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

In summary, Padmanabhan's Dialogue argues that entropy is observer dependent, and that this gets rid of Penrose's objection to cosmological bounce scenarios.
  • #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
 
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  • #2
marcus said:
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 this is something similar in a 1995 paper, if i remember right. There may be something to it. Both Jacobson and Padmanabhan are recognized as world class GR experts. The fact that they both had a similar intuition could be significant.

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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  • #3
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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  • #4
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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  • #5
marcus said:
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.

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?
 
  • #6
atyy said:
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'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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  • #7
friend said:
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?

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.
 
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  • #8
marcus said:
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.

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.)
 
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  • #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.
 
  • #10
If no information survives the bounce, then you could not tell the difference between a bounce and a creation.
 
  • #11
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:
marcus said:
Observers are not simply "points in space".
marcus said:
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.
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.
marcus said:
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.
marcus said:
I suspect that a regime where observers can meaningfully exist is the essential meaning of this tricky word "emergence".
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
 
  • #12
Fra said:
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.

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."
 
  • #13
Fra said:
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.

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.
 
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  • #14
friend said:
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 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 believe 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 believe 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 won't 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.

friend said:
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.

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

/Fredrik
 
  • #15
atyy said:
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."

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
 
  • #16
Dmitry67 said:
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.

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.
 
  • #17
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
 
  • #18
marcus said:
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".

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.

marcus said:
What is an observer where no rods exist?

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.

marcus said:
How can entropy continue to be defined when there are no thermometers? ... The microscopic degrees of freedom which underlie both geometry and matter DO however survive.

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?
 
  • #19
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:

marcus said:
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 [at a scale] where no rods [could] exist? How can entropy continue to be defined when there [could be] no thermometers?

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.
 
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  • #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?
 
  • #21
Thomas Larsson said:
Entropy is the log of the number of states.

Yes, in a given macrostate. One can ask "whose macrostate?"
Padmanabhan has what I think is an interesting discussion of entropy and why it is observer dependent.

One of the thought experiments involves a classical largescale black hole and two observers: one standing at a distance from it and one falling through the horizon. The inertial observer falling through the horizon does not, according to Padma, see the horizon as having a temperature. He doesn't see the Hawking temperature, or the entropy, that we associate with the horizon.

Padma declares a principle of democracy :biggrin:. He says that observer is just as good as any other observer. I suppose one can think of the black hole as very big and the inertial observer as having many happy hours of life still remaining to him, even though he is just now passing thru an horizon (which to him is invisible.) In Padma's view the entropy of a black hole is definitely not an absolute. It seems to depend strongly on which observer is looking at the hole.

This seems to have a partial overlap with what you were asking, suggestive (though not exact) similarity. Please let me know if you see a flaw in Padmanabhan's discussion on pages 7 and 8. I tend to think of him as one of the top experts in the field, so it would be very helpful if you could find some questionable point in the argument.
 
  • #22
Dmitry67 said:
Do different states 'merge' just before the BB so the number of states decreases?

Hi Dima, entropy is based on counting the number of microstates per macrostate.

The macrostates depend on the variables like temperature and density and pressure which matter to us, or to whatever beings are doing the physics. We don't distinguish between different microstates which we perceive as indistinguishable---it's all the same macrostate to us.

So you can picture state-space like a wide stretch of sandy beach on which you draw a map of macrostates. The tide is out. You take a stick and scratch boundaries in the wet sand, dividing the beach into regions. These regions are the macrostates and each grain of sand inside the boundary of some region is a microstate. After that, you only care which region of state space, not which grain of sand.

In this oversimple cartoon, the entropy associated with some region is the log of the number of grains of sand in it.

The true state of the universe wanders randomly from grain to grain and it has come into one of the very large regions that you drew. Therefore the entropy according to your measure is large.

Now the tide comes in. You the observer die. Your map of borderlines and regions that you drew in the sand is erased.

The tide goes out again and a new observer appears, who with his stick draws a new map, his macrostates. He happens to draw a small macrostate region around the grain where the true state of the universe currently happens to located. For him the entropy of that macrostate is small. It is a region containing comparatively few grains of sand, so the log of the number of states is small.

New observer, new map of macrostates (still the same same space of microstates but) a new ball-game.

This is not a physical explanation, just a way to visualize. Maybe your way, where you picture microstates merging, is just as good a way. I can't say, your picture may be even better---but it is not intuitive for me, so I sketched this alternative one.
 
  • #23
I understand your analogy, this is very cool.

but marcus, can the whole universe be considered one macrostate in the birds view?
 
  • #24
You could poll Tom Stoer, Thomas Larsson, Fra, and others about that. My tentative view is that the state of the universe could be one quantum state, one vector in a grand Hilbertspace. If only we knew how to construct that Hilbertspace.

Then a macrostate would be a linear subspace of that grand Hilbertspace. The entropy would be the log of the dimension of that subspace.

In classical thermo one counts the microstates in a macrostate, like beans or grains of sand, and take the log.
In quantum one looks at the dimensionality of the macrostate, and takes the log.

Essentially the beans that one is counting are "basis vectors" or vectors in a minimal spanning set.

You need to ask others. I worry that there could be something philosophically wrong with imagining that one could ever have a "wave function of the universe". Or that such a thing is satisfactorily constructible even in principle. But as a matter of fact people do construct simplified approximations to that. You know how in classical cosmology one makes the simplifying assumption of symmetry (homogeneous isotropic universe, a uniformized approximation to the real thing) and gets the Friedman model. Then all the work is done using versions of the Friedman model. The same thing happens in quantum cosmology---in that simplified sense one does have a wave function of the universe and recent simulations show it undergoing a bounce. The wavefunctions used are typically peaked around some classical state. I suppose that preliminary sort of work suggests that it might be OK to imagine a Hilbertspace of states for the real thing.
 
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  • #25
ok, another question.

Do you think that it is possible that entropy decreases before the big bounce?
In that cases there are no problems at all with the entropy. it was very small at BB and then increased on both sides. On the both sides observers interpret it as a EXPANSION and 2 big bangs.
 
  • #26
marcus said:
You need to ask others. I worry that there could be something philosophically wrong with imagining that one could ever have a "wave function of the universe". Or that such a thing is satisfactorily constructible even in principle.

While reading this post I got to thinking about whether it is possible to construct one "wavefunction" of the universe. I'm not an expert, I'm on the edge of my understanding in this, and everyone is welcome to correct me if I'm wrong, but as I recall, a wavefunction is also considered a propagator, or green's function, and looks like a Dirac delta function. The integration of one Dirac delta function is equal to one. But this integral can be equated to a multiple integral of a multiple of delta functions which in turn can be equated to Feynman's path integral. See the following link for this easy calculation:

http://hook.sirus.com/users/mjake/delta_physics.htm [Broken]

My point is that it seems physics can be broken down into one delta function or wavefunction. Does this mean that there is one wavefunction that describes the universe?
 
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  • #27
Dmitry67 said:
ok, another question.
...Do you think that it is possible that entropy decreases before the big bounce?...
We have to keep in mind that current cosmo models involving a bounce might not be right. There's an ongoing effort to derive predictions that can be looked for. Say in the spectrum of fluctuations in the CMB.
But if they do happen to be at least approximately right, the stuff I'm familiar with has pretty ordinary time evolution. A collapse, a bounce, an expansion. Behavior is essentially classical except for a tiny fraction of a second right around the bounce. Ordinary classical GR and classical thermodynamics work, except in the quantum regime where conditions are at such extreme scales that conventional physics apparently does not apply.

So entropy is increasing with time all the way along. But before the bounce it is the pre-bounce observer who determines the map of microstates and defines entropy. After the bounce it is a different observer who determines what is distinguishable and defines the entropy. They have radically different perspectives and define radically different entropies.
But in the current models I know about, I don't think that the Second Law is violated.

I could be quite wrong about this, collapse might cause a big decrease of entropy, as you suggest---but does that happen during the collapse of a star to form a black hole? We think that it does not, at least not from the standpoint of a stationary observer well outside the black hole. I know that doesn't prove anything, but I suspect that from a pre-bounce perspective collapse can involve increasing entropy just as the Second Law teaches us to expect. Hope some others will comment on this.
 
  • #28
no, marcus, it is not a big bounce which cause a decrease in entropy. entropy decreased all the way down to the big bounce.

So what I suggest is that arrows of time point in the opposite directions of the big bounce.

Not this:

-inf >>> time >>> BB >>> time >>> inf

but

-inf <<< time <<< BB >>> time >>> inf

I am curious, why all people silently assume that arrow of time does not change the direction at the BB? if would be so easier if it did for so many reasons!
 
  • #29
Dmitry67 said:
-inf <<< time <<< BB >>> time >>> inf

I am curious, why all people silently assume that arrow of time does not change the direction at the BB? if would be so easier if it did for so many reasons!

Your picture of time arrow changing direction seems to violate the 2nd Law. It is hard for me to understand how it makes things easier. :confused:

collapse and expansion are quite asymmetrical, as I picture it. I keep the time arrow running in the same direction and during collapse I see a huge increase in entropy because of the formation of zillions of black holes. From the perspective of a before-bounce observer, he sees a sky full of black holes and he sees a huge sum of all the individual entropies, plus whatever other entropy.

A black hole is the epitome of where lots of microstates belong to a macrostate because you can't see inside, because of the horizon. As time goes on the universe gets more and more like that---essentially entropy is going to infinity.

Then the universe enters quantum mode and starts to bounce. All the black holes are abruptly erased. How could they exist in the quantum regime where you don't have classical observers or horizons or any of that structure? After a little while we have big bang conditions. A smooth expanding geometry. A universe filled with radiation etc etc. The usual story.
It is not the reverse picture of the collapse, and not merely playing the collapse movie backwards :-D. It represents starting off with an almost clean slate. Low entropy. The geometry hasn't had a chance to wrinkle, pucker, develop pimples and warts. As it will with time.

This is just an impressionistic what-if kind of sketch, but it may help you see why I can't follow your backwards time scenario. You seem to me to be running into trouble with the 2nd Law. Maybe this is just a difference in the way we think about gravitational collapse and the big bang---we may simply picture things differently and not be able to resolve it.
 
  • #30
marcus, arrow of time points to the direction where entropy increases. So on the fundamental level 2nd law is telling us that entropy increases in the direction, where entropy increases :)

I don't like your assymetric picture for 2 reasons:
1. complicated initial conditions at t=-inf
2. dramatic decrease of entropy few Planck times before the BB

I just suggest evaluting the symmetrical scenario: double-sided BB, in t>0 area coordinate time and apparent time point in the same direction, in t<0 area - in opposite direction. For both observers initial conditions are very simple at BB. Observers can not tell if they are at t>0 or t<0

To make it even more beautiful, in MWI (and only in MWI) both sides must be absolutely identical. So BB is a mirror. events at t=x are equivalent to events at t=-x. I am really shocked by the beauty of that picture
 
  • #31
I'm wondering, if things start to converge close to the plank length during the collapse, then wouldn't all thing start to become entangled and indistinguishable so that you end up with fewer possible states to describe the whole? This would sound like entropy decreasing, wouldn't it? If everything crunched down to a single particle, wouldn't information be lost and entropy decrease?
 
  • #32
Another way of making it intuitive why entropy is relative is from the point of view I have:

Thomas Larsson said:
Entropy is the log of the number of states.

I think the original purpose of "entropy" is that it is supposedly a measure of missing information. The very obvious question is - you know what you know, but how do you actually measure your own ignorance, given that you don't know what you don't know?

The thing is simply that it relies on a "microstructure of information" and the ergodic hypothesis.

This renders the information measure at least relative to this choice and hypothesis.

In my view, the microstructure of information and the ergodic hypothesis are both part of the observers identity in a similar sense of Zurek's words (what the observer knows, is indistinguishable from what the observers is). Different observers, have different expectations, and therefor may act in ways that make them "interact" in ways that doesn't preserve the status quo.

So for me, this means that the microstructure, which somehow defines the set of distinguishable states, and the corresponding prior distribution on that, are a result of the observers evolution. At each "present", the observer "sees" and arrow of time that simply is the direction of the "expected future" calculated from the observers distinguishable state space and prior relative information about it's own environment.

However, this arrow of time is only of a local differential nature, there is no global arrow of time because as time progresses, the arrow adjusts in response to the observers own evolution as the number of microstates changes.

I think the clarify comes when you required the representation of distinguishable microstates to be physical - this means that as an observer looses mass and cmoplexity, it's space of distinguishable events are decreasing.

So I for one think the relative notion of entropy is plausible and natural. There is no physical sense in trying to define a global observer independent notion of entropy for me.

/Fredrik
 
  • #33
friend said:
I'm wondering, if things start to converge close to the plank length during the collapse, then wouldn't all thing start to become entangled and indistinguishable so that you end up with fewer possible states to describe the whole? This would sound like entropy decreasing, wouldn't it? If everything crunched down to a single particle, wouldn't information be lost and entropy decrease?

That's where detailed calculation is needed, I would imagine. Do things have time to coalesce? If concepts like observer and horizon still mean anything at that point, then does a merger have time to occur? Does a larger horizon have time to form? Does the observer have time to see the new horizon and determine the new entropy?

I haven't read much about collapse or "crunch", and the thermodynamics involved, but I will make a small point.

Keep in mind that the Schwarzschild model of a black hole is a rather "equilibrium" type thing, so in this very messy rapid confusion of collapse it is a crude approximation.
But I suppose that in this huge complex collapsing mess, black holes of many masses and spins will predominate (spin determines shape, or oblateness, not all are spherical).

And in the Schwarzschild approximation entropy of horizon (i.e. seen by remote hypothetical observer) is proportional to square of mass.

So if M and M' merge, the entropy increases.

(M+M')2 > M2 + M'2

==================

Intuitively, as I picture the collapse of what is by now an incredibly complex stew of black holes, the observer (as long as the concept of observer remains viable) becomes more and more ignorant of what is going on. More and more information is occluded by dynamical effective horizons. Less and less time remains for information to reach him. And he may also be becoming more and more indifferent to detail. Differences which might earlier have meant something become mere indistinguishable "microstates".

Essentially, as I picture gravitational collapse from the standpoint of an observer participating in it, the entropy diverges to infinity.

The little algebraic inequality about the merger of Schw. black holes is just a token or toy model of the realworld explosion of entropy which I reckon to be considerably more drastic.

================

Fra, thanks for your comment. It helped me develop an intuitive picture. I'd still be interested to find out what other people might say about this, and I'm particularly curious about how Padmanabhan would describe a bounce.
 
  • #34
may be I am not understanding something obvious, but why all people are talking about the CRUNCH before the Big Bounce?

't' is just a coordinate. There are no signs on that axis showing 'Future -> In that direction'. 2nd law works ONLY because of the initial conditions at Big Bang: low entropy at the BB. Otherwise (Loshmidth paradox) 2nd law would not exist.

So if we assume that universe is smooth enough, and entropy at BB was low, now it is higher, isn't that obvious that the same logic must be also applicable before the BB, at t<0?

Pre-BB era (t<0) and After-BB era (t>0) can share the same time (varibale t), but for God's sake, why everybody assumes that arrow of time at t<0 points in the same direction? arrow of time ALWAYS points away from a state with low entropy!
 
  • #35
Dmitry67 said:
may be I am not understanding something obvious, ...

... ALWAYS points away from a state with low entropy!

The obvious thing you are missing is contained in pages 7,8 of the paper which is the topic of this thread.
There is no such thing as a state with low entropy in some absolute sense.

Entropy depends on the observer. Therefore it is not an intrinsic property inherent to the state. Therefore you cannot make a statement like "time points away etc etc" without specifying the observer who observes the entropy.

But there are now hundreds of papers relating to the cosmological bounce. Many researchers have studied bounce cosmo models. There are equation models and computer models. They all proceed by time evolution starting with collapse and proceeding to expansion. This does not violate the second law for any observer. I think this has been explained enough now, Dmitry.
 

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