Do black holes determine time's arrow?

[PeterDonis]

to have an observer with functioning memories, you have to have an entropy difference between the two ends of time.

The idealized GR models we are considering do not have to have observers with functioning memories; they just have to have worldlines with proper time that increases in a consistent direction, either towards the singularity (black hole) or away from it (white hole).

The gross structure of spacetime doesn't determine which direction is low entropy.

In the idealized GR models we are considering, the entropy is zero everywhere, since the microstate of the universe at every event is exactly known.

You can add entropy and observers with functioning memories to the model, but then we are talking about a more complicated model, where you have to include some more detailed description of the matter that allows entropy to increase in one direction or the other based on some kind of coarse-graining of the matter's state space. Then the question would be whether such a more complicated matter model can be consistently added to both of the idealized models (black hole and white hole) or only to one (presumably the black hole). I don't see why it wouldn't be possible for both (since we already expect that we can construct consistent models in which entropy increases when things fall into black holes, and since the white hole exploding into a star model, at least in its matter portion, is just like an expanding FRW universe, and we already expect that we can also construct consistent models in which entropy increases in the direction of time in which the universe is expanding). But that still doesn't make them the same model; they are still physically different.

 

[PeterDonis]

If one is the time reverse of the other, then they are the same manifold, since manifolds are equivalence classes.

GR is a theory of physics, not math. The fact that the two solutions might belong to some mathematical equivalence class does not make them physically the same. Physically, they are different solutions, and that's the sense that matters for GR.

 

[stevendaryl]

GR is a theory of physics, not math. The fact that the two solutions might belong to some mathematical equivalence class does not make them physically the same. Physically, they are different solutions, and that's the sense that matters for GR.

I'm claiming that physically, they are NOT different solutions. They become different solutions when you throw in observers who have a thermodynamic arrow of time.

 

[stevendaryl]

The idealized GR models we are considering do not have to have observers with functioning memories; they just have to have worldlines with proper time that increases in a consistent direction, either towards the singularity (black hole) or away from it (white hole).

Proper time is ambiguous up to a sign. We choose the sign of the proper time so that the timelike path is future-pointing, but that assumes that you already have a notion of which direction is future. It's circular reasoning to say that proper time tells us which direction is the future.

 

[stevendaryl]

The universe doesn't contain just one observer. It contains lots of them, all of whom observe that they share a common future direction of time.

Yes! That is a fact about thermodynamics. That's my point.

For whatever reason, the time immediately after the Big Bang was very low entropy (comparatively). The entropy sets the arrow of time, and defines the difference between a Big Bang and a Big Crunch. If the singularity is in the thermodynamic past, it's a Big Bang, and if it's in the thermodynamic future, it's a Big Crunch.

 

[stevendaryl]

Yes. In the cases under consideration, the vector field ##X## is the tangent vector field of the appropriate timelike congruence. For the star collapsing to the black hole and the white hole exploding into the star, the appropriate congruence is the congruence that is comoving with the matter.

A tangent vector is ambiguous up to a sign! If you have a parametrized path ##\mathcal{P}(s)##, it will have a certain tangent vector. If you parametrize it differently, say using ##\lambda = -s##, then the resulting tangent vector will point in the opposite direction.

It's circular to use tangent vectors to specify the arrow of time, because the tangent vectors of timelike paths are chosen to be future-pointing, in the first place.

 

[PeterDonis]

I'm claiming that physically, they are NOT different solutions.

And this claim is wrong, because the direction of proper time of observers comoving with the matter, relative to the singularity (toward vs. away) is part of the physical interpretation of the solution.

Proper time is ambiguous up to a sign.

Only for a time symmetric solution. The direction of proper time for a time asymmetric solution is part of the geometric properties of the solution. Reversing that direction means a physically different solution. Again, GR is a theory of physics, not math; proper time increasing towards the singularity is physically different from proper time increasing away from the singularity. I am frankly baffled as to how you can fail to accept this.

Yes! That is a fact about thermodynamics.

No, it isn't, it's a geometric fact about the solution: there is a congruence of timelike worldlines comoving with the matter, and that congruence has a tangent vector field. That tangent vector field's future direction, relative to the singularity, is different for the two solutions (toward for black hole, away for white hole). That is true for the idealized solutions we are discussing, which, as I have already pointed out, have zero entropy everywhere and do not have the thermodynamic properties you refer to.

For whatever reason, the time immediately after the Big Bang was very low entropy

In the idealized solutions we are considering, the entropy is zero everywhere, as I have already pointed out: the microstate of the matter is exactly known everywhere.

If you want to talk about a universe with a low entropy Big Bang and entropy increasing away from the Big Bang, you are talking about a different model, in which there are two arrows of time: the entropy arrow you describe, and the geometric proper time arrow for the congruence of comoving worldlines that I described; and for the solution to be physically valid for our actual universe, those two arrows have to match. But that does not mean that in an idealized solution where there is no thermodynamic arrow, the proper time arrow doesn't exist.

 

[PeterDonis]

A tangent vector is ambiguous up to a sign!

No, it isn't. The two possible signs are two physically different solutions. That is true even in the absence of a thermodynamic arrow, which, as I have repeatedly pointed out now, is not present at all in the idealized solutions we have been discussing.

 

[Dale]

But the point is that, absent the 2nd law of thermo, it is impossible to experimentally determine if you are going forward in time in a collapsing black hole or backwards in time in an exploding white hole. That is the arbitrariness.

 

[stevendaryl]

No, it isn't. The two possible signs are two physically different solutions.

I don’t think what you’re saying is true. The parameter used for parametrizing a path is a choice for how the path is described. It’s not physically meaningful.

 

[stevendaryl]

And this claim is wrong, because the direction of proper time of observers comoving with the matter, relative to the singularity (toward vs. away) is part of the physical interpretation of the solution.

I don’t think what you’re saying is true. There is no physical meaning to the choice of one sign over the other, unless the direction is chosen for a physical reason, such as pointing in the direction of the thermodynamic arrow of time.

 

[PeterDonis]

absent the 2nd law of thermo, it is impossible to experimentally determine if you are going forward in time in a collapsing black hole or backwards in time in an exploding white hole.

Sure it is; if it's a black hole, you can fall into it and hit the singularity, and you can't have come out of it because none of it is in your causal past. If it's a white hole, you came out of it, from the singularity, and it's in your causal past, and you can't fall back into it. These situations are distinguishable experimentally, although in the black hole case you won't be able to communicate your results back to any journals. And the experiments don't require any knowledge of thermodynamic properties; there is no need to even measure any entropy or any other thermodynamic parameter.

The parameter used for parametrizing a path is a choice for how the path is described. It’s not physically meaningful.

Yes, it is. Every GR textbook I've read gives the curve parameter along a timelike curve the physical interpretation I have described. If you dispute it, please give me a reference that says otherwise.

There is no physical meaning to the choice of one sign over the other, unless the direction is chosen for a physical reason

Putting the singularity in your past vs. your future is a physical reason, and can't possibly require any correspondence with thermodynamics in and of itself, since, as I have pointed out several times now, there is no thermodynamics in the idealized models we have been discussing, yet there is still the physical difference of which way the curve parameter increases relative to the singularity.

As I said above, this is a basic matter of physical interpretation of GR, and what I am saying is in accord with what I have seen in every GR textbook that I have read. I have never seen anything in any GR literature that says you can freely reverse the sign of the curve parameter along a timelike curve without changing the physical interpretation; all the GR literature I have read says the opposite.

 

[stevendaryl]

I’m perfectly fine with a convention that a specification of a solution to GR includes an assignment of an arrow of time to each timelike path. However, I think that such an assignment has no physical meaning unless it aligns with the thermodynamic arrow of time.

We can perform measurements to determine whether the universe is expanding from a Big Bang or contracting to a Big Crunch, relative to the thermodynamic arrow of time. But there is no measurement that can distinguish between the two if we allow for the thermodynamic arrow of time to be inconsistent with the cosmological arrow of time. There is no measurement that can determine whether proper time is increasing or decreasing along a path except by comparing it to a process that has a preferred arrow of time by thermodynamics.

What is the empirical evidence that would distinguish between (1) our universe is in a Big Bang cosmology and our thermodynamic arrow is pointing in the direction of the expansion? (2) our universe is in a Big Crunch cosmology and our thermodynamic arrow of time is pointing in the opposite direction of the contraction?

I claim that there isn’t any empirical distinction, so we may as well call both Big Bang cosmologies.

 

[stevendaryl]

Sure it is; if it's a black hole, you can fall into it and hit the singularity, and you can't have come out of it because none of it is in your causal past.
If it's a white hole, you came out of it, from the singularity, and it's in your causal past, and you can't fall back into it. These situations are distinguishable experimentally,

No, they are not! Not without a thermodynamic arrow of time. Thermodynamics is what distinguishes between “causal past” and “causal future”. The laws of physics are symmetrical under time reversal (or at least electromagnetism and gravity are). The fact that we remember the past and not the future is a fact about thermodynamics. If you somehow arranged the universe so that it had lowest entropy in the far future, we would remember the future, rather than the past.

 

[Dale]

If it's a white hole, you came out of it, from the singularity, and it's in your causal past, and you can't fall back into it.

Not if you are going backwards in time. If it is an exploding white hole and you are going backwards in time then it is indistinguishable from a collapsing black hole with you going forwards in time (absent thermodynamics).

It is thermodynamics that allows you to experimentally distinguish the two. If the ice cubes in my drink melt then I know I am going forward in time to a black hole, and if the ice cubes in my drink are forming then I know I am going backwards in time to a white hole.

 

[stevendaryl]

Let me illustrate the problem with empirically determining whether you or rising or falling without assuming a thermodynamic arrow of time.

Suppose you are near a planet with very weak gravity. You want to figure out if you are rising or falling. Here’s a toy model for doing this. Suppose that someone constructs a tall tower, maybe 400 meters tall. On the outside of the tower, there are “sticky notes”, at one-meter intervals, there is a pad of sticky notes on which is written the distance above the ground.

So someone who is in slow freefall next to the tower can measure his progress by once per minute taking one of the nearest sticky notes and pasting it into his notebook, filling the pages in order.

If he is falling, then the numbers in his notebook will be decreasing—maybe 100, 81, 64, 49, …, 1

If he is rising, then the numbers will be increasing—1, 4, 9, 16, …, 100.

But now the trickster god of thermodynamics messes with the initial conditions. The scientist starts at a height of 100 meters, the notebook already filled with the numbers 1, 4, 9, …, 100. And all the processes inside the scientist’s body ard reversed, so that instead of taking a sticky note from the tower and placing it into his notebook, he takes the last sticky note from his notebook and places it onto the tower.

Then even though the scientist is falling, the numbers in his notebook will be in increasing order. So the ordering of the numbers give the exact wrong impression.

As long as all the fundamental laws of physics are reversible, there will always be a way (in principle) to set up initial conditions so that the question of whether the scientist is rising or falling will give the wrong answer.

You can only do normal empirical reasoning except under the assumption that your arrow of time isn’t messed with.

 

[PeterDonis]

If the ice cubes in my drink melt then I know I am going forward in time to a black hole, and if the ice cubes in my drink are forming then I know I am going backwards in time to a white hole.

Here you are actually agreeing with me: you are implicitly making use of two distinct concepts of "direction of time". One direction is the direction in which the ice cubes melt; the other direction is the direction in which your proper time increases. Since your scenario says these are not the same, you agree with what I have been saying all along.

You could observe that both of the concepts you use, ice cubes melting and proper time increasing, are local; but so is the direction in which the singularity is, since if the singularity is in your past you can see it, and if it is in your future you can't, and that is a local test. That particular local test just happens to reflect a global property of the spacetime you're in, whereas the ice cube melting test and the proper time increasing test don't.

 

[PeterDonis]

If he is falling, then the numbers in his notebook will be decreasing—maybe 100, 81, 64, 49, …, 1

If he is rising, then the numbers will be increasing—1, 4, 9, 16, …, 100.

In other words, you are taking the ordering of the pages, a spatial ordering, to reflect the ordering in time; you have set up a physical process that records a time ordering in a spatial ordering. So once the experiment is done, we can look at the ordering of the pages and what sticky notes are on them to determine what happened. Ok so far.

But now the trickster god of thermodynamics messes with the initial conditions. The scientist starts at a height of 100 meters, the notebook already filled with the numbers 1, 4, 9, …, 100. And all the processes inside the scientist’s body ard reversed, so that instead of taking a sticky note from the tower and placing it into his notebook, he takes the last sticky note from his notebook and places it onto the tower.

Then even though the scientist is falling, the numbers in his notebook will be in increasing order.

No, his notebook will be empty at the end of the experiment, so it will convey no information whatever.

Also, when you say "all the processes" inside the scientist are reversed, is that supposed to include his consciousness as well? Is he supposed to experience this experiment backwards somehow? (And what would that even mean?) Or is he still experiencing it forwards, but experiencing himself following a different set of rules (put the notes onto the tower instead of taking them off)?

 

[PeterDonis]

Thermodynamics is what distinguishes between “causal past” and “causal future”.

Not according to every GR textbook I have ever read. Again, if you disagree, please give me a reference that supports your claim.

I don't see the point of continuing to just assert our respective positions. I submit that if you look in any GR textbook, you will find it using the terms "causal past" and "causal future" as geometric properties, without any hint of thermodynamics whatever. The same goes for "proper time" and the other terms I have used in previous posts. I take what I have described to be the standard physical interpretation of GR used by physicists. If you insist on adopting your own idiosyncratic interpretation, I can't stop you, but I'm not going to agree with you either without at least some reference to go by.

 

[PeterDonis]

Thermodynamics is what distinguishes between “causal past” and “causal future”.

Btw, if you were to assert this claim as an empirical claim about our actual universe, rather than as a theoretical claim about properties of models in GR, I would have no problem with it. Or if you were to say that, yes, you can have idealized solutions in GR where there is no meaningful thermodynamics at all (for the reasons I have already described), but there is still proper time along timelike curves and there is still a physical distinction being made between corresponding pairs of solutions like "star collapsing to black hole" and "white hole exploding into star", even though that distinction, in those idealized models, has no other theoretical basis and is just stated as a rule of physical interpretation without any deeper justification (in the context of those models)--but then you were to say that you don't consider those idealized models to be physically realistic, because there is no thermodynamic arrow of time, I would have no problem with that either.

But you are making the much stronger claim that the rule of physical interpretation I have described is simply invalid, and that is what I disagree with. And, as I have said, every GR textbook I have ever read says that such a rule of physical interpretation is valid. So that's what I'm going with unless I see a reference that says otherwise.

 

[stevendaryl]

Btw, if you were to assert this claim as an empirical claim about our actual universe,

Yes, it's a general fact about physics in a universe with time-symmetric laws. There is no notion of "future" outside of the thermodynamic arrow of time.

Or if you were to say that, yes, you can have idealized solutions in GR where there is no meaningful thermodynamics at all (for the reasons I have already described), but there is still proper time along timelike curves and there is still a physical distinction being made between corresponding pairs of solutions like "star collapsing to black hole" and "white hole exploding into star",

No, I don't think that there is a physically meaningful distinction in the absence of a thermodynamic arrow of time.

Every GR textbook I have ever read says that such a rule of physical interpretation is valid.

I don't know what you can possibly mean by "valid". Certainly, given a choice of an arrow of time, you can distinguish between a black hole and a white hole. It's relative to that choice, though.

 

[stevendaryl]

Not according to every GR textbook I have ever read. Again, if you disagree, please give me a reference that supports your claim.

I think you're misinterpreting those textbooks. They are focusing on General Relativity, not on the general problem of establishing causality in a universe with time-symmetric laws. They are assuming an arrow of time.

This is really not specifically about General Relativity. General Relativity is in the same boat as Maxwell's equations and Special Relativity. The laws of physics don't distinguish future and past (leaving out weak interactions). They don't distinguish between causal past and causal future. The word "causal" in a world with time-symmetric, deterministic laws is all about thermodynamics and entropy.

 

[stevendaryl]

The significance of the "causal past" of an event is that, with deterministic, time-symmetric laws governing the universe, everything that is needed to predict what happens at an event is determined by that event's past light-cone.

But it's ALSO true that everything that is needed to predict what happens at an event is determined by the event's future lightcone.

When the laws of physics are deterministic and time-reversible, then knowledge of the past allows you to predict the future, and VICE-VERSA. The notion of causal influences does not make a distinction between future and past.

 

[stevendaryl]

Here are lecture notes about Causal Structure of General Relativistic Spacetimes

https://www.pitt.edu/~jdnorton/teaching/GR&Grav_2007/pdf/Notes on CausalStructure.pdf

Here's a quote:

Suppose that ##M, g_{ab}## is temporally orientable. Choose one of the two possible orientations as giving the future direction of time

It goes on to define the causal structure RELATIVE to the choice of what direction is future versus past.

 

[stevendaryl]

From this paper:
http://philsci-archive.pitt.edu/800/1/The_Arrow_of_Time_in_Cosmology.pdf

The main difficulty to be encountered in answering this question lies in our anthropocentric perspective: the difference between past and future is so deeply rooted in our language and our thoughts that it is very difficult to shake off these asymmetric assumptions. In fact, philosophical discussions around the question are usually subsumed under the label “the problem of the direction of time”, as if we could find an exclusively physical criterion for singling out the direction of time, identified with what we call “the future”. But there is nothing in physics that distinguishes, in a non-arbitrary way, between past and future as we conceive them. It might be objected that physics implicitly assumes this distinction with the use of asymmetric temporal expressions, like “future light cone”, “initial conditions”, “increasing time”, and so on. However this is not the case, and the reason can be understood in simple conceptual terms...

The paper goes on to discuss the problem of defining a "cosmological arrow of time", but along the way dismisses the idea that our use of "future light cone" means by itself that there is a fundamental difference between past and future.

 

[stevendaryl]

Another quote from the above paper that is directly relevant to the discussion:

However, we know that, if t is the cosmic time, then if [hij(t, x 1 , x 2 , x 3 ), φ(t)] is a solution of the Einstein’s field equations, [hij(-t, x 1 , x 2 , x 3 ), φ(-t)] is also a solution. In other words, we obtain two solutions, each one of which is the temporal mirror image of the other, that are both possible relative to the laws of general relativity...

But why the two possible universes are different?

...
it makes no sense to say that, when we obtain two solutions of the field equations, one the temporal mirror image of the other, they describe two possible universes whose difference consists in being opposed in time: on the contrary, such solutions are different but equivalent descriptions of one and the same possible universe

 

[PeterDonis]

it's a general fact about physics in a universe with time-symmetric laws. There is no notion of "future" outside of the thermodynamic arrow of time.

I disagree. Time-symmetric laws is not the same thing as time-symmetric solutions, and the latter are what describe possible universes.

I don't think that there is a physically meaningful distinction in the absence of a thermodynamic arrow of time.

I disagree.

I don't know what you can possibly mean by "valid".

I mean that I am giving a rule of physical interpretation, and you are denying it.

Certainly, given a choice of an arrow of time, you can distinguish between a black hole and a white hole. It's relative to that choice, though.

Now I'm the one who doesn't understand what you can possibly mean. Having the singularity in your future is physically different from having it in your past. This physical difference is reflected in the theory by having two different models, each of which is the time reverse of the other. Again, I am baffled as to why you seem unable to accept this simple fact.

The notion of causal influences does not make a distinction between future and past.

In a fully deterministic theory, yes, the past can be retrodicted from the future just as the future can be predicted from the past.

However, that is a weaker claim than the one you make in the quote. The notion of "cause" does make a distinction between future and past: causes come before their effects.

You would probably say that this distinction requires a thermodynamic arrow of time; however, that is an empirical claim, not a rule that excludes any theoretical model that does not abide by it.

I'll take a look at the two references you give and comment on them in a separate post.

 

[PeterDonis]

Here are lecture notes about Causal Structure of General Relativistic Spacetimes

These notes do not discuss proper time along worldlines at all, let alone its physical interpretation.

It goes on to define the causal structure RELATIVE to the choice of what direction is future versus past.

No, it defines the terminology we use for causal structure relative to the choice of what direction is future versus past.

What it does not do anywhere, as above, is talk about actual physical interpretation. To put it another way, it does not talk at all about why you would choose which direction is future versus past. And the only specific spacetimes it discusses, Minkowski and Godel, are time symmetric, so for them it's easy to argue that the choice of future vs. past makes no difference physically. Whereas the discussion in this thread is specifically about time asymmetric spacetimes, where the choice of which direction is future vs. past does make a physical difference.

 

[PeterDonis]

From this paper:

This paper is making a proposal, not describing the standard rules of physical interpretation of GR that appear in GR textbooks.

Also, if we're going looking for quotes, how about this one:

From our perspective, it is possible to address the problem of the arrow of time in cosmology in terms of the geometrical properties of the space-time, independently of thermodynamic arguments. In this sense, we follow Earman’s “Time Direction Heresy”, according to which the arrow of time, if it exists, is an intrinsic feature of space-time “which does not need and cannot be reduced to nontemporal features” (Earman, 1974, p.20). In other words, the geometrical approach has conceptual priority over the entropic approach, since the geometrical properties of the universe are more basic than its thermodynamic properties: the definition of entropy and the calculation of the entropy curve for the whole universe are possible only if the space-time has certain definite geometrical features.

Another quote from the above paper that is directly relevant to the discussion

You left out a key part of the last snippet you quoted: "If this point is accepted, it makes no sense..." I don't accept the point referred to in the phrase I italicized (basically the previous part of the same paragraph, and the paragraph before that). This paper makes the same omission here as the other one you referenced: it does not discuss the obvious physical difference between having the singularity in your past vs. in your future; in the former case, you can see it, and in the latter, you can't. Saying that these two models are just different descriptions of the same universe makes no sense.

I think we've reached an impasse.

 

[stevendaryl]

This paper is making a proposal, not describing the standard rules of physical interpretation of GR that appear in GR textbooks.

Yes, but it reviews the current state of things when it comes to the arrow of time. The suggestion that the author is looking for a "geometric" definition of the arrow of time works exactly against the point you are making. He claims that two different solutions that are time-reverses of each other are not actually different, which is the opposite of what you're claiming.

I really don't understand your point of view, at all. And for all your call for references, you haven't posted a quote that supports your point of view.

The time-reversal of someone falling into a black hole and yelling "Help, I'm falling into a black hole!" is not someone rising from a white hole yelling "Wow! A white hole, and I'm rising out of it!". The time reversal of the first scenario is someone yelling "Help, I'm falling into a black hole!" (speaking backwards). The way to get a situation in which someone notices that they are arising from a white hole is by reversing that observer's internal sense of time, so that farther from the center seems like later, rather than earlier.

 

[stevendaryl]

What it does not do anywhere, as above, is talk about actual physical interpretation. To put it another way, it does not talk at all about why you would choose which direction is future versus past.

There is no reason, unless you introduce observers with an internal arrow of time. You say that there is a physical distinction between, say, a black hole cosmology and a white hole cosmology, but your explanations of what that distinction is are circular. There is no possibility of observing the difference unless you assume that the observer has an internal arrow of time aligned in a particular way. What looks like a black hole to one observer looks like a white hole to a time-reversed observer.

 

[PeterDonis]

I really don't understand your point of view, at all.

And I don't understand yours (more precisely, I don't understand why you are unable to see the obvious physical difference between the two solutions, star collapsing to black hole vs. white hole exploding to star), so I guess we're even.

And for all your call for references, you haven't posted a quote that supports your point of view.

As I said, I'm traveling and don't have my copies of textbooks like MTW and Wald handy. But I have already explained that the rule of physical interpretation I have been describing is what I get from reading textbooks like those. I have never seen any claim in any GR textbook that a thermodynamic arrow of time is required for the physical interpretation of proper time along a timelike worldline. The rule as I have described it is what is used throughout those textbooks. It permeates them. I am frankly baffled as to why this is not already an obvious fact to you.

The time-reversal of someone falling into a black hole and yelling "Help, I'm falling into a black hole!" is not someone rising from a white hole yelling "Wow! A white hole, and I'm rising out of it!".

Um, yes, it is. (Except for the yelling, which is not part of the models we have been discussing. You keep adding in extra features which are not part of those models, and then using those extra features to make claims about those models. That is unjustified.) Remember we are talking about two solutions which are time reverses of each other. One solution is a star collapsing to a black hole; the other, the time reverse of that, is a white hole exploding into a star. If you add an observer (or better, a mechanical device that registers proper time along its worldline--see further comments below) comoving with the matter, they fall into the black hole in the first solution, and they rise out of the white hole in the second.

The time reversal of the first scenario is someone yelling "Help, I'm falling into a black hole!" (speaking backwards).

This is adding an extra feature that is not present in the idealized models we have been discussing, and then talking as though it proves something about those idealized models. Sorry, not buying it.

The way to get a situation in which someone notices that they are arising from a white hole is by reversing that observer's internal sense of time, so that farther from the center seems like later, rather than earlier.

Here you are agreeing with me. "Reversing that observer's internal sense of time", in the idealized models we have been discussing, means reversing the direction of increasing proper time along their worldline, relative to the singularity--proper time increases away from the singularity, instead of towards it. That is how GR models the observer's "internal sense of time". And the "observer" here does not have to be conscious; it could be a mechanical clock. It could be anything that registers the proper time parameter along the curve. And for the idealized models we have been discussing, it needs to be, to avoid confusing yourself by adding extra features (like thermodynamics) that are not present in those idealized models.

 

[PeterDonis]

You say that there is a physical distinction between, say, a black hole cosmology and a white hole cosmology, but your explanations of what that distinction is are circular.

No, it isn't. See below.

There is no possibility of observing the difference unless you assume that the observer has an internal arrow of time aligned in a particular way.

In GR, you don't "assume" this, you model it as the proper time parameter along the observer's worldline. This mathematical property of the model (which direction, towards the singularity or away from it, the proper time increases) models the physical property of the observer (which, as I said in my previous post, should actually be a mechanical device to avoid confusion). Again, I am frankly baffled as to why this is not already an obvious fact to you. This is how every GR textbook I've read does it, all throughout the textbooks.

 

[PeterDonis]

The suggestion that the author is looking for a "geometric" definition of the arrow of time works exactly against the point you are making.

No, it works against the point you are making. You are basically claiming that I can't define the proper time parameter along an observer's worldline without introducing thermodynamics. The paper, correctly, recognizes, in the quote I gave, that that is not the case; proper time is a geometric parameter and can be included in a geometric model without any thermodynamics at all.

He claims that two different solutions that are time-reverses of each other are not actually different

But not based on the viewpoint in the quote I gave; the paper bases this claim on other grounds, which I have already said that I reject.

 

[Ibix]

Borrowing the Penrose diagram from figure 10 of the paper Peter linked earlier, switching a few + and - signs in the right hand copy (and I should probably have flipped the arrows on the shock wave and the event horizon but that was too fiddly), and adding a worldline with a few ticks of its proper time:

Is this argument essentially about whether those two diagrams represent distinct physical models, and/or exactly what changes are needed to make them become distinct or not distinct?