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Entropy depends on observer (Dialogue on the Nature of Gravity)

  1. Oct 11, 2009 #1

    marcus

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    In the past several major advances in physics have been associated with the discovery that something wasn't absolute, but depended on the observer.

    Padmanabhan just posted A Dialogue on the Nature of Gravity, which is remarkably readable, and which argues among other things that entropy is observer dependent.

    See section 3, pages 7 and 8.

    One could conclude that this gets rid of Penrose's objection to cosmological bounce scenarios. In 2003 Penrose expressed the opinion that a Big Bounce would violate the Second Law, because the collapsing region would have high entropy (as seen by an observer with the bounce in his future), and the subsequent expanding region would have low entropy (as seen by an observer with the bounce in his past). Entropy seems to have been reduced, a violation of the Second Law. But since they are two different observers, and since entropy, instead of being absolute, is relative to the observer, the Second Law is not violated. Mr. Before and Mr. After do not define/measure the same entropy. In any case that is one possible conclusion one might draw from Padmanabhan's Dialogue.

    Apart from a few isolated tough spots, the first third or so of the Dialogue is fun reading. Thought experiments and general arguments without many equations. Dialogue can be an effective vehicle for communicating science.

    The latter half gets more technical because he is trying a tour de force---he attempts to derive the Einstein equation of General Relativity from thermodynamics. Curiously enough Ted Jacobson tried something similar, perhaps not quite so ambitious, in a 1995 paper which Padma cites. There may be something to it. Both Jacobson and Padmanabhan are recognized world class. The fact that they both had a similar intuition could be significant. As I understand it, TJ made stronger assumptions, so his result is limited but still suggestive. I have the impression that TP assumes less and derives more, so in this case he may have done more heavy lifting. This comparison could be in error. Also parts of Padma's paper refer to work still in progress.

    Here's Padmanabhan's Dialogue
    http://arxiv.org/abs/0910.0839

    Here's Jacobson's 1995 paper
    http://arxiv.org/abs/gr-qc/9504004
     
    Last edited: Oct 11, 2009
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  3. Oct 11, 2009 #2

    Fra

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    Thanks for the post, I'll try to raead Padmanabhan's paper later.

    I'd like to add to these attempts also some others. I don't know what Olaf Dreyer will come up with since his work is still in progress but he clearly expressed a vision that his "intrinsic perspecive" of internal relativy should yield imply both SR and GR. But how remains to see.

    I am very much in tune with such vision. I look forward to his future papers.

    Also Ariel Caticha, has expressed a vision to derived at least classical GR from the principles of inductive reasoning. And if you look at that, inductive reasoning based on probability theory has strong similarities with the thermodynamic reasoning of TJ.

    I think this direction is very interesting, and all of these angles are probably contributing to a new emergent understanding.

    Edit: some references to thes guys

    "My recent work explores whether the laws of physics might be derivable from principles of inductive reasoning. These principles - consistency, objectivity, universality and honesty - are sufficiently constraining that they lead to a unique set of rules for processing information: these are the rules of probability theory and the method of maximum relative entropy...

    ...The many formal similarities with the theory of general relativity suggest that the latter might be a form of entropic dynamics."
    -- http://www.albany.edu/physics/ariel_caticha.htm [Broken]

    Olaf Dreyer, progress report
    -- http://www.matmor.unam.mx/eventos/loops07/talks/7A/Dreyer.pdf

    Part of this mission statement found on fqxi grant page,

    "...When metric notions as well as notions like mass and energy are defined purely internally the emergent space-time ceases to be flat. We argue that if this is done consistently the equivalence principle and the Einstein equations emerge naturally.."
    --http://www.fqxi.org/grants/large/awardees/view/__details/2006/dreyer

    /Fredrik
     
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  4. Oct 11, 2009 #3

    marcus

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    Thanks for the extra pointers, Fra.
    I should say something about Padma's standing, since some people will find what he is saying a shock.

    He has over 200 publications on Spires, of which 15 are in the 100+ cites. These topcited papers are mainly solo, not group papers. One of his solo papers has more than 1000 cites.
    http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=a+padmanabhan%2C+t&FORMAT=WWW&SEQUENCE=citecount%28d%29 [Broken]
    And in 2005, when the premier Einstein Centennial conference was held in Paris, Padmanabhan was an invited speaker. What that says is that as a relativist (a GR-expert) he's on the all-star team.

    At this point, if Roger Penrose (78) and Thanu Padmanabhan (52) go head to head, I would not bet on Penrose. It's just how it is. Everybody is fallible, so Padma could be wrong in this paper, but you have to take it seriously.
     
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  5. Oct 11, 2009 #4

    atyy

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    A more concise version, although I'm not sure it's exactly the same, is Padmanabhan's "Gravity: The Inside Story", which took first prize in the 2008 Gravity Research Foundation essay competition. http://www.gravityresearchfoundation.org/pdf/awarded/2008/Padmanabhan_2008.pdf [Broken]

    A technical version was published in PRD in 2006. http://arxiv.org/abs/hep-th/0607240

    I would read Padmanabhan's view as being in favour of string theory or some other emergent approach, rather than being about entropy in bouncing universes. Ted Jacobson's earlier thermodynamic reasoning also led him to say "This perspective suggests that it may be no more appropriate to canonically quantize the Einstein equation than it would be to quantize the wave equation for sound in air."

    One can quantize some sound waves - such as the phonons in a solid, but in an interacting theory, they are generally effective and not renormalizable - and as we know, phonons are indeed emergent.

    Brett McInnes has an essay about the arrow of time in the string theory landscape. http://arxiv.org/abs/0711.1656
     
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  6. Oct 11, 2009 #5
    I'm not sure I agree that these are two different observers. Is he saying that it is impossible to keep track of a single point (observer) throughout a bounce? But if you can keep track of a point throughout a bounce, then wouldn't a single observer at this single point see things getting hotter before the bounce and colder after the bounce?
     
  7. Oct 11, 2009 #6

    marcus

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    I'd be interested to know if anyone finds the 2008 and 2006 papers helpful. As you say, the former is more concise and the latter is technical. The concise version struck me as couched in shorthand aimed primarily at experts, the technical version looked like wall-to-wall equations with little attempt to provide intuition. Here in the Dialogue I think he has something of a communication masterpiece. I expect it to spread understanding to a wider audience and cause a change in the conversation. We'll see.
     
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  8. Oct 11, 2009 #7

    marcus

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    Friend, you'll just have to read, say, page 8 of the dialog and decide for yourself. He gives an example of two observers which can be at the same location but have different motion---one sees a horizon, one does not. And two observers at the same location can measure different temperature of space. Observers are not simply "points in space".

    I'm not not sure that in Padma's reality "points in space" exist. You know Einstein said that they had no objective or physical reality. I'm not sure that observers can exist at Planck density or be meaningful at Planck scale. There are paradoxes and vagueness here that I can't help resolve---that you may just need to come to terms with on your own for the time being.

    I suspect that a regime where observers can meaningfully exist is the essential meaning of this tricky word "emergence".

    When Ashtekar discusses the Loop cosmology bounce, which happens at around 40% if Planck density (as normally defined), he talks about "the quantum regime". It is not clear to me that a meaningful idea of observer exists in that regime, any more than one would exist down at smaller than Planck scale (where one cannot make any measurement).

    What is an observer where no rods exist? How can entropy continue to be defined when there are no thermometers? At this point I think a lot of us confront a bare conceptual wall and for the time being, until somebody explains more to us, we just have to decide for ourselves.

    Anyway, to the best of my ability I will try to answer your question. I suspect that no observer survives Planck scale bounce, no macroscopic physical quantity like entropy survives, and the Second Law does not survive.

    The microscopic degrees of freedom which underlie both geometry and matter DO however survive. These are what we would see if we had a zoom microscope and could examine the tabletop in front of us and see how it looks at Planck scale.

    Renate Loll has a nice cartoon of herself doing that, looking down at the weird chaotic microdegrees of freedom. Lee Smolin writes in the same terms, about the "atoms" of space/time. This is the same language as Padmanabhan occasionally uses in his dialogue.
    This idea of underlying microscopic degrees of freedom is also basic to Loop gravity as Rovelli presents it.

    The basic idea of emergence from a so-far-undefined Planck scale physics, in Loop-and-allied approaches, is different from some other versions of the "emergence" story.
    In Loop-and-allied approaches the underlying ground still has locality. It is microscopic and different from what we're used to by way of geometry+matter, but it is there.

    It is not a holodeck projection from some distant screen, or figment of abstract algebra. There is something here and now, down at Planck scale, and the geometry+matter we see here and now arises from it, but those micro degrees of freedom are hard for us to imagine. And I suspect the concept of an observer with his rod and clock does not apply down there. Still, it has locality, perhaps even a causal structure (not sure though.) So Loop, CDT, etc have a fairly rudimentary idea of emergence, as compared with some other approaches.
     
    Last edited: Oct 12, 2009
  9. Oct 11, 2009 #8

    atyy

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    Doesn't Ashtekar say something like time, or at least a cosmological arrow of time, does not survive?

    p181, http://books.google.com/books?id=ZNr0jue-b9cC&dq=solvay+time+conference&source=gbs_navlinks_s

    With regard to emergence, while Padmanabhan (like me) seems to prefer true emergence such as strings, quantized sound such as phonons can provide a statistical mechanics underlying thermodynamics. The problem is interacting phonons are usually not renormalizable, so they'll be unreliable at high energies. In the true true emergence point of view, even QCD should be emergent, even though it can in principle can hold at arbitrarily high energy due to asymptotic freedom. (The fake true emergence point of view is string theory, since string theory is not emergent.)
     
    Last edited: Oct 11, 2009
  10. Oct 11, 2009 #9
    What about "birds view" observer?

    Lets talk about entropy as the number of states. If in BB-Big Bounce there is only one possible state (some sort of vacuum) and there were more states before the BB then evolutions is not unitary. Period.
     
  11. Oct 11, 2009 #10
    If no information survives the bounce, then you could not tell the difference between a bounce and a creation.
     
  12. Oct 11, 2009 #11

    Fra

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    I haven't gotten around to reading Padmanabhan's paper yet, but I'd like to add my emphasis to general, but KEY points raised by marcus:
    I think these points are good and crucial and no sound reasoning can IMO escape confronting these at face. These are typical point raised if you take the inside view seriously.
    The problem of how to describe emergence, without having a fixed something to start with is difficult but this is IMO where the idea of evolving constraints really seem like a natural solution.

    But I think we need something more radical than smolins CNS. We are getting closer I think if we combine smolins idea with Padmanabhan's idea to not distinguish general horizons from black hole horizons. If we take this one step further the horizon could simply be seen as a distinguishable window of fixed resolution to the environment. Then that is starting to look even closer to how I envision the abstraction of an "observer". The generalisation would even remove the space interpretation of the horizon, and it's instead a more abstraction information channel, that "indexes" events to the inside observer. And one could then work it around the other way and define space from a more general framework.

    The very notion of "thermodynamics" really means that we think of the einstein equation as a statistical state equation, which essentially is an EXPECTATION, based on some max ent reasoning on the choice of microstructure. But if this EXPECTATION is to describe also the actual processes as real time flows, one must also add the condition of a kind of equilibrium. IE. an equilibrium where the microstructure is not changing.

    This as I see it, makes this fully compatible qith the idea of evolving law, since the evolutions really corresponds to off-equilibrium, and there the expectations clearly aren't valid, not more that ordinary thermodynamical state equations apply to non-equilibrium systems far from equilibrium - consider say the gas laws for a highyl radioactive and decomposing gas.

    It's in this sense I think gravity can be emergent - if say Einsteins equations are to be seen as an equilibrium condition in the fundamental microstructure, that also selectes the specific "law". The evolving law could be nothing but the "equilibration".

    I'm looking for clues howto describe this process. I think what we really are looking for is an "inside view" of (statistical) inference, where there exists no external objective microstructure. Thermodynamics is a prime example of a statistical inference, but where the microstructure is frozen.

    This faces problem of both the meaning of "statistics" and thus how to count evidence in such an intrinsic theory. But I think this is questions we have to face, and resolve.

    /Fredrik
     
  13. Oct 11, 2009 #12

    atyy

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    What about the renormalization group? Take a look at the "Epilogue: Beauty is Truth" in Kerson Huang's http://books.google.com/books?id=q-CIFHpHxfEC&dq=kerson+huang+quantum&source=gbs_navlinks_s

    "A fixed point is a structure of pure mathematics, a thing of beauty .......... Physics is truth. It sails down a trajectory in the space of Lagrangians when the energy scale shrinks from that set by the Big Bang. It gets attracted to fixed points and lingers in their neighborhoods - as it must by nature of fixed points. The journey thus proceeds from fixed point to fixed point, and only at these ports of call do we have the opportunity to observe and understand it. And at these times, beauty and truth become one."
     
  14. Oct 11, 2009 #13
    Do you recognize this as an attempt to derive physics from "inference" alone? By definition it would be hard to argue with if you find it.

    You should consider the Dirac delta function, which is a type of distribution about which information and entropy can be calculated. It turns out that the Dirac delta function is transitive. The integral of a single delta function can be equated to a multi-integral of a multiple of delta functions. And when these delta functions take the form of a complex gaussian, the multi-integral can be manipulated into the path integral for a free particle. So perhaps the entropy of a gaussian delta function without reference to any underlying objects could be a constraining factor in what kind of particles exist and how they interact. PM me if you want to see the details. Does anyone know the information contained in or the entropy of a gaussian distribution or a Dirac delta function? I suspect it's zero, or perhaps not. Thanks.
     
    Last edited: Oct 11, 2009
  15. Oct 12, 2009 #14

    Fra

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    You have a point. But my previous objection to your physics from pure logic was that I think of this in a different way that I THINK you meant it.

    The scientifinc process itself IS an inference process, I also think PHYSICAL processes also fit into inference processes IF you take seriously the inside view.

    But the inference system itself, doesn't come from nowhere, it is evolving and the only way for getting real feedback is to put it to work and let it interact with it's own environment. So since a human is actually interacting with it's environment all the time, the pure thought inference is not really free from environmentally induced evolution. A human brain would not develop if it was isolated in a mason jar. We need stimulation and challanges.

    I think our difference is this:

    We both believe in "inference" or logic...

    ...but you seem to beleive in deductive logic and hold a somewhat realist view of the deductive system itself. So that somehow there is a unique set of axioms and interpretations that describe reality, that is independent of the observer.

    ...I think take the evolution of the infernece system itself to be part of reality. Since there is in my view an uncertatatiny in the inference system itself, the inferences are not deductive, the are more inductive. And in my view, the inference system at hand today, is a result of past inference processes. So the inference system is also inferred. This leads to an origin problem, which I envision solved by starting at the zero complexity limit.

    So while you seem to say that we could DEDUCE the laws of physics from logic, I think we have no choice! but to GUESS/INDUCE the laws of physics from the information we have at hand, and this information defines a natural inference system, that is closely resembling probabilistic reasoning, thermodynamics and statistical inference. But there are more complications since statistical records must also be estimated from inside information, meaning that there are no 100% certain distributions.

    My conjecture is that this game, does produce stable equilibriums, that comes with effective laws. So if we can understand this game, we could perhaps predict some but not all things!

    I have no illuision that any kind of inference can predict the future! What we can do though, and very well os, is GUESS the future. All that is required is that the actions based on our expected future serve us well enough so that we survives the ACTUAL future. In here is also a selection, since bad inference systems that fail to be adapative and flexible simply have to fitness and they become supressed in the population.

    So I think I believe in evolving soft logic, and you belive in harder logic? I think the problem with hard logic is that it's subject to running into a halt, if it fails to resolve a situation. Soft logic wont do that, instead the stability is ensured by constraints, usually weights os that although even weird things are allowed, they have sufficiently low weight to not destabilise everything.

    I don't think I got this remark? I'll PM you on that.

    /Fredrik
     
  16. Oct 12, 2009 #15

    Fra

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    I'll try to check that later, this week will be tight for me as I'll be assisting a fair.

    There are strong similarities with what I envision about scaling laws, or inside views of laws that depends on the complexity scale. But regular renormalisation theory is too simple, and is built on far more realist foundations. Wether that paper is some new view of it, I have to read it and check.

    IF the radical views I advocate would work, then the right normalisation scheme would be built into the theory and be a proper integral part of it, not just a fix. The correct physical description must respect the right complexity scale. This is why I think as the inside observers shrink, there is no other choice but to face unification. As there is no ROOM for diversity.

    Then the other way around to see how this again self-organises as the complexity increases and larger and larger confined energy systems form.

    I think the complexity renormalisation, is tightly related to the origin of mass and inertia and this also constrains the complexity of distinguishable law. But I try to work from the inside and out, this is where it's evolution. If you do the outside-in approach, you can just average out information which doesn't I think reflect the true inside view. It also doesn't work fully since the amount of information one has to reduce in the first place is overwhealming, so it's only a partial success, that works when you study small subsystems of which you can monitor the environment.

    /Fredrik
     
  17. Oct 12, 2009 #16
    Actually, I was wrong, I forgot that for the bird-view observer the total information in the universe is 0

    It is possible that universe collided and bounced, but if entropy at BB was very small, then entropy increased AT BOTH SIDES of the BB. So, in pre-BB time entropy decrased over time. Hence, all observers in pre-BB era interpreted it not as contraction, but expansion from the BB!

    So instead of contraction->BB->expansion we have 2 mirror Big Bang scenarios. These 2 BB 'worlds' can be isomorfic if we replace t with -t. So an answe to 'what was before the Big Bang/Big bounce is very unusual.
     
  18. Oct 12, 2009 #17

    Fra

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    More: I do not think of the renormalisation flows as mathematical abstractins, in the proper inside view, a complexity renormalistaion is a physical process, it's the acquisiion of mass(confidence), and this process runs in real time, and the "transformations" must be constrained by the physical constraints and inertia(also related to complexity).

    This is taking the correct inside observational perspective seriously from start when reconstructing the interactions, rather than starting with a given interaction and try to "renormalise it". The results will I think be different. It doesn't make sense ot have a UN-normalised interaciton, since it would correspond to a non-physical interaction for me. And the only physical correspondence of such shifts, are actual processes like for example acquisition of mass. How and observer gains control and mass from its' environment and as that happens, new interactions also become distinguishable.

    /Fredrik
     
  19. Oct 12, 2009 #18
    But an observer may simply be "a moving point in space" - a position and a velocity. At least the two objections mentioned above can be overcome if we just equip the observer with a velocity.

    One can of course consider spatially extended observer's, but that is a reducible case. It also opens up a can of worms about how different parts of the observer observe each other; how does the left hand know what the right hand is doing? Irreducible observers are pointlike and trace out trajectories in spacetime.

    Which brings me to my favorite slogan: the outcome of every physical experiment depends on the observer's physical properties, in particular his mass and charge.

    I suspect that this question is ill-posed. It is similar to asking what is the simultaneous position and momentum of an object. You can ask that question, but Heisenberg told us that it does not have a meaningful answer.

    This stance gets rid of Einstein's hole argument at once. If physics cannot say anything about regions where there are no observers, any questions about matter-free regions of space are meaningless.

    Entropy is the log of the number of states.

    This reminds me of something that I don't understand with the Bekenstein-Hawking relation between entropy and area of black holes. The number of states can be counted, and all observers should agree about this number; or at least their disagreement should be an integer. OTOH, an observer which undergoes a Lorentz transformation will see a different area due to length contraction. A black hole with radius R has area 4 pi R^2 in its rest frame, but an ultra-relativistic observer will see it flattened to two discs, with total area 2 pi R^2. How can something which transforms in this way be equal to the number of states?
     
  20. Oct 12, 2009 #19

    marcus

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    Hi T.L.
    The post you quoted wasn't written well. (Yesterday was hectic, being in a rush didn't help.) I could insert "at a scale", to make it clearer. Let me try to say it this way:

    In classical relativity, the Hole Argument works because one can imagine (operationally defined) observers even where there is no matter. I am not asking for actual material rods :smile:. I'm talking about the possibility of measurement.

    I think what I am saying is that the concept of an observer becomes dubious at extremely small scale. Also at very high density. I don't feel I understand conditions in what is called "the quantum regime" at the moment of an hypothetical bounce, but at least see no reason to suppose that conventional classical measurements could conceivably be made.

    My question which you quoted is in part a philosophical one. What is an observer that cannot (even in principle) make measurements? I try to define concepts operationally.

    You may have a more satisfactory conception of what "points" are at planck scale, and at near-planck density. You may have a better understanding than I do of "moving points", under those conditions, and "point particles". My perhaps quite unsatisfactory conception is that, if the cosmological bounce can be real at all, there is a brief episode when all that exists is the wave function.

    The conventional features of reality with which one does classical thought experiments therefore operationally break down, or at least become doubtful.

    Nevertheless, the researchers can run computer models of the quantum state evolving through a bounce. Something seems to exist, that we can do physics with. There is a model of existence which contracts and then expands according to the postulated equations.
    After a few tens of planck times (in the simulations) it begins to look approximately classical and thereafter it reproduces what we expect from the classical cosmological model.
     
    Last edited: Oct 12, 2009
  21. Oct 12, 2009 #20
    marcus, what these models tell us about the information of the pre-big bounce era? because when we look at simulations we have the birds view.

    Do different states 'merge' just before the BB so the number of states decreases?
     
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