space
    Authors: Luke A. Barnes, Matthew J. Francis, J. Berian James, Geraint F. Lewis

  • Geraint

    > E=-p.u at the beginning and the end does it– yes, for Doppler and Gravitational redshifts. But in each case you need consider only the event of emission and the event of detection. If you only consider those two events, then it becomes very tempting to take u as a relative velocity between the source and observer…

    Tempting, but clearly wrong :) Just thinking of two observers who are spatially at rest at two different radii in the schwarzschild metric shows this.

    Personally, I feel the problem lies with the with to label redshifts as being “different” – gravitational, cosmological, doppler – when in reality E=-p.u is it and the components of g, p and u depend on which coordinate system you choose –

    i.e. in the FRW u has zero spatial components (for a comoving observer) and so people say the redshift is “cosmological”, where as the conformal representation of the same spacetime has non-zero spatial component for the same observer and now there is a doppler component to the redshift – but it’s exactly the same situation, with exactly the same observable – the only thing that changed was the coordinate system you threw down.

  • Speedy Gonzalez

    Rob Knop, I’m going to be a little bit rough here because I have been going through a sort of intellectual core meltdown in this post here, here and here, but it’s nothing personal, just physics.

    Before I start, I must proudly announce the birth of a new acronym; Hazy English Language of Physicists – HELP

    I have also formulated a pseudoscientific law saying: HELP = HELP, and I urge everyone to shout for HELP when physicists talks woolly in the hazy smog. :)

    Okay Rob, there seems to be a clear case of HELP in your post about Randall Munroe and the Size of the Observable Universe.

    Why then isn’t the observable Universe at most 28 billion light-years? If something emitted light and it took 14 billion years to reach us, and it was moving the other way as fast as it could, it would only be 28 billion light-years away right now. What’s with the 46?

    For physicists it’s probably clear what the observable Universe represents mathematically, for all others observable correspond to a visual object that you can see with your eyes.

    I hope that you are not saying that we can receive photons here on earth that has been travelling for 46 billion years? Alternative; that you are not saying that we can receive photons here on earth that has been travelling for 14 billion years at 3.28 times the speed of light in vacuum?

    A picture is worth a thousand words and this one is the best I’ve seen explaining the observable universe and Understanding the expansion of space.

    It’s high time to demystify our universe and use a proper language for everyone!

  • Geraint

    Actually – I find Tamara Davis’s conformal representation as the best for explaining why the observable universe is 46 billion LY in radius.

    http://www.dark-cosmology.dk/~tamarad/astro/scienceimages/Spacetime_diagrams.pdf

    As for use of proper language, we do already.

  • Speedy Gonzalez

    Geraint, when saying “observable universe”, are you saying that we can see (receive photons) from an object that is 46 billion years away?

  • Geraint

    No – as shown in the conformal picture, more most distant objects we can see (effectively the lumps in the CMB) are *now* 46 billion light years away.

  • Speedy Gonzalez

    Thanks Geraint, that’s a relief!

    My guess is that there are plenty of people (made of ordinary matter ;) ) out there who just give up on trying understand the universe because of this “lost in translation” situation. I have talked to science journalists about this “46 billion question” (those who are supposed to bring this info to the public) and they are besides “lost in translation” completely “lost in space” as well…

    It’s probably a tricky problem to find one or two words that say; The largest piece of universe that we can know anything about is at visual distance of 14 billion light years, which represents an actual present physical position of 46 billion light years away, even if it’s problematical to talk about *now* according to Einstein’s general theory of relativity.

    Did I get that right?

  • Geraint

    > Did I get that right?

    Yeah – except the bit of the universe we can ever know something about is given by the event horizon, and is currently at a radius a little over 60 billion Lyrs away.

  • http://www.sonic.net/~rknop/blog/ Rob Knop

    I hope that you are not saying that we can receive photons here on earth that has been travelling for 46 billion years? Alternative; that you are not saying that we can receive photons here on earth that has been travelling for 14 billion years at 3.28 times the speed of light in vacuum?

    Er.

    You are slamming on me by quoting the question from a blog post that’s written in a “hypothetical questioner and answer” format. I invite you to read the next paragraph after the one that you quoted, in which I explain what’s going on.

  • http://www.sonic.net/~rknop/blog/ Rob Knop

    And, in any event, talking about the *distance* to very distant objects is troubling, because there are lots of different distances involved… proper distance at the time the photon was emitted, proper distance now, both of those measured by setting the FRW t parameter to constant; or the distance the photon travelled…

    When I give public talks, I talk about lookback time, because it’s conceptually a lot cleaner.

  • Lawrence B. Crowell

    The speed of light determines a relationship for a distance and a time locally. There can exist two frames F and F’ where observers in both will see that d = ct works. However, the two frames F and F’ may have their lightcones oriented differently. And the further away an observer on the frame F detects things on frame F’ this deviation may become more extreme. It is because of this with cosmology that as one observes further out the general relativistic physics of particles comoving in a frame becomes significant. The lightcone on the frame of a distant galaxy has an orientation different than the lightcone for your local frame. This corresponds to points on the spatial surface that galaxy is embedded in are being “slid” away. This then can lead to the discrepancy between time and distance (13.7 billion years vs 47 billion light years).

    This 47 billion light years is only the distance to the CMB region some 370,000 years after the big bang. If we could get the neutrino telescopes or gravity wave interferometers to peer much further back to the inflationary period of the universe this distance will become far greater. On a local frame the light cone defines the projective space and the local projective Lorentz group. This is naturally defined because of the null property of light rays, ds^2 = 0. Globally, where these local frames “mesh together” on the whole spacetime, this projective spacetime has a more complex geometry, so that the distance “infinity” is parameterized by a finite time interval. That distance “infinity” is, or close to, the initial quantum event giving rise to the observable universe. That might be a quantum fluctuation of some vacuum state, the collision of branes or … , which is infinitely far (or approximately so), but is also the single point from which the universe emerged.

    Lawrence B. Crowell

  • http://www.nutcase.org H.M. Amir al-Mumenin al-Mutawakkil ‘Ala Allah Rab ul-Alamin Imam Yahya bin al-Mansur Bi’llah Muhammad Hamidaddin, Imam and Commander of the Faithful, and King of the Yemen.

    Geraint said: “the FRW “metric” is a coordinate system on the underlying geometry.”

    At this point I can only say: “Huh?”

    “The important thing is the observables are the same.”

    If we are really going to be hard-headed positivists then we should give up all talk about hypothetical objects like “galaxies” and confine ourselves to discussions of optics in telescopes etc. The point of these discussions is to find a way of *thinking about* what we mean when we say “space is expanding”.

    Let’s try this. Pythagoras came up with a formula for the distance between two points. Naturally enough it did not occur to him that his formula should include any functions of time. But fascinatingly enough it turns out that he was wrong: the corrected version of Pythagoras’ formula *really does* have an *intrinsic* time dependence. So in order to understand the distance between two objects, it is no longer enough to know where they are and how they are moving: *superimposed* on that, the laws of geometry are dependent on time. This time-dependence of the laws of geometry is what we call “the expansion of space”.

    I find that infinitely simpler and more interesting than a tedious addition of infinitely many Doppler shifts etc etc etc. It is just a translation into English of the mathematics of GR applied to cosmology. It has also the virtue of being true.

  • Geraint

    > At this point I can only say: “Huh?”

    You may say huh, but the statement is correct. The FRW metric is a coordinate choice, but there are others that can equally be thrown over the geometry of the universe. In FRW (comoving) galaxies are stationary, in others they are not.

    The point is that all of these coordinate systems are equal, FRW is no more “fundamental” or special than any other (like choosing cartesian over polar on a piece of paper – both are just coordinate systems).

    I know what I think about “the expansion of space” – if you look at the 3 papers at the start of this thread, I wrote one of them.

  • Geraint

    >I find that infinitely simpler and more interesting than a tedious addition of infinitely many Doppler shifts etc etc etc.

    Again, the point is that this viewpoint is as valid as anyone elses.

  • Lawrence B. Crowell

    Geraint on Oct 8th, 2008 at 9:39 pm

    You may say huh, but the statement is correct. The FRW metric is a coordinate choice,

    That is true, the metric is given by a coodinate choice, which underlies the connection coefficients, which in turn are used to compute curvatures. The metric is a tool, and points defined in a particular metric are calculational entities of sorts.

    Lawrence B. Crowell

  • neophyte

    Geraint: “I note that several posts in this thread are on the verge of declaring space as a “thing” that can bend and expand. This is where the problems begin!”

    neophyte “So, what are you saying space is, if it is not some thing?”

    Geraint “Nothing”

    Oh yeah? Where’s the geometry then?

  • Geraint

    >Oh yeah? Where’s the geometry then?

    It’s a mathematical construct, just like the wave function, magnetic fields and all the other constructs.

  • Geraint

    i.e. – it’s nowhere.

  • http://www.nutcase.org H.M. Amir al-Mumenin al-Mutawakkil ‘Ala Allah Rab ul-Alamin Imam Yahya bin al-Mansur Bi’llah Muhammad Hamidaddin, Imam and Commander of the Faithful, and King of the Yemen.

    Before I give up, I have to correct

    “You may say huh, but the statement is correct. The FRW metric is a coordinate choice,”

    A metric is a particular kind of tensor. It is not a coordinate choice, it can be defined without ever mentioning coordinates, and it doesn’t care about coordinate choices.

    Likewise the fact that a particular spacetime has the FRW structure is a property of that spacetime’s geometry. It is not a coordinate choice, it can be defined without ever mentioning coordinates, and it doesn’t care about coordinate choices.

    Everything about FRW spacetimes can be stated without ever mentioning any coordinates. With a few [extremely non-generic] exceptions, namely the ones with maximal isometry groups, one can say definitely whether they are expanding or not. Generically they do expand or contract. This statement is not a coordinate choice, it can be defined without ever mentioning coordinates, and it doesn’t care about coordinate choices.

  • http://www.nutcase.org H.M. Amir al-Mumenin al-Mutawakkil ‘Ala Allah Rab ul-Alamin Imam Yahya bin al-Mansur Bi’llah Muhammad Hamidaddin, Imam and Commander of the Faithful, and King of the Yemen.

    LB Crowell said “That is true, the metric is given by a coodinate choice”

    No, that most certainly is *not* true. See the early chapters of Misner Thorne and Wheeler.

  • Jason Dick

    Please, can anybody explain this in plain English!?

    I can try.

    1) Exactly at what precise distance are the normal human thoughts about measuring velocities breaking down; on one tenth of a light year, or 800 million light years, or 13 billion light years, or what?

    At any distance. Comparing velocities at different spatial locations is simply not a valid operation in General Relativity. Doesn’t matter whether it’s a millimeter, a light year, or a billion light years.

    Now, then, that said, it is something that you can do in special relativity, which assumes perfectly flat space-time. So you can go ahead and compare relative velocities in different locations as long as the area has an approximately flat space-time.

    Therefore, since the curvature of the universe is essentially set by its expansion rate, the expansion rate of the universe determines how far away assuming special relativity works (which is typically as far as the expansion is negligible, so within a megaparsec or so, and also far away from any really dense objects, such as black holes or neutron stars). So as long as you stick with special relativity, and as long as that works as an approximation, you’re golden.

    Now, does this mean that in General Relativity there is no speed of light limit? Certainly not! The speed of light limit in General Relativity just means something different: no object with mass can ever outrun a light ray. That is to say, if I use a laser to pulse a beam of light off in some direction, and at the same time launch a rocket ship from that same location, that rocket ship, provided it takes the same path as the laser beam, can never ever catch up to the beam of light, no matter how much acceleration it has or how fast it moves.

    Of course, if the space ship was launched before the beam of light, in some special circumstances it is possible for the beam of light to never catch up either. This depends entirely upon the curvature of the space-time through which the ship travels, and it’s exactly why we can see things today that are some 20 billion light years away: when that light was emitted, they were much, much closer than that. But the universe has expanded since then, and they’ve moved so far away in the intervening time that we can no longer ever reach them with a beam of light, nor they us.

    2) Are Michael S. Turner/Judy Jackson right when claiming; “There is no speed limit on the universe.”, or is Sean right when claiming; “There is no such thing as expanding faster than the speed of light.”?

    (I sure hope that everybody agrees that No. 2 is perfectly contradictory?)

    Well, no, they’re saying basically the same thing. After all, if there’s no such thing as expanding faster than the speed of light, then it doesn’t make sense for there to be a speed limit on it, does there?

    As for why this is, it’s simple: expansion of space is not a speed. Expansion of space is speed per unit distance (or, equivalently, inverse time). The Hubble constant, for instance, is often given in units of km/sec/Mpc. You just can’t compare this number to the speed of light because it’s got the wrong units.

  • Jason Dick

    Geraint,

    While it may be true that things like wave functions, magnetic fields, manifolds, metrics, etc. are mathematical constructs, mathematics is the most specific and accurate way which we know to describe the universe around us. A “magnetic field” exists in the exact same way that a tree exists. While the mathematical equations that describe the status and behavior of a magnetic field are not in and of themselves the field, they are a description of a real, physical system which we call by the name “the magnetic field”.

  • Lawrence B. Crowell

    H.M. Amir … King of the Yemen. on Oct 9th, 2008 at 5:47 am

    LB Crowell said “That is true, the metric is given by a coodinate choice”

    No, that most certainly is *not* true. See the early chapters of Misner Thorne and Wheeler.
    —————————-

    What is invariant is the interval ds^2 = g_{ab}x^adx^b. However, for a particular spacetime problem how one assigns coordinates is given by a coordinate condition or a gauge-like choice.

    Lawrence B. Crowell

  • Speedy Gonzalez

    Jason Dick, thanks a lot for taking time! I must let this sink in to my little brain ;) this is not easy stuff for a layman.

    Geraint, thanks and I’ll be back with some questions about – Expanding Space: the Root of all Evil?

    Rob Knop, sorry man. It was not my intention to slam on *you*, just to “stir the pot” of language confusion. The real nutcase here is *me*, not understanding. Physicists are my heroes!

  • Geraint

    Yes, FRW is a coordinate choice on a particular geometry. There is nothing special about the choice.

    I disagree on the magnetic field statement above – The classical “magnetic field” of Maxwell is not observable, only its consequences. Is it “there” filling space with little red field lines (with little blue field lines of its friend, the electric field)? I suggest you have a read of a little Feynman and the development of QED on that one.

  • Lawrence B. Crowell

    The question might be asked whether the electric or magnetic field in quantum mechanics are Hermitian operators. Of course they are not being of the form

    E ~ int dk a^*e^{i@} + a e^{-i@}, @ = kx – omega*t,

    and so the matrix elements are off diagonal. Strictly speaking an observable in QM is determined by a Hermitian operator.

    I indicated yesterday how the global relationship between distance and time can be seen according to projective geometry of null rays. One is from there free to hang the spatial surfaces on this framework as one want (shift functions) and how they foliate together (lapse functions).

    Lawrence B. Crowell

  • Speedy Gonzalez

    “Everything should be as simple as it is, but not simpler.” — Einstein

    Ehhh… I’m not sure what you are talking about here Jason Dick, Geraint and Lawrence B. Crowell, but surely the magnetic field could be observable with a little aid?

  • Geraint

    > Ehhh… I’m not sure what you are talking about here Jason Dick, Geraint and Lawrence B. Crowell, but surely the magnetic field could be observable with a little aid?

    No – you can’t “see” the magnetic field – you see an interaction – in QED the “magnetic interaction” is mediated by photons, which, in the large number limit, looks like a “classical magnetic field”. If there were no iron filings there, there would be no photons mediating the magnetic interaction and hence no classical magnetic “field”.

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

    Jason Dick:

    Well, no, they’re saying basically the same thing. After all, if there’s no such thing as expanding faster than the speed of light, then it doesn’t make sense for there to be a speed limit on it, does there?

    As for why this is, it’s simple: expansion of space is not a speed. Expansion of space is speed per unit distance (or, equivalently, inverse time). The Hubble constant, for instance, is often given in units of km/sec/Mpc. You just can’t compare this number to the speed of light because it’s got the wrong units.

    No, it’s not the units that’s the point. At a large enough distance (added up successive “steps” of concatenated local separations) that still generates a separation rate of c, and farther away the rate is even higher. You’re just hiding the separation velocity itself under a rug (making the ration seem to be the point.) There is no limit because we are talking about the rate of change in total distances between various galaxies in a case with no true physical edge (no place where anyone can’t see yet more galaxies in all directions) nor is there a small-enough closed universe (e.g. hypersphere.) Like I said, you imagine this as a “realist” thinking that those galaxies exist and next to one far from us is another one, and from them yet another, and so on – even if we can’t see all of that and never will.

    You just have to get out of thinking in terms of SRT and being able to compare local objects that can move *right past* each other. Yes, it is like a “rubber sheet” because as the whole sheet expands, the bumps on it separate accordingly in a classical-type way (I mean, effectively in context, don’t go thinking I meant it literally is a classical process.) Of course this has to be thought of in terms of “cosmic time” to make sense. I am surprised not to hear more about CT in this discussion, do you guys appreciate its significance? Check out the Wikipedia piece:

    Cosmic time
    From Wikipedia, the free encyclopedia

    Cosmic time (also known as “time since the big bang”) is the time coordinate commonly used in the Big Bang models of physical cosmology. It is defined for homogeneous, expanding universes as follows: Choose a time coordinate so that the universe has the same density everywhere at each moment in time (the fact that this is possible means that the universe is, by definition, homogeneous). Measure the passage of time using clocks moving with the Hubble flow. Choose the big bang singularity as the origin of the time coordinate.

    Cosmic time is the standard time coordinate for specifying the Friedmann-Lemaître-Robertson-Walker solutions of Einstein’s equations.

  • Lawrence B. Crowell

    Ehhh… I’m not sure what you are talking about here Jason Dick, Geraint and Lawrence B. Crowell, but surely the magnetic field could be observable with a little aid?

    ————–

    A charged particle will move according to

    F = g(E + vxB)

    in the presence of an electric and magnetic field. This does not tell us that these fields are “real” as such. They might just be ways in which we organize things to account for the motion of charged particles.

    This is one of those frustrating things about physics. A lot of what we use as tools, methods and mental images and constructions might not have quite the hard reality we would like them to have.

    Lawrence B. Crowell

  • http://web.maths.unsw.edu.au/~brewer/ Brendon Brewer

    >>I disagree on the magnetic field statement above – The classical “magnetic field” of Maxwell is not observable, only its consequences. Is it “there” filling space with little red field lines (with little blue field lines of its friend, the electric field)? I suggest you have a read of a little Feynman and the development of QED on that one.<<

    Geraint and I had an ongoing argument about the reality of magnetic fields years ago, the conclusion of which is (in my mind) that his criteria for something being called “real” are far too strict and excludes things like trees, as a previous poster mentioned. I think restricting the word that much is unhelpful.

    From hearing these expanding space discussions over the last couple of years, I summarise it to myself in the following way. Yes, space is expanding*.

    * May not mean exactly what you think it means.

  • Geraint

    Brendon – I still suggest you read a little QED and think again (I said this last time also :)

  • Jason Dick

    No, it’s not the units that’s the point. At a large enough distance (added up successive “steps” of concatenated local separations) that still generates a separation rate of c, and farther away the rate is even higher.

    Except that’s not a valid operation to perform in General Relativity. You can’t do it.

  • Jason Dick

    A charged particle will move according to

    F = g(E + vxB)

    in the presence of an electric and magnetic field. This does not tell us that these fields are “real” as such. They might just be ways in which we organize things to account for the motion of charged particles.

    This is one of those frustrating things about physics. A lot of what we use as tools, methods and mental images and constructions might not have quite the hard reality we would like them to have.

    Lawrence B. Crowell

    Okay. Now why not consider Maxwell’s equations? In Maxwell’s equations, we find that a changing magnetic field can cause an electric field. And a changing electric field can cause a changing magnetic field. Change one or the other in the right way, and you start off a traveling wave. This wave can be shown to carry momentum: if it reflects off an object, it imparts momentum to said object.

    And whenever there is an electric field, magnetic field, or both, they carry energy (equal to the integral of E^2 + B^2, modulo units, over the region in question).

    So what, exactly, isn’t real here? The electric and magnetic fields describe a real phenomenon that has real effects upon the world around us. As Brandon mentions, saying that the electromagnetic field is not real would also exclude a tree as being real.

  • Geraint

    >As Brandon mentions, saying that the electromagnetic field is not real would also exclude a tree as being real.

    No – it is not quite the same question. If you think Maxwell’s B and E are “real” there are red and blue lines threading the room, even when there is no charge there to interact with. What I mean by “real” is that they are there – something physical, even if we are not trying to interact with them. Clearly, this is not the case in QED – which is amongst our most accurate pictures, so where are the B and E if they don’t appear in QED (except when pushed to the classical limit)

  • Lawrence B. Crowell

    What is real or directly observable about the EM field is contained in the momentum-energy tensor, which for T^{00} is the energy T^{ii} the momentum and off diagonal terms are Poynting vector terms. The fields are in a way the “square roots” of these terms. In QM the momentum energy terms are of the sort a^dagger times a, which are hermitian, while the square root involves linear equations in a and a^dagger terms, which are not hermitian.

    The E and B fields, as is the case with all Yang-Mills field theories, simply reflect symmetries of the energy-momentum of the field. These fields we have been told have all sorts of pretty vector field interpretations, with some nice mathematics such as Gauss’ law, Stokes law and so forth. In these mathematics we have all types of ideas of vector fields crossing imaginary surfaces, vector fields in vortices and others radially arrayed, vector potentials associated with loops and currents and so forth. Yet these are really just mathematical ways of representing symmetries of the field.

    These symmetries are internal symmetries, and so things such as fields are curvatures on a principal bundle F_{ab} = D_bA_a – D_aA_b, for D_a a covariant differential. As such these fields are really in a way “lifted” off the base manifold. Their connections to measurable physics on the base manifold is with the motion of charged particles, energy and momentum.

    It is interesting to reflect on the fact that position and momentum are also represented according to linear equations in a and a^dagger. Yet these quantities are “observables.” The difference is that they are external symmetries — ultimately involved with the Lorentz group. So there appears to be two different types of symmetries here, which are extended to three symmetries with the CPT discrete symmetry. That physics has these three symmetries is the Coleman-Mandula theorem. Yet what ties the apparent dichotomy between internal and external symmetries is supersymmetry.

    I REALLY am looking for the LHC to find evidence of SUSY, at least some particle physics for broken SUSY.

    Lawrence B. Crowell

  • neophyte

    Geraint, do you believe space is static? If not, what is space doing? Justify your answer.

  • Geraint

    > Geraint, do you believe space is static? If not, what is space doing? Justify your answer.

    Yes. My justification is written for all to see in paper number 3 up there at the start of the thread. Please have a read.

  • Geraint

    ps – the paper was refereed and has appeared in an international journal.

  • Geraint

    > What is real or directly observable about the EM field is contained in the momentum-energy tensor, which for T^{00} is the energy T^{ii} the momentum and off diagonal terms are Poynting vector terms

    I don’t quite agree – what is observable is how charged particles move.

  • Geraint

    “I have asked you to imagine these electric and magnetic fields. What do you do? Do you know how? How do I imagine the electric and magnetic field? What do I actually see? What are the demands of the scientific imagination? Is it any different from trying to imagine that the room is full of invisible angels? No, it is not like imagining invisible angels. It requires a much higher degree of imagination (…). Why? Because invisible angels are understandable. (…) So you say, “Professor, please give me an approximate description of the electromagnetic waves, even though it may be slightly innacurate, so that I too can see them as well as I can see almost-invisible angels. Then I will modify the picture to the necessary abstraction.”

    I’m sorry I can’t do that for you. I don’t know how. I have no picture of this electromagnetic field that is in any sense accurate. (…) So if you have some difficulty in making such a picture, you should not be worried that your difficulty is unusual.”

    Feynman Lectures

  • Geraint

    “Suppose there was no field. Then perhaps the circularity could be broken. Each electron would act directly on another. Only the direct interaction between charges would be permitted. … The interaction was light, in the form of radio waves, visible light, X rays, or any other manifestations of electromagnetic radiation. “Shake this one, that one shakes later, “Feynman said later.

    No field; no self-interaction”

    Genius; Richard Feynman and Modern Physics

  • Geraint

    [ps – I see students dearly hanging onto ideas learnt at school when they enter university, so electrons are “really” particles that sometimes have wave-like properties, while photons are “really” waves that sometimes have particle-like properties, that the classical magnetic fields of maxwell’s equations “really” permeate space and that space “really” expands]

  • Lawrence B. Crowell

    Geraint wrote

    1) Q) Geraint, do you believe space is static? If not, what is space doing? Justify your answer.

    A) Yes. My justification is written for all to see in paper number 3 up there at the start of the thread. Please have a read.

    2) I don’t quite agree – what is observable is how charged particles move.

    3)”Suppose there was no field. Then perhaps the circularity could be broken.
    ———-

    When it come to #1) I’d say that we might ask whether space even fundamentally exists. What we might say has a concrete reality in physics are null rays, congruences of null geodesics and projective geometries. These are invariants of the theory. These projective spaces, or null congurences can then have a fibration over then from which connection terms and curvatures are computed. BTW, this is how I in fact have been reworking GR. This then makes general relativity similar in structure to quantum mechanics according to the Fubini-Study metric. In this approach the metric is not that fundamental. Anything which might be called space or spacetime is then something which we hang on projective geometry or sets of null congruences. How we want to do this “decorating” is up to the analyst.

    When it comes to #2) I can meet you half way. I tend to think of the expectation of a Hermitian operator as observable. The most important observable is the EM field of a photon H = 1/2a^dag a. The photon is a particle and I tend to think of particles as observable. The photon has a helicity or spin, momentum and energy. So I would consider the photon as observable.

    When it comes to something such as a static field, of course we don’t observe them! We might say that in a region of a magnetic field we can insert a Hall probe and measure the magnetic field. However, all we are doing is calculating what might be called a field effect because we have found that an electric current has been effected. Charged particles in motion are all we really measure. The B field is then inferred. This becomes of course particularly interesting with quantum hall effects.

    Much the same holds for quantum waves. We really observe particles. The wave is more of a complex valued field effect which models how quantum particles behave. But interestingly we really don’t measure the wave at all.

    Oh and while we are at it about things which don’t exist in the way we might think we might throw in vacuum energy as well.

    With respect to #3) The fields are useful only as calculational devices for computing propagators. If the field is just a way of computing the symmetry of the bosonic field, such as with photons, then there are no real fields which couple back on the electron. Feynman got this one right.

    Lawrence B. Crowell

  • Speedy Gonzalez

    Geraint,
    What I mean by “real” is that they are there – something physical, even if we are not trying to interact with them.

    Does this imply that this Cup of Levitron uses an “unreal magnetic field” to hold the spinning top floating in the air?

    Or, does this imply that the magnetic field is real while the top is spinning, and become unreal when the top stops? If so, how can a spinning top decide what’s real or unreal?

  • Speedy Gonzalez

    Hehe, found this one with more “unreal music”!

  • Geraint

    The cup of levitron floats due to the electromagnetic interaction which is a direct propagation of photons (a’la QED) – In the large number limit, this looks like the classical B field in maxwell’s equations.

  • Geraint

    > But interestingly we really don’t measure the wave at all.

    Exactly – the “wave function” is the QM equivalent of the B field (and of course are when you look at quantized em field they are the same :)

  • Speedy Gonzalez

    “If you can’t explain it simply, you don’t understand it well enough” — Einstein

    Geraint, have done some more reading. Can we say that?

    magnetic field = electromagnetic field (or electromagnetic waves)

    And, that the “mechanical force” that hold the Levitron Spinning Top floating in the air is photons?

    If this is the case I think I can understand: Magnetic field – doesn’t exist – is unreal – is not observable – because it belongs to the quantum world of approximations, right? And an approximation can never be a “real” thing; it’s just an approximation, right?

    If my “hobby speculation” is anywhere near scientific truth, I have 2 questions:

    1) Light is “made off” photons, I can see the light with my eyes. Is light a real thing?

    2) According to Einstein matter and energy is the same thing E=MC2, and matter can be regarded as “frozen energy”. Energy/matter cannot be destroyed. We all agree a tree as being a real thing. If have a “container” for burning trees that would not let anything out. Could one say that after burning a real tree, we get a “tree” in the form of light, heat and carbon, which is also real? Or is it just the carbon that counts for real?

    If it’s NO on both questions I suggest we make it very simple for everyone and say:

    All that is not matter is unreal because Quantum Mechanics has to big influence, so the best we can do is give (pretty god) predictions and approximations.

  • neophyte

    Geraint, to what extent, if any, in your opinion, is curvature real?

  • Lawrence B. Crowell

    Curvatures on a bundle define the fields. The electromagnetic field tensor constains the electric and magnetic fields, and this is the curvature on the principal bundle. The difference with spacetime curvatures is that it is given on a fibre bundle of connections pertaining to the base manifold, or that it is an extrinsic curvature. It this curvature real? Well we can use that curvature to compute the deflection of light around a gravitating body, and find that measurements confirm the prediction. Does this mean the curvature “exists,” or does this mean that it is a geometrical calculational device for predicting a measurement?

    When it comes to points moving apart in an expanding cosmology, say with a deSitter (like) metric, we might say that this moving of points is a solution to the Einstein field equations. As I indicated the main thing which might be real in gravitation are projective and congruent configurations from null geodesics. Spacetime is what we dress this framework with. If so then on the Hubble frame (a convenient coordinate condition) points are found to be sliding away from each other on a large scale. Is this business of points moving apart real? Maybe it is just a solution which permits us to compute some things about the universe, such as comoving of frames.

    Remember, general relativity is not about points! Given a point in spacetime one can chose two spatial metrics which contain that point and then “evolve” that point into two different points. What matters in general relativity is the relative motion of particles or massive bodies.

    As for waves and the rest, of course physics has lots of wave equations. Maxwell’s equations for waves of electric and magnetic fields, Schrodinger wave equations, and on and on. These are nifty mathematical devices, and they permit us to predicts lots of stuff. Even general relativity for N-type of Petrov-Pirani solutions are wave equations (gravity waves). There is nothing wrong with talking about fields and waves and all the rest, including points sliding apart in cosmology. It is however, important to remember that these things do appear to be more mathematical representations of nature than how nature herself actually operates.

    Lawrence B. Crowell

  • neophyte

    (1) Is there any form of mathematics that pertains in any way whatsoever to reality?

    (2) Is there a reality for mathematics to pertain to?

    (3) Is there any reasonable sense in which a (healthy growing) tree is expanding, but space is not expanding?

  • Speedy Gonzalez

    neophyte, I’m going to try to answer in a “layman way”, surely the “real” guys are going to correct me. ;)

    (1) Is there any form of mathematics that pertains in any way whatsoever to reality?
    A: Yes, one popular formula is: If you take one banana and then one more banana, you have two real bananas. Mathematically that would represent the famous equation: 1 +1 = 2 (which allows you to go bananas). :) Seriously, of course there is lots of mathematics that connects direct to reality.
    (Some mathematician gurus say that mathematics is the reality, but I cannot comment on that.)

    (2) Is there a reality for mathematics to pertain to?
    A: Yes, the whole universe.

    (3) Is there any reasonable sense in which a (healthy growing) tree is expanding, but space is not expanding?
    A: No, therefore both the healthy tree and space is expanding, but in a very different way, and for very different reasons.

  • neophyte

    Ah, yes. Good common sense answer.

    Now let’s see what the “experts” have to say.

  • neophyte

    Oh, and Sean, feel free to chime in.

  • Geraint

    > Geraint, to what extent, if any, in your opinion, is curvature real?

    As we say in our papers, “curvature of space” is as “real” as the “expansion of space”. Space is not a thing that curves and expands.

    Weinberg has a great section in his (IMHO fantastic) textbook on “The Geometric Analogy” (which I keep bookmarked to show students) that because the maths looks like curved space-time that there actually is a curved space-time.

    ‘Imagine looking at a galaxy which is, say, a billion light years away. Then imagine a fellow in that galaxy looking at a galaxy along the line of sight which is another billion light years further away. Imagine, the galaxy you are looking at is travelling at 10 000 kilometres per second. But the fellow in the second galaxy must also see the third galaxy travelling at 10 000 kilometres per second. So the third galaxy, which is twice as far away from you as the second galaxy, is travelling away at 20 000 kilometres per second – twice as fast from you.

    ‘You can build this up into a proof that the speed of a galaxy is proportional to its distance,’ says Weinberg. ‘And it’s all derived from the principle that the Universe looks the same from all positions.’

    Popular accounts, and even astronomers, talk about expanding space. But how is it possible for space, which is utterly empty, to expand? How can ‘nothing’ expand?

    ‘Good question,’ says Weinberg. ‘The answer is: space does not expand. Cosmologists sometimes talk about expanding space – but they should know better.’

    (Steven Weinberg quoted in New Scientist)

  • Geraint

    > (3) Is there any reasonable sense in which a (healthy growing) tree is expanding, but space is not expanding?

    The universe is expanding (things are moving apart) but it’s not because the space between them is stretching.

  • Geraint

    > If this is the case I think I can understand: Magnetic field – doesn’t exist – is unreal – is not observable – because it belongs to the quantum world of approximations, right? And an approximation can never be a “real” thing; it’s just an approximation, right?

    Not quite. In QED, the thinkgo floats because there is an exchange of virtual photons between the base and the floating thing. Now, this is a classical device and so there are quadrabazzilions of photons being exchanged, mediating the EM force between the two.

    Now, take away the floaty thing – what does classical physics say – well, Maxwell’s equations would say that there is a magnetic field there, even when there is nothing there to interact with, little red lines with arrows on them looping through.

    What does QED say – well, with nothing there to interact with, there are no virtual photons flying around (there will be between the atoms in the base, but not up to where the floaty was. The classical B-field is not there. Now, bring a compass in, the exchange of virtual photons begin in earnest, and viola, it “feels” a magnetic force.

  • Speedy Gonzalez

    Geraint, thanks a lot! I was just reading about virtual photons!

    The debate of the magnetic field is close to end, and then we should all be proper “on-topic guys”. ;)

    But, before I stop rambling I must go in to virtual photons (which should have a lot in common with virtual particles in empty “expanding” space).

    Questions:
    1) Just imagine that the carrying force of the magnetic field was ordinary (real) photons. Would those photons have to “go any ware”, i.e. excite on the Levitron Spinning Top and making it glow like a light bulb (if the wavelength was in the visual spectrum)?

    2) Could ordinary (real) photons ever have this “mechanical momentum” as virtual photons have, i.e. if I would try to make the Levitron Spinning Top float in the air using a real powerful laser, it’s would just burn a hole in the poor thing, or?

    3) In vacuum (or empty space) there are vacuum energy “made off” quantum fluctuations in virtual particles. My understanding is that this is “okay” only because it’s an extremely short “loan” from reality, so if you borrow 100 bucks – you must repay 100 bucks immediately – ending up with zero, right? In what way does quadrabazzilions of virtual photons in the classical magnetic field get “unlimited credit” (like Wall Street! ;) ) to create a real mechanical force that holds real matter floating in the air (and even lift up heavy cars in the junkyard)?

    PS – Brilliant Weinberg quote.

  • Speedy Gonzalez

    Sorry for misspelling, my “soft-where” is taking me “any ware”…!? :)

  • Geraint

    “Virtual” photons are normal photons, it’s just this issue of borrowing and giving back energy that makes them somewhat different (basically, for a virtual photon, both the energy and momentum are not conserved at a vertex in a feyman diagram, but these quantities are conserved overall). Yes, all photons carry momentum and so can push on things (even the classical em-waves of maxwell’s equations carry and transfer momentum).

    Photons are only exchanged, so they arn’t randomly fired off with the hope of meeting an absorber, they can only be transfered from one particle to another (sometimes that other is in your eye so you “see” the photon).

  • Speedy Gonzalez

    Cool, even if I feel that the feyman diagrams are “above” my capabilities. In “my world” it feels like if I’m a virtual photon – forced to undo everything I do, not to mess-up with reality – if I push a real thing 1 cm forward, I have to immediately pull it back 1 cm, to repay my “loan”, or?

    It’s completely new to me that all photons carry momentum, fascinating! But it’s also weird since momentum the product of the mass and velocity of an object (p = mv), and photons don’t have any mass??

    By the way; I’ve found the Feynman’s lectures on QED on video! Better start learning!

  • Speedy Gonzalez

    “Imagine, the galaxy you are looking at is travelling at 10 000 kilometres per second. But the fellow in the second galaxy must also see the third galaxy travelling at 10 000 kilometres per second. So the third galaxy, which is twice as far away from you as the second galaxy, is travelling away at 20 000 kilometres per second – twice as fast from you.”

    Brilliant and simple enough for everyone to understand, thanks Steven Weinberg!

    If we call them G1, G2 and G3 for galaxy one, two and three and space is — it would look like this:

    G1 — G2 — G3

    The weird thing is that we who lives in G1 are perfectly sure that we are at rest. And the folks in G3 think the same, so when they look at us we are moving away at 20 000 kilometers per second!?

    AND, the folks in G2 think absolute the same, so when they look at G1 and G3 they are moving away at 10 000 kilometers per second!?

    Weird and unreal, but a fact.

  • neophyte

    Geraint said

    (Steven Weinberg quoted in New Scientist) said
    Popular accounts, and even astronomers, talk about expanding space. But how is it possible for space, which is utterly empty, to expand? How can ‘nothing’ expand?

    ‘Good question,’ says Weinberg. ‘The answer is: space does not expand. Cosmologists sometimes talk about expanding space – but they should know better.’

    Well it’s possible for a neophyte to be right and a nobelist to be wrong (assuming you’re correctly portraying him as agreeing with you). I think it’s clear that it is the people who confuse “empty space” with “nothingness” who are the ones getting confused by their own bad intuition.

  • Geraint

    > I think it’s clear that it is the people who confuse “empty space” with “nothingness”

    General relativity doesn’t say than empty space is anything but nothingness. It is those that attribute empty space with physical properties are those going askew.

    That’s the point of the three papers quoted at the start of the thread. No, I am not misquoting Weinberg (or Rees) – in fact, it’s these comments that started our thoughts on this issue (see Expanding Space: The Root of All Evil?)

  • neophyte

    Where are all the physical constants stored?

  • Geraint

    > Where are all the physical constants stored?

    What does that mean?

  • neophyte

    Everything that exists is information, and information is everything that exists. That includes all the physical constants and the physical laws . And if you want any kind of locality these physical constants and physical laws have to be essentially everywhere, permeating all of space, as are rulers and clocks.

    That’s how I see it.

    How do you see it? (I’m guessing you have a different view.)

  • Geraint

    Sorry Neo – but I have not idea what you are talking about. The “fundamental constants” describe things – they don’t “exist” anywhere. There is no Harry Potter like Gringolts (sp?) where their values live.

  • Lawrence B. Crowell

    The expansion of space is just a solution to the Einstein field equation. The spatial surface might be flat in the Hubble frame, a particularly convenient coordinate (gauge-like) choice, but these surfaces are not embedded in a flat spacetiime. As such the local time direction (or lapse parameter chosen) is not equal to the time direction at some distance region. More importantly null directions are not universally the same. Because of this we get this model of points of space moving apart.

    This is not that different from what happens with black holes. In the case of a Kerr metric the rotation of the black hole is often seen according to points of space being rotated around (frame dragging) the black hole. The comotion of frames in the universe is analogous to this frame dragging, though there are some departures due to the difference in the isometries of the spacetime (Killing fields etc) in the two examples.

    The point here is that space and spacetime are similar to fields in electromagnetism. These are inferred quantities which we don’t measure directly. The existential qualities of these types of entities is of course a matter of some debate, but these things do not have the same physical observable status as other directly observables. Things which are directly observable might simply only be those things which are associated with Hermitian operators in quantum mechanics.

    Lawrence B. Crowell

  • Geraint

    >The expansion of space is just a solution to the Einstein field equation.

    You mean FRW is a solution of the field equations, and the interpretation of a(t) is that space is expanding – but other solutions of field equations for exactly the same geometry (but sliced differently) behave differently and have a more complex form for a(t) than FRW – and would not necessarily be interprested as “expanding space”.

    We, therefore, return to the question of what a(t) is (which I guess is the point of this thread) – and what the papers at the start basically say is that you can’t embody space with physical properties and say that it is actually expanding.

  • Lawrence B. Crowell

    The spatial portion of the metric is well known and the solution involves spatial surfaces in a foliation where volumes contain there in are variable. This is a well understood. For spatial slices according to an inconvenient coordinate condition will result in oddball solutions. These might correspond to what an observer on a highly relativistic spaceship would see of the universe.

    Again the problem is not so much whether space expands, but the physical reality of space. Space is a geometric quantity, and its dynamics in general relativity is similar to the dynamics of field-waves in electromagnetics. These fields are not directly measurable, but are inferred from the measurements of other quantities. In EM we talk a lot about fields, waves and we design attenna to couple to electric or magnetic field components of a wave and so forth. So these things are a part of the language we use. In fact we could not get away from them, even if these things exist only according to inferences from certain measurements.

    Within the solution of GR on the Hubble frame points of space do separate. It is similar to points of space being frame dragged around a rotating black hole, or points on a spatial surface moving towards a Schwarzschild black hole.

    Lawrence B. Crowell

  • Speedy Gonzalez

    Lawrence B. Crowell, this sends shivers down my spine:

    “The point here is that space and spacetime are similar to fields in electromagnetism. These are inferred quantities which we don’t measure directly.”

    I’m no physicist or mathematician, but I have always “felt” that there must be a “connection” between gravity/spacetime and (electro)magnetism, and here is obviously one similarity.

    I know that the Graviton is not discovered get (maybe at LHC?) but if it exists, wouldn’t gravity have a lot in common with electromagnetism, in the way virtual particles make up the carrying force?
    (of course gravity must be “monopole” only)

    If they find the Graviton would that mean the end of curved spacetime as a model/explanation of gravity?

    I love Einstein, he is one of the greatest genius we ever had, and for me curved spacetime looks like an excellent solution when talking about objects like the Earth and the Moon (where one can use the “terrible” rubber sheet to make a working picture).

    But when you stand on the Earth and try to imagine a spacetime that “warps” you to the ground, it doesn’t give you the same “intuitive” feeling.

    I would be much more pleased if gravitons “glued” me to the Earth like a magnet.

    And that would also solve a much greater problem; Quantum gravity/TOE. Please, LHC hurry up! ;)

    Wait… the Higgs boson and the Graviton is the “same” particle, right? And the Higgs boson works like a syrupy and thus slowing down particles with mass… right? So it will not “glue” me to the Earth like a magnet… or? I prefer magnets before syrupy, syrupy is messy…

  • Speedy Gonzalez

    Geraint, sorry I missed to address to you, but do you have any comments on virtual photons and the mass of photons, and the weird things that goes on with G1 – G2 – G3?

  • Lawrence B. Crowell

    The monopole of the gravity field is the black hole, the Petrov-Pirani type D solution. This is analogous to the near field solution of the Maxwell equations. The analogue of the far field solution in electromagnetism in general relativity are the type N solutions, which correspond to gravity waves. There are other solution types, some which define intermediate field solutions, and one called type O for cosmologies. The solution types are determined by eigenvectors of the Weyl curvature and their eigenvalues.

    The type N solutions are not dipole as can be the case with an electromagnetic wave. The type N solutions are vectors V^d which are eigenvectors of the Weyl tensor by

    C_{abcd}V^d = 0,

    which by zero eigenvalue means they are null. Gravity waves move at the speed of light. Further momentum is an isometry of this spacetime, so momentum is conserved. Hence a dipole p = mx (mass along a distance) is constant and does not oscillate in order to conserve momentum. Gravity wave are generated by quadrupole moments or higher.

    For a weak gravity wave, say a metric of the form

    $latex
    g_{ab}~=~eta_{ab}~+~h_{ab}
    $

    for the perturbation h_{ab} small one gets a Maxwellian-like sort of wave equation with helicity 2. This can be quantized in this weak linearized form, which then defines what might be called the graviton.

    As for the graviton being a Higgs, well that is speculation which is somewhat outside the domain of physics. A Higgs particle is spin-0, and the graviton as described above is spin-2. So there is a problem right away with this idea. If the Higgs in a technicolor like theory is composed of something it might be a top-quark condensate.

    Lawrence B. Crowell

  • Speedy Gonzalez

    Thanks Lawrence B. Crowell, it’s absolutely amazing; gravity and electromagnetism do have a something in common!

    To continue with “expanding” space: There seems to be some “disagreement” among physicists whether space is expanding or not (finally on-topic!), and I have one question:

    1) No one could argue with the fact that the distance between galaxies are increasing, we do have physical hard proof as this picture of The 2dF Galaxy Redshift Survey from John Peacock’s personal webpage. Why can we not skip the discussion on “expanding space” and just say; The distances between galaxies are increasing – or maybe even simpler – The Universe is getting bigger – or maybe even better – The Universe is in a state of universal expansion?

    (For those who like 3D there is also an amazing 2dF redshift survey Rotating Slice Movie)

  • Lawrence B. Crowell

    The redshift factor for special relativity and cosmology exhibit some departures from each other. The standar defintion for the redshift factor is

    $latex
    z~+~1~=~lambda_o/lambda_e,
    $

    where the right hand is the observed wavelength -:- the emitted wavelength. In special relativity this is given by the formula

    $latex
    z~+~1~=~sqrt{frac{1~+~v/c}{1~-~v/c}}.
    $

    The hubble relationship was demonstrated by Cepheid variables that have a precise relationship between their average absolute luminosity and periodicity of luminosity (they pulsate). Using the well known relationship between absolute and apparent luminosities Hubble found that the velocity of galaxies, based on redshift, and their distance measured by Cepheid variables was

    v = Hd

    where the velocity and distance (v, d) are related by this constant H = 64km/sec/Mpc. For for every megaparsec (1pc = 3.26 ly and the distance out to where one AU subtends a one second arc) the further out one observes that galaxies are moving an average of 64 km/sec faster. This law works best the further out you look where galaxies are not subject to local gravity of the local group of galaxies — the Andromeda galaxy is actually moving towards us! Further the obsered redshift when factored into the Hubble relationship indicates that 1 + z = exp(v/c). Yet clearly there are some departures with the special relativistic rule. If you take a binomial rule on the special relativistic formula you do get to first order v = cz + …, which conforms to the Hubble law. However, the two exhibit departures for larger velocities. Hence the special relativistic coordinates of Minkowski spacetime are not the same as cosmological coordinates.

    It is tempting to say that maybe the Hubble law breaks down for large distances. If we directly look at the Hubble relationship it is easy to see that for d = 4687.5 Mpc or 15.3 billion light years that galaxies would be moving faster than light! It is tempting to think that something is going awry here. However, let us consider the CMB. This is due to the deionization of the plasma of material at the end of the radiation dominiated period. The photons emitted were comparable to optical photons ~ 1 micron wavelength, and now are redshifted into microwave wavelengths. Just ballparking this is clearly a z ~ 10^6. For the Hubble law this gives a v ~ 6c for the velocity of the material we are observing. We see stuff reach us from emitters traveling at an apparent velocity faster than light!!! More on this later, and how we actually detect photons from this material. The distance to this material is also

    $latex
    d~=~(c/H)ln(1~+~z)~simeq~6c/H~=~90 billion ly.
    $

    this is one reason for this much larger distance to the CMB opacity barrier than predicted by d = ct.

    Now let us assume that there is some departure from the Hubble law which folds cosmology into a Minkowski spacetime. If we compute this redshift using the special relativistic rule then the velocity of this stuff is moving at v/c ~ 1 – 10^{-12}, or very very close to the speed of light. The distances also fold in accordingly as well so we no longer have this huge distance to the CMB opacity barrier.

    So is there a special relativistic recovery? No, for these departures would show up much closer to home than at these distances. Even for 100Mpc distant galaxies these departures would be apparent. With the Hubble space telescope and some of the other mega-scopes it has become clear that these departures do not exist. In other words Cepheid variables and other standard candles used to benchmark distances would exhibit these departures, but our direct observations have not found them. For better or worse, even as the “root of all evil,” observations bear out the reality of the Hubble relationship to incredibly large distances.

    So how is it that we can detect photons from material flying away at velocities which appear to be faster than light? Remember that the “no faster than light” rule is a local rule which holds in a local Lorentz frame. The Hubble relationship tells us that the spacetime of the universe is curved. In fact it means that the time direction of a distant galaxy is different from our local time. Further, the light cone centered at that distant galaxy is pointed mostly away from our direction — it is squashed relative to our light cone. Thus locally a photon on this cone centered at an emitted with v > c will indeed receed away from us! Yet a photon emitted towards us by an emitter way out there with an apparent v > c will travel on the local light cone that connects up with different local light cones. That local light cone is a local tangent to the null geodesic of the photon, where these local tangents (light cones tangent to the photon path) become more oriented in the same way our local light cone is. As a result that photon which may initially receeed away from our position will enter into local regions where it receeds less and less and then eventually approaches us.

    So the Hubble law appears pretty solid. There are however deviations, but not those which recover special relativity. These deviations in fact do the opposite. We might call the year 1997 the year of breaking a cosmic barrier. Two big developments happened. The first is that Perelmutter found that not only is there a law which breaks down special relativity, but that velocities are receeding faster than thought. This means that the universe is a deSitter-like cosmology with the line element

    $latex
    ds^2~=~-dt^2~+~e^{Lambda t/3}(dr^2~+~r^2dOmega^2),
    $

    which is an exponentially expanding space. The Omega just stands for spherical angular coordinates. The “Lambda-factor ” is of the form

    $latex
    Lambda~=~3H^2Omega/c^2,
    $

    for H the Hubble factor and Omega the infamous factor which accounts for all the mass-energy in the universe. The total Omega turns out to be near unity, where only 5% of it is ordinary matter, another 25% is dark matter and the rest is dark energy. The dark energy part has some strange properties, in particular it appears to give a negative pressure on space, which expands things ever faster.

    The other development in 1997 of great interest is something called the AdS/CFT correspondence of Maldacena. This result hinges upon the dual of the deSitter cosmology, the Anti-deSitter spacetime, which is dual by having a negative Gaussian curvature and two time directions in its embedded 5 dimensions. On the horizon of this spacetime, where time increments become huge or “infinite” is a barrier to the outside with field theory. The horizon provides a conformal map or boundary, and this leads to a fascinating result that the AdS and conformal field theory are equivalent. Further, since the Gaussian curvature is negative a black hole is repelled from the horizon, and so maintains an “eternal” equilibrium with the horizon and conformal fields define there. That the observable universe is deSitter-like and this AdS/CFT result has taken us considerably closer to an understanding of quantum gravity.

    This post has been much longer than I had intended, but I wanted to write on some of these issues to attempt to clarify some things. Now as I have previously said, things like space, spacetimes, field etc are inferred and in someways appear to be constructions. Yet in doing physics it is nearly impossible not to refer to them — they appear to be lasting aspect of our lexicon.

    Lawrence B. Crowell

  • Geraint

    > Space is a geometric quantity, and its dynamics in general relativity is similar to the dynamics of field-waves in electromagnetics.

    Well, the metric is, but space does not have physical properties in GR – it does not bend, stretch or expand.

    Speedy – Everyone is happy saying the universe expands – but some of us are saying that this is because “space expands” is not the best way of putting it (cos it leads to horrible misconcetions)

    [Several of my posts did not appear – hope I haven’t upset someone so am now moderated :/ ]

  • Lawrence B. Crowell

    The matter of a metric changing or the space or spacetime changing does not matter much. The standard old fashioned way of writing a line element is with Gaussian coordinates

    $latex
    ds^2~=~g_{ab}dx^adx^b,
    $

    but I can just as well write this as

    $latex
    ds^2~=~eta_{ab}{underlineomega}^aotimes{underlineomega}^b,
    $

    which is according to the basis one-forms of the spacetime. In the first approach we can say that a metric tensor is what is changing, but in the second case the basis elements of the space or spacetime are the dynamical entities. Both views are reasonable.

    Again as I have said space and spacetime are inferred quanitities when it comes to measurement. They are model dependent quantities. Yet within general relativity it is perfectly acceptable to talk about points moving around, such as points moving in a black hole geometry. The motion of galaxies by the outward motion of points of space is a form of frame dragging, similar to the Penrose-Kerr effect of particles moved inside the ergosphere of a rotating black hole. One might be more precise and talk about the relative structure of local light cones and avoid all this discussion of moving points. In fact in some ways I do prefer that language. The classic text by Misner Thorne and Wheeler has in chapter 21 a good discussion of the “space plus time” or ADM approach to general relativity and the nature of lapse and shift functions on points of a spatial surface.

    As I indicated above the motion of galaxies outward simply can’t be reduced to the motion of particles in a Minkowski spacetime. Observational data pretty stronly rules that out. So we are pretty much forced into the idea of space, as the classical field or model, in a dynamical evolution.

    Lawrence B. Crowell

  • Geraint

    > As I indicated above the motion of galaxies outward simply can’t be reduced to the motion of particles in a Minkowski spacetime. Observational data pretty stronly rules that out. So we are pretty much forced into the idea of space, as the classical field or model, in a dynamical evolution.

    I don’t think anyone suggests that a general FRW universe can be globally represented as motion through a minkowski metric – which is obvious as the underlying geometries are not the same. But the point is that the choice of FRW and the interpretation “that its because space expands” is one choice of many.

    But saying “cos space expands” also leads some to adopt the rubber sheet analogy as being somehow “real” and hence inferring that whacky things happen cos space expands, pushes, pulls, twists, bends or wobbles it. Space doesn’t do any of these things to objects. That’s the point of the papers at the top.

  • Speedy Gonzalez

    eraint, glad that you are “back”! ;)

    [Several of my posts did not appear – hope I haven’t upset someone so am now moderated :/ ]

    I’m pretty sure that you are *not* moderated by Cosmic Variance, same thing has happened to me several times.

    I know more about programming than physics, and it seems to be a problem of “transaction handling” (i.e. what do you do when two or more users are trying to do the same thing at the same time), but I don’t know if Cosmic Variance uses a back-end database (probably they do). Anyhow this is what you do:

    How-To Avoid “Pseudo Moderating”

    1) Always write you comment in an editor, if it’s long (and you don’t want to lose it).

    2) Copy and paste the text in the reply-form and hit Submit.

    3) Always check that it worked OK.

    4) If Murphy’s Law decides that you have too much spare-time (and therefore sends your text to Cyberspace), repeat No. 2-> 3.

    5) If you get an error message (after No. 4 -> 2 -> 3) saying “This comment is already saved” (or similar). Change one character and repeat No. 2-> 3.

    And you are OK!

    (Lawrence, I’ll be back)

  • Speedy Gonzalez

    (G)eraint,

    6) Also remember to copy the first character in the text! :D

  • Lawrence B. Crowell

    The idea of space expanding can of course be removed. We can consider the whole spacetime, or look at local light cones in spacetime, without any direct reference to space expanding. So the notion of space as some “rubber sheet” which stretches or contorts is not needed. That picture of things only comes about if one looks at the spacetime as a foliation of spatial surfaces linked by lapse and shift functions. How one considers this folation is a matter of coordinate condition one imposes of course. Of course one normally does so with respect to the Hubble frame. Each spatial surface is linked to the other by the diffeomorphisms of general relativity, which we identify (with some subtle issues I am ignoring for now) this with a temporal evolution of spatial surfaces. In this sense the spatial surfaces of a cosmology can be said to be stretching.

    This picture is of course coordinate dependent. There is something in gauge theory called the elliptic sequence. So a system of one-forms or connections are mapped to the field two-forms through an intermediate set of form which “mod-out” group actions or diffeomorphisms. This might be seen as

    $latex
    Omega^{1}(ad~g)~^Mrightarrow~{tildeOmega}^{1}(ad g)~^Drightarrow~Omega^{2}(ad g)
    $

    where the map “M” takes connection terms on the left hand side and maps them to

    $latex
    M:A~rightarrow~A/diffeo(g),
    $

    and defines a moduli space. This is done by imposing gauge conditions on the problem, where each gauge condition is a “moduli” in the moduli space.

    The problem with focusing too much on pictures such as rubber sheets expanding, twisting or in general evolving is that one is focusing a lot on a particular coordinate condition and not on the more general problem. So in that sense focusing too much on this is problematic. It is not so much that it is “wrong” to look at GR according to moving points or shifting spaces, but rather one is best not to focus exclusively on this aspect of the problem.

    Lawrence B. Crowell

  • Speedy Gonzalez

    Lawrence B. Crowell, just a short question:

    Do you think that it is ever possible to translate the elegant equations that explain the geometry of the Universe, in to a 3D movie (and export in to a Flash on web for the public)?

    (I’ll be back with more questions later)

  • Speedy Gonzalez

    Clarification: We saying *3D movie* – I mean using a 3D software where you have vertices that can be manipulated and visualized in a 3D space (x, y, z), and using animation in the 3D software you get the fourth dimension of spacetime.

  • Lawrence B. Crowell

    I am not sure, and it must might be a movie of expanding space! The big issue I was driving at is with moduli spaces. There has been considerable mathematical work in this arena. Interestingly the moduli space for general relativity, due to the hyperbolic nature of the connection one-forms, is non-Hausdorff. This makes things very interesting, for it means that sequences of gauge connections may not converge as Cauchy sequence.

    I wrote elsewhere recently about my sense that technology makes us stupid. Call it “Amusing Ourselves to Death.” It seems to me that our multi-media world is taking the place of that inner visual-auditory system in the brain or mind. As a result I have growing suspicions that it kills imagination and reasoning. I sometimes wonder if technology is self-limiting, for at some point you end up with people who are information rich, but reasoning poor and thus incapable of sustaining the technological trajectory. Of course you can combine that with resource depletion and planetary ecospasm, and — well you get the picture.

    People should maybe exercise the discipline to use that marvelous multi-media machine we have had from our evolutionary roots.

    Lawrence B. Crowell

  • Geraint

    > Personally, I think “expanding space” is an extremely useful concept. My universe will keep expanding.

    Hi Sean – We arn’t saying that the universe isn’t expanding, just that you have to be careful with talking about expanding space – thinking about the universe as a rubber sheet can lead to problems.

  • neophyte

    “rubber sheet” is a bit of a straw man don’t you think?

    Although it’s probably closer to the truth than saying space is nothing.

  • Geraint

    > .Although it’s probably closer to the truth than saying space is nothing.

    No – it isn’t. Did you read any of the papers at the top?

  • Speedy Gonzalez

    Geraint, do you have any comments on momentum and the mass of photons?

  • Geraint

    >> It’s completely new to me that all photons carry momentum, fascinating! But it’s also weird since momentum the product of the mass and velocity of an object (p = mv), and photons don’t have any mass??

    p – mv is momentum in classical physics – in special relativity there is a relation between energy, momentum and mass

    E^2 = (mc^2)^2 +(pc)^2

    for photons, m =0

    So they carry momentum and have no mass.

    (actually – em radiation carries momentum in classical physics).

  • Speedy Gonzalez

    Lawrence B. Crowell, I guessed that it wouldn’t be that easy. It’s a little “sad” though that the “sexiest thing” there is for the non-mathematical public to visualize our expanding universe is this raisin bread

    It might be impossible to simulate real spacetime since the four dimensions are (obviously) connected (by speed of light) in a way that is never(?) possible in a 3D software.

    I agree in much of what you are thinking about new technology. But I think it’s a never ending story in evolution of society. Take the hunter-gatherer society 10,000 years ago. If they saw us now – sitting inside an office, writing weird stuff on paper or hammering on a keyboard – they would think that we had lose it all, the deeper knowledge and feelings about the nature is gone.

    But we got other knowledge and skills that are not all bad, and the best I think we can do is to make the right choices to push civilization in the right direction, using all tools available to make it happen.

    We can’t go back to slide rule or hunter-gatherer, except if we find some way to change the direction of time.

  • Speedy Gonzalez

    Ok, thanks Geraint! I have to go to bed it’s 02:50 here and it’s work tomorrow. But I shall be back.

  • neophyte

    I guess what I’m saying, Geraint, is that when you say “empty” space is nothing, you couldn’t be more wrong.

    In any case, it’s absurd to suggest that GR says that “empty” space is nothing. You don’t need a differentiable manifold to mathematically model nothing.

    I read Sean’s book on GR. If “empty” space were nothing, then Sean’s book would only need to be zero pages long.

  • Geraint

    >I guess what I’m saying, Geraint, is that when you say “empty” space is nothing, you couldn’t be more wrong.
    In any case, it’s absurd to suggest that GR says that “empty” space is nothing. You don’t need a differentiable manifold to mathematically model nothing.
    I read Sean’s book on GR. If “empty” space were nothing, then Sean’s book would only need to be zero pages long.

    I too have read Sean’s book – where in there does it say space is a thing in GR? The “manifold” describes the action of gravity in the presence of mass – it is not a property of “empty space”.

  • Jon Corthell

    I have an idea for a very simple interpretation of the cosmological redshift. This interpretation does not rely on “space itself” expanding nor on the special relativistic Doppler Effect.

    To set the context, we know that cosmological redshift follows the relationship:

    ?o/?z = a(o)/a(z) = (z+1),

    where ? is wavelength and a is the scale factor. We also know that:

    Do = De*(z+1),

    where Do is the distance to a galaxy at the time of observation and De is the distance at the time of emission of a photon we see now. For example, a photon with redshift z=3 was emitted from a galaxy which is now 4 times as distant as it was then.

    I believe that the cosmological redshift effect is simply a Doppler-like reconciliation of the net MEAN velocity of the photon as measured in the observer’s reference frame with the MEAN velocity as measured in the emitter’s reference frame.

    In the observer’s rest frame, a photon is emitted at z=3 from a distant galaxy which is moving away from the observer at about 1.6c (in the LCDM model with Ho=71). The photon initially moves away from the observer (figuratively climbing upstream AGAINST the decelerating Hubble flow), and only at about z=1.5 begins closing on the observer. The observer measures the “net” travel distance as De, about 5.3GLy. (“Net” as distinguished from the “gross” travel distance of the photon moving first away from the observer and then doubling back past the original emission distance.)

    In the emitter’s rest frame, the emitting galaxy at z=3 is at rest and the observer’s galaxy initially recede away at the same 1.6c. Viewed in this frame, the photon never moves away from the observer. The photon always moves away from the emitter in a motion rather like “surfing WITH the wave” of the receding and decelerating Hubble flow. The photon begins at a travel speed in the range of hundreds of c in this frame, and its speed decelerates smoothly over the length of the trip. The photon finally overtakes the receding observer at about 21.1Gly. This is exactly 4 times the net travel distance measured by the observer.

    Despite their disagreement about the net distance traveled, the observer and emitter agree on the same elapsed time between emission and reception, because clocks tick at a uniform rate for all comoving galaxies in the FLRW metric. Thus, the observer measures a mean net travel velocity which is 1/4 that measured at the emitter. At any given wavelength, the observer calculates that 1/4 as many wave cycles (peak-to-peak) will fit into the travel distance as the emitter measures. Therefore the observer measures 1/4 the frequency and 4 times the wavelength as the emitter measures. This is a Doppler-like pseudo-time dilation.

    Although its nature is Newtonian, this is not the classical Doppler Effect, because the latter measures the discrete velocity differential between the emitter and observer at the instant of emission. Instead, cosmological redshift is generated by the total (= mean) velocity over the total net travel path, because photons are either accelerating or decelerating (depending on you frame of reference) dynamically over the entire travel path.

    Why don’t we observe a combination of the mean-velocity Doppler Effect I describe and the classical Doppler Effect? I believe we would, except that the redshift of the classical Doppler Effect is exactly cancelled out by the gravitational blueshift caused by the cosmic gravitation field. If the observer pictures herself at the center of a homogeneous cosmic sphere with the approaching photon at the surface, Gauss’ Law implies a gravitational acceleration force on the photon in the direction of the observer at the center. In other words, cosmic gravity applies an acceleration force to the photon like it does to the galaxies in the Hubble flow that the photon passes along its journey. This is the gravitational blueshift effect that Prof. Peacock describes in his “diatribe” and which Matt, Geraint, Luke and Berian allude to in their recent radar ranging paper.

    This also is not the SR Doppler effect. I think SR is entirely inapplicable at cosmological distances in a non-empty GR universe, first because there is no global inertial frame, second because the photon passes every local galaxy at exactly c, and third and most importantly because there simply is no place in the FLRW metric to arbitrarily insert an SR time dilation factor which aggregates a quasi-infinite set of infintesimal local time dilations. As stated previously the local clocks of comoving galaxies in the Hubble flow keep identical time, regardless of any choice of reference frame in the Hubble flow. I am puzzled why Prof. Peacock expresses strong confidence that cosmological redshift is related to SR Doppler Effect, with a sort of double-doppler fudge factor stirred into the mix. In the mean-velocity Doppler model, the blueshift acceleration experienced by the travelling photon is essentially the same contractive gravitational acceleration experienced by the galaxies in the Hubble Flow, so the photon does not experience any gravitational time dilation which differs from the underlying time dilation inherent in the FLRW metric.

    Finally, in case it isn’t clear, here is an example using tosses of a ball to show why the observer and emitter agree on the photon’s travel time even though they disagree on the travel distance. Imagine that you and a teammate are standing together on the field, and you start running away from him at a constant 3m/s. When you cross the 10m mark, you throw a ball to him at a speed of 5m/s (measured in your rest frame). The ball approaches him at a net 2m/s and he catches it after an elapsed time of 5s.

    Next, the same example, except he throws the ball to you as you cross the 10m mark running away from him. You will catch the ball at the 25 meter mark (from him) and the elapsed time will be the same 5s. The time equation is t = De/(Vo-Ve), where De=10m, Vo=5m/s, Ve=3m/s, and V(net) = 5m/s-3m/s = 2m/s. Do = t*Vo = 25m. If the units are changed to c and ly’s, the cosmological redshift in this non-realistic example is z = Do/De-1 = Vo/V(net)-1 = 1.5.

    Recognition of this scenario becomes subtle when neither party can tell who is moving and who is standing still. In cosmology, each party tends to simplify his/her own calculations by assuming he/she is the one standing still. Therefore he/she will calculate that the ball always travels further and faster when he/she is the thrower than when he/she is the catcher. At cosmological distances, we calculate that the proper speed of contemporaneous photons is always much faster when moving away from us than when approach us. This leads to other interesting consequences.

    Jon

  • Speedy Gonzalez

    Jon Corthell, this is absolutely brilliant!!

    This is what I’m talking about, to get the public a chance to understand and visualize the problem:

    “Finally, in case it isn’t clear, here is an example using tosses of a ball to show why the observer and emitter agree on the photon’s travel time even though they disagree on the travel distance. Imagine that you and a teammate are standing together on the field, and you start running away from him at a constant 3m/s. When you cross the 10m mark, you throw a ball to him at a speed of 5m/s (measured in your rest frame). The ball approaches him at a net 2m/s and he catches it after an elapsed time of 5s.

    Next, the same example, except he throws the ball to you as you cross the 10m mark running away from him. You will catch the ball at the 25 meter mark (from him) and the elapsed time will be the same 5s. The time equation is t = De/(Vo-Ve), where De=10m, Vo=5m/s, Ve=3m/s, and V(net) = 5m/s-3m/s = 2m/s. Do = t*Vo = 25m. If the units are changed to c and ly’s, the cosmological redshift in this non-realistic example is z = Do/De-1 = Vo/V(net)-1 = 1.5.”

    On this one could even make a very instructive 3D animation on what’s going on in the universe!!

  • Lawrence B. Crowell

    Speedy Gonzalez wrote: “Take the hunter-gatherer society 10,000 years ago. If they saw us now – sitting inside an office, writing weird stuff on paper or hammering on a keyboard – they would think that we had lose it all, the deeper knowledge and feelings about the nature is gone.”

    This is absolutely true. Now to be fair they would be unaware of the fact a mathematician or scientist might be working on deep relationships they could not fathom. However, for every person doing that you have dozens tapping away on keyboards as telemarketers and accountants. We might live longer than our Pleistocene ancestors, but I think on balance “life for life” they had it better than your average modern person today. Which seems more fun?; stalking a herd of bison or mastadons in the wilderness or driving to to your office building, logging onto your computer and spending 8 hours managing other people’s accounts?
    —————————-

    Jon Corthell wrote:”I believe we would, except that the redshift of the classical Doppler Effect is exactly cancelled out by the gravitational blueshift caused by the cosmic gravitation field. ”

    The cosmological expansion, again to use the “root of all evil” the idea of the expanding spatial sheet, means that distant galaxies are comoving with their local frames away from our position, and indeed every position will observe the same thing. Further, a photon will reflect this in its redshift. This redshift can be seen in this expanding space perspective as well. If space is expanding then so too is any volume. We might think of that volume as being a sort of virtual resonance cavity, for every photon which enters the volume is on average compensated for by a photon which exits. So if the volume expands so does the average wavelength of these photons. So the cosmological redshift can be modelled according to an expanding space.

    Lawrence B. Crowell

  • Speedy Gonzalez

    Lawrence B. Crowell, LOL this is really good!

    “Which seems more fun?; stalking a herd of bison or mastadons in the wilderness or driving to to your office building, logging onto your computer and spending 8 hours managing other people’s accounts?”

    Well, if Sean could have a Self-Driving Car & Sexbot, he would choose the office, and so would I! :D

    No seriously, this is one of the weirdest and most troublesome questions ever in the history of human. We have marvelous machines and a material status then never before (i.e. 12% of us), but are we happy? Well, the consumption of Prozac and alcohol hasn’t directly reduced since Pleistocene.

    Many of us are not the masters of our own life, but slaves in the rat race for (more) money.

    So of course, our Pleistocene ancestors lived a freer and healthier life, but the rules where much much tougher. If you got seriously ill, you were dead. (= no health insurance)

  • Jon Corthell

    Oops, here are two corrections to my post on cosmological redshift:

    1. I was wrong when I said “The photon begins at a travel speed in the range of hundreds of c in [the emitter’s frame]. The initial “instantaneous” travel speed of a photon emitted at z=3 is about 4c in the emitter’s frame. I accidentally looked at my spreadsheet cell for the instantaneous speed of a photon emitted at z=1023, which is greater than 1000c in the emitter’s frame.

    2. I was wrong to characterize Prof. Peacock’s diatribe reference to SR being related to cosmological redshift as a “double-doppler fudge factor.” I meant for this to refer to the SR cosmological redshift equivalence equation in Tamara Davis’ excellent contribution in Appendix A to the recent paper “Time Dilation in Type Ia Supernova Spectra at high redshift” by Blondin et al, 4/08.

    Prof. Peacock combines an integration of SR redshift and gravitational blueshift. I think that’s the most reasonable approach for applying SR, but I think it is incorrect to apply SR to cosmological redshift at all for the reasons stated in my post.

    One conceptual point to consider is whether the geodesic of a photon emitted by a galaxy in the Hubble flow is properly categorized as purely “peculiar motion”. I submit that it is not. We know that a particle’s peculiar motion “decays” as the universe expands, causing the photon’s motion to eventually be sort of “absorbed” into the Hubble flow, i.e. indistinguishable from it locally. That effect never happens to the photon, which continues to “skate across” the ever-changing local Hubble flow at a constant rate of c, in perpetuity. Conceptually then, the geodesic of a photon emitted by a galaxy in the Hubble flow is fundamentally governed by the same FLRW metric that governs the geodesics of the galaxies the photon passes. This reinforces the point that any geodesic incorporating an element of SR time dilation would be incongruous at cosmological distances in an FLRW universe.

    Jon

  • Speedy Gonzalez

    Jon Corthell, I have been thinking about the “throwers” point of view:

    “The initial ‘instantaneous’ travel speed of a photon emitted at z=3 is about 4c in the emitter’s frame”

    … and …

    “Therefore he/she will calculate that the ball always travels further and faster when he/she is the thrower than when he/she is the catcher.”

    But, you can never throw a “ball” faster than 1c (the speed of light), can you?? The thrower must always see the “ball” leaving at maximum 1c … or??

  • Jon Corthell

    Hi Speedy,

    Yes you are correct, the photon can’t initially be moving at 4c from the emitter. The instantaneous speed of the photon compared to the emitter starts at exactly 1c of course, but then it accelerates rapidly as the photon “surfs away” with the receding Hubble flow. The AVERAGE speed of the photon is about 2.7c over the travel leg starting at z=3 and ending at z=2. As compared to an average speed of about 5.44c if it started at z=7 and ended at z=3.

    In the emitter’s frame, the Hubble flow moves faster as a function of distance away from the emitter, but the entire Hubble flow also decelerates as a function of time, which somewhat correlates to the photon’s distance from the emitter as well since the photon is moving constantly away. The resulting geodesic nets the two effects.

    If you are interested, here are the figures from my spreadsheet for a photon’s AVERAGE travel speed away from the emitter on each individual segment of its path starting at z=1089 (the CMB surface of last scattering) and approaching the observer:

    z1089 => z1023: 1048c
    z1023 => z511: 686c
    z511 => z255: 346c
    z255 => z127: 174c
    z127 => z63: 87c
    z63 => z31: 44c
    z31 => z15: 22c
    z15 => z7: 11c
    z7 => z3: 5.4c
    z3 => z1: 2.7c
    z1 => observer: 1.4c

    These are calculated simply as travel distance divided by elapsed time for each segment. Note that (z+1) for each segment represents a halving of the redshift compared to the segment above it on the chart, except for the z1089 leg. The average photon recession speed also roughly halves during each successive segment; but this relationship is not exact in a universe with a cosmological constant dark energy.

    Jon

  • Geraint

    Groan…

  • Speedy Gonzalez

    I’m not sure I’m with you here Jon…

    “then it accelerates rapidly as the photon ‘surfs away’ with the receding Hubble flow”

    Ehhh, how can the photon “surf” and on what? And doesn’t the “Hubble flow” have a “slowing down effect” all the way from start up to my nose??

  • Speedy Gonzalez

    Jon Corthell, I think you’ve missed an important part on the ball field.

    Let’s put 3 guys on the field:
    A are standing still
    B are running
    E(instein) is watching from beside

    B is throwing a ball to A. Initially it would look like this:

    A :

    E

    B will throw the ball after running 10m at 3m/s.
    B will see the ball leaving at 5m/s.
    A will see the ball approaching at 2m/s.
    A will catch the ball after 5s, when B has been running another 15m
    B will get confused since he was able to run another 15m before A catches the ball, and he should only have been able to run another 6m??

    E smiles secretly because he knows that the clocks for A & B are not synchronized…

  • Speedy Gonzalez

    Initially it would look like this:

    A <– B -> :

    E

    (darn those < and > ;) )

  • Speedy Gonzalez

    Geraint, lets mess up things even a little bit more… :D

    And talk about Dark Energy, Expanding Universe and Empty Space.

    How does your paper deal with DE? I can see the reasoning about; “the energy density will not increase with time and bound structures will remain bound and stable”

    But what about the argument on Empty Space, is it really empty? If 73% of the universe is made of DE, it must be somewhere …?

  • Jon Corthell

    Hi Speedy,

    “A will catch the ball after 5s, when B has been running another 15m

    B will get confused since he was able to run another 15m before A catches the ball, and he should only have been able to run another 6m??”

    You must state clearly whether A and B are aware of who is standing still and who is moving. If both parties have perfect knowledge, then nobody is confused about why B runs another 15m in 5s at 3m/s. And if A thinks he is standing still and B is running away, his calculations will be correct. On the other hand, if B thinks he is standing still, he won’t perceive himself to have moved at all, let alone 15m. He will perceive that A has run a total of 25m, which is the correct answer in his frame of reference.

    “E smiles secretly because he knows that the clocks for A & B are not synchronized…”

    We should not refer to a non-relativistic Doppler Shift as a clock synchronization problem. A’s and B’s clocks are entirely in synch in this example. The classical Doppler Effect is a “pseudo-time dilation”, because it looks like one but it’s not.

    Jon

  • Jon Corthell

    Hi Speedy,

    “Ehhh, how can the photon “surf” and on what?”

    Please understand that I’m using informal terminology to try to make the explanation as intuitive as I can. In that spirit, imagine a two-dimensional infinite plane expanding universe. As a photon moves radially away from the emitter in its frame of reference, it MUST accelerate to catch up to successively more distant galaxies, because the Hubble rate increases in direct proportional to distance. The photon must pass each successive galaxy at a local speed of exactly c. (Think of the receding galaxies as the waves being surfed, ok maybe it’s a weak analogy.) If you think of the distribution of galaxies being extremely granular, then the acceleration (relative to the emitter) is smooth and continuous. After a moderate amount of cosmic time has passed (e.g., well before the scale factor doubles), the photon will start decelerating (relative to the emitter) because the cosmic gravitational deceleration starts to exceed the rate of increase in the Hubble rate (relative to the emitter).

    “And doesn’t the “Hubble flow” have a “slowing down effect” all the way from start up to my nose??”

    Yes, but there are two separate effects at work here: (1) the Hubble rate which increases with distance, requiring the photon to accelerate, and (2) the gravitational contraction, which slows the Hubble rate as a function of time.

    I agree with your implication that there is an interesting dilemma here. Surely all changes in the momentum and speed of the photon should result directly from gravitational force. So how is it that the FLRW metric causes the photon first to accelerate rapidly, and then to decelerate more slowly (in the emitter’s frame)? At this point I can’t give you a crisp answer.

    Gauss’s Law seems to give a gravitational “free ride” to the photon when calculated from the observer’s perspective. That is, the collapse action of the cosmic gravitation imparts a blueshift (like an accelerating moving sidewalk) to the photon, which exactly offsets and compensates for its classical Doppler redshift. The photon does not need to “expend” any energy/momentum of its own in order to accelerate. On the other hand, there is no apparent gravitational source to “boost” the photon up to the increasing recession velocity of the Hubble flow, as a function of distance from the emitter.

    I suppose a theoretical answer is that, if the photon is “required” to accelerate to keep pace with the Hubble flow, then it must surrender a corresponding amount of energy/momentum, relative to both the emitter and the observer. That loss of energy/momentum then is manifested as the cosmological redshift. While this thought seems somewhat tidy, I am quite bothered by the concept that the photon can spontaneously accelerate its speed, without any gravitational boost, merely because the higher speed is “required” in order to pass each successive local galaxy at exactly c. And I’m not ready to accept the concept that there is some GR “frame dragging” effect at work here, with the receding motion of the galaxies itself applying a force directly onto the photon. And as I’ve said, I don’t think SR time dilation provides a useable answer.

    Well, it’s all food for more thought.

    Jon

  • Geraint

    >How does your paper deal with DE?

    In GR, you have fluids that describe the energy density – and dark energy is added by putting in a fluid of a particular equation of state.

    NOWHERE in relativity does it say dark energy is a property of space – that is only achieved with some quantum-mechanically hand waving.

    Jon – I’ll stick with E=-p.u

  • Jon Corthell

    Hi Geraint,

    E=-p.u is “merely” a mathematical equation, not a physical description of what’s happening. This equation is indispensible, but alone I don’t see how it gives us a robust understanding of the complexities of cosmological redshift.

    I want to understand how a long series of infintesimal SR time dilations can accumulate as a photon travels the cosmological distances (z>1) between Galaxy A and Galaxy B, without violating the FLRW constraint that all clocks in the Hubble flow remain synchronized.

    I want to understand how cosmic gravitational time dilation can explain cosmological redshift if the emitting and receiving galaxy clocks remain in synch.

    I want to understand why cosmological redshift is PRECISELY equal to the ratio between the distance of a galaxy at the time of emission and at the time of reception of a photon. Surely a convoluted integration of SR and gravitational time dilation in a universe with or without expansive dark energy thrown into the mix would not be expected to serendipitously generate such a profoundly simple relationship.

    I want to understand why we calculate a photon to reposition itself exactly (z+1) times as far away when viewed from the emitter’s frame as when viwed from the observer’s frame, yet the parties in both frames calculate the same elapsed travel time.

    I want to understand how cosmic gravitation can explain how a photon emitted from Earth will accelerate (in the sense of repositioning itself a relatively longer distance away in a short time interval) and then decelerate (reposition itself a a relatively shorter distance away in a longer time interval), as viewed from our frame of reference.

    And, as something of a diversion, I want to understand your comment in an earlier post that photons are only exchanged between particles, not shot blindly into empty space. When the CMB surface of last scattering set some photons on a path roughly toward where our solar system would someday form, how did the source particle “anticipate” that the photon would eventually hit our orbiting satellite which we wouldn’t decided to launch until gigayears after the photon began its journey? If the Australian space agency cuts the budget before the photons arive, are the photons instantly recalled to home base, or are they permitted to retroactively decide to never have begun the journey at all? (No, because the CMB source particle may subsequently no longer exist or may have relocated.) Are you suggesting instantaneous action or quantum entanglement across cosmological distances? Does the source particle’s energy level change when it first emits the photon, or only later when the photon becomes assured of striking an identified target? If a tree falls in the forest and no one is there, did it make a sound?

    Jon

  • Lawrence B. Crowell

    These calculations of the comoving velocity for z =~ 1100 by Jon strike me as off the mark. Given the Hubble rule (FRW cosmology etc) that

    1 + z = exp(v/c)

    and for z = 1100 indicates that v/c = ln(1100) = 7, or an apparent velocity of 7c. Things are not moving nearly as fast as is being presumed here.

    Lawrence B. Crowell

  • Speedy Gonzalez

    Jon Corthell, Thank you very very *MUCH*!!

    In my opinion this comment is the most interesting and intelligent in this post so far. To cover the feeling in my heart in one line:

    “The important thing is not to stop questioning. Curiosity has its own reason for existing.” — Einstein

    Jon, I’m particularly happy/impressed by the line: “E=-p.u is ‘merely’ a mathematical equation, not a physical description of what’s happening.”

    We have a lot of truly intelligent guys here who clearly grasp the math beyond the public’s imagination. But, if you can’t communicate the “product” to the public in plain language, it must be something wrong, or at least a reason to rethink.

    Sometimes I get the feeling that it is more or less “taboo” for physicists to say: “Well guys, we don’t know everything yet, there some really weird things going on in the universe, but we are working on it.”

    It’s obviously safer to say: “Well guys, everything is perfectly clear, we have run the equations and it works, there is nothing to discuss about the fundamental behavior of the universe. It’s a problem though, that you don’t understand the math.”

    Michael S. Turner who coined the term dark energy, elaborate his thoughts in this video (mov 18.4 MB) about where science stands today (June 22, 2003) in the understanding of the universe. In an open and sincere way he comes to the conclusion that “we are a kind of six blind cosmologists and the universe” as an allegory to the Six Blind Men and An Elephant.

    I’m confused…

    Some really heavy Nobel Laureates like Steven Weinberg says: “…how is it possible for space, which is utterly empty, to expand? How can nothing expand? The answer is: space does not expand. Cosmologists sometimes talk about expanding space, but they should know better.” (Quoted in – Expanding Space: the Root of all Evil?)

    Some says that there must be an expanding space to explain the stretching of light wave frequencies from very distant objects in the universe, sending photons in our direction.

    Some says: “There is no speed limit on the universe.”

    Some says: “There is no such thing as expanding faster than the speed of light.”

    Some says: “For the Hubble law this gives a v ~ 6c for the velocity of the material we are observing.”

    Some make logical acrobatics and says: “…there’s no such thing as expanding faster than the speed of light, then it doesn’t make sense for there to be a speed limit on it, does there?”

    Some says: “…clocks tick at a uniform rate for all comoving galaxies in the FLRW metric.”

    Some says: “Comparing velocities at different spatial locations is simply not a valid operation in General Relativity.”

    Michael S. Turner says: “Only knowing everything there is to know about the Universe would be worse than knowing all the questions to ask about it. Without doubt, as our understanding deepens, new questions and new surprises will spring forth.”

    I’m confused…

    (and maybe I’m not the only one)

    And Jon, finally a question to you: “…if the photon is “required” to accelerate to keep pace with the Hubble flow…”

    What framework does the photon use to “calculate” and “adjust” its speed? How does the photon know who is watching (thrower/catcher)? It’s getting even worse, since there is no way of comparing velocities at different spatial locations? Is that little bastard the almighty God??

  • Lawrence B. Crowell

    Photons don’t accelerate. It is that the null geodesics exist in arcs. In fact if you project the spatial surface into Fermat coordinates, you get a Poincare disk (3-ball) where null geodesics are great arcs on the disk. A look at an Escher print of tessilations on a disk, fish or devils and angels. gives an illustration of this.

    Looking at this according to null geodesics is preferrable to language about expanding spatial surfaces.

    Lawrence B. Crowell

  • Geraint

    E=-p.u is not *merely* an equation – it is *the* equation that you are trying to find a picture for – but the point is that the E is the observable, a coordinate independent quantity, but the other side, the p, the u and even the . are coordinate dependent. So, the picture you want to paint depends of the coordinates you choose. *But*, and again this is the point, there is no choice of coordinates that are “more correct” than another. Some might make calculations easier, or make a picture somewhat more pretty, but none are the “correct” choice.

    If I choose FRW, then there is no spatial component to u for comoving observers, and so we say “oooooh – they aren’t moving and so the redshift is due to “space expanding in between”.

    But if I transfer FRW into its conformal representation, which describes exactly the same geometry, then there is a spatial component to u, but the redshift is exactly the same, then we go “ooooooh – now it’s moving and so some of the redshift must be Doppler”

    When we perform a series of transformations into orthonormal frames at a series of points along the path, and the redshift is still exactly the same, and we go “ooooh look, now we have a series of Doppler shifts along the path”.

    Or I could play coordinate games between now and the end of (conformal*) time, and I could continually reinterpret the same redshift in a myriad of ways.
    But none of them is *the* correct description – every description is coordinate dependent.

    – Geraint

    * conformal time is bounded into our future

  • Jon Corthell

    Hi Geraint,

    Thanks for the reply, but if I am interpreting your response correctly, we are talking past each other. I am pretty familiar with the characteristics of different coordinate systems such as FLRW, conformally flat Minkowski, Milne, etc. I read your Coordinate Confusion paper as well as all the relevant papers by your team, Davis & Lineweaver, Whiting, Chodorowski, Abrahmson, etc.

    My comments and questions relate to Proper Distance and Proper Speed, not Comoving Distance and Speed. I understand that comoving galaxies are stationary in comoving coordinates, that’s why it’s so good at obscuring interesting things that are going on. It doesn’t make it wrong, just limits its usefulness. I know that there is more than one way to characterize redshift.

    I would appreciate if you could respond specifically to as many of my redshift questions as you feel comfortable with. I have some very specific concerns and I hope you can help me with them.

    My recollection is that the papers you and your team wrote did not directly address the question of whether cosmological redshift can be formulated in terms of infintesimal SR and/or gravitational time dilations (in appropriate coordinate systems). You ducked the question in your papers it seems to me. If you believe that time dilation is the answer, please let me know whether you’ve run calculation using those equations that yield cosmological redshift solutions that match the traditional (observed) results at both low and high z values. I.e., DOES IT ACTUALLY WORK? I have yet to see anyone run the results that way and generate the correct answer with observational data.

    Thanks, Jon

    p.s., what about my question about photon exchanges?

  • Speedy Gonzalez

    YES! FINALLY AN EXPLANATION IN PLAIN LANGUAGE!

    Universal Expansion
    The expansion of the universe causes distant galaxies to recede from us faster than the speed of light, if comoving distance and cosmological time are used to calculate the speeds of these galaxies. However, in general relativity, velocity is a local notion, so velocity calculated using comoving coordinates does not have any simple relation to velocity calculated locally. Rules that apply to relative velocities in special relativity, such as the rule that relative velocities cannot increase past the speed of light, do not apply to relative velocities in comoving coordinates, which are often described in terms of the “expansion of space” between galaxies. This expansion rate is thought to have been at its peak during the inflationary epoch thought to have occurred in a tiny fraction of the second after the Big Bang (models suggest the period would have been from around 10^-36 seconds after the Big Bang to around 10^-33 seconds), when the universe may have rapidly expanded by a factor of around 10^20 – 10^30.

    Astronomical Observations
    Apparent superluminal motion is observed in many radio galaxies, blazars, quasars and recently also in microquasars. The effect was predicted before it was observed by Martin Rees and can be explained as an optical illusion caused by the object partly moving in the direction of the observer, when the speed calculations assume it does not. The phenomenon does not contradict the theory of special relativity. Interestingly, corrected calculations show these objects have velocities close to the speed of light (relative to our reference frame). They are the first examples of large amounts of mass moving at close to the speed of light. Earth-bound laboratories have only been able to accelerate small numbers of elementary particles to such speeds.

    From Wikipedia

    This of course doesn’t deal with redshift, as this webpage do.

  • Speedy Gonzalez

    And here’s an animation showing the changing views of spacetime along the world line of a rapidly accelerating observer (i.e. not comoving).

  • Geraint

    > how did the source particle “anticipate” that the photon would eventually hit our orbiting satellite which we wouldn’t decided to launch until gigayears after the photon began its journey?

    Have a read of the Wheeler-Feyman absorber theory (or transaction theory).

    Speedy – that’s really no different to what we’ve been saying.

  • Speedy Gonzalez

    “that’s really no different to what we’ve been saying.”

    Geraint, thanks and of course you are absolutely right. Those last posts from me only prove what a complete nutcase I am in physics! :D

    I have to explain something though (to save my face ;) ). English in not my native language and I’m not a physicist, so if everyday talks runs pretty okay, I’m completely lost in space when pros start talking about “null geodesics” and “gauge condition” etc, and I have to run thru half the Internet before I get the picture. And then add “hieroglyphic” equations to that and you got the picture of a totally confused amateur very late at night! :D

    Lawrence B. Crowell is of course also absolutely right when saying; “People should maybe exercise the discipline to use that marvelous multi-media machine we have had from our evolutionary roots.”

    Law No. 1: There is only one way to learn – use your brain.

    Sorry guys, I’ve been rambling on too much about “it must be something wrong”, and I take it back.

  • Jon Corthell

    Hi Geraint,
    OK so I read about the Wheeler-Feynman absorber theory, and it’s about as wacky a theory as one could imagine. From a web article that describes it as the most like cause of mass having inertia:

    “This theory says that when you push on something, it creates a disturbance in the gravitational field that propagates outward into the future. Out there in the distant future the disturbance interacts with chiefly the distant matter in the universe. It wiggles. When it wiggles it sends a gravitational disturbance backward in time (a so-called “advanced” wave). The effect of all of these “advanced” disturbances propagating backward in time is to create the inertial reaction force you experience at the instant you start to push (and cancel the advanced wave that would otherwise be created by you pushing on the object).”

    This travel back and forward in time is right up there with string theory and colliding branes on the wacky scale. I understand that a lot of brilliant people contributed to these theories, and the math really does work. But there is no guarantee that a theory supported by valid math is itself physically valid. I like many people think we need to apply more common sense to evaluating these far out theories.

    Jon

  • Jon Corthell

    Hi Lawrence,

    >”These calculations of the comoving velocity for z =~ 1100 by Jon strike me as off the mark. Given the Hubble rule (FRW cosmology etc) that

    1 + z = exp(v/c)

    and for z = 1100 indicates that v/c = ln(1100) = 7, or an apparent velocity of 7c. Things are not moving nearly as fast as is being presumed here.”

    I believe you are looking at the instantaneous recession velocity of the EMITTER as measured in the OBSERVER’S (Earth’s) frame of reference. According to my spreadsheet and the Wright and Morgan online cosmic calculators, an emission source at z=1089 had a recession velocity of 56.6c then and 3.3c now, as measured in the observer’s frame of reference. Not sure why your equation calculates a different number.

    The figure I gave of 1048c is measuring something quite different: the average TRAVEL SPEED of a PHOTON during the SEGMENT of its trip between z=1023 and z=511, as measured in the EMITTER’S frame of reference.

    Jon

  • Jon Corthell

    I have an idea how cosmic gravity might first cause the redshifted photon to accelerate and then later to decelerate, thereby enabling it to pass each succeeding galaxy in the Hubble flow at exactly 1c.

    I submit that, rather than applying Gauss’ Law to a cosmic sphere centered on EITHER the observer or emitter, it should be applied to BOTH such cosmic spheres, at every point along its path, and then netted, to yield a combined “forward and backward” figure for gravitational influence at each point. This set of effects can then be integrated to calculate the geodesic across the entire path.

    Intuitively, early in the photon’s travel the gravity of the sphere centered on the observer will dominate, because the radius of that sphere is enormously larger, and during this historical epoch the cosmic mass/energy density is also relatively very high. So the initial acceleration toward the observer (which causes blueshift) is very high. Late in the photon’s travel the sphere centered on the emitter will now dominate, because the radius of that sphere is enormously larger. So the net effect of cosmic gravity will be to decelerate the photon. However, this deceleration will be milder than the early acceleration, even though the sphere’s radius is larger, because the cosmic density has decreased by much more proportionally than the propoprtion by which the late observer sphere’s radius exceeds the early emitter sphere’s radius.

    The math remains to be done, but I am encouraged by the logic. I believe that the cosmic gravity field MUST provide the sole explanation for the photon’s early acceleration and late deceleration. In the absence of accumulated SR time dilation (which seems to be ruled out by the FLRW metric), the photon can’t self-accelerate just because it is “required to” in order to pass every galaxy at exactly 1c.

    Jon

  • Lawrence B. Crowell

    Jon Corthell on Oct 19th, 2008 at 4:49 pm
    I have an idea how cosmic gravity might first cause the redshifted photon to accelerate and then later to decelerate, thereby enabling it to pass each succeeding galaxy in the Hubble flow at exactly 1c.

    ————————

    Photons don’t accelerate! Null geodesics might be curved and the photon red or blue shifted, but there is no acceleration of a photon.

    Lawrence B. Crowell

  • Lawrence B. Crowell

    Jon Corthell: According to my spreadsheet and the Wright and Morgan online cosmic calculators, an emission source at z=1089 had a recession velocity of 56.6c then and 3.3c now, as measured in the observer’s frame of reference.

    ——————

    Again something is amiss. SNI data tells us that the recessional velocities of galaxies in increasing, not decreasing.

    Lawrence B. Crowell

  • Geraint

    >This travel back and forward in time is right up there with string theory and colliding branes on the wacky scale. I understand that a lot of brilliant people contributed to these theories, and the math really does work. But there is no guarantee that a theory supported by valid math is itself physically valid. I like many people think we need to apply more common sense to evaluating these far out theories.

    Why do you think your “common sense” in anyway is a good predictor of the way the universe works?

  • Jon Corthell

    Hi Geraint,

    Well I can’t say the absorber theory is definitely wrong, but I think it is a fundamental principle of the scientific method that all possible approaches should be exhausted that rely on close-to-conventional physics before radically exotic “new” physics is accepted. Time travel is just inherently too radical, and is not used in any other mainstream physics theory. And the concept of time travel is known to have many theoretical impediments. For example, both the emitter and receiver will move substantial distances during the wave travel period. I don’t see how there’s anything in the theory to accomodate that spatial relocation angles between the past, present and future.

    In my humble opinion the closer a cosmology theory is to purely kinematic (with GR gravity of course) the more likely it is to be correct.

    Jon

  • Jon Corthell

    Hi Lawrence,

    > “Again something is amiss. SNI data tells us that the recessional velocities of galaxies in increasing, not decreasing.”

    Dark energy is causing recessional velocities to increase in late times (e.g., since about 7Gy), but it will be many Gy before the are as fast as they were shortly after the inflation era ended. Gravity caused recession speeds to slow dramatically during the first 7 Gy before they turned around and started increasing again.

    > “Photons don’t accelerate! Null geodesics might be curved and the photon red or blue shifted, but there is no acceleration of a photon.”

    I agree that photons don’t accelerate LOCALLY. But at cosmological distances, their travel speed relative to both the observer and emitter MUST change. Otherwise, how could distant galaxies have been receding at superluminal velocities at the time of emission, yet the photons approach us at exactly c today?

    GR terminology such as “spacetime curvature” is all well and good, but we should not slavishly constrain ourselves to use terminology which obscures the fact that something real and tangible is occuring out there. Terminology is here to help us communicate, not to get in the way. When I talk about photons accelerating, I am simply referring to the distance they relocate over some elapsed period of time, as measured from a particular frame of reference. Let’s focus on the substance rather than the terminology.

    Jon

  • Geraint

    > Terminology is here to help us communicate, not to get in the way. When I talk about photons accelerating, I am simply referring to the distance they relocate over some elapsed period of time, as measured from a particular frame of reference. Let’s focus on the substance rather than the terminology.

    Sigh – this is a coordinate dependent quantity and so there is no single “correct” answer.

  • Lawrence B. Crowell

    General relativity removes the whole notion of force and acceleration from gravitation. Photons exist on curved geodesics in cosmology which loop back (so to speak) so distant objects comoving at apparent v > c can be observed. But this really does not involve accelerations as such.

    Lawrence B. Crowell

  • Jon Corthell

    Hi Geraint,

    > “Sigh – this is a coordinate dependent quantity and so there is no single “correct” answer.”

    So much sighing and groaning… I feel like the foolish Kung Fu Grasshopper at the knee of the great master.

    I have agreed that there are an infinite number of coordinate systems which yield an infinite number of different perspectives. BUT, I think there is at least one coordinate system in which the relationships I proposed might be correct.

    What’s important here is not the *absolute* values of distance, speed and acceleration, it’s the relationship of relative values as a function of time and density as perceived in the distinct frames of the emitter and observer. Surely one or both of those frames has some special logical relevance to the issue of observed redshift.

    Geraint, your papers refer frequently to superluminal recession velocities, which you say are inevitable and open ended at large distances in both the FLRW and conformally Minkowski metrics. You also apply Gauss’ Law in your radar ranging paper in the same manner I do, and you specifically apply it to round-trip velocities in your two selected coordinate systems. You also specifically state that redshift is a result of a discrete transformation at the observer’s frame rather than an accumulation of infintesimal redshifts en route. The terminology I’m using and the points I’m trying to make are similar to those in your papers, although the particular redshift mechanism is original.

    Why not address my specific questions and ideas rather than reciting broad mantras: “There are no absolutes my son … everything is relative… ”

    Jon

  • Speedy Gonzalez

    Jon Corthell,

    “I agree that photons don’t accelerate LOCALLY. But at cosmological distances, their travel speed relative to both the observer and emitter MUST change. Otherwise, how could distant galaxies have been receding at superluminal velocities at the time of emission, yet the photons approach us at exactly c today?”

    You grasp the math better than me, but I think you have got trapped in the same “logical confusion” as me. It’s probably “over bold” for an amateur like to tell you how to think, but after debating this topic over the last weeks, the logic finally make sense:

    * We cannot visually see anything that has moved toward us at superluminal speed, including redshift or photons.

    * We can calculate, using comoving distance and cosmological time, that the objects that emitted light towards us 700 million years after the big bang, *NOW* should be accelerating at superluminal speeds, at physical distances further than 13,7 light years. BUT please observe – we cannot physically see these objects *NOW*.

    Take a good look at this picture of the embedded Lambda-CDM geometry

    The brown line on the diagram is the worldline of the Earth (or, at earlier times, of the matter which condensed to form the Earth). The yellow line is the worldline of the most distant known quasar. The red line is the path of a light beam emitted by the quasar about 13 billion years ago and reaching the Earth in the present day. The orange line shows the present-day distance between the quasar and the Earth, about 28 billion light years.

    Here is very basic and helping information from good old Wikipedia – Understanding the expansion of space

    Speedy

  • Speedy Gonzalez

    Correction: “…further than 13,7 billion light years.”

  • Speedy Gonzalez

    NOTE: THIS MATERIAL COULD BE COPYRIGHTED!
    (I honestly don’t know. Since this is from The Caltech Years, Sean can probably decide if it’s ok?)

    Anybody want to listen to Richard Feynman for 9 hours explaining the laws of nature? Guessed so!

    I’ve found very rare Richard Feynman’s lectures on Physics for all physicists and amateurs!

    The following are a collection of rare lectures by the man himself (MP3 Sound):
    V1 Ch07 Theory Of Gravitation – 51:42 (20.4 MB)
    V1 Ch08 Motion – 53:46 (23.3 MB)
    V1 Ch09 Newton’s Laws of Dynamics – 54:42 (23.9 MB)
    V1 Ch10 Conservation of Momentum – 53:44 (23.4 MB)
    V1 Ch11 Vectors – 52:41 (23.2 MB)
    V1 Ch12 Characteristics of Force – 59:36 (26.1 MB)
    V1 Ch13 Work and Potential Energy 1 – 55:45 (24.4 MB)
    V1 Ch14 Work and Potential Energy 2 – 52:15 (22.8 MB)
    V1 Ch15 Special Theory of Relativity – 50:00 ( (25.6 MB)
    V1 Ch16 Relativistic Energy And Momentum – 54:57 (24.7 MB)

    You can download all from RapidShare for free. The lectures are stored in RAR files, and can easily be unpacked using the free tool 7-Zip (for Windows and Linux):

    RapidShare – Feynman Lectures 7-9.rar (66.2 MB)
    RapidShare – Feynman Lectures 10-12.rar (71.3 MB)
    RapidShare – Feynman Lectures 13-15.rar (71.6 MB)
    RapidShare – Feynman Lectures 16.rar (24.3 MB)

    Each of the first three RAR files has three lectures in them, and the last one has lecture 16 alone.

    Enjoy!

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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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