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

[friend]

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?

 

[Fra]

Another way of making it intuitive why entropy is relative is from the point of view I have:

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

 

[marcus]

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

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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.

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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.

 

[Dmitry67]

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!

 

[marcus]

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.

 

[Bob_for_short]

Let me intervene in your learned discussion. If you take a couple of charges in QED (a target and a projectile) and make them scatter, then in the final state, apart from the scattered charges, you will obtain a lot of soft photons. This process cannot be practically reversed, can it?

Of course, one can play with an oscillator equation (or alike) and imagine that it describes everything in a reversible way, but is it fair enough?

 

[marcus]

, apart from the scattered charges, you will obtain a lot of soft photons. This process cannot be practically reversed, can it?

... is it fair enough?

Yes Bob, and thanks! It is fair enough.

In a classical universe, similar to ours except it is collapsing, things will be colliding and smashing and scattering soft photons. Entropy will obviously be increasing.

As long as there is ordinary matter it will do the kind of thing you say, and entropy will increase. You have explained it very well with an example.

And when enough mass collects it will collapse to make a black hole---this process converts a considerable fraction of the mass into radiation too.

So the arrow of time clearly runs forward with the collapse, towards a singularity (if you believe time can end) or a bounce, or something we didn't think of yet.

The only part of the scenario some of us didn't imagine carefully yet is late in the collapse when much of what is collapsing is black holes. Millions of black holes falling together, some black holes already inside the horizons of other larger ones. It is a pimply mess and horribly complicated. Maybe a large fraction of the mass is being turned into gravitational radiation. Whatever it is, it is very brief, there is no time for any equilibrium behavior.

Even though your QED example does not explicitly cover this chaotic crowd of black holes, I think in the same spirit as your example that the entropy has to be increasing rapidly (for any observer unfortunate enough to be caught in such a debacle!)

But to me it seems plausible that a different physics takes over as one approaches Planck density. In what is called the 'quantum regime' there is no meaningful idea of a classical observer ( measures things, who has to be prevented from building perpetual motion machines, and all the other classical legal things). I have to go to lunch. Anyway maybe you have response?

 

[Fra]

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.
...
arrow of time ALWAYS points away from a state with low entropy!

As I read your reasoning, I would say that you consistently refuse to acknowledge the importance of the intrinsic perspective. This is the root of the confusion I think.

You say that the arrow of time always points away from the state of low entropy - I would say that the arrow of time is an intrinsic propery of the an inside perspecitve of an observer that points in the direction of the EXPECTED future. And the actions of this observer, is in consistency with this expectations - in this sense the second law, is just defined locally and differentially and has more the form of the least action principle. Since entropy is relative, the least action principle is pretty much a principle of differential entropy.

But clearly expecations change as real progress is made and the observer evolves, and so does the arrow of time.

IMHO: The expectations are what defines the arrow of time and makes it "subjective" or observer independent. The problem of your reasoning is that you assume that expectations are frozen, and are NOT updated in the light of new information. This is why you think that your CURRENT expectations would be valid also at some envision big bang or other chaotic condition. This is why you are forced into the odd position that the initial condition is "improbable" (this is what low entropy means), but this EXPECTATION is not the proper expectation the proto-observer at the big bang would have.

/Fredrik

 

[Fra]

I envision that our "entropy ruler" so to speak, is our own complexity, this is why the entropy as seen from the inside, a particular state doesn't necessarily become infinitely improbable at some picture BB because our "entropy rulers" also scales along with it. I think most would agree that during the chaotic conditions around the BB one would not expect very massive coherent systems(observers). This is why there set of available entropy measures is constrained enough to not run into the conceptual issues of improbable initial conditions.

Not beeing the topic of this thread but I also think this is why we expect unification at this scale, since the ACTION of each observer is based on it's simpler and simpler expectations (as complexity is stripped).

The way I personally envision the coding of the measure of missing information of the environment, is by the amount of from the inside-disitnguishable combinations of microstates that is consistent with the structure of the space of distinguishable events that pretty much defines the communication surface between the observer and it's environment. This should suggest that as the complexity is dropped, this entropy itself becomes quantized. This is why I think the ordinary continuum basis for information theory based on probability theory contains a large redundancy.

/Fredrik

 

[Dmitry67]

Fra, I am not surprised: for your "evolving law" you need some global time where law evolves.

But regarding the 2nd law, I can tell you what it truly means. It means that all observers observe an increase of entropy. In another words, observer's arrow of time points to the same direction as the system which is observed. In another words, it declares some 'smoothness' of the arrow of time. In another words, arrow of time can not change direction unless isolated by an event horizon.

Of course, it is not applicable to the before- and after- the BB.

2 marcus: I did not miss these pages, but I believe you're all trying to solve the problem (2nd law, black holes, increasing ignorance, relativity of information) which does not exist.

 

[Chronos]

Im not sure you would go about distinguishing observer dependence from independence, All our Earth bound observations are observer dependent so far as I know.

 

[Fra]

Fra, I am not surprised: for your "evolving law" you need some global time where law evolves.

(I'm really tired today so this is a short rsponse.)

I see why you conclude this, but from my point of view there is no global time! Because what ou mean by global time is not an instrinsic construct. It's simply not physical.

I do see that the real difficult thing seems to understand from the point of view of eternal law, that there is no external view of this "evolution". Instead there are only internal views. Objectivity and somewhat global times say like cosmological style times are emergent as evolutions of a common environment, but there is no background context IN WHICH in emerges. Even this cosmological time would (IMHO) be relative, BUT since the local environment of causally connected observers unavoidably equilibrate with their local time, eventually a kind of consensus of an approximately cosmological evolution emerges. But this can not in my view be described by a fixed deductive logic, it's a different kind of inference logic.

I know this sounds strange and circular, but I think we debated this already. But I see why you think there must be a background, it's somehow coming from your more realist position than me.

/Fredrik

 

[Fra]

But regarding the 2nd law, I can tell you what it truly means. It means that all observers observe an increase of entropy. In another words, observer's arrow of time points to the same direction as the system which is observed. In another words, it declares some 'smoothness' of the arrow of time. In another words, arrow of time can not change direction unless isolated by an event horizon.

Throwing in some more of my personal views here

- One should not forget that the second law is really a statistical statement, meaning that it
really says that the entropy by construction is highly likely to increase, rather than beeing bound to incresease in the logical sense.

- Then one way of blurring the arrow of time, is to reduce the weight of the statistical inference. As the complexity is very low, the statistical conclusions become less and less peaked, at some point the arrow of intrinsic time is completely lost.

- Then, if you look at "statisitical inference" that works from data, and since all observers have different information the statistical inference of each observer will differ from others. But the more they differ, the more will their actions be at variance with the neigbouring observers - which ultimatley leads to physical interactions and a mutual selection for emergent consesus (a mutual interest), this is the evolution I see.

- In a certain sense, I picture EVERY observer always come with a kind of "horizon". You can picture the horizon from two ways, from the inside or from the outside. From the inside, the event horizon is simply the horizon of distinguishable events, I personally don't interpret this in it's basic form as a surface in regular space, I rather abstractly view this horizon as an information theoretic abstractin that rather is a key to *building* space. In this way, the complexity of the observer limits the size of this surface. Building space is in my view part of the the emergent consensus between the interacting observers. Thus spacespace corrseponds to an equilibrium. Off-equilibrium, spacetime as we know it is I think not distinguishable as a structure.

All of the three above poitns, are keys to reconstruct the physical basis for a new statistical inference framework in physics. The normal way of just assuming that limits of probability theory are well defined and objective are ignoring I think fundamental issues already from the starting points. I think it's about time at least someone raises these questions and not let them go until resolved.

/Fredrik

 

[Fra]

I skimmed 80% of the paper last night. I prefer shorter papers, because longer papers tend to ultimately not get read :)

From my personal perspective, I think Padmanabhan's thinking is in the right direction and I wouldn't be surprised if some more interesting papers comes from him in the future.

However, since I am one of those who already hold the view that information measures, like entropy, are observer relative constructs - this part isn't new to me - I didn't think this paper contains something revolutionary since he sort of first used what we know, to show that there is another principle from which it can be derived, which makes is a weak argument from the plausability point of view. Also he seems to take the existence of the spacetime manifold for granted (although geometry/gravity is emergent).

I guess what I am looking for, and I think ca be done - is something that Harold in the paper asked for also on page 12 - an plausible argument independent of the field equations we already konw, for why a particular say entropy functional, and a variational principle is valid and then show that gravity follows from this more general principle.

In any case, I think his various analogies in this paper is onto something, but I think from the point of view of trying to find an independent argument for the statistical gravity I found no real convincing new first principle arguments.

/Fredrik