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

#### marcus

Gold Member
Dearly Missed
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

2018 Award
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

Staff Emeritus
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.

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#### Demystifier

2018 Award
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

Gold Member
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 occuring 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.

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#### stevendaryl

Staff Emeritus
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).

#### wabbit

Gold Member
Agreed - I don't claim these observations solve the mistery : ) it just suggests that the "background" initial singularity and accelerating expansion may not be the obstacle in finding alternate perspectives - something that wasn't clear to me initially.

Regarding your comment, I have a question. The history we describe is one of gradual differentiation and structure formation - or order arising out of chaos to put it in wholly unscientific terms. Intuitively there seems to be a lot more "relevant" information in later states than in early ones - the initial state being perhaps some kind of undifferentiated hot soup of unified field quanta (even suggestive of a thermal state). Might there be a choice of coarse graining where this picture translates into decreasing entropy rather than increasing, or is this hopelessly misguided?

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#### wabbit

Gold Member
Just quicly, another rambling thought - Actually, I don't expect an alternate perspective to be easy to identify (e.g as from the picture above which I do suspect is misguided (it seems too easy not to be naive), it should be truly and completely foreign to us if it exists. But maybe starting with the universe as information, a set of bits, the subdivision into interacting systems corresponds to different interpretations of those bits - the same string of bits encoding two different pictures when decoded differently. If so, an alternate perspective might correspond to such a thorough scrambling of all bits (cryptography?) and coarse graining (steganography?) that it is completely unrelated to any aspect we can perceive, and it might be completely impossible to reconstruct any relevant observable in the alernate view, using ours.

OK I'll shut up before I get thrown out for empty philosophising:)

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#### stevendaryl

Staff Emeritus
Regarding your comment, I have a question. The history we describe is that of gradual differentiation and structure formation. Intuitively there seems to be a lot more "relevant" information in later states than in early ones - the initial state being perhaps some kind of undifferentiated hot soup of unified field quanta (even suggestive of a thermal state). Might there be a choice of coarse graining where this picture translates into decreasing entropy rather than increasing, or is this hopelessly misguided?
I don't know whether there is a way to make sense of that, or not, but I have had a similar idea. Roughly speaking, the entropy of a system can be thought of as the number of bits needed to completely describe a system. So if you have a cube filled uniformly by hydrogen in its ground state, that is completely described in a few words. If through thermonuclear processes, the hydrogen is turned into helium, nitrogen, carbon, iron, and all the rest of the elements, and those elements are assembled into humans and buildings and cars and planets and so forth, then it takes vastly more words to completely describe the state, in all its detail. So this is a much higher-entropy system. But now imagine trillions of years of history. The buildings crumble into dust, as do the living creatures and cars, etc. Eventually, you have no large-scale structure at all, just microscopic dust, thoroughly mixed, so that each speck of dust is indistinguishable from any other. This situation to our minds seems very uniform, and simple to describe, just as the initial uniform collection of hydrogen did.

So if we could somehow separate macroscopic entropy from microscopic, macroscopic entropy does not increase forever, it starts off low in the early universe, increases for a while, and then decreases again. So it seems roughly time-symmetric.

#### marcus

Gold Member
Dearly Missed
The ideas of the paper http://arxiv.org/abs/1407.3384
which is the topic of the thread were presented and discussed at the September 2014 Tenerife conference
5YqQaWEss74
52 minutes. About 33 minutes of presentation followed by discussion.
Lots of questions and discussion at the end (Robert Wald, George Ellis, Jim Hartle, Simon Saunders, David Alpert...)
Thanks to Fuzzyfelt for pointing this out! It's a really interesting youtube.
In fact the questions raised evidently helped to motivate the next paper on this subject which Demystifier just gave the link to:
http://lanl.arxiv.org/abs/1505.01125
Is Time's Arrow Perspectival?
Carlo Rovelli
(Submitted on 4 May 2015)
We observe entropy decrease towards the past. Does this imply that in the past the world was in a non-generic microstate? I point out an alternative. The subsystem to which we belong interacts with the universe via a relatively small number of quantities, which define a coarse graining. Entropy happens to depends on coarse-graining. Therefore the entropy we ascribe to the universe depends on the peculiar coupling between us and the rest of the universe. Low past entropy may be due to the fact that this coupling (rather than microstate of the universe) is non-generic. I argue that for any generic microstate of a sufficiently rich system there are always special subsystems defining a coarse graining for which the entropy of the rest is low in one time direction (the "past"). These are the subsystems allowing creatures that "live in time" ---such as those in the biosphere--- to exist. I reply to some objections raised to an earlier presentation of this idea, in particular by Bob Wald, David Albert and Jim Hartle.
6 pages, 4 figures.
Here is the schedule of talks (with abstracts) for the Tenerife conference

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#### wabbit

Gold Member
So if we could somehow separate macroscopic entropy from microscopic, macroscopic entropy does not increase forever, it starts off low in the early universe, increases for a while, and then decreases again. So it seems roughly time-symmetric.
Indeed, macroscopic and microscopic entropy, didn't quite see that so clearly.
With luck in some toy models at least there might even be a symmetry exchanging the two. That would be nice:)

But maybe the suggestion to follow is that of Rovellis examples, ball colorings and the small ball/big balls: these toy models seem like they could have a lot in store.

#### marcus

Gold Member
Dearly Missed
Personally I suspect that all subsystems are obliterated at cosmological bounce (at near Planckian density).
The problem they are wrestling with is how does it happen that expansion starts at a low entropy state.
The universe begins expanding at what is considered a very unlikely state, that gives the direction to time.
I don't see the problem because I do not see how you can even define subsystems, or macroscopic variables, or entropy at planckian density. Gravity is repellent at extreme density (quantum effects) which is what causes geometry to bounce.
How do you define a region, or a "thing", or even a locality under such conditions? I think entropy is a meaningless idea at such high density.

Rovelli's point is that the definition of entropy involves interaction with a subsystem in an essential way, he emphasizes that.
Yes there is strong dependence on how the subsystem interacts with the universe.
But he does not make what I think is a reasonable conjecture that therefore (when the idea of a subsystem, or a split of the Hilbert space into a tensor product of two or more factors is itself unrealizable) entropy cannot be defined at bounce.

One would have to wait for some expansion to occur and density to get well below planckian, gravity stops being repellent, more normal version of geometry, locality settles down. Definite subsystems begin to emerge. *Then* we know what entropy is. This is just my suspicion.

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#### marcus

Gold Member
Dearly Missed
Since we've turned a page, I'll bring forward the most relevant links:
The ideas of the paper http://arxiv.org/abs/1407.3384 which is the topic of the thread
were presented and discussed at the September 2014 Tenerife conference
52 minutes. About 33 minutes of presentation followed by discussion.
Lots of questions and discussion at the end (Robert Wald, George Ellis, Jim Hartle, David Alpert...)
In fact the questions raised evidently helped to motivate the next paper on this subject which Demystifier just gave the link to:
http://lanl.arxiv.org/abs/1505.01125
Is Time's Arrow Perspectival?
Carlo Rovelli
(Submitted on 4 May 2015)
We observe entropy decrease towards the past. Does this imply that in the past the world was in a non-generic microstate? I point out an alternative. The subsystem to which we belong interacts with the universe via a relatively small number of quantities, which define a coarse graining. Entropy happens to depends on coarse-graining. Therefore the entropy we ascribe to the universe depends on the peculiar coupling between us and the rest of the universe. ..
.... These are the subsystems allowing creatures that "live in time" ---such as those in the biosphere--- to exist. I reply to some objections raised to an earlier presentation of this idea, in particular by Bob Wald, David Albert and Jim Hartle.
6 pages, 4 figures.
Here is the schedule of talks (with abstracts) for the Tenerife conference

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