Dark Matter: Still Dark.

By Julianne Dalcanton | January 16, 2008 5:01 pm

ESA has just done the first big press release for the Integral gamma-ray telescope, and the big woosh you’re hearing is the sound of numerous dark matter models flushing down the toilet.

For several years the community has been carefully eyeing an extended, apparently spherical excess of gamma-rays from the center of the galaxy. Theorists have been busy generating crafty models where the excess in gamma-rays comes from the direct annhilation of dark matter particles, or from a decay chain from the dark matter particles themselves. These models were attractive because the shape and extent of the gamma-ray detection was wrong for just about any Galactic source except for the dark matter halo itself. The dark matter halo would produce just the right sort of signal, since it’s presumably highly cuspy in the center, leading to high rates of the sorts of interactions which might lead to detectable photons, but only near the center of the galaxy. The halo is also expected to be mostly spherical, as was consistent with the previous observations.

integral detection

Well, with the higher resolution of the new Integral telescope, the distribution of gamma-rays looks distinctly disklike and lopsided, which smells much more like a boring old astronomical explanation (where “boring” means something to do with neutron stars and black holes, but still — no one’s expecting the Nobel Prize for this one, yet).

CATEGORIZED UNDER: Science
  • http://www.sunclipse.org Blake Stacey

    Black holes are now boring? How I love the twenty-first century!

  • http://countiblis.blogspot.com Count Iblis
  • Shantanu

    Anyone know if they have a paper on this somewhere?

  • onymous

    Yay! I never liked those weird dark matter models.

  • Tony

    Any word on the WMAP Haze?

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

    Can someone explain whether “shadow matter” (sometimes put as, theoretical classes of particles, their existence intimated by supersymmetry theory, that participate in few if any of the four known fundamental forces – but most likely just gravity) is still to be taken seriously now, especially as a candidate for at least some dark matter? SM in most hypotheses would interpenetrate ordinary matter, and only be detected by gravitational attraction – sounds about right overall.

  • http://blogs.discovermagazine.com/cosmicvariance/julianne Julianne

    Tony — I haven’t run into Doug Finkbeiner recently, so I don’t have any recent updates. If someone reading this runs into him, send him over!

    I also haven’t seen limits on what fraction of the Integral results could still be in an axisymetric component, so there may still be room for some fraction of the gamma-ray signal to be related to dark matter. We’ll know a lot more when they look at nearby dwarf galaxies, which should have even denser cores, and thus higher interaction rates. If there’s no signal there, then MeV dark matter and its ilk become a lot less compelling.

  • http://xspector.blogspot.com/ Keith

    Minor nitpick: Integral is not new – it was launched in late 2002. It just takes a long time to collect enough gamma-rays to perform this sort of analysis. The press release result is based on four years of observations.

  • http://countiblis.blogspot.com Count Iblis
  • John Merryman

    Hmmm… Dark matter is still a mystery and the most extreme gravity wells radiate the most extreme energies. Doesn’t shoot down a convective cycle of collapsing mass and expanding energy as opposing curvatures of space…

  • Lawrence B. Crowell

    Dark matter clearly exists, but the problem might be the word “matter.” Who ever said this stuff had to be made of particles? It may well be the case that we will never find so much as a WIMP of anything out there. This dark matter appears to be just clouds that only have gravity. There is no decay process coming from it, there are no X-rays or gamma rays coming out of this stuff if it should decay. It looks about as dead as anything can be, except a black hole. So what might this stuff be?

    Think of the universe at its most early moments or at time = 0^+ as nothing more than a set of quantum vacuum states. There is no real space or time or anything we can put our “finger on,” but just this unstable set of vacua. These vacua are largely unitarily inequivalent, which means they are not related to each other by the nice compact operators of quantum mechanics, but instead by hyperbolic groups that are not compact. Things get sort of messy here, but the frame of an accelerated observer is not unitarily equivalent to an inertial observer. This results in Unruh radiation, and a similar physics is involved with black hole radiation. Now this set of vacua are unstable because they are conformal and the dilaton field of the conformal group of symmetries will evolve in a “higgsian” manner to settle the universe into a more stable vacuum (vacua) configuration.

    BOOM!!! the big bang is off and running.

    Now let us think of spacetime, and for that matter 10-11 dimensional superspace, according to some choice of tesselation into Planck units of volume. This is not too different from what the Loop Quantum Gravity people do. In various dimensions there is a minimal lattice configuration, such as in four dimensions this is the 24-cell. This is the Weyl-Coxeter representation for the F_4 group, so imagine the quantum gravity as a solid state physics system with analogues to phonons which are and so(3,1) subgroup, a so(4) subgroup we will just call “weak interactions,” and short roots (4 x bar-4) which we might just think of as being analogous to electrons. So let us just reduce this mess to phonons and electrons. Think of this lattice as similar to atoms in a crystaline lattice, in particular an exotic lattice similar to the cuprates explored in Hi-TC’s. The electrons can exist in a phase called a Landua fluid, but a phase transition can also occur where the electron becomes “heavy.” This phase transition in solid state physics carries over to a phase transition in the vacuum state for gravity.

    The following reference discusses the solid state aspect of this

    Anisotropic Violation of the Wiedemann-Franz Law at a Quantum Critical Point

    M. A. Tanatar, J. Paglione, C. Petrovic, L. Taillefer

    Science 1 June 2007:
    Vol. 316. no. 5829, pp. 1320 – 1322

    A phase transition point for fermi heavy electron fluid, anti-ferromagnetic and magnetic phase meet at a quantum critical point and zero temperature. This quantum critical point is in cosmology the w = -1 phase condition. The three states around it for w -1 is dark energy and for E >~ 0 is a strange state similar to quintessence. Here the energy refers to a ZPE-like term. This latter phase may well be what we call dark energy. To the extent that it is a “particle,” there is a quasi-particle state associated with this phase transition.

    So back to the big bang. There are lots of vacua which are “destroyed” by the inflaton, and at the end of inflation only two are present, where phantom energy (big rip cosmology) phase was turned off after inflation. So two remain, and most of it is what we call dark energy and the rest is dark matter. So if this is right there are no particles in the standard sense of the meaning associated with dark matter.

    As the universe expands the percentage of ordinary matter will be reduced as well as dark matter. As these approach zero percent and the universe becomes 100% dark energy its configuration approaches that of a deSitter cosmology. The quantum vacuum of the universe goes from great complexity to great simplicity, as the entropy of the universe increases. Due to Hawking-Gibbon radiation the cosmological horizon recedes to infinity and the attractor point for the universe is a Minkowski spacetime — the same conformal infinity for the Anti-deSitter spacetime in the su(4) ~ so(4, 2) conformal group.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    You know I like great simplicity to begin with and you don’t really like ZPE.

    All we really know is that the outer edges of galaxies spin faster than they ought. Is this due to internal attraction? Or could it be external pressure? If space expands, but the universe doesn’t, due to it being infinite, there is the pressure.

    I might be wrong, but this particular data points toward my view, in that gravity doesn’t collapse mass infinitely, but cycles back out as radiation, not away from it.

  • Jason Dick

    All we really know is that the outer edges of galaxies spin faster than they ought. Is this due to internal attraction?

    It’s due to dark matter. We’ve been pretty darned confident of this since the Bullet Cluster observation.

    The pressure you’re talking about is nonexistent.

  • Lawrence B. Crowell

    Galaxies rotate almost as a solid disk, which is not a Kepler law type of rotation one might expect. Galaxies have halos, which are composed of this mysterious dark matter. Their gravity field is what permits this strange rotation. Further galaxies are not solitary objects, they exist in clusters which have tendrils of dark matter and dwarf galaxies connecting them, and these clusters are connected by tendrils of dark matter and dwarf galaxies in a vast web that connected them together in a vast array.

    It would be like opening an attic door after a decade of never entering and the room is laced with billions of cobwebs spun every which way. A shaft of light enters the room and glints off each dust particle on each web fiber, those are galaxies or clusters of galaxies. The tension on each web fiber is akin to the dark matter gravity field. But then you realize the room is expanding in size and the web is being stretched further out, assuming the web is sufficiently elastic so as not to break. The walls of the room are pushing out by absorbing energy, or doing “negative work” so that the net vacuum energy of the universe remain constant —- dark energy. Now remove the picture of walls and replace them with a huge bubble that extends out into the neighborhood, that is the CMB.

    If I am right another picture of dark matter is an ice cube. Take a good look at one and you see these needle shaped bubbles in there. Those are where water is in a gaseous phase. The pressure is sufficient in the bubble to keep the H_2O in that phase. Those are models of a dark matter region, a region where the vacuum state is in a different phase from the phase of the vacuum in most of the universe. There are other exceptional vacuum phases as well, such as condensates of quark-gluon plasmas or strings bundles drawn into huge tendrils or cosmic strings during the inflationary big bang. There is some evidence for the existence of these as seen in CMB textures due to the Einstein lensing of the CMB around these.

    Then back to the cobwebbed filled attic room. We are on one of those glinting dust motes, the Milky Way, or more precisely on one tiny particle in that glinting dust mote around one little star — Jonothan Swift’s fleas with fleas that bite their back.

    Lawrence B. Crowell

  • John Merryman

    Jason,

    I’ll give you that one, in that the lensing effect seems stronger for the mass state, then the gas state. It still leaves my point that black hole gravity wells emit lots of radiation.
    It is interesting how these binary systems are clustered around the core black hole. As if the gravitational vortex has centrifugal properties pulling it apart, or that it is otherwise spawning smaller vortexes, like a hurricane will create tornados. Gravity tends toward this individuation, in that a galaxy is composed of numerous gravitational objects and is not just one swirl of gases.

    Lawrence,

    Galaxies rotate almost as a solid disk, which is not a Kepler law type of rotation one might expect. Galaxies have halos, which are composed of this mysterious dark matter. Their gravity field is what permits this strange rotation. Further galaxies are not solitary objects, they exist in clusters which have tendrils of dark matter and dwarf galaxies connecting them, and these clusters are connected by tendrils of dark matter and dwarf galaxies in a vast web that connected them together in a vast array.

    I realize you are a company man on the subject, but you might consider some of what the plasma cosmologists have to say. I’m not saying they have anything to teach you, but it’s always good strategy to know what the other side is thinking, even if you think you are winning.

    http://www.thunderbolts.info/tpod/2006/arch06/060904bulletcluster.htm

    The cluster has a redshift of z=0.3, exactly the value of the Karlsson quantization peak that is typical of BL Lac objects. Because it therefore does not need to be normalized to the base redshift of another galactic group, it is likely a member of our Local Group. This is confirmed by its location in the ejection cone of M31 (Andromeda Galaxy), which includes M33, 3C120, many QSOs, and hydrogen plasma cells strung between M31 and the Milky Way. Because of its proximity to the Milky Way and the Large Magellanic Cloud, its precursor QSO was probably ejected from one or the other. Statistically, as astronomer Halton Arp has pointed out again and again, galaxy clusters occur preferentially near large, low-redshift galaxies.

  • Lawrence B. Crowell

    Jason Dick on Jan 18th, 2008 at 11:45 am

    It’s due to dark matter. We’ve been pretty darned confident of this since the Bullet Cluster observation.

    ————

    Yes, this pretty much clinched the case for dark matter. The galaxies collided with the luminous stuff being slowed or nearly stopped by the friction of the collision and the dark matter stuff from both galaxies kept on going. The dark matter was detected by its Einstein lensing of light in the more distant universe.

    Lawrence B. Crowell

  • Lawrence B. Crowell

    John Merryman on Jan 18th, 2008 at 1:20 pm
    Jason,

    I’ll give you that one, in that the lensing effect seems stronger for the mass state, then the gas state. It still leaves my point that black hole gravity wells emit lots of radiation.

    —————–

    Sorry, but you are wrong. I have been over this with you a number of times. A black hole by elementary definition is a region of gravity that is strong enough to prevent the escape of light. Black holes do not emit radiation. It is the stuff being violently pulled into a black hole that can emit radiation. There is also no counter gravity pressure due to radiation either, as you keep proposing.

    As for galaxy structure, that is not my domain of work, though I follow this stuff some. I read some astronomy articles and pull out my 8″ scope now and then and look around out there. The description, almost an allegory, of the webbed universe is pretty much how things look out to z = 2 or beyond. The Sloan Digital Sky Survey has revealed that the matter dominated universe dating back about 10 billion years has this structure. As a result it is really a dark matter dominated phase of the universe, or at least what appears to dominate the clumping of structures which emerged from fluctuations in the earliest moments of the universe. Dark energy really dominates the show, and will over the next few 10′s of billions of years pull this web apart into a thin almost nothingness. Woe to any astronomers who evolve on some planet 25 billion years from now. Things will look dark and boring out there beyond their fading galaxy.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    I know what black holes are defined as. Does the reality match the description? Radiation still climbs out of gravity wells. Nothing else does, unless it has a lot of energy behind it.

    I’m just sold on BBT. Or on time as the basis of motion, rather then a measure of it. So I find a cosmology that describes the universe as a narrative unit that goes from start to finish as potentially subject to unexamined assumptions. Because the structure of time goes from future potential to past circumstance, while the actuality goes from past events to future ones, much like film on a projector goes from being in the future to being in the past, as the projector light flashes from past scenes to future ones. It’s reasonable for me to see what is a common pattern in the universe, with energy going out to new form, as form contracts in. Maybe I’m wrong and there really is a God’s eye view of all time and we just happen to be little lines of events, but it is this time as dimension I find to be the fairy tale. Along with the narrative universe.

    Sorry to be so hard-headed, because I really like you for having tolerated me to the extent you have. Most people who don’t see the basic logic in this quickly lose patience with it, but it runs pretty deep in me. I’m more of a taoist, then a monist.

  • John Merryman

    Lawrence,

    A large part of my sense of confidence on this topic, even though I’m obviously self educated and therefore a rube, is that your worldview fits half the equation. Essentially you have an extended watchmakers paradigm of a mechanistic universe that if you examine all the pieces on a small enough scale, eventually you will figure out how they all fit together. The problem is that this is biased toward the (ideal)form side of the equation, so it amounts to a modern Platoism, where the equations are the Bible, TOE is God and Newton, Einstein, etc. are the prophets. Time becomes one dimension of units, stretching from the start of the grand unit of the universe to its conclusion, just like a watch, once wound, runs down. As units, time is only really the face of the clock and there the hands are is incidental, if they even matter at all.
    In terms of space, as expanding singularity, it is a set. One unit defined by its contents, not a state of equilibrium. The absolute is that dimensionless point of the singularity, not a neutral state. Monotheism makes the same assumption. It reductionistically assumes that one is the ideal form of oneness. That the set defines the state. Obviously physics is based on the study of the physical, so it’s understandable it should focus on what can be held and examined, but sometime you just have to step back and unfocus. It’s the raw expanding energy that goes toward the future and stucture that falls away into the past. That’s why you see the universe as entropic and finite, because all you can hold is falling apart and the energy dispersed just seems to fade away, but it does come back together in the most unfocused, unexamined ways and reality keeps going on. The old dies and falls away and the new grows up to take its place and repeats the cycle.
    Meanwhile physicists search for ever smaller units of measure, like they are diamonds. Not recognizing any value in all they have to throw away to find them.

  • Lawrence B. Crowell

    A classical black hole (no quantum mechanics etc) is a spherical region of gravity or spacetime curvature where for a radius smaller than r = 2GM/c^2 light rays are focused into the hole. The time and radial directions flip their Lorentzian signatures and the inward radial direction becomes the future time direction. Nothing gets out of a black hole, “Abandon all hope all ye who enter these gates,” to use Dante.

    BTW, this spherical assumption is for a nonrotating black hole, the Schwarzschild solution. For a rotating black hole there are frame dragging issues and complexities, but for this discussion the same rule generally still applies.

    The radiation we observe to detect black holes is due to all the violent hydrodynamics and heating of stuff that falls into a black hole before it passes this event horizon at r = 2GM/c^2. We don’t detect anything coming from the interior. A black hole sitting isolated without stuff falling into it is utterly invisible. We might if we get lucky measure a microlensing to light passing by it from a more distant source, similar to the bending of light around the sun. But nothing, including radiation, will be emitted by a black hole — period!

    There is Hawking radiation and quantum effects, but these are only apparent for a small black hole, such as one with the mass of an asteroid and the radius of a micron or smaller. This is a quantum tunnelling of quanta in the interior of the hole to the outside world. Yet a large astrophysical black hole, such as thundering ones in galactic centers or a 10 solar mass BH accreting mass from a companion star, will not intrinsically emit radiation. What radiation we detect is from the violence of stuff being gravitationally pulled in.

    Lawrence B. Crowell

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

    Lawrence (or anyone), Greg E. isn’t around for awhile and I want to get a second opinion about some non-linearities in gravitational attraction. It might apply to black holes/DM concentrations etc, but our original example was a very extended planar mass PM providing a very uniform (but not Rindler-style) g field. GE said that a mass zipping parallel to the PM would have higher acceleration (defined in rest observer’s simple fashion, z dot dot with z perp. to the PM.) I thought that was weird enough in light of the equivalence principle saying, that the field should be like in a giant accelerating elevator – in which case the side-moving mass must hit the floor at the same time as one dropped straight down.

    But to make it more confusing, GE then seemed at least to contradict himself and say, that this differential acceleration really didn’t violate the EP after all (and even after said that even in a small region, different accelerations could not be transformed away in tandem – the falling observer would know he was not in true inertial space.) GE provided what seemed competent but rather sophistic reasoning to support his counterintuitive claims. What’s you knowledge/opinion on this?

  • John Merryman

    Lawrence,

    What actually falls in is the real question. Yes, black holes are massively powerful gravitational wells, but they also generate enormous energy;

    http://www.space.com/news/new_black_hole_000321.html

    “Many more quasars (and their supermassive black hole power sources) may be hidden in otherwise innocuous galaxies,” Smail said. “When astronomers come to do an audit of the total energy output in the universe, they have to take all these hidden quasars into their calculation — or theyll get a very wrong answer.”

    “This can change our perspective on what the main sources of power in the universe are,” explained Fabian. “Quasars may go from being a rarity of little overall consequence to being more common and of wider import.”

    So could they effectively be the equivalent of the eye of a hurricane, in that the real activity and energy is what goes on around the center? If not, what is that center? A well into infinity, or some physical object? What are the percentages of the energy of what is falling in vs. the energy of what is radiating out?

    http://www.space.com/news/x-ray_background_000113.html

    The Chandra telescope has given these scientists a glimpse at the source of the diffuse X-ray glow that seems to permeate the entire universe, said Richard Mushotzky, a researcher at NASAs Goddard Space Flight Center.
    —–
    Most likely, the sources in all these cases are super-massive black holes, either in the centers of galaxies or galaxy clusters, or hidden from view by surrounding clouds of dust, Barger said.

  • John Merryman

    Michael Strauss of Princeton University explains that powerful black holes are more common in the last eight billion years of cosmic history than had previously been thought. “Moreover, because the light from these hidden quasars previously had been unaccounted for, black holes turn out to be more efficient in converting the energy of in-falling matter into light than we had thought.”

    This result also has implications for theoretical models of quasars. “The relative numbers of hidden versus normal quasars tell us something about how dust and gas typically are distributed around these objects,” explains Julian Krolik, a collaborator from Johns Hopkins University. “If the dust covers a large fraction of the area around a black hole, this object would more likely appear as a hidden quasar. So the large number of hidden quasars discovered by the SDSS team implies that most of the light emitted by quasars is actually obscured.”

    http://www.physorg.com/news119115673.html

  • http://lablemminglounge.blogspot.com/ Lab Lemming

    “If I am right another picture of dark matter is an ice cube. Take a good look at one and you see these needle shaped bubbles in there. Those are where water is in a gaseous phase.”

    Actually, those bubbles are where dissolved gasses in the water exolved as the water crystallized, due to a lower solubility in ice than in liquid water.

  • spaceman

    More negative results wrt to our searches for the hypothesized dark matter. It seems like every observation that attempts to detect dark matter fails to do so. How much longer, given that this is the case, will cosmologists cling to the particle DM idea?

  • Hal S

    I have played around with the idea of how virtual particles behave in a gravitational field. There seems to be a slight asymmetry in how negative energy particles and positive energy particles would behave.

    The asymmetry arises due to the fact that the acceleration due to gravity changes with respect to distance from the center of gravity. When virtual particles pop into existance, they should gain our lose some tiny amount of kinetic energy depending on their direction of travel.

    I’m am still struggling with this, but it would seem that some of the kinetic energy gained by positive energy virtual particles will not be completely offset by changes in kinetic energy of the negative energy particles.

    This creates conditions for a gradient to exist in the vacuum energy surrounding any massive object. Higher vacuum energy would exist closer to the center of gravity, and relatively lower vacuum energy would exist further away.

    In this conception; dark matter and dark energy are really related to the gradient of the vacuum energy and are just the opposite effects of the same process; I just haven’t reached a good way to calculate whether this effect is adequate to explain the additional rotational velocities of galaxies.

    Any comments or insights would be greatly appreciated.

  • Lawrence B. Crowell

    I stand corrected with the ice cube, though there is H_2O vapor in these bubbles. I knew at the time my description was incomplete, but I was trying to drive home the point that these bubbles are regions with a different phase.

    As for black holes generating energy. They don’t generate anything except entropy. If a black hole absorbs some mass the area of its event horizon increases which is directly proportional to it entropy increase.

    Gravity does not “generate energy,” but is a field with a potential energy. If you walk up 10 flights of stairs and drop a mass it will impact the ground with a velocity V and have a kinetic energy T = 1/2mV^2. Now think!, did this kinetic energy come from mining gravity or that gravity was some “public utility” that you got energy from? Or might it be better to say that this energy was stored energy in the gravity potential which came from your muscles that worked to get you and the mass up 10 flights of stairs? The second is of course more on the mark.

    An accretion disk around a black hole is dropping matter into the black hole. An orbit of a isolated small mass will generally have a constant total energy, such as the planets around the sun which are nearly eternal. Yet the disk of hot gas has friction and the rest which converts some of the orbital energy of each unit or atom of the gas into heat — lost energy. A loss of total energy means you go more negative in energy and down further into the potential well. In doing so the process is similar to dropping a mass from a great height on Earth and watching the violent collision at the bottom as that kinetic energy is dissapated into other forms.

    As for: Neil B. on Jan 19th, 2008 at 1:09 pm

    Lawrence (or anyone), Greg E. isn’t around for awhile and I want to get a second opinion about some non-linearities in gravitational attraction. It might apply to black holes/DM concentrations etc, but our original example was a very extended planar mass PM providing a very uniform (but not Rindler-style) g field.

    —————-

    Let me read your question a bit more closely to figure out what you are asking exactly.

    Lawrence B. Crowell

  • Lawrence B. Crowell

    I think the argument for why a mass moving with a velocity v would fall faster involves special relativity. If we consider the planar “infinite” mass as Newtonian, then if I place a Gaussian surface (a pillbox that encloses the planar mass with the circular cap of the cylinder parallel to the plane) the Newtonian lines of force will be normal to the pillbox cap and will give a constant force proportional to the mass per unit area of the plane. Let this acceleration be g, and any mass m experiences a force F = mg. Now let us consider a mass m moving parallel to the plane with velocity v.

    If this velocity is fast enough the momentum of the mass is a four vector

    P = m(Yv, Yc) = mcY(v/c, 1)

    (I use Y since it looks similar to gamma)

    where Y is the Lorentz gamma factor Y = 1/sqrt{1 – (v/c)^2}. Now before I push on with this the “v” part is a three momentum vector and the “c” part is the energy -:- by c part of the four momentum. The square of this vector is

    P*P^T = (mc)^2Y^2(v/c, 1)*(-v/c, 1)

    = (mc)^2Y^2(1 – (v/c)^2) = (mc)^2.

    The change in the sign on the v/c under the transpose “T” is due to the signature of spacetime. The square of the four momentum is (mc)^2 which is a constant or invariant.

    Now to do something that is a bit of an adulteration in the first equation we can say that the mass of the moving particle has been changed by Ym. Mind you, the mass of the body is an actual invariant, which is why I went through the stuff above. Yet an observer at rest with respect to this motion could interpret the mass of the body as having been shifted by the gamma factor Y = Y(v) >= 1. So the force on the moving body is F = Ymg. To obtain the force per mass we divide through by m to get a Lorentz transformed acceleration g’ = Yg >= g.

    In an approximate sense we can see this with the precession of Mercury. As it approaches the sun at its orbital apherion its speed increases and there is a slight Lorentz shifting of its mass. The gravity of the sun then has a higher gravity acceleration on the planet, which increases its angular velocity and shifts its perihelion.

    Lawrence B. Crowell

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

    Lawrence, thanks but some clarification about this problem. We must remember to invoke tangential (to velocity) force and acceleration transformation laws to get a handle on this. First we talk in terms of values defined in the rest frame RF. If we assume that a mass in motion has higher effective mass than rest value m_0, then the force on it in RF is gamma*m_0*g_0. But that doesn’t translate into higher acceleration in RF because of the transformation of force and acceleration. In the moving frame the lateral force is even higher, gamma^2*m_0*g_0. That corresponds to a higher acceleration in that frame, which makes sense since the RF g should transform to that higher value. But in turn, the value we should see in the RF should be transformed back down to the value of g (same as for simply dropped masses) by the acceleration transform, that (a_perp) = gamma^2 (a_proper_perp). But GE kept sophisting around that IMHO, and left it a muddle for me. Once thing he said of interest, is that the field around a planar mass is not like that of Rindler coordinates, and in the latter an object dropped straight “down” and one shot off to the side must of course hit the floor at the same time, since the accelerating “elevator” must intercept them accordingly. This whole thing needs deeper reflection.

    Hal S, I may get this wrong but I don’t think physics distinguishes between negative and positive energy particles as such. Non-virtual particles always have positive energy, and virtual ones are in a borrowed state best left for others to clarify. BTW, negative energy mass is absurd since how could it be converted into radiant “negative energy” – the Maxwell equations don’t have for negative-energy radiations of any sort.

  • Lawrence B. Crowell

    I will get to positive and negative masses later today. I am a bit tied up. This is an intersting story. The Dirac equation says a lot about this.

    Lawrence B. Crowell

  • Lawrence B. Crowell

    Neil B. on Jan 20th, 2008 at 3:58 pm
    Lawrence, thanks but some clarification about this problem. We must remember to invoke tangential (to velocity) force and acceleration transformation laws to get a handle on this. First we talk in terms of values defined in the rest frame RF. If we assume that a mass in motion has higher effective mass than rest value m_0, then the force on it in RF is gamma*m_0*g_0. But that doesn’t translate into higher acceleration in RF because of the transformation of force and acceleration. In the moving frame the lateral force is even higher, gamma^2*m_0*g_0.

    —————

    I have to make this quick. From the perspective of the particle, on its frame the planar mass has been Lorentz contracted, which will increase the gravity force just as with the case of watching the particle on the frame of the planar mass. This gravity force due to Lorentx contraction effectively increases the mass per unit area of the graviting mass of the planar mass as seen in the particle frame.

    Lawrence B. Crowell

  • Hal S

    Neil B. #29

    I think I need to be more careful when I say “pop into existance”, I don’t want to make the mistake of saying there are “real” negative energy particles. My idea along this lines right now is that a if a virtual particle borrows energy, from one section of space, and then gains energy along the way, wouldn’t it deposit more energy into a different section of space when it gets re-absorbed?

    Acceleration in a gravitational field is inversely proportional to the square of distance; and it changes inversely to the cube of distance; If one assumes a virtual particle can have initial momentum in any direction and with no preferred direction; the momentum and energy lost by particles decelerating against the gravitational field will be less than the momentum and energy gained by particles accelerating with the gravitational field.

    In this way one could conceptualize a gradient being produced in the vacuum energy.

  • Hal S

    Once again…for the record…I do not want to imply there is such a thing as a “real” negative energy particle.

    I am just thinking hypothetically

  • Lawrence B. Crowell

    The issue of negative energy is curious. Nature does not operate symmetrically with respect to positive and negative energy. I am going to connect this to the Dirac equation and the “sea.” In spinor form the wave-field is psi = (psi_A, psi_{A’}). These two fields are coupled to each other according to the two equations

    nabla^A_{A’} psi_A = 2^{-1/2}m psi_{A’}

    nabla^{A’}_A psi_{A’} = 2^{-1/2}m psi_A.

    This can be thought of as two particles that “zig,” psi_A, and “zag,” psi_{A’}. The mass is the coupling constant between these two particles. The mass which couples the two equations is due to the Higgs field with the Yukawa Lagrangian L = bar-psi H psi which in spinor components is

    L = psi_A H psi^A + psi_{A’}H psi^{A’},

    where the m psi_A and m psi_{A’} are found with the Euler Lagrange equations so that m ~ H.

    The negative energy states are removed by “filling them in,” or by not permitting any unoccupied states. If energy is applied to the “sea,” this positive energy creates a hole in the sea that is the anti-particle. So nature does not particularly permit things with negative mass-energy. I will state more on this later in the context of gravitation.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    http://en.wikipedia.org/wiki/Black_hole

    Hitting the singularity
    As an infalling object approaches the singularity, tidal forces acting on it approach infinity. All components of the object, including atoms and subatomic particles, are torn away from each other before striking the singularity. At the singularity itself, effects are unknown; a theory of quantum gravity is needed to accurately describe events near it. Regardless, as soon as an object passes within the hole’s event horizon, it is lost to the outside universe. An observer far from the hole simply sees the hole’s mass, charge, and angular momentum change slightly, to reflect the addition of the infalling object’s matter. After the event horizon all is unknown. Anything that passes this point cannot be retrieved to study.

    So we have vortexes of collapsing space and the space between these wells expands, but there is no connection? Oh.

    I suppose it’s like Scotland and the highlanders and the lowlanders just don’t mix.

  • John Merryman

    Damn. I waited an hour for that to post, before reposting it. MODERATOR!!!

  • John Merryman

    Lawrence,

    My basic point still holds;

    http://en.wikipedia.org/wiki/Black_hole

    Event horizon
    This is the boundary of the region from which not even light can escape, but at the same time, light does not get sucked into the black hole. Stephen Hawking, in his book A Brief History of Time, describes the event horizon as “the point of which light is just barely able to escape (I like to think of it as being chased by the police but just barely managing to stay one step away!).” Another way to think of this is that the light is running on a spacetime “treadmill;” the light is moving away from the black hole at the rate of c, but the spacetime is being sucked into the black hole at the same rate, so the two cancel each other out, much like a treadmill.

    Whether it’s light escaping from the accretion disk, or “spacetime” and the energy/matter manifesting it, falling into a blackhole and re-emerging through some other dimension as dark energy, ZPE, whatever, or even if these are two separate phenomena and we are exchanging energy and space with other universes, IF Omega is anywhere close to one, the space expanding between galaxies is falling into them, so that the entire universe is not expanding, or is only to the difference between gravity and expansion.

  • Lawrence B. Crowell

    Again I must say that I think that you do not have a clear idea of things.

    I am going to disabuse you and others of this idea that space or spactime are really fundamentally real. Think of spacetime as a series of spatial (three dimensional spaces) foliated like pages in a book within spacetime. This folation is a bit strange for there are many ways in which one can do this, and someone on another frame will folation things differently. Yet given that you have made a choice of foliation you then put a flag at a point. Somebody else has made another choice of folation and they put their flag at the same point. In different frames there are different metrics. These two metrics at the same point p will have g_{ij}(p) = g’_{ij}(p), but if that point p is extended to another point in the two metrics the result will not be the same point. The flags of these respective observers are not coincident. This means that general relativity does not give an absolute definition of points and their coordinates, but rather can only determine the location of physical bodies with respect to each other. General relativity does not determine the position of bodies with respect to a manifold or space or spacetime. This is the fundamental meaning of general covariance. It also suggests that spacetime is really not a physical entity at all, but is more of an auxiliary calculational device.

    Space and spacetime are really mathematical objects, they are things we define or construct in order to calculate or predict things which involve the motion of objects or particles. The black hole is really a part of such a construct, but it has an invariant of the theory which is the event horizon. This is a congruence of null geodesics, where null geodesics are zero length in spacetime and paths (geodesics) light follows. These are invariant, and have a fundamental physics. They are associated with the mass of the black hole and they demark in outer and inner regions of the black hole.

    The event horizon is a fundamental bifurcation of spacetime, and anything that on their frame passes through that horizon has effectively left the universe. From the outside the observer never sees the object pass through due to a dilation of time, but the object becomes ever more redshifted until it effectively becomes invisible. Nothing comes out of the interior region of a black hole. Yet a black hole and its gravitational influence can cause all sorts of havoc in regions outside its horizon. This is what we observe.

    And BTW, when ever I read or hear somebody refer to gravitation with terms such as “vortex” that is often an indication they don’t really understand things.

    Lawrence B. Crowell

  • Hal S

    On a side note:

    If anyone is interested in the discussion about negative energy solutions in quantum mechanics, and isn’t entirely sure where to look; I highly recommend P.A.M. Dirac’s book “The Principles of Quantum Mechanics”

    From a historical perspective it is THE source book for relativistic quantum mechanics.

    The relavent section is section 73, “Theory of the Positron”

    This book is about $60-70 if you buy it new, but you can pick up good used copies in the $30-40 range (and probably beat up copies for less). I wouldn’t spend more than that (unless your Paris Hilton).

    If you just want to check out the sections on positrons, you can find them on Google books…just search for the book by title and go to the appropriate place in the table of contents.

    This book is really a must have for those interested in quantum mechanics.

  • Lawrence B. Crowell

    The Dirac equation is essentially the “square root” of the Klein-Gordon equation in a quaternionic form. Just as there are positive and negative solution to quadratic equations, the Dirac equation does as well. The negative energy states form what he labelled as the “sea,” which were anti-particles with negative mass. With further work it was understood that if you give one of these negative energy states, say with negative energy -(E + mc^2) twice this energy 2(E + mc^2), ignoring threshold energy issues, then the negative mass-energy anti-particle becames a postive mass-energy anti-particle.

    The Dirac sea is filled. Otherwise there would be this huge cascade of states to fill unoccupied negative energy states and a huge amount of radiation emerging from the vacuum.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    I understand space and time are considered framing devices for physical properties, so it’s undersandable different frames give different solutions.
    You are the expert and obviously the details of what I’m trying to say don’t make any more sense to you, then the big picture cosmology has drawn from studying the details makes to me. Maybe I’ll wise up. Maybe cosmology will come apart at what seem to me to be the various seams. More likely though, we are in the tail end of the current golden age and these questions will have to wait for another renaissance.

  • Hal S

    Some of the framework in my thoughts about dark energy and dark matter being caused by a gradient in the vacuum energy seems to be closely linked to the following:

    The Quantum Interest Conjecture of Ford and Roman
    http://arxiv.org/abs/gr-qc/9901074

    and the follow on work by Fewster

    Quantum Energy Inequalities
    http://maths.york.ac.uk/www/PhysicsQIneq.htm

    Although this is general used to limit the size of wormholes, I have to wonder if its possible to have a very tiny gradient across all of space.

  • Hal S

    Lawrence,

    “With further work it was understood that if you give one of these negative energy states, say with negative energy -(E + mc^2) twice this energy 2(E + mc^2),”

    “The Dirac sea is filled. Otherwise there would be this huge cascade of states to fill unoccupied negative energy states and a huge amount of radiation emerging from the vacuum. ”

    I was thinking about this too, and I was wondering if rather than thinking of virtual particles as pairs of particles, but as pairs of pairs (4 instead of 2).

    So pair production actually involves 4 particles, the positive energy electron and positron and the negative energy electron and positron.

    In the absence of a strong EM field, the 4 particles do “a little dance” and happily interact to keep charge, mass and spin in balance.

    But when exposed to the EM/gravitational field of an atom, the 2 positive charges (one with + energy and one with – energy) and the 2 negative charges (one + energy one – energy) align based on the EM field; and also align do to the gravitational field caused by the mass of the nucleus.

    This next part is tricky, and in order for me to go further I have to consider the spin of my particles. The photon that started this whole interaction carries energy and integer spin (+/-) 1, our network of 4 particles, carries a net zero spin, but each particle carries (+/-) 1/2 spin (with the absolute value of spin equal to 2).

    Due to the alignment caused by the EM and gravitational field; the negative energy particles (one electron one positron), combine with the photon. These particles are required to have the same value of spin, with a combined value of opposite that of the photon’s spin (+/- 1). (the end result is that the charge, energy and spin goes to zero)

    The positive energy particles (electron and positron) are now free to head off in their appropriate directions, in this case both carrying the same value of spin.

    This sketch is somewhat uncomfortable, because the spin of the two positive energy particles are the same and not opposite of each other (as in our current understanding of pair production).

    It is also possible to come to an uncomfortable implication that the 4 particle arrangement is similar to both a Higgs particle and a graviton (or one or the other, or none…although I am still to illequipped to rule out the implication)

    I was wondering what your thoughts are about the feasability of such a scheme, is their a way to improve it?

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  • Lawrence B. Crowell

    The Dirac equation is the square root of the Klein-Gordon equation. The four momentum interval in special relativity is

    E^2 – p^2c^2 = (mc^2)^2.

    The standard quantization is that momentum p is replaced with the operator (hbar/i)nabla (nabla is a directional derivative) and E = ihbar &/&t (& = partial). The four momentum invariant interval becomes the wave equation

    nabla^2 psi – &^2psi/&t^2 = m^2 psi c —> 1 for simplicity.

    This is a nice wave equation, similar in some ways to what the Maxwell equations give for electromagnetic waves. This is for a spin 0 particle, such as the Higgs field or su(4) dilaton.

    For a spinning particle this equation fails to describe that spin. So we then say that a spinless particle might be built from two spin 1/2 particles in opposite directions. So what do we do? We simply say that the Klein Gordon equation is the square of a wave equation for a spin 1/2 particle. The four momentum vectors p_a contribute as

    (Y^ap_a)Y^bp_b + m^2 = 0.

    So this becomes

    (Y^ap_a + m)psi = 0

    where the field psi is a spinor essentially the same as Y^ap_a + m !!! The term Y^a are the infamous Dirac matrices which are quaternions, and these are in the field and the field equation. The solution to the Dirac equation is essentially the same as the Dirac operator, for if D = Y^ap_a + m, then D^2 = 0 is the same as Dpsi = 0.

    If I had more time I could go into all sorts of fascinating things about this! D^2 = 0 is “boundary of a boundary is zero,” which is always true. The boundary of a 3 dimensional of a ball is a two dimensional sphere, but that has no boundary! This then leads us into some very rich theory of the algebraic topology of the Dirac operator and something called quantum cohomology. Cohomology is an aspect of algebraic topology.

    I will turn to the subject of gravity, but before doing that I should at least mention electromagnetism, or gauge fields. The photon is a vector field, or that has spin = 1. So we can think of it as being build up from to spin 1/2 fields with spins aligned. Using the Weyl approach to the Dirac equation, where the Dirac equation is two equations for left and right parts, we can write the electromagnetic field as

    F_{ab} = eps^{AA’BB’}_{ab} F_{AA’BB’}

    = eps^{AA’BB’}_{ab} a_{AA’} b_{BB’}

    where the spinor fields a_{AA’} a_{BB’} obey the Weyl equation (half the Dirac equation) and the action of the Weyl-Dirac operator nabla _{CC’} will give wave equations or a spinorial form of the Maxwell wave equations for electromagnetic radiation.

    For gravity I turn to the Weyl tensor C_{abcd}, which is the traceless component of Riemann curvature tensor for spacetime, and in spinor form this may be written as

    C_{AA’BB’CC’DD’} = a_{AA’}b_{BB’}c_{CC’}d_{DD’},

    where a_(AA’} = (a_A, a_A’). Now let us consider a basis spinor s_{AA’} = nabla_{AA’} the covariant basis for the vector. We then have that this spinor is an eigenvector of the Weyl tensor by

    s^{AA’}C_{AA’BB’CC’DD’} = (nabla^{AA’}}a_{A} +

    nabla^{AA’}a_{A’})b_{BB’}c_{CC’}d_{DD’} + … .

    The ellipsis involves derivatives of the other spinors and delta functions etc. We then have the differential equation

    nabla_{AA’}a_{A’}) = lambda a^A.

    The plus sign in the equation for the application of the vector X on the Wely tensor gives

    lambda (a^A, a^{A’}) = lambda a^{AA’}.

    This equation is essentially a covariant form of the Dirac equation (or really the Weyl equation). If lambda = 0 this is the neutrino equation. The annullment of eigenvectors on the Weyl tensor gives the N-type solutions, of which the pp-waves for gravity waves are an example of. Various outcomes for these eigenvalues determine the Petrov type for the spacetime solution. For non-zero outcomes these spinor wave equations are forms of the Dirac equation. I will not go into that because it is an exhaustive subject. I leave it to the reader to research this up.

    Now just as the Dirac equation has its Dirac sea of negative energy solutions filled up by the “sea,” I think the same happens with GR. There have been various solutions that science fiction afficianados have come to love, such as wormholes, warpdrives and Krasnikov tubes. However, Ford Pfenning and others have shown that the violations of the weak energy conditions T^{00}

  • Lawrence B. Crowell

    That darn carrot problem again!

    weak energy conditions T^{00} &lt 0 renders these solutions problematic, indeed impossible. However, I think these are still remarkable results, not because I think we can warp factor 9 our way to Betelgeuse, but because these have an analogue with the Dirac sea. The Alcubierre warpdrive is really a form of gravity wave. Now for gravity waves its quantization for strong fields results in gravitons that couple to each other. The whole thing becomes an unrenormalizable tangle. Yet, what if these divergent Feynman diagrams exactly cancel those for the Alcubierre warpdrive? If so then we can fill up the analogue of the Dirac sea. Indeed, the loop diagrams for gravity have causality issues similar to those of the warpdrive. Yet if they cancel out, then all we are left with is the stuff on the “tree level.” To be honest I suspect that things don’t completely cancel, but that the loop diagrams left to q-gravity are renormalizable by standard regularization methods. But this is TBD.

    So as the adage goes, one man’s trash is another’s treasure. At any rate, I think this is a somewhat deeper or foundational approach to cancelling infinite positive energy with negative energy.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    And BTW, when ever I read or hear somebody refer to gravitation with terms such as “vortex” that is often an indication they don’t really understand things.

    Since real vortexes are a tranfer of energy between layers in a gravitational field, why don’t they apply to the theory of gravity?

  • Lawrence B. Crowell

    A vortex is usually a circular flow of a fluid. If we consider the tangent velocity of any atom or mass unit in the fluid it obeys a flow equation curl F =/= 0. Curl is a cross product between a directional derivative and a vector, here F being a flow vector. In the theory of quantum fluids Feynman quanitzed these, called rotons.

    When I hear people talk about vortices in gravity I often sense they are thinking according to Descarte’s idea that the motion of planets was due to a circular flow of a medium. The theory was supplanted by Newton, who’s gravitation has lines of force radially directed towards the sun.

    Accretion disks around black holes might look like hurricanes, but the physics of the two are very different. Hurricanes occur because of bulk atmospheric flows on the rotating Earth, and such motions experience Coriolis accelerations. This is a pseudo-force, one which is apparent due to motion on a non-inertial frame. Accretion disks are hydrodynamic flows of material around a gravitating body, usually modelled in a Newtonian framework, with a disappative loss mechanism due to frictional loss and the loss of energy in radiation. Just because a hurricane and an accretion disk look the same and have rotational dynamics does not mean they are due to the same physics.

    Lawrence B. Crowell

  • John Merryman

    Lawrence,

    My point of reference is the relationship of rising heat interacting with descending cold. Then corresponding this to atomically stable mass falling in, as radiant energy expands out. Spin and all its variations is a consequence, not a cause.

  • Hal S

    Lawrence

    The book you wrote said you were affiliated with the Alpha Institute for Advanced Study; I sent a question about this dark matter stuff via the “contact us” page on their website asking them if they could forward it to you, just wanted to let you know.

  • John R Ramsden

    Jason Dick [#13] wrote:
    >
    > It’s due to dark matter. We’ve been pretty darned confident of this since the Bullet Cluster observation.

    As I recall, the Bullet Cluster includes that galaxy which slowed so abruptly, in collision with another or with gas, that its associated dark matter blob went flying through the windscreen, so to speak, and carried straight on, no longer within the galaxy. Presumably you were referring to that.

    If so, and assuming dark matter causes faster than expected rotation rates in the outer reaches of galaxies, doesn’t that imply there should now be no such anomalous rotation rate in this particular galaxy? That should be fairly easy to check with red-shift measurements.

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

    People may have already touched here, but I can’t go over with comb, in any case: DM should encounter black holes and fall in, and that must ?produce radiations etc. – it would likely have a different signature that ordinary gas, and be a way to say, there’s definitely “something” that is filling space at that point (or is it too tenuous? I would suppose, but not even being able to make an envelope calc., a powerful black hole would do something to it we can notice.

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

    OK, I mentioned black holes re DM directly since the original post didn’t use that term or (nor the comments I’ve had time to read, some of which did mention black holes in tangential ways) give an idea of just what we could expect as evidence of “dark matter” flowing into an event horizon rather than ordinary matter, what results would be indications of what types of DM etc. What did the phrase “the direct annhilation of dark matter particles” mean, since BHs don’t “annihilate” particles in common parlance.

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

    OK, I’ve got to break before I get more carelessly muddled, “didn’t use that term” – yeah it did, but the other questions remain, sorry, tx.

  • John Merryman

    Neil,

    I think that’s what the original blog posting by Julianne was about, that they thought they’d found evidence of gamma-rays from dark matter falling into the black hole at the center of the MW, but that it seems to map more closely to the binary stars in its vicinity and be associated with normal activity. So it’s still very dark.

  • Lawrence B. Crowell

    A lot of theory has been written about dark matter and its potential decay. Some theories have suggested that it decays into Z^0 particles or photons. The problem with that is that in any gauge interaction the decay products usually carry a signature of that interaction, such as a quantum number associated with that process. Dark matter clearly does not interact by the electromagnetic interaction, so that to my mind questions the emission of photons directly. Photons might be generated by the subsequent decay of the Z^0 particle. A theory that has dark matter interacting by weak interactions might have been reasonable, but we now know that gamma or X-rays rays do not appear to come from the extragalactic tendrils or halos of dark matter. So these theories now look at best suspect.

    Dark matter will of course enter a black hole if it is attracted in there. Maybe this is how these thundering galactic black holes were formed. Yet I think it suspect that there is anything in the environs of a black hole which would cause dark matter to decay. The stuff would be quietly drawn in and “reprocessed” by the quantum gravity transitions in its interior. The reprocessed quanta will become measurable in the very distant future as the black hole quantum mechanically decays over a 10^{90} year time frame. The human species will be dust long before that happens.

    I wrote last week a rather long email post about just this issue of dark matter and black holes. I can transmit it here if there is any interest, but it is long and the interest here is for shorter posts. There are all sorts of unknowns here, including the “classical” nature of dark matter and how it would interact with a black hole. If the stuff is treated as a fluid there are all sorts of conundrums involved. If we don’t understand its classical behavior well, then understanding how it interacts with a black hole is hard to cypher.

    I think the most qualified statement we can come up with this is “I dunno.”

    Lawrence B. Crowell

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

    tx, does that direct to the issue of what was meant by the strange wording, “the direct annhilation of dark matter particles” ? I assume fundamental particles are meant, which again are not annihilated normally by fall into BH unless loose use here of idea of crushing at the singularity?

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

    Lawrence you may send your email post etc. to my address at neil_delver at (caloricmail, a metaphor) dot com, tx.

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

    LC said….

    “Dark matter clearly exists, but the problem might be the word “matter.” Who ever said this stuff had to be made of particles? It may well be the case that we will never find so much as a WIMP of anything out there. This dark matter appears to be just clouds that only have gravity. There is no decay process coming from it, there are no X-rays or gamma rays coming out of this stuff if it should decay. It looks about as dead as anything can be, except a black hole.”

    This, it seems to me, is a very appropriate reflection on “Dark Matter”. There are vast numbers of stellar sized black holes scattered throughout the galaxies. The overall effect of this “invisible mass” could very well create the “Dark Matter Halo”. The distribution of such invisible mass within the galaxies would have the effect of creating the overall phenomenon of “soupy space”…

    Dark matter may well be only another form of dark energy…indeed many scientists speak of dark energy as constituting 96% of the mass of the universe.

  • Ed A

    According to recent work by David Wiltshire , dark matter can be explained away purely within general relativity by taking into account the inhomogeneity of the universe. Here is a media teaser .

    The shadowy world of particle dark matter just isn’t needed if general relativity is thought through carefully.

    This would be a bold and beautifully elegant solution to the problem. So beautiful, you just have to hope it is true :-)

  • Ed A

    sorry, I mistyped that link somewhere or other … here is
    David Wiltshire

  • Hal S

    Going back to my post #43

    Under this scenario, it would be possible to construct a new form of “Hawking radiation” involving massive particles instead of photon’s. This radiation might be detectable.

  • Lawrence B. Crowell

    I am looking at Wiltshire’s paper

    http://arxiv.org/PS_cache/arxiv/pdf/0712/0712.3984v1.pdf

    “Dark Energy Without Dark Energy.” I appears to be largely a classical paper, where gravitation and its source are not treated quantum mechanically. I can see in part how one might object to the equation of state approach for a quantum vacuum state. The cosmological constant enters into the Einstein field equation, where if the matter-energy sources are zero the spacetime is one where the Ricci curvature is proportional to the metric. The constant of proportionality is the cosmological constant. So there is a basic difference between using the so called zero point energy of quantum fields and treating the cosmological constant responsible for dark energy as a pure Einstein space.

    I suspect that with quantum gravity this classical distinction is removed and we will understand this issue more clearly.

    I think dark matter is simply a different phase for the quantum vacuum of the universe that exists in local regions. I question these ideas that dark matter is composed of particles in the usual sense, but are more quasi-particles (or particle-like) which manifest themselves in this difference of phase.

    Lawrence B. Crowell

  • Hal S

    I liked this so much I thought I’d post it again to see if anyone had thoughts on it.

    $latex P_{avg}=dfrac{Delta m}{Delta t} c^2=dfrac{Delta p}{Delta x} c^2$

  • Hal S

    One quick note, this equation (if true) implies that average power can never equal zero since

    $latex Delta E Delta t ge dfrac{hbar}{2}$

    and

    $latex Delta p Delta x ge dfrac{hbar}{2}$

  • Hal S

    Please if anyone thinks this is all wrong; let me know

  • Lawrence B. Crowell

    I am not exactly sure what it is that you are trying to show. The uncertainty “Delta” of any operator O means

    $latex Delta O~=~sqrt{langle O^2rangle~-~langle Orangle^2}$

    while the Delta used in the power expression is a finite difference term that enters a calculus limit.

    Lawrence B. Crowell

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

    An additional reflection on Post 60…

    Using an age of the universe since the big bang as 13.7BY and realizing that more massive stars exist as luminous bodies for only a cosmologically brief period of time, it could be reasonably assumed that most of the mass of the universe already exists in the form of black holes…which in turn correlates with the fact that 96% of what exists is invisible.

    Ed A said:

    “According to recent work by David Wiltshire , dark matter can be explained away purely within general relativity by taking into account the inhomogeneity of the universe. Here is a media teaser .

    The shadowy world of particle dark matter just isn’t needed if general relativity is thought through carefully.

    This would be a bold and beautifully elegant solution to the problem. So beautiful, you just have to hope it is true”.

    The hypothesis described in this work is a very reasonable conclusion as we relate what we know from field work with the most precise and verified models available.

    It is not possible to fully explore all the conclusions of these relationships… those between QM, GR, SRT and congruent field results….but the implication that our expanding, accelerating universe may only be a frame of reference phenomenon is truly significant in the light of the kind of cosmology Einstein sought…not just because of the convention of his time, but also in his search for the kind of cosmological engineering constaints which could form a basis for explaining the presence of embedded stable information in the universal structure.

    The DNA in our bodies is, while changed in organization, chemically identical to the DNA which existed 3.2 billion years ago. In fact, in that sense, as we presently exist, we have never really known death.

    That part of us which is at the heart of our existence, far from being random and fleeting in nature, is existentially tenacious; it has existed for almost 25% of the time since the big bang occurred. A persistence and development of information and complexity with that kind of stability has to be cosmologically significant, and relates to the geometric link between observation and existence which is so fundamental to QM, GR and SR….

  • Hal S

    This will have to wait until this evening, but for the moment, think from an engineer’s perspective, where the delta just means change

  • Hal S

    Actually, to be more precise (and not to confuse the situation) delta is the difference between to quantities, where as the derivative d is instantaneous

    we engineer’s aren’t usually about nuance; sadly

  • Hal S

    correction

    two quantities

    and instantaneous change

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  • Lawrence B. Crowell

    What is surprising is that the universe does not exist primarily is the form of black holes. Black holes may form the largest percentage of the cosmological entropy S ~ 10^{100}GeV^4, but the early universe appears not to have produced many black holes. The universe appears to have started out with a very low entropy.

    I think the interiors of black holes are dual to a condensate phase of gauge fields, such as gluon plasmas probed at RHIC, and that these objects are determined by a dilaton field to contain information for an AdS (Anti-deSitter) spacetime and its conformal infinity. This suggests that the structure of elementary particles and black holes provide the information for the conformal completeness of the AdS. The conformal infinity of AdS, or rather a patch on this, is a Minkowski spacetime for four dimensions. So it is not possible to time develop a spatial surface of three dimensions into this final configuration without sufficient auxilliary information. As a result the physical cosmology we observe may have been selected from all other quantum amplitudes for cosmologies in the earliest phase as the one which had the structure of elementary particles and an early entropy in black holes so as to give this conformal completeness. This might be why the universe is not packed full of black holes, but is configured with a black hole entropy and the dual of BH interiors with the structure of elementary particles so as to give this completeness of AdS conformal infinity.

    Lawrence B. Crowell

  • Hal S

    In regards to posts 65 and 66

    What I am trying to address here is that from a naive engineer’s perspective we have made an observation that

    $latex Delta E Delta t ge dfrac{hbar}{2}$

    If we imagine a plane where one axis is Energy and the other is time; this implies that there is a minimum are we can define. The diagonal of that minimum area is the slope, which is;

    $latex sl = dfrac{Delta E}{Delta t}$

    It turns out that this ratio is the definition of average power.

    Since this slope must always be finite positive (do to our definition of uncertainty) we can say with confidence that the average power of the universe must always be greater than zero

    $latex P_{avg} > 0 $

  • Hal S

    “If we imagine a plane where one axis is Energy and the other is time; this implies that there is a minimum are we can define”

    just to correct grammar

    If we imagine a plane wher one axis is change in Energy and the other is change in time; this implies there is a minimum area we can define.

  • Hal S

    actually I liked it better like this

    If we imagine a plane wher one axis is Energy and the other is time; this implies there is a minimum area we can define.

  • Hal S

    okay its still early

  • Hal S

    Hey do any cosmologists read this blog?

    Can anyone prove the logic of posts 65, 66 and 72 wrong?

    Am I the only one who sees the implication of such a simple statement?

  • Hal S

    $latex H_e_l_l_o$

    $latex H_e_l_l_o$

    $latex H_e_l_l_o$

    $latex E_c_h_o$

    $latex E_c_h_o$

    $latex E_c_h_o$

  • Lawrence B. Crowell

    Given the uncertainty principle

    $latex Delta EDelta T~ge~frac{hbar}{2},$

    your power equation would amount to

    $latex P~=~frac{Delta E}{Delta T}~ge~frac{hbar}{2Delta T^2}.$

    We need to step back a minute as ask what does this mean. The uncertainty in time is just an interval defined by the sampling time in a measurement. This results in the uncertainty in energy. This power equation tells us that in that spread of time there is this “quantum power” involved with generating this spread of possible energy outcomes. Yet this power is not likely something observable in a direct way. Cleary

    $latex PDelta T^2~ge~frac{hbar}{2},$

    which suggests that this power is a “fluctuation” that exists within the uncertainty of quantum mechanics.

    Look at

    http://blogs.discovermagazine.com/cosmicvariance/2008/01/14/boltzmanns-universe

    to see my derivation (last entry as of now) of where the uncertainty in the energy comes from.

    Lawrence B. Crowell

  • Hal S

    if true:

    Quantum mechanics $latex D I C T A T E S$ the the universe at a $latex M I N I M U M$ is a $latex P E R P E T U A L$ $latex M O T I O N$ $latex M A C H I N E $ that is a $latex N E T$ $latex P R O D U C E R$ of energy.

    And Therefore

    There must always be a $latex N E T $ $latex P O S I T I V E$ amount of energy in the universe.

  • Hal S

    Your equation

    $latex P Delta T^2 ge dfrac{hbar}{2}$

    dictates the minimal state of the universe

    congrats!

  • Lawrence B. Crowell

    This does not imply that the universe has a net creation of energy within it. The time rate of change for the expectation of the energy of a system is given by

    $latex frac{partial}{partial t}langlepsi|H|psirangle~=~Big(frac{partial}{partial t}langlepsi|Big)H|psiranglelanglepsi|H|~+~langlepsi|Hfrac{partial}{partial t}|psirangle$

    where I have assumed the Hamiltonian has no explicit time dependency. We now use the Schrodinger equation

    $latex ihbarfrac{partial}{partial t}|psirangle~=~H|psirangle$

    which has its complement

    $latex ihbarfrac{partial}{partial t}langlepsi|~=~-langlepsi|H$

    where the sign change is due to complex conjugation. Now plug this into the above equation

    $latex frac{partial}{partial t}langlepsi|H|psirangle~=~langlepsi|HH~-~HH|psirangle$

    which is trivially zero. If there is some time rate of change for the Hamiltonian this is modifed to

    $latex frac{partial}{partial t}langlepsi|H|psirangle~=~langlepsi|frac{partial H}{partial t}|psirangle.$

    This obtains for a problem where there is some sort of driving source, such as a hamiltonian which describes the input of energy by an electromagnetic wave.

    This little equation you are playing with describes how an uncertainty fluctuation in the energy during a measurement obtains over an interval of time of the measurement.

    Lawrence B. Crowell

  • Lawrence B. Crowell

    I forgot the i hbar in part of this derivation. TeX and LaTeX is sometimes funny, but the conclusion holds. Quantum mechanics obeys energy conservation perfectly and the Heisenberg uncertainty principle does not imply that there is a continual creation of energy in the universe.

    Lawrence B. Crowell

  • Hal S

    This may take some time.

    In the meantime, think on this; we require probability to be conserved. We also require that all negative states be filled.

    Therefore, in order for there to be positive energy, all the peaks associated with positive energy states must be slightly higher than the peaks associated with negative energy states.

  • Lawrence B. Crowell

    Clearly I made a TeX goof in the first equation — oops.

    The Heisenberg uncertainty principle is not a dynamical equation. The Schrodinger equation is, and that is where one finds that energy is conserved. The Heisenberg uncertainty principle is a quantum analogue of the Nyquist rule in electromagnetism and mechanical vibrations. This is a result of dynamics, but not itself a dynamical principle.

    Snce the Schrodinger equation is deterministic there are no intrinsic stochastic fluctuations. Fluctuations are a phenomenology of measurement, and our ignorance of the myriad of states in the measurement apparatus. I could write a very long discussion on this issue: the problem of measurement, decoherence and how quantum states are einselected.

    The conservation of probability and the Born rule come about from the Schrodinger equation. The Schrodinger equation is a deterministic wave equation which has a set of observables which are constants of the wave motion. The filling in the negative energy states, or Dirac’s sea, is a matter of the Dirac wave equation. The spinor solutions of the Dirac equation have positive and negative solutions, just as the quadratic equation often has positive and negative solutions. In other words the simple equation

    y = x^2

    has two roots x = sqrt{y} and x = -sqrt{y}. Since the Dirac equation is the “square root” of the Klein-Gordon equation there are similar +/- roots.

    Lawrence B. Crowell

  • John Merryman

    http://space.newscientist.com/article/mg19726401.400
    ——————
    Other physicists certainly listen to him. When Georgi made his idea public last March, he provoked a flood of research activity. More than 95 papers have now been written investigating the peculiar facets of unparticles – a level of research on a subject that has not been seen since 1998, when theorists including Dimopoulos proposed that extra dimensions could be large enough to be detected (Physics Letters B, vol 429, p 623). “Unparticles are such a novel idea,” says Pran Nath at Northeastern University in Boston, Massachusetts. “They excite people because they are completely different from anything anyone has seen before.”

    We might even spot unparticles soon. According to Georgi, they could make a surprise appearance in collisions at the Large Hadron Collider (LHC) particle accelerator, due to turn on later this year at the CERN laboratory near Geneva, Switzerland. “To my mind, unparticles would be a much more striking discovery than supersymmetry or extra dimensions,” says Georgi. “Unparticle stuff would astonish us immediately.”
    ————————-
    An unparticle does not have one particular mass, but can take on any possible mass or have all possible masses at the same time, depending on how you look at it. That sounds weird, but anyone who has ever tried to measure the length of a coastline has seen a similar effect. If you are trying to find out how long a coastline is, you will get a different answer depending on how closely you look at it and the size of the measuring stick you use. Zooming in on a jagged coastline reveals finer and finer detail, first the bays and harbours, and then smaller coves, nooks and crannies. Each time you try and take all this extra detail into account, the coastline’s overall length appears to increase.
    ———–
    Georgi reserves judgement on whether his unparticles really could be the key to solving the dark matter problem until more work is done, but he’s pleased that people are investigating the possibility. “All I knew was that I had found something cool and I wanted other people to take a look and see what kinds of weird things they might be capable of doing – what mysteries they might solve,” he says. “I’m happy because that’s exactly what people are now doing.”

  • Lawrence B. Crowell

    This is a regularization scheme, where there emerges a nonintegral number of particles in an amplitude. It is a curious prospect. Georgi’s main paper on this can be found at:

    http://arxiv.org/PS_cache/hep-ph/pdf/0703/0703260v3.pdf

    Lawrence B. Crowell

  • John Merryman

    It will be interesting to see where it goes. I guess my attention was drawn by it seeming to be something of a field theory from a particle perspective.

    It’s going to be interesting to see what the LHC does show and what further questions it raises.

  • Hal S

    Lawrence

    I want to first clarify that I do not believe in the “free energy” claims people make when they talk about zero-point energy.

    I began building a very interesting logical argument over the weekend, but in the interest of time and courtesy, I think I can reduce it significantly.

    1) The first matter is whether the uncertainty priniciple is an unfortunate result of measurment, or if it represents “real” energy.

    The simple logical argument is that QED and experiment have demonstrated the reality of vacuum pair production (vacuum decay)

    http://en.wikipedia.org/wiki/Virtual_particles

    This situation can be conceptualized by showing that on the momentum-position plane or the energy-time plane, the “box” around our expected value point will not disappear even if our particle does; instead it simply centers itself around the origin of our plane.

    2) The second matter is to postulate what this “box” represents.

    There is a great discussion on wikipedia about uncertainty

    http://en.wikipedia.org/wiki/Uncertainty_principle

    The following equation from this discussion helps demonstrate that “uncertainty” is related to our imaginary part in QM

    $latex Delta X Delta P ge | langle psi | hat{X} hat{P} | psi rangle | ge | langle psi | I m ( hat{X} hat{P} ) | psi rangle | = dfrac{hbar}{2}$

    The odd thing is that Einstein “discovered” this relationship before it was formulated and it has had the unfortunate name of “zero-point energy” and “vacuum energy” in popular culture and science ever since.

    http://en.wikipedia.org/wiki/Zero-point_energy

    http://en.wikipedia.org/wiki/Vacuum_energy

    $latex E = dfrac{hbar omega}{2} $

    So it seems intuitive that our “box” is in fact the non-reducible imaginary component of a particle.

    3) The third issue is how do we interpret this “box”

    It is obvious that the energy represented by uncertainty is “real” in the sense that it reacts to the gradient of a field.

    Although we generally restrict vacuum pair production to strong fields; we must consider the fact that in quantum mechanics, states of particles are superposed and scaled based on their relative probability. This requires there to be a positive probability that vacuum pair production can occur in a weak field as well, just not as probable.

    This brings us to a more pressing question as to the nature of fields.

    4) What is a field?

    The nature of a field is to cause the release of internal potential energy from an object or to reduce kinetic energy of the object. It serves to transform those two types of energy into one or the other. It also serves to reduce the total relative energy of an object.

    Although initially counterintuitive that an object moving rapidly in a close orbit has less energy than an object moving slower in a more distant orbit; physics tells us that in all cases involving fields, we must add energy in order for a bound object to become unbound.

    It is also less intuitive that a black hole actually represents a bound state of matter where the matter has reached a constantly collapsing ground potential. The inability for objects to escape is due to their inability to increase their potential energy as fast as it is being converted to kinetic energy.

    With this conceptual framework, we can now see that “vacuum energy” is the non-reducible positive imaginary components of particles and represents a continuous reservoir of potential energy; but since all the energy is strictly potential, it can only be converted into kinetic energy when exposed to the gradient of field.

    5) Our last question is then; where do fields come from?

    Here is an interesting question. Fields and curves in space are generated simply by the presence of energy. Any amount of energy, no matter how small; will generate a field.

    This nature of energy also tells that since “imaginary” energy interacts with fields in the same manner as “real” energy, than it is “real” as far as the field is concerned. It also tells us that “imaginary energy”, in the absence of “real” matter should also generate its own field.

    The nature of this field will have to be discussed later, but as a closing note; the “power” we discussed in comments 81 and 83, could be correctly described as “imaginary” power.

  • Lawrence B. Crowell

    The box you refer to is the probe you use to measure the ZPE. This is the Casimir effect, where the plates in the apparatus are a probe. We do not detect virtual pairs of particles directly. What is done is to impart energy in a small location of space, as measured by the wavelength of input scattering states, and some of this energy enters into amplitudes or scattering channels for the production of particle anti-particle pairs. We don’t measure free virtual particles.

    Also, things like loops and the like in Feynman diagrams are perturbation terms with a summation over their momenta. Just as in calculus summation variables are called dummy variables these loops are really mathematical artifacts, or in a sense dummy variables.

    Since the classical variables commute, one could easily rewrite the Hamiltonian for the Hamonic oscillator

    $latex
    H~=~frac{1}{2}[p^2~+~omega^2 q^2]
    $

    as

    $latex
    H~=~frac{1}{2}[p^2~+~omega^2 q^2]~+~frac{iomega}{2}(qp~-~pq).
    $

    Since pq = qp classically, all we have added is zero and this is the same Hamiltonian. Now with hbar = 1 if we quantize this Hamiltonian with

    $latex
    a~=~sqrt{1/2omega}(omega q~+~ip),~
    a^dagger~=~sqrt{1/2omega}(omega q~-~ip),
    $

    the quantized Hamiltonian is

    $latex
    H~=~omega a^dagger a
    $

    and there is no [a, a^dagger] commutator often interpreted as the zero point energy. The ZPE has been completely removed, there is nothing “funny” or hand waving about this. For this reason often the raising and lowering operators are just “normal ordered” and the ZPE term removed.

    What happens with pair creation is that something is coupled to the Harmonic oscillator. The usual equations coupled together are the Dirac equation and the Maxwell equation. The Dirac field acts as a current in the Maxwell equation and the momentum operator in the Dirac equation is put in a gauge invariant form with the EM vector potential. Then things start to get a bit complicated. What does happen is the occurrence of particle pairs that would not obtain if hbar were zero.

    The zero point energy is then a very subtle thing, particularly with cosmology. I don’t want to digress into that right now, but there is a whole lot of stuff that goes on, often in published papers, where the ZPE is assumed to be a real “thing.” Instead the cosmological constant is better thought of as a subtle quantum effect of fields coupled to spacetime (analogous to the Dirac equation plus Maxwell equation), or rather better said the gravity field, which results in this term so the cosmology is globally an Einstein space with spacetime curvature proportional to its own metric.

    The same is the case with the Heisenberg uncertainty principle and the notion of fluctuations. These are phenomenological results which describe a measurement or the distribution of possible outcomes. The Schordinger wave equation is a perfectly deterministic equation and there is nothing intrinsically stochastic about its time development of a wave. Stochasticity enters into the picture when you try to observe the system, or if the system is coupled to some large classical-like system or one with many modes, and is a tool we use.

    Lawrence B. Crowell

  • Hal S

    Interesting; I’ll need some more time.

    I suspect that uncertainty principle and the lorentz transformation are fundamentally related.

  • Lawrence B. Crowell

    In order to ponder how spacetime physics is related to quantum mechanics requires that one consider the two arenas of physics as systems of relationships between particles.

    In different frames there are different metrics. These two metrics at the same point p will have

    $latex
    g_{ab}(p)~=~g^prime_{ab}(p),
    $

    but if that point p is extended to another point in the two metrics the result will not be the same. This means that general relativity does not give an absolute definition of points and their distances, but rather can only determine the location of physical bodies with respect to each other. General relativity does not determine the position of bodies with respect to a manifold. This is the fundamental meaning of general covariance. It also suggests that spacetime is really not a physical entity at all, but is more of an auxiliary calculational device. General relativity is fundamentally a theory on the relationship between particles which we describe according to geometry.

    Quantum entanglement tells us there is a completely different way in which two particles can be related to each other than by their relative location as given by relativity. This is through quantum entanglement. Two quantum
    states may exist in a superposition where one state if up the other is down plus the first down and the second up. This can happen in the decay of a spin 0 particle into two spin 1/2 particles. Angular momentum must be conserved, so the total state is

    $latex
    |psirangle~=~{1oversqrt{2}}big(|+rangle_1|-rangle_2~+~e^{itheta}|-rangle_1|+rangle_2big)
    $

    This state vector is written independent of an spatial or momentum value. The wave function that is defined through space is

    $latex
    psi(r_1,~r_2)~=~langle r_1|langle r_2|psirangle
    $.

    This can be extended to the domain of special relativity. An optical analogue of this can be obtained with entangled pairs of photons in orthogonal polarization states produced in a parametric down shift by a sapphire crystal.

    If two detectors at positions R and -R measures the particle there are two possible outcomes:

    $latex
    |-rangle_1$,~|+rangle_2,~or~ |+rangle_1$,~|-rangle_2
    $

    These two measurements may be performed instantaneously in a mutual rest frame. Yet no information is communicated from one measurement to the other, for the information obtained in both measurements are identical. Nothing is communicated, but the conservation of angular momentum demands this outcome. This is a relationship between particles that exists independent of any spacetime interval or distance between them.

    These are the two relationship systems, and quantum gravity is the area of physics where these two relationship systems are specific examples of a single relationship system.

    Lawrence B. Crowell

  • John Merryman

    http://space.newscientist.com/article/mg19726401.400

    The reason that coastlines, with their jagged edges, don’t have a definite length is because they are examples of fractals. It doesn’t matter how much you magnify a fractal, you always see pretty much the same pattern – in the case of a coastline, another jagged edge. The pattern is the same whatever the scale – fractals are “scale invariant”.

    Under scale invariance, matter loses all sense of perspective, and distance is no longer important, says Francesco Sannino of the Niels Bohr Institute in Copenhagen, Denmark, who has also studied unparticles.

    This has a remarkable effect on the strength of the force holding unparticles together. Sannino likens it to being able to hear a quiet whisper as easily as a loud yell. “In the normal world, if two people are sitting in different countries and they want to have a conversation, they must use a phone,” he says. “But in a scale-invariant world, even if they were separated by 2000 kilometres they could speak to each other as if separated by just 2 metres.”

    These two measurements may be performed instantaneously in a mutual rest frame. Yet no information is communicated from one measurement to the other, for the information obtained in both measurements are identical. Nothing is communicated, but the conservation of angular momentum demands this outcome. This is a relationship between particles that exists independent of any spacetime interval or distance between them.

    These are the two relationship systems, and quantum gravity is the area of physics where these two relationship systems are specific examples of a single relationship system.

    Could there be some connection here?

  • Hal S

    Just on a side note:

    Lawrence, this is a very useful discussion and it is helping me a lot.

    From a philosophical standpoint, I really have no preference on how the universe works, other than it should work like the one I’m in.

    My current default view of things is to picture the “vacuum energy” or “cosmological constant” as acting like a power source, and black holes act as grounds. (or from a mechanical standpoint, you’d have a boiler or pumping station, and blackholes are the ocean). Sure its a naive toy model, but from a starting point I think its just as good as anything else; sources and sinks.

    Anyhow, I also like the analogy that physics is similar to reverse engineering in a lot of ways; and sometimes you have to “break” things to see how they work.

    I tend to have a very deep respect for physicists and mathematicians; so I particularly appreciate the time spent discussing these topics. Thanks.

    Now about that whole universe thing…

  • Hal S

    Just for fun:

    we find the following equation for a single harmonic oscillator at wikipedia;

    http://en.wikipedia.org/wiki/Zero_point_energy

    $latex epsilon = dfrac{h nu}{e^{frac{h nu}{k T}} – 1} + dfrac{h nu}{2}$

    which can be rewritten as;

    $latex 1 = dfrac{epsilon}{h nu} = dfrac{1}{e^{frac{h nu}{k T}} – 1} + dfrac{1}{2}$

    which is;

    $latex 1 – dfrac{1}{2} = dfrac{1}{e^{frac{h nu}{k T}} – 1}$

    and then;

    $latex e^{frac{h nu}{k T}} – 1 = 2$

    thus;

    $latex e^{frac{h nu}{k T}} = 3$

    making

    $latex dfrac{h nu}{k T} = l n 3 = 1.098612289 $

  • Hal S

    Its just interesting when compared to the dervation of the constant x in Wien’s displacement law

    http://en.wikipedia.org/wiki/Wien%27s_displacement_law

  • Hal S

    sorry…derivation

  • Lawrence B. Crowell

    I can’t give a definative answer to whether the unparticle theory is related to my thinking that gravitation and quantum mechanics are particle relationships that are specific cases in a more general physical relationship system. The unparticle theory is a type of regularization scheme. The fractal-like nature of this, eg the coastline argument, is a regularization. In QED the cut-off in energy at high energy is permitted because the structure of the theory below the cut-off is self-similar to the physics above. So the cut-off is permitted in a way similar to a Julia set algorithm can cut off the calculation on a certain scale without adulterating the set at a larger scale. The foundational nature of renormalization is encoded in the renormalization group equation, Wilson and Polchinski, which has a fluid mechanics analogue and describes a Hausdorff dimension for the scalability of the theory.

    There is a whole lot more I could go on about this, such as the role of conformal groups and dilaton fields, or with zeta functions, and … . But that would take things a bit far afield.

    In quantum gravity not every wave function(al) has a configuration variable, which is a geometry or metric, that is a classical space or spacetime. How a classical universe emerges from this is not well understood. So these wave function(al)s over non-classical metrics are in a sense what might be called “un-spaces” or “un-spacetimes.” The spacetime geometries are these strange or “fake” manifolds found in the Uhlenbeck-Donaldson theorems on the moduli for four dimensional spaces. Again, this gets into some very deep mathematics and physics/cosmology it might describe.

    Lawrence B. Crowell

  • Hal S

    This situation is well discussed at:

    http://en.wikipedia.org/wiki/Equipartition_theorem

    under the section called:

    Failure due to quantum effects

    Where in our equation describes the situation when Z = 3/2

  • Hal S

    This situation is well discussed at:

    http://en.wikipedia.org/wiki/Equipartition_theorem

    under the section called:

    Failure due to quantum effects

    Where our equation describes the situation when Z = 3/2

  • Hal S

    I also like this approach:

    The uncertainty principle is tied to the concept of reactive power in AC electrical theory

    Reactive Power (Q):
    The power which is exchanged between reactive elements (inductors and capacitors) is called reactive power, Q, and is measured in vars (volt-ampere-reactive) or kilovars. This power does no useful mechanical work, but must be alternately absorbed and supplied by the reactive elements.

    another link about this;

    http://en.wikipedia.org/wiki/Reactive_power#Real.2C_reactive.2C_and_apparent_power

    So in a naive way, you could consider “ZPE” as meaning that the circuitry of the universe is always in an energized state. (pre-energized).

    Just interesting.

  • Hal S

    Of course what makes this more interesting is how it relates to Entropy:

    $latex S = k ln Omega $

    $latex int frac{delta E}{T} = frac{h nu}{T} = k ln 3 $

    hmmm…3 microstates….hmmm

  • Hal S

    funny how 3 seems to pop up a lot in nature

    hmmmm

  • John Merryman

    Lawrence,

    In QED the cut-off in energy at high energy is permitted because the structure of the theory below the cut-off is self-similar to the physics above. So the cut-off is permitted in a way similar to a Julia set algorithm can cut off the calculation on a certain scale without adulterating the set at a larger scale. The foundational nature of renormalization is encoded in the renormalization group equation,

    Why does this sound like some form of fractals all the way through?

  • Lawrence B. Crowell

    With reactive power I would say the analogue is with an uncertainty in energy that emerges by probing of the vacuum. The question to ponder is whether that ZPE is there if it is not measured, or if there is nothing coupling to it.

    I am not sure how the equipartition theorem comes into this picture.

    The number three plays a most interesting role with the triality in group theories, such as the 3 + bar-3 long roots of SU(3) which have some connection to the three families of quarks. The number 5 also comes in with my work in the Steiner group as the representation of a sporadic group. A subgroup of this is S^3xSL_2(7), which is a three sphere with each point identified with a projective map of E_8 onto the Fano plane. So here the numbers 3 and 7 come in, 7 being a favorite number of the bible types. This is a sort of three dimensional Bloch sphere where each point is a set of states given by E_8, with three independent E_8′s required.

    There is no intrinsic notion of time in the Wheeler DeWitt equation. The ADM classical constraint equation H = 0 becomes H*Y[g] = 0, and where time enters into the picture it is something the analyst inputs. The lapse functions N are determined by a coordinate condition, analogous to a gauge. One way in which we can do this is to impose a field on the metric g. For that field F we give a wave equation and it is not hard to introduce a phase on the wave functional Y[g, F] so that the W-D equation is extended to

    $latex
    ifrac{delta Y}{delta t}~=~HY~rightarrow~iK’_tY~=~HY.
    $

    for K_t a Killing vector. Now remember, this field is defined within some scaling or conformal setting. We can just as well chose another field conformally scaled otherwise. This wave equation is perfectly time reverse invariant, even if this “time” is in a sense fake. If we have another metric g’ it has a similar wave functional X[g', F'] and wave equation

    $latex
    ifrac{delta X}{delta t’}~=~HX~rightarrow~iK’_tX~=~HX.
    $

    Yet covariance requires that K_t =/= K’_t and so we can’t describe a superposition of states, and a path integration over possible states

    $latex
    Z~=~int delta [g]exp^{iS},
    $

    where S includes NH, is not defined in the usual sense as some parameterization of states in a time ordered sense. There is no single definition of time.

    The course graining of these metric configurations leads to an energy uncertainty functional

    $latex
    delta E_g ~sim~ |nabla (g~-~g’)|^2,
    $

    which describes a coarse graining over many metric configurations. Most of these wave functionals are over metric configuration variables which have no classical description, or in fact have no possible dynamical (diffeomorphic) description. These 4-manifolds are “fake” and this course graining of possible metric configurations, with these as well, introduces this error functional. The Cartan center of E_8 describes the set of possible M^4′s and these “fake” manifolds. This is in part why I think quantum gravity requires the S^3xSL_2(7) subset M_{24} or more fundamentally M_{24} as a quantum error correction code, which embeds three E_8′s — an E_8xE_8 for the graded heterotic supergravity field theory and the third for this configuration of all possible spacetimes. In the restricted S^3xSL_2(7) this is the Bloch sphere where each point on it is a “vector” in a three space spanned by the Fano planes associated with these three E_8′s. S^3xSL_2(7) has 1440 roots and is itself a formidable challenge, but this represents a best first approach.

    So fundamentally there is no such thing as time, or a time which describes the vacua at or “near” the start point of the path integral of the universe. It is hard to avoid tensed language here, and English is very time ordered. Russian might actually be a better language to use. Time is something which obtains on a larger scale as a coarse graining over all possible states with different metric configuration variables.

    It is interesting that in our world time is probably the second most feared thing, with the first being death. Of course the two are related in that death is a sort of ultimate deadline. Yet when one thinks about these matters with some depth these worries are put in a proper perspective. Ultimately what we fear the most is an sort of illusion, or a holographic projection.

    Lawrence B. Crowell

  • Lawrence B. Crowell

    As for fractals, there is a Hausdorff dimension with the renormalization group of running parameters. So there is a fractal-like nature to this physics.

    Lawrence B. Crowell

  • Hal S

    Lawrence,

    For benign unrelated reasons I don’t plan on posting comments for some time, I just want to thank you for your comments :-)

    Thanks.

  • John Merryman

    Lawrence,

    I agree that time isn’t a fundamental dimension, rather that it is a consequence of motion, rather than the basis for it. As such, this makes it similar to temperature, rather than space, but that doesn’t make it any less real from our perspective, as anyone who has been burned can tell. What it means is that we are more illusion than time is. To the extent there is some fundamental unity of being, it is as essential basis, rather than ideal form.

  • TERRY FRASER

    Hi, I think there is a good piont in this conversation and it is that no one wants to see a simple picture of an oval circle that has photon sensitivity in the center. The dark matter is most likely created by photon layer plates with dark matter plates separeting each other.When the plates compress there is more speed , heat , and visible electromagnetic field,and when the plates are more space the plates cool,slow down and no visible electromagnetic field.The center of the galaxy most likely is like a black hole that has cool plates entering or sucked in,then compressed to super heat, plates ejecting the very visible electromagnetic field,the gravity that is created is the plates transfer particle mass through closeing and opening of the collecting plates.Just to make life fun think of what is making this enery hole since you might now know of how black holes work,something besides collapsing stars are doing this,excuse me if this ending sounds strange.

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