The 'time oriented coarse graining' hypothesis -- "Rovelli"

[John86]

http://arxiv.org/abs/1407.3384

Why do we remember the past and not the future? The 'time oriented coarse graining' hypothesis
Phenomenological arrows of time can be traced to a past low-entropy state. Does this imply the universe was in an improbable state in the past? I suggest a different possibility: past low-entropy depends on the coarse-graining implicit in our definition of entropy. This, in turn depends on our physical coupling to the rest of the world. I conjecture that any generic motion of a sufficiently rich system satisfies the second law of thermodynamics, in either direction of time, for some choice of macroscopic observables. The low entropy of the past could then be due to the way we couple to the universe (a way needed for us doing what we do), hence to our natural macroscopic variables, rather than to a strange past microstate of the world at large.

Is Rovelli saying that the low entropy state of the universe plusminus 13.7 bilion years ago is not the whole story ? I don't fully understand what he is trying capture here.
Could t be that the discrete strutcture of the low entropy state universe thet whe vision after singularity or Bounce or whatever the universe state was 13.7 billion years ago, has something to do with our macroscopic ensemble view.

 

[marcus]

http://arxiv.org/abs/1407.3384
Why do we remember the past and not the future? The 'time oriented coarse graining' hypothesis
... The low entropy of the past could then be due to the way we couple to the universe (a way needed for us doing what we do), hence to our natural macroscopic variables,...

Is Rovelli saying that the low entropy state of the universe plusminus 13.7 bilion years ago ... has something to do with our macroscopic ensemble view.

Yes. Entropy is not an intrinsic/absolute quantity. It depends very much on the choice of macroscopic variables.
So you are right: the fact that we reckon the entropy of the universe, then, to have been low has VERY MUCH to do with our natural macroscopic variables (those through which we, by our nature, couple to the universe).

 

[John86]

Yes. Entropy is not an intrinsic/absolute quantity. It depends very much on the choice of macroscopic variables.
So you are right: the fact that we reckon the entropy of the universe, then, to have been low has VERY MUCH to do with our natural macroscopic variables (those through which we, by our nature, couple to the universe).

But than Marcus, macroscopic statements as singularity continuüm or discreet states will also be generalized.

 

[marcus]

My problem is with my own imagination. I cannot imagine anything more interesting and important than what we call "life forms" and I cannot imagine a life-form that does not couple to the universe via macroscopic variables we call "frequency" and "energy".

The "time oriented coarse graining" paper is primarily about that: about defining alternative sets of macro variables, alternative maps of macro states, if you can do that then obviously the definition of entropy changes. Entropy of where you are is just the "size" of the macro state you are in (i.e. log of number of microstates it comprises). If you change the map of macro countries, you change all their sizes and it is a new game. TOCG paper sets up a toy model balls-in-box universe where we can easily SEE alternative macro variables. My difficulty is in imagining how to extend that to the real universe we see and live in: what other macro variables could IT have?

 

[atyy]

Is Rovelli's paper related to this paper which also investigates whether the second law of thermodynamics can be derived by examining whether subsystems of an isolated quantum system can come to local equilibrium?

http://arxiv.org/abs/1402.3380
The approach to equilibrium in a macroscopic quantum system for a typical nonequilibrium subspace
Sheldon Goldstein, Takashi Hara, Hal TasakiGolstein and colleagues trace their work back to von Neumann. Here is a commentary on von Neumann's paper.

http://arxiv.org/abs/1003.2129
Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
Sheldon Goldstein, Joel L. Lebowitz, Roderich Tumulka, Nino Zanghi

"For a "typical" finite family of commuting macroscopic observables, every initial wave function ψ₀ from a micro-canonical energy shell so evolves that for most times t in the long run, the joint probability distribution of these observables obtained from ψ_t is close to their micro-canonical distribution."

 

[John86]

My problem is with my own imagination. I cannot imagine anything more interesting and important than what we call "life forms" and I cannot imagine a life-form that does not couple to the universe via macroscopic variables we call "frequency" and "energy".

The "time oriented coarse graining" paper is primarily about that: about defining alternative sets of macro variables, alternative maps of macro states, if you can do that then obviously the definition of entropy changes. Entropy of where you are is just the "size" of the macro state you are in (i.e. log of number of microstates it comprises). If you change the map of macro countries, you change all their sizes and it is a new game. TOCG paper sets up a toy model balls-in-box universe where we can easily SEE alternative macro variables. My difficulty is in imagining how to extend that to the real universe we see and live in: what other macro variables could IT have?

Yes i see, this surpasses my horizon of imagination to.

 

[marcus]

macroscopic statements ... singularity ... will also be generalized.

If I understand the gist, I think you are making a good point. What about the "start of expansion"?

How do we define macro variables on it? Who is coupled to it, interacting with it, experiencing it?
What are the relevant macro variables? It is a very dense state, as we understand dense. A lot of energy, as we understand energy. Perhaps there is a bounce. Does the bounce happen very quickly? Who or what is keeping time?

There have been several papers recently arguing that in the quantum regime at bounce there is a signature change---from Lorentz (with lightcones and extended present) to Euclidean (as if the speed of light suddenly for a flickering instant became infinite). This troubles me, this suggested "signature change". Only one or two people are talking about it, so perhaps for the time being one should simply be aware that it is being mentioned in the literature but not pay very close attention.

 

[atyy]

I just came across an intriguing paper about signature change from a non-LQG group.

http://arxiv.org/abs/1403.0580
Emergent Lorentz Signature, Fermions, and the Standard Model
John Kehayias, Shinji Mukohyama, Jean-Philippe Uzan

 

[marcus]

In reply to post #5, "is Rovelli's paper related to [a paper by Sheldon Goldstein]?"
I think probably not. Both use the word "entropy" but otherwise don't see much overlap.
If interested, here's an interview with Goldstein (b. 1947, math dept Rutgers)
Here's a less technical, less specialized paper of his to give an idea of his turn of thought:
http://arxiv.org/pdf/cond-mat/0105242v1.pdf

I think Rovelli's concern is with the perception of low entropy at start of expansion---e.g. at the LQC bounce. And our perception that change (time) has a direction. Why don't we remember the future? The TOCG hypothesis (rightly or wrongly) assumes that different coarsegrainings are possible, different choices of macro variables, and that our set of macros is part of our identity, so that the direction of time is somehow rooted in who we are. This idea comes as a shock and goes against one's strongly held preconceptions.

I'm not sure that either signature change or signature emergence (two different ideas) is relevant to the TOGC paper. I mentioned the former (brief episode of Euclidean signature RIGHT AT the bounce) because it might be relevant to the TOGC hypothesis. It might turn out that, like a horse that throws off its rider, no coarsegrainings are possible in that moment when the signature is Euclidean and the U throws off all its macroscopic variables. Then a moment later it is back to normal, Lorentzian signature is resumed.

The assumption is that underlying spacetime reality has Lorentz invariance (except according to some people right at the bounce).

This is different from the "emergent Lorentz signature" idea where people study models in which underlying reality is Euclidean forever and the Lorentz signature somehow constantly emerges from that. E.g. http://arxiv.org/pdf/0806.4239v2.pdf (Girelli, Liberati, Sindoni)
"In the first section, we have considered fields that live in a Euclidean space, and showed that there exists a class of Lagrangians such that the perturbations around some classical solutions ψ ̄ propagate in a Minkowski spacetime. In this case ψ ̄ is essentially picking up a preferred direction, so that we have a spontaneous symmetry breaking of the Euclidean symmetry. The apparent change of signature is free of the problems usually met in signature change frameworks since the theory is fundamentally Euclidean. Lorentz symmetry is only approximate, and in this sense it is emergent.
The main lesson we want to emphasize here is that Lorentzian signature can emerge from a fundamental Euclidean theory and this process can in principle be reconstructed by observers living in the emergent system. In fact, while from the perturbations point of view it is a priori difficult to see the fundamental Euclidean nature of the world, this could be guessed ..."

 

[atyy]

In reply to post #5, "is Rovelli's paper related to [a paper by Sheldon Goldstein]?"
I think probably not. Both use the word "entropy" but otherwise don't see much overlap.
If interested, here's an interview with Goldstein (b. 1947, math dept Rutgers)
Here's a less technical, less specialized paper of his to give an idea of his turn of thought:
http://arxiv.org/pdf/cond-mat/0105242v1.pdf

I think Rovelli's concern is with the perception of low entropy at start of expansion---e.g. at the LQC bounce. And our perception that change (time) has a direction. Why don't we remember the future? The TOCG hypothesis (rightly or wrongly) assumes that different coarsegrainings are possible, different choices of macro variables, and that our set of macros is part of our identity, so that the direction of time is somehow rooted in who we are. This idea comes as a shock and goes against one's strongly held preconceptions.

Perhaps the two papers are not related, but the part of Rovelli's paper that caught my eye was the quantum section "The point here is not to assume the tensorial structure of H a priori. Instead, given a generic state, we can find a tensorial split of H which sees von Neumann entropy grow in time." (Entanglement Entropy )

This seems similar to Goldstein et al's "We prove that, for a typical choice of "nonequilibrium subspace", any initial state (from the energy shell) thermalizes..." Actually, it may be closer to an earlier paper from Goldstein, Lebowitz, Tumulka and Zanghi http://arxiv.org/abs/cond-mat/0511091, as well as the similar paper of Popescu, Short and Winter http://arxiv.org/abs/quant-ph/0511225, both of which use the entanglement entropy explicitly. But I don't think either of those had an argument for the arrow of time.

 

[atyy]

Here are some bits of the Goldstein paper http://arxiv.org/abs/1402.3380 in which the notion of "equilibrium state" or "non-equilibrium state" is said to depend explicitly on the choice of macroscopic observable, which I think is similar to Rovelli's point.

"Consider the simplest situation where one is interested in the behavior of a single macroscopic quantity $\hat{O}$ , whose equilibrium value is $\bar{O}$. Then one can define H_eq as the subspace spanned by the eigenstates of the nonnegative operator $(\hat{O} − \bar{O})^{2}$ corresponding to sufficiently small eigenvalues." (p5, footnote 14)

"Given the energy shell H, the nonequilibrium subspace H_neq, in reality, is determined not in a random manner, but through the values of macroscopic quantities that we use to characterize the system." (p10)

 

[atyy]

Here are two papers by Sugiura and Shimizu that further explain the role of macroscopic observables in determining whether a state is an equilibrium state or not.
http://arxiv.org/abs/1112.0740v4
http://arxiv.org/abs/1302.3138v2

From the introduction of the first:
"It was shown in Refs. [1–4] that almost every such vector gives the correct equilibrium values of a certain class of observables $\hat{A}$ by $\langle\psi|\hat{A}|\psi\rangle$. This property was proved in Refs. [1, 2] for observables of a subsystem, which is much smaller than the whole system. The case of general observables, including observables of the whole system (such as the total magnetic moment and its fluctuation), was analyzed in Refs. [3, 4]. It was shown that the above property holds not for all observables but for observables that are low-degree polynomials (i.e., their degree $<< N$) of local operators [3]. We here call such observables mechanical variables."

 

[MathematicalPhysicist]

http://arxiv.org/abs/1407.3384

Why do we remember the past and not the future? The 'time oriented coarse graining' hypothesis

Cause the future never occurs in actuality, the past had occurred and that's why we remember it.

Kindergarten question really. :-D

 

[John86]

Cause the future never occurs in actuality, the past had occurred and that's why we remember it.

Kindergarten question really. :-D

Remembering historical events or measuring them, is quite patchy or grainy if you like, never exact in a way that al information is available.

 

[John86]

If I understand the gist, I think you are making a good point. What about the "start of expansion"?

How do we define macro variables on it? Who is coupled to it, interacting with it, experiencing it?
What are the relevant macro variables? It is a very dense state, as we understand dense. A lot of energy, as we understand energy. Perhaps there is a bounce. Does the bounce happen very quickly? Who or what is keeping time?

.

But would a bouncing state of the universe in the past or the future not also inhabit the same marcroscopic variables questions as discretenes states and continuüm problems whe have now in our theoretical physics descriptions of these situations.

It would be interesting to see if there is a way to generalize them.

 

[MathematicalPhysicist]

Remembering historical events or measuring them, is quite patchy or grainy if you like, never exact in a way that al information is available.

Well, if this measurement is quite patchy then all our measurements are in the same way, "quite patchy".

 

[Berlin]

It is amazing that Rovelli gets us thinking with every single paper he writes. Very original thoughts to me. The responses here however, seem weird to me. Why talk about 'Who we are' or what 'IT' will be? Don't we allready know that we, defined as the known particles and energy in the universe, are only the 4% or so discovered so far? My physics question would be: all the dark mass and energy only seems to couple with us only through gravity. Is there room (or 'space' :) ) in rovelli's thinking to speculate about that? Can we give boundaries in physical, or new, parameters describing those other forms?

Berlin

 

[Demystifier]

The circularity problem

In my opinion, the main problem with the Rovelli's idea is circularity. To see this, one must ask obvious questions which Rovelli, for some reason, refuses to ask. When the obvious questions are answered by obvious answers, one gets the following logical loop:

- Entropy increases because humans define macroscopic variables in a specific way.
- But why do humans define macroscopic variables in such a specific way? Because that's how their mind works.
- But why their mind works so? Because that's how their brain works.
- But why their brain works so? Because the brain, as a part of nature, obeys the laws of physics.
- But what these laws of physics say? Different laws say different things, but here the crucial law is the second law of thermodynamics which says that entropy increases.

In other words, Rovelli's argument says that entropy increases because entropy increases. Circularity!

 

[atyy]

In my opinion, the main problem with the Rovelli's idea is circularity. To see this, one must ask obvious questions which Rovelli, for some reason, refuses to ask. When the obvious questions are answered by obvious answers, one gets the following logical loop:

- Entropy increases because humans define macroscopic variables in a specific way.
- But why do humans define macroscopic variables in such a specific way? Because that's how their mind works.
- But why their mind works so? Because that's how their brain works.
- But why their brain works so? Because the brain, as a part of nature, obeys the laws of physics.
- But what these laws of physics say? Different laws say different things, but here the crucial law is the second law of thermodynamics which says that entropy increases.

In other words, Rovelli's argument says that entropy increases because entropy increases. Circularity!

But what if we take Goldstein et al's version of the argument? QM is already an instrumental theory, in which macroscopic observers and detectors are necessary, so that doesn't seem a problem - except for the measurement problem. In that sense, one could say that Goldstein et al merely push the problem back to the establishment of Bohmian quantum equilibrium?

 

[Demystifier]

But what if we take Goldstein et al's version of the argument? QM is already an instrumental theory, in which macroscopic observers and detectors are necessary, so that doesn't seem a problem - except for the measurement problem. In that sense, one could say that Goldstein et al merely push the problem back to the establishment of Bohmian quantum equilibrium?

I don't see how it helps. In Bohmian mechanics particle positions and wave function are fundamental (not merely instrumental), while observers and detectors are made of these fundamental particles. The second law implies that the initial condition for the wave function must be special, which cannot be explained by referring to observers and detectors.

 

[atyy]

I don't see how it helps. In Bohmian mechanics particle positions and wave function are fundamental (not merely instrumental), while observers and detectors are made of these fundamental particles. The second law implies that the initial condition for the wave function must be special, which cannot be explained by referring to observers and detectors.

I agree that in Bohmian mechanics, a second law for quantum equilibrium would suggest special initial conditions, the same way we usually think of the second law of thermodynamics (that's what I meant by "push the problem back").

But a separate question was what do you think of Goldstein's derivation of a something that looks like the second law in http://arxiv.org/abs/1402.3380? What it seems to say is if there are observers who care about almost any given set of macroscopic observables, there will be a second law of thermodynamics for those observables? That seems in the spirit of what Rovelli is saying.

 

[Demystifier]

But a separate question was what do you think of Goldstein's derivation of a something that looks like the second law in http://arxiv.org/abs/1402.3380?

Interesting paper, but I don't think that they derive the second law in it.

What it seems to say is if there are observers who care about almost any given set of macroscopic observables, there will be a second law of thermodynamics for those observables? That seems in the spirit of what Rovelli is saying.

First, they do not talk about observers, so it is not in the Rovelli's spirit at all. Second, they show that for most initial conditions the approach to equilibrium is VERY FAST, much faster than observed in nature. That means that one can NOT explain why the observed approach to equilibrium is so slow, and that IS the point of their paper.

In short, they sharpen the well-known problem that statistical physics cannot explain the second law without assuming very special initial conditions. By sharpening the problem they do not solve it. In fact, they make the problem even harder.

 

[julcab12]

In other words, Rovelli's argument says that entropy increases because entropy increases. Circularity!

..That is really the consequence of thinking in the perspective of relational view
.It has no definite direction and meaning. It is just a new interpretation of an existing formalism. It's been done in the past like how Einstien postulate an axioms of a theory; invariance of C from the motion of the source and universal principle of relativity until the geometrization of the theory--relativization of quantities. In Rovellis point. He pick the very obvious mechanism of each part with some possession of an intrinsic property of the subject and viewed it as purely relational. Like how he's been picking apart the structure of time/space.

 

[atyy]

Interesting paper, but I don't think that they derive the second law in it.

First, they do not talk about observers, so it is not in the Rovelli's spirit at all. Second, they show that for most initial conditions the approach to equilibrium is VERY FAST, much faster than observed in nature. That means that one can NOT explain why the observed approach to equilibrium is so slow, and that IS the point of their paper.

In short, they sharpen the well-known problem that statistical physics cannot explain the second law without assuming very special initial conditions. By sharpening the problem they do not solve it. In fact, they make the problem even harder.

Although Goldstein, Hara and Tasaki don't talk about observers, their notion of an equilibrium subspace depends on a choice of observables, so this seems similar to Rovelli's viewpoint. Actually, as far as I know, all conceptions of the second law require a choice of coarse grained observables, even those which explain it by a special initial condition, since the microscopic dynamics are time-reversible. I think what Rovelli is suggesting is that traditionally one requires a special initial condition and a coarse graining, but maybe a coarse graining is sufficient.

It is true that Goldstein, Hara and Tasaki sharpen the problem, but it does seem very close to deriving the second law in the sense that they show thermalization for generic choice of macroscopic observables, ie. there seems to be a "direction of time" regardless of initial condition. That's why it seems similar to Rovelli's suggestion. I do agree that the question of a realistic equilibration time is open.

 

[marcus]

It might be useful to give a little background. I think it is well-known that entropy is not an ABSOLUTE. It is observer-dependent. In particular it depends on the observer's coarse-graining, how he divided the world's microstates up into macros according to the variables that affect him and he interacts with.
To give some of the flavor I'll quote a bit from the conclusions of Don Marolf's 2004 paper, A few words on Entropy, Thermodynamics, and Horizons:

==quote http://arxiv.org/abs/hep-th/0410168 from conclusions==
the realization that observers remaining outside a black hole associate a different (and, at least in interesting cases, smaller) flux of entropy across the horizon with a given physical process than do observers who themselves cross the horizon during the process. In particular, this second mechanism was explored using both analytic and numerical techniques in a simple toy model. We note that similar effects have been reported³⁵ for calculations involving quantum teleportation experiments in non-inertial frames. Our observations are also in accord with general remarks^36,37 that, in analogy with energy, entropy should be a subtle concept in General Relativity.
We have concentrated here on this new observer-dependence in the concept of entropy. It is tempting to speculate that this observation will have further interesting implications for the thermodynamics of black holes. For example, the point here that the two classes of observers assign different values to the entropy flux across the horizon seems to be in tune with the point of view (see, e.g., Refs. 38,39,40,41,42) that the Bekenstein-Hawking entropy of a black hole does not count the number of black hole microstates, but rather refers to some property of these states relative to observers who…
==endquote==
Since entropy is observer dependent, clearly in order for the "2nd law" to hold you have to STICK WITH THE SAME OBSERVER. If you suddenly change observers, or change the map of macrostates--which micros belong to which macros--then you can't expect entropy to be consistently non-decreasing.

It seems to me that the Rovelli paper John86 called attention to in post#1 draws a possible conclusion from that observer-dependence.

http://arxiv.org/abs/1407.3384
Why do we remember the past and not the future? The 'time oriented coarse graining' hypothesis
Carlo Rovelli
(Submitted on 12 Jul 2014)
Phenomenological arrows of time can be traced to a past low-entropy state. Does this imply the universe was in an improbable state in the past? I suggest a different possibility: past low-entropy depends on the coarse-graining implicit in our definition of entropy. This, in turn depends on our physical coupling to the rest of the world.
I conjecture that any generic motion of a sufficiently rich system satisfies the second law of thermodynamics, in either direction of time, for some choice of macroscopic observables. The low entropy of the past could then be due to the way we couple to the universe (a way needed for us doing what we do), hence to our natural macroscopic variables, rather than to a strange past microstate of the world at large.
5 pages

 

[marcus]

The difficulty I have in understanding and interpreting this is that everything which is contemporary to "us" and comparable in scale to "us" seems to have the same basic coupling to the rest of the world. that goes for a singlecell amoeba and for me and for the solar system. We all depend on (what is needed for us to do what we do) the same macroscopic variables and processes. We, collectively, are the observer. I cannot imagine an alternative collection of entities. So I cannot imagine a different overall direction of time.

 

[atyy]

The difficulty I have in understanding and interpreting this is that everything which is contemporary to "us" and comparable in scale to "us" seems to have the same basic coupling to the rest of the world. that goes for a singlecell amoeba and for me and for the solar system. We all depend on (what is needed for us to do what we do) the same macroscopic variables and processes. We, collectively, are the observer. I cannot imagine an alternative collection of entities. So I cannot imagine a different overall direction of time.

Suppose there are macroscopic observables A and macroscopic observables B, and that both are sufficient to induce arrows of time for generic initial conditions, will the two arrows of time point in the same direction? I think the Goldstein, Hara and Tasaki paper says they will, because observables A and B will each induce their notion of equilibrium, and that if one starts in a non-equilibrium state, the observables will tend toward their equilibrium values. So I think the paper confirms Rovelli's ideas (at least in the quantum case).

 

[Demystifier]

Although Goldstein, Hara and Tasaki don't talk about observers, their notion of an equilibrium subspace depends on a choice of observables, so this seems similar to Rovelli's viewpoint. Actually, as far as I know, all conceptions of the second law require a choice of coarse grained observables, even those which explain it by a special initial condition, since the microscopic dynamics are time-reversible. I think what Rovelli is suggesting is that traditionally one requires a special initial condition and a coarse graining, but maybe a coarse graining is sufficient.

It is true that Goldstein, Hara and Tasaki sharpen the problem, but it does seem very close to deriving the second law in the sense that they show thermalization for generic choice of macroscopic observables, ie. there seems to be a "direction of time" regardless of initial condition. That's why it seems similar to Rovelli's suggestion. I do agree that the question of a realistic equilibration time is open.

I think that the Goldstein et al result can be demystified by expressing it in different words. They show that most initial conditions are not the exact equilibrium states, but states which are VERY CLOSE to the equilibrium. This is in fact quite expected, intuitive and even obvious. In this way it is obvious that it is very likely that there will be a time arrow, but unfortunately a very fast time-arrow, which is very unlike the observed one. So if one wants to explain the OBSERVED time arrow (and not just any time arrow), the Goldstein et al result does not help. So in my view, even if there is some similarity with the Rovelli's suggestion, I don't see much relevance of it.

 

[stevendaryl]

Yes. Entropy is not an intrinsic/absolute quantity. It depends very much on the choice of macroscopic variables.
So you are right: the fact that we reckon the entropy of the universe, then, to have been low has VERY MUCH to do with our natural macroscopic variables (those through which we, by our nature, couple to the universe).

I understand that there is a certain amount of subjectivity in the definition of entropy. However, we can remove entropy from question by describing the asymmetry of the time evolution of the universe in concrete terms. The early universe (a few minutes after the Big Bang) consisted of mostly hydrogen and helium, more or less uniformly distributed. Later, the matter clumped together into stars. Fusion and supernova explosions produced heavier elements.

So the progression is

Hydrogen + Helium $\Rightarrow$ Stars + Heavier Elements

That's an asymmetry in the time evolution of the universe. You never see heavy elements convert into hydrogen and helium. You never see stars dissipate into clouds of hydrogen and helium.

This asymmetry in the time evolution of the universe cannot possibly be an artifact of a particular coarse-graining choice, can it?

 

[atyy]

I think that the Goldstein et al result can be demystified by expressing it in different words. They show that most initial conditions are not the exact equilibrium states, but states which are VERY CLOSE to the equilibrium. This is in fact quite expected, intuitive and even obvious. In this way it is obvious that it is very likely that there will be a time arrow, but unfortunately a very fast time-arrow, which is very unlike the observed one. So if one wants to explain the OBSERVED time arrow (and not just any time arrow), the Goldstein et al result does not help. So in my view, even if there is some similarity with the Rovelli's suggestion, I don't see much relevance of it.

I agree with your technical points. I thought the relevance was that although Goldstein et al point our some major difficulties for Rovelli's suggestion, I think they came to it by a programme similar to Rovelli's. Perhaps it is more obvious from an earlier paper by Goldstein with other co-authors, when they hadn't discovered the problem yet http://arxiv.org/abs/cond-mat/0511091. There's also http://arxiv.org/abs/quant-ph/0511225 which is related work by another group. So I think it could be interesting to see how Goldstein and colleagues follow up on their work.

 

[atyy]

I understand that there is a certain amount of subjectivity in the definition of entropy. However, we can remove entropy from question by describing the asymmetry of the time evolution of the universe in concrete terms. The early universe (a few minutes after the Big Bang) consisted of mostly hydrogen and helium, more or less uniformly distributed. Later, the matter clumped together into stars. Fusion and supernova explosions produced heavier elements.

So the progression is

Hydrogen + Helium $\Rightarrow$ Stars + Heavier Elements

That's an asymmetry in the time evolution of the universe. You never see heavy elements convert into hydrogen and helium. You never see stars dissipate into clouds of hydrogen and helium.

This asymmetry in the time evolution of the universe cannot possibly be an artifact of a particular coarse-graining choice, can it?

I think it is unlikely that coarse graining without a special initial condition is the whole story, since the special initial condition is the well accepted answer. However, I think it is interesting to see how far one can get without invoking the expansion of the universe, especially since quantum mechanics allows some possibilities that classical systems don't, eg. http://arxiv.org/abs/1007.3957.

 

[atyy]

I think that the Goldstein et al result can be demystified by expressing it in different words. They show that most initial conditions are not the exact equilibrium states, but states which are VERY CLOSE to the equilibrium. This is in fact quite expected, intuitive and even obvious. In this way it is obvious that it is very likely that there will be a time arrow, but unfortunately a very fast time-arrow, which is very unlike the observed one. So if one wants to explain the OBSERVED time arrow (and not just any time arrow), the Goldstein et al result does not help. So in my view, even if there is some similarity with the Rovelli's suggestion, I don't see much relevance of it.

Goldstein, Hara and Tasaki's paper is very general, could additional restrictions to make the system more "realistic" help to get more realistic times? For example, in http://arxiv.org/abs/1103.2683 or http://arxiv.org/abs/1311.1200 thermalization is dual to black hole formation in classical general relativity, which is a somewhat realistic theory.

 

[Demystifier]

Rovelli now uploaded a new version of his argument:
http://lanl.arxiv.org/abs/1505.01125

In Sec. IV he discusses various objections to his idea, together with his responses to these objections. In particular, the first objection and his response are the following:
"1. Isn't this just shifting the problem? Instead of the mystery of a strange (low past entropy) microstate of the universe, we have now the new problem of explaining why we belong to a peculiar system?

Yes. But it is easier to explain why the Earth happens to rotate, rather than having to come up with a rational for the full cosmos to rotate. The next question addresses the shifted problem."

In a sense, this response provides also an answer to my circularity objection in post #18. It's easier to explain why a small system is in a peculiar state, then why a big system is in a peculiar state.

 

[wabbit]

Trying to think about how cosmology can be "perspectival" and seeking to picture alternate perspectives of our history, this reminded me of two things which I find intriguing - not directly related, more tangential to the topic, but it seems so suggest some intuitive obstacles to switching perspective may not be as strong as they sound - or I could be reading far too much in these, or misinterpreting.

1. With a cosmological constant and nothing else, we get de Sitter space. But as noted in http://www.bourbaphy.fr/moschella.pdf, (portions of) that same manifold can be interpreted as representing a flat universe expansion (plenty of choices of those too), a flat universe contraction, or a closed universe (non-singular) bounce. The choice is made by the preferred time slicing, i.e, by the choice of a set of comoving observers and associated cosmological time. At least for a good part of its history, a single trajectory can be interpreted as occurring in any of these scenarios. As it is a vacuum these observers are virtual, but this suggests that the cosmological constant by itself does not break "perspective symmetry".

2. A closed matter dust FRW spacetime is fully time symmetric. We can interchange the initial bang and final crunch, and a single trajectory can be viewed as happening in either scenario. This is not a vacuum so we do have observers here, and this suggests that the big bang by itself does not break all "perspective symmetry" if it is otherwise correct.
To get something interesting though, we need a perturbation of this FRW, which kills the symmetry - but at least this suggests that the "low early entropy" in a FRW spacetime may have little to do with the bang itself, but with the kind of perturbations we consider.

 

[stevendaryl]

2. A closed matter dust FRW spacetime is fully time symmetric. We can interchange the initial bang and final crunch, and a single trajectory can be viewed as happening in either scenario. This is not a vacuum so we do have observers here, and this suggests that the big bang by itself does not break all "perspective symmetry" if it is otherwise correct.

But the whole issue where time asymmetry comes from is sparked by the evolutionary aspects of the universe. We start off with huge balls of hydrogen, which collapse into stars, which ignite and eventually burn themselves out. That evolution is not time-symmetric.

You say that we have observers in the dust spacetime described, but observers require planets to evolve on, which require suns to revolve around, which require big balls of hydrogen. If it's just dust throughout history, then there wouldn't really be any observers (in the sense of organic creatures doing the observing).