# Heat Death?

I have been reading the archives of Physics Forums, some threads about the expansion of the universe and also the upcoming Heat Death that people keep talking about. However, there are a few things that keep bugging me:

First of all, atoms have not so far shown any tendency not to cluster together, like they do today in galaxies and so forth, so why is there a reason to believe that all matter should be ripped apart?

Increasing entropy, they tell me, but that brings me to another question which as that as to howt eh universe is considered a closed system or not. Because as far as I know, Boyle's law only applies to closed systems. I was reading something about this once, about how life came to be, because it shouldn't really have if there is a constant strife for increasing entropy, as cells and all kinds of living organisms are really a very orderly form of being. However, since the earth is not a closed system as such this was possible, and I gather this is because it is in space, and therefore the universe should not be striving towards entropy. But it is?

What am I missing out on?

SpaceTiger
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shingetsunohimitsu said:
First of all, atoms have not so far shown any tendency not to cluster together, like they do today in galaxies and so forth, so why is there a reason to believe that all matter should be ripped apart?

Let's be careful to distinguish between the heat death and the "Big Rip". For the former, remember the second law of thermodynamics -- entropy always increases in a closed system. Heat death basically refers to this gradual movement towards the maximum entropy state. Atoms aren't exactly "ripped apart", as you say.

As for the Big Rip (in which atoms are eventually ripped apart), it's a new idea that comes from some theories of dark energy. It only arises if the dark energy has certain properties (specifically an equation of state less than -1), but this cannot yet be tested by observations. The basic idea is that the universe expands so quickly that, eventually, the different parts of individual objects (like atoms) can no longer communicate with one another and they get ripped apart.

Increasing entropy, they tell me, but that brings me to another question which as that as to howt eh universe is considered a closed system or not.

What am I missing out on?

An excellent question. In fact, the observable universe is not a closed system (things are entering our horizon all of the time), but if the cosmological principle holds (homogeneity and isotropy), then things outside our horizon should have basically the same properties as those inside and the heat death would still occur. The validity of the cosmological principle on scales outside of our horizon will depend on whether or not we can experimentally confirm the predictions of inflation.

Overall, I wouldn't put much confidence in any predictions about the fate of our universe, particularly since we don't yet know what this "dark energy" really is. For all we know, it could reverse its equation of state ten billion years from now and the universe would start contracting.

Chronos
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SpaceTiger said:
... In fact, the observable universe is not a closed system (things are entering our horizon all of the time) ...
We have a rare difference of opinion on that count. I think the portion of the universe that will ever be causally connected [observable] to us was fixed during the inflationary epoch of the big bang. Which means we have always, and will always be causally connected to [able to see] everything possible to view from our observational outpost. In that sense, it is a closed system - although most objects will eventually redshift beyond practical limits of detectability.

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Chronos said:
We have a rare difference of opinion on that count. I think the portion of the universe that will ever be causally connected [observable] to us was fixed during the inflationary epoch of the big bang. Which means we have always, and will always be causally connected to [able to see] everything possible to view from our observational outpost.

If inflation is correct, then the universe was once causally connected, but is not at the present epoch. If it weren't for portions of the universe entering the the horizon and coming into causal contact with rest, the acoustic oscillations of the CMB would not be possible.

Here's a quote from Joanne Cohn's website:

A special feature of inflation is its effect on horizons. The horizon demarcates the boundary of causally connected regions, regions that light rays (which travel at the fastest speed that any signal can travel) can reach since the time of the big bang. These regions grow over time, as light has more time to travel, but the expansion of the universe means that over time there is more space to cross as well. When the universe isn't inflating, such as now, regions which are larger and larger come inside the horizon and become causally connected.

The basic reason is that inflation shrinks the comoving horizon (note, astronomers are usually thinking in comoving coordinates when they talk about cosmology). When inflation ends and we enter the radiation- and matter-dominated epochs, then the evolution of the scale factor is much slower and the comoving horizon begins to grow with time.

Right now, it's not clear exactly what's going on because we don't know what the dark energy is. If it's a cosmological constant, then we're right on the boundary between the matter-dominated epoch and "vacuum energy dominated" epoch. The latter will cause the horizon to shrink, so we won't see much more of the universe and it will be a closed system from here on out. If, on the other hand, it's something more complicated than that, there's no telling how much more of the universe we'll see. Whether or not the observable universe is a close approximation to a closed system will depend upon these details, but I don't think it's safe to assume at this point.

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Chronos
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That is a powerful argument, and one I cannot handily refute. I merely have an opinion... more like a hunch... that it's wrong. I lean that way because of horizon issues with black holes. Studies suggest horizons are real and the universe has one. Don't mean to be argumentative, just curious.

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SpaceTiger
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Chronos said:
That is a powerful argument, and one I cannot handily refute. I merely have an opinion... more like a hunch... that it's wrong. I lean that way because of horizon issues with black holes. Studies suggest horizons are real and the universe has one.

I'm not disputing the existence of horizons, Chronos. Could you please clarify, because I don't see what you're objecting to.

SpaceTiger said:
Let's be careful to distinguish between the heat death and the "Big Rip". For the former, remember the second law of thermodynamics -- entropy always increases in a closed system. Heat death basically refers to this gradual movement towards the maximum entropy state. Atoms aren't exactly "ripped apart", as you say.

As for the Big Rip (in which atoms are eventually ripped apart), it's a new idea that comes from some theories of dark energy. It only arises if the dark energy has certain properties (specifically an equation of state less than -1), but this cannot yet be tested by observations. The basic idea is that the universe expands so quickly that, eventually, the different parts of individual objects (like atoms) can no longer communicate with one another and they get ripped apart.
I'd like you all to consider that the cosmologcial event horizon may fix the amount of entropy in the visible universe just as the surface area of the event horizon of a black hole fixes the entropy of a black hole. The observable effects are the same: as objects approach the cosmo event horizon, they redshift and become slower, just as they do for a black hole event horizon. I've seen articles from Ph.D's that suggest that the information inside our cosmological event horizon is fixed by the surface area of that horizon using the same equation as for that of a black hole.

You talk about "heat death" and "big rips" as though entropy is free to increase without limit. But I have my doubts. Consider that we have just discovered that space is expanding ever faster, accelerating. This means that the cosmological event horizon is getting smaller, that the constraint on entropy is decreasing. I suspect that this may be the cause for the emergence of highly complex structures such as life. Curious that life started to arise at about the same time that the universe started to accelerate its expansion, about 4 billion years ago. Perhaps this is not a coincidence.

So, will there be a heat death or a big rip, leaving nothing left to speak of? Or will ever greater complex, stable structures arise as the entropy inside the observable universe is forced to decrease by the ever shrinking horizon?

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Mike2 said:
I'd like you all to consider that the cosmologcial event horizon may fix the amount of entropy in the visible universe just as the surface area of the event horizon of a black hole fixes the entropy of a black hole.

That does not seem unreasonable to me, but there is one problem: we don't know what the event horizon is. Without understanding all of the components of the universe, including dark energy, the relevant integral cannot be done. It's possible that it diverges.

You talk about "heat death" and "big rips" as though entropy is free to increase without limit.

For the former, there would be a theoretical "maximum entropy state", just as there is for a gas. For the latter, the situation I described is not in any way dependent upon entropy.

This means that the cosmological event horizon is getting smaller, that the constraint on entropy is decreasing. I suspect that this may be the cause for the emergence of highly complex structures such as life.

That seems like a big stretch to me. Why would the total entropy of the universe have such a dramatic impact on local processes? The second law of thermodynamics still applies.

SpaceTiger said:
That does not seem unreasonable to me, but there is one problem: we don't know what the event horizon is. Without understanding all of the components of the universe, including dark energy, the relevant integral cannot be done. It's possible that it diverges.

....

That seems like a big stretch to me. Why would the total entropy of the universe have such a dramatic impact on local processes? The second law of thermodynamics still applies.

I agree that this would certainly be a mysterious process. It would seem that it cannot be described in terms of particles and forces. But then again, so is any entropy. Entropy doesn't seem to be describable in terms of particles and forces. In fact it seems that the physical laws at the micro scale don't seem to distinguish the direction of time. They seem symmetric with respect to a reversal of the time coordinate. What do they call that, unitary?

However, entropy is a number ascribed to the state of an entire system. It does not depend on the mass of particles or how fast the particles are moving. It is a given number for the system. And if that number should change then it can change in various ways, faster particles, or more massive particles to effect the same change in entropy, etc. So if the entropy of our observable universe is changed by the cosmological event horizon, then this would have an immediate effect, not needing time for that information to travel to us at the speed of light, for example. For it is a number ascribed to the entire system.

As for not knowing what exactly the horizon is, I don't think it matters. All we do need to know is that it does effect the system as a whole.

SpaceTiger
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I agree that this would certainly be a mysterious process. It would seem that it cannot be described in terms of particles and forces. But then again, so is any entropy. Entropy doesn't seem to be describable in terms of particles and forces. In fact it seems that the physical laws at the micro scale don't seem to distinguish the direction of time. They seem symmetric with respect to a reversal of the time coordinate.

But the increase of entropy is due only to the laws of physics and the axiom of causality. The change in entropy is not itself the cause, but is the result of other causal laws. In other words, it doesn't make sense to say something like, "because the entropy is increasing, the particle velocities are increasing." Unless you're suggesting that the laws of physics changed 4 billion years ago, I don't think that your idea works.

As for not knowing what exactly the horizon is, I don't think it matters. All we do need to know is that it does effect the system as a whole.

Even if it diverges? How does one compute the entropy (or time derivative of entropy) if there is divergence?

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SpaceTiger said:
But the increase of entropy is due only to the laws of physics and the axiom of causality.
As I understand it, the quantum mechanical equations are symmetric with respect to the direction of time and don't say anything about entropy whatsoever. If you are referring to the 2nd law of thermodynamics, it is an equation of state and doesn't care how the particles properties change to accomadate it. For all the 2nd law cares, the mass of particles can increase instead of the velocity increase in order to have a higher temperature. There simply is no cause and effect reasoning why the 2nd law exists. It is simply and outside observation about the probabilities involved in the way things progress. The probability of what state a system may evolve into does not seem to be encoded in the particles or their interactions. So it seems entropy at any level is not a properties that can be reduced to particles, forces, space, and time.

SpaceTiger said:
The change in entropy is not itself the cause, but is the result of other causal laws.
I don't think you could prove that. You would have to show that the first could exist without the second in order to prove that the second in not the cause of the first. But since both exist in conjunction, it is logically impossible to prove that one is the cause of the other but not the other way around.

SpaceTiger said:
In other words, it doesn't make sense to say something like, "because the entropy is increasing, the particle velocities are increasing."
I think they say things like this all the time. Take for example a gas contained by a partition to one side of an enclosure. Take away the partition and we say that because entropy increase, the particles on average will move towards the other side. The existence of entropy imposes a prediction on the velocity of particles.

SpaceTiger said:
Even if it diverges? How does one compute the entropy (or time derivative of entropy) if there is divergence?
Sorry, I don't follow you here. If what diverges? What do you mean by diverges?

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Mike2 said:
I don't think you could prove that. You would have to show that the first could exist without the second in order to prove that the second in not the cause of the first. But since both exist in conjunction, it is logically impossible to prove that one is the cause of the other but not the other way around.

I don't need to prove it, someone already did, or at least they showed that the second law arises naturally from time-symmetric physical laws, given, as I said, the axiom of causality. Since this isn't a religious forum, I'm prone to outright reject the opposite suggestion -- that the change in a single quantity, entropy, is the cause of all of the laws of physics. One might say that our understanding of causality is a consequence of increasing entropy, but that's a philosophical point.

I think they say things like this all the time. Take for example a gas contained by a partition to one side of an enclosure. Take away the partition and we say that because entropy increase, the particles on average will move towards the other side. The existence of entropy imposes a prediction on the velocity of particles.

You're right, I should have been more precise. We can speak of the entropy as being a cause of phenomena that are more general than those from which it's derived. For example, it makes sense to say,

"The seasons are caused (in part) by the earth going around the sun."

However, it does not make sense to say,

"That the force of gravity falls off as 1/r2 is caused by the earth going around the sun."

In the case we're discussing, you're suggesting that the changing total entropy of the universe would somehow be altering the basic behavior of matter and energy on a global scale, yet it is this basic behavior from which the second law arises.

I've not seen the derivations, but I suspect that the fact that the entropy decreases with the event horizon has only to do with the fact that a smaller event horizon contains less matter and energy.

Sorry, I don't follow you here. If what diverges? What do you mean by diverges?

The cosmological event horizon is given by

$$r_e = \int_{t_0}^{\infty}\frac{dt}{a(t)}$$

If the above integral does not converge, then the event horizon is effectively infinite in size, implying an infinite entropy within the universe. The open universe ($$\Omega<1$$) is an example of a case where the integral diverges.

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Chronos
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IMO, the surface of last scattering [z~1100] is the horizon, and eternal limit of our observable universe. The only variable is distance and recession velocity. Everything inside this horizon always has, and always will be observationally accessible and nothing beyond that barrier will ever be observationally accessible to us. No 'new' structures will ever pop into view. Nor will any objects currently inside our horizon pass beyond it and suddenly disappear.

Expansion causes time dilation. High redshift objects appear to evolve more slowly than their low redshift counterparts. For example, we know expansion accelerated in the recent past is because high redshift supernova are not at the brightness expected based on time dilation of their light curves. If the rate of expansion [or inflation] changed at other times in the early universe, it could be detected [and may already have been] through anomalies in the CMB. If the universe suddenly stopped expanding, distant objects would gradually become less redshifted and appear to evolve more quickly. If expansion continues to accelerate indefinitely, objects will become increasingly redshifted and appear to evolve more slowly - eventually appearing to be virtually frozen in time.

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SpaceTiger said:
I don't need to prove it, someone already did, or at least they showed that the second law arises naturally from time-symmetric physical laws, given, as I said, the axiom of causality. Since this isn't a religious forum, I'm prone to outright reject the opposite suggestion -- that the change in a single quantity, entropy, is the cause of all of the laws of physics. One might say that our understanding of causality is a consequence of increasing entropy, but that's a philosophical point.
The laws of physics on which this theorem is derived are at question. How would the calculation change if it were discovered that spacetime were quantized, for example. What is causality below the quantum gravity level? If this Fluctuation theorem is so general that it would encompass any equations invariant with time reversal, then this theorem does not depend on physics at all. And this theorem only relates entropy to statistical situations. We already know that.

No, if entropy is derived by these underlying equations (laws of physics) in particular, then it would be that the existence of entropy would prove that these were the one and only unique equations of physics. For if the underlying equations were different, then we would not have the Fluctuation theorem. But if the Fluctuation theorm held under many supposed time reveral invariant laws of physics, then it is not physics that proves entropy.[/QUOTE]

JesseM
SpaceTiger said:
I don't need to prove it, someone already did, or at least they showed that the second law arises naturally from time-symmetric physical laws, given, as I said, the axiom of causality.
The fluctuation theorem doesn't really help you explain the asymmetric arrow of time, though. Yes, it says that given a certain low-entropy state observed now, if you observe the system again at a later time the entropy is more likely to have increased than decreased. But without imposing any special prior boundary conditions, exactly the same reasoning should lead you to predict that if you had observed the system at an earlier time, the entropy would be much more likely to have been higher in the past than lower. Without making assumptions about boundary conditions, statistical mechanics will always lead to the prediction that entropy should increase in both the positive time direction and the negative time direction from any given low-entropy state.

SpaceTiger
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Chronos said:
IMO, the surface of last scattering [z~1100] is the horizon, and eternal limit of our observable universe.

This first part of your argument has a rather simple flaw in that it assumes photons to be the only observable particles. In fact, there are other things that carry information about the cosmos. In particular, neutrinos and gravity waves have their own "surfaces of last scattering" at z>>1100. This is a relatively minor point, however. There is, I believe, a more fundamental misunderstanding at work here:

Everything inside this horizon always has, and always will be observationally accessible and nothing beyond that barrier will ever be observationally inaccessible to us. No 'new' structures will ever pop into view. Nor will any objects currently inside our horizon pass beyond it and suddenly disappear.

The observable universe consists only of those objects whose photons are observable at the present time. Within the context of the standard model, this is not, and has not been, a constant with time. To understand why this is, consider some examples. First, imagine a completely stationary and flat universe (no expansion) that suddenly pops into existence at a time that we'll call t=0. Now, if you agree that information can only be carried at or below the speed of light, then the size of the observable universe will simply be the distance that light can travel since the beginning of time:

$$r_u=ct$$

I hope we would all agree that, in this simple case, the size of our observable universe is changing with time and new structures are popping into view.

This is not the universe we live in, however, and things are a bit (to put it mildly) more complicated. First of all, we have expansion. The most basic consequence of this is that, while light is traveling further and further with time, things are also moving further and further apart. To make things even worse, we find that this expansion appears to have both accelerated and decelerated at several points in cosmic history! Needless to say, the presently favored equivalent of the equation I gave above would not be in any way intuitive to someone not familiar with relativity, but the important point is that it is not a constant. This should be intuitive from the simple fact that the both the rate of expansion and its time derivative have been changing with time.

Although a full understanding of the evolution of the universe requires a detailed knowledge of general relativity, one can nonetheless develop an intuition for it by considering some basic results:

- The exact conditions at the beginning of the universe are unknown, but suffice it to say that all of the universe (or at least a much larger portion than we see now) was in causal contact and could be observed from any reference point.
- During the inflationary epoch, expansion is superluminal, in the sense that objects recede from us more quickly than the speed of light. (note: this is not in contradiction with relativity, as is explained here ) A hypothetical observer living through inflation will find that, as time goes on, their telescopes can observe fewer and fewer objects.
- After inflation, the expansion begins to decelerate and the dynamics are dominated by radiation and matter, respectively. One consequence of this is that the size of the observable universe begins to increase, again revealing some of the parts that were rendered unobservable by inflation. In fact, one of the original motivations for inflation was that it explained how the observable universe could have been increasing in size (that is, objects were "popping" into view), and yet have still been uniform on scales that had seemingly never communicated with one another before.
- Very recently (by cosmic standards), the universe has started accelerating again, possibly indicating the beginning of another inflationary epoch. If this is the case, the observable universe will begin to shrink once again. However, the answer will remain highly uncertain until we reach a consensus on the origin of the acceleration.

I hope that helps. All of this depends, of course, on the correctness of the standard model, but I figured that wasn't the issue, since you've always embraced it in the past.

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SpaceTiger
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JesseM said:
The fluctuation theorem doesn't really help you explain the asymmetric arrow of time, though. Yes, it says that given a certain low-entropy state observed now, if you observe the system again at a later time the entropy is more likely to have increased than decreased. But without imposing any special prior boundary conditions, exactly the same reasoning should lead you to predict that if you had observed the system at an earlier time, the entropy would be much more likely to have been higher in the past than lower. Without making assumptions about boundary conditions, statistical mechanics will always lead to the prediction that entropy should increase in both the positive time direction and the negative time direction from any given low-entropy state.

I was under the impression that this was the purpose of the axiom of causality (note, an assumption and not a proof) that i mentioned in the passage that you quoted. Besides, the direction of the arrow of time is not really the issue being debated, since this would seem to me to be a binary question (that is, it's either causal or anti-causal). Rather, Mike2 is suggesting that in a more generalized sense, the changing total entropy of the universe is changing the behavior of the contents of the universe in some way not described by the laws of physics.

JesseM
SpaceTiger said:
I was under the impression that this was the purpose of the axiom of causality (note, an assumption and not a proof) that i mentioned in the passage that you quoted.
Where did you read about the axiom of causality? If this axiom can't be derived from any of the fundamental laws of physics it seems like it isn't really explaining anything. Anyway, in a deterministic system it is always possible in principle to prepare an initial state that will lead the system to decrease in entropy, would doing so violate the axiom of causality?
SpaceTiger said:
Besides, the direction of the arrow of time is not really the issue being debated, since this would seem to me to be a binary question (that is, it's either causal or anti-causal).
A system at maximum entropy won't show an arrow of time in either direction (if you play a movie of its behavior backwards it won't look any different from a forward movie)--is it "causal" or "anti-causal"? I have never seen any physicists talk this way--when they discuss the arrow-of-time problem, they always seem to argue that its origins lie in the low-entropy state of the universe at the time of the Big Bang, which itself has no widely-agreed-upon explanation.
SpaceTiger said:
Rather, Mike2 is suggesting that in a more generalized sense, the changing total entropy of the universe is changing the behavior of the contents of the universe in some way not described by the laws of physics.
OK, if that's his argument I wouldn't agree with it. But the arrow-of-time question is an interesting side issue, anyway.

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Mike2 said:
The laws of physics on which this theorem is derived are at question. How would the calculation change if it were discovered that spacetime were quantized, for example. What is causality below the quantum gravity level?

Speculating on future physics is not really the point here. As far as we know at the moment, the physical laws are time-reversible and your reasoning doesn't apply. There are an infinity of things that we can speculate about for the future of physics, but I see no compelling reason to believe that they will be so different as to have induced the change you're suggesting at such a recent moment in cosmic history.

If this Fluctuation theorem is so general that it would encompass any equations invariant with time reversal, then this theorem does not depend on physics at all.

It depends on the laws of physics being time-reversible. How does that translate into "does not depend on physics at all"? If they weren't time-reversible, it wouldn't apply.

And this theorem only relates entropy to statistical situations. We already know that.

As far as I know, entropy has only been shown to be physically meaningful in statistical situations. If you know of an experiment that shows otherwise, I would be curious to see it.

No, if entropy is derived by these underlying equations (laws of physics) in particular, then it would be that the existence of entropy would prove that these were the one and only unique equations of physics. For if the underlying equations were different, then we would not have the Fluctuation theorem.

First of all, the "existence of entropy" cannot be shown by science, it can only show that the quantity is of physical significance. Second of all, this would not lead naturally to the laws of physics, it would show only that they were time-reversible. Finally, proof and causality are different things. For example, I can use the orbits of the planets as "proof" of the Newton's Law of gravitation, but that does not mean that the orbits caused the law.

Chronos
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This a very interesting subject and makes for lively discussions. Mathematically, it is difficult to quantify the relativistic consequences of superluminal expansion. But I can see ways to preserve causal contact between different regions no matter how fast they recede. One way is to observationally freeze them in place until the retarded photons have a chance to catch up. This approach makes sense to me. Time and space preserves the causal link between connected regions by stretching the wave fronts of photons [or neutrino] that connect them. This apparent violation of SR would not be detectable by inertial observers because their 'rulers' would also be stretched. It would, however, result in some very confusing observational consequences.

SpaceTiger
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JesseM said:
If this axiom can't be derived from any of the fundamental laws of physics it seems like it isn't really explaining anything.

If it were derivable, it wouldn't be an assumption. The fluctuation theorem is not a proof of the arrow of time, I was agreeing with you. I'm invoking it only to show that it does not make sense to use the "total entropy of the universe" as an additional causal agent in the behavior of physical systems.

Anyway, in a deterministic system it is always possible in principle to prepare an initial state that will lead the system to decrease in entropy, would doing so violate the axiom of causality?

If we're talking about macroscopic systems here, then as I understand it, yes, it would be a violation of the second law of thermodynamics, which rests on the assumption of a specific arrow of time (to use your preferred terminology).

A system at maximum entropy won't show an arrow of time in either direction (if you play a movie of its behavior backwards it won't look any different from a forward movie)--is it "causal" or "anti-causal"?

I suppose that a universe with no thermodynamic arrow of time is possible, in principle, but again, I don't think that's relevant here and it seems a bit picky.

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SpaceTiger
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Chronos said:
This a very interesting subject and makes for lively discussions. Mathematically, it is difficult to quantify the relativistic consequences of superluminal expansion.

Not at all, in fact, it's standard theory. It may be a bit difficult to conceptualize, but it's a relatively simple computational problem compared to those that GR experts do on a regular basis.

But I can see ways to preserve causal contact between different regions no matter how fast they recede. One way is to observationally freeze them in place until the retarded photons have a chance to catch up. This approach makes sense to me. Time and space preserves the causal link between connected regions by stretching the wave fronts of photons [or neutrino] that connect them. This apparent violation of SR would not be detectable by inertial observers because their 'rulers' would also be stretched. It would, however, result in some very confusing observational consequences.

I think you're approaching crackpot territory here.

JesseM
SpaceTiger said:
If it were derivable, it wouldn't be an assumption. The fluctuation theorem is not a proof of the arrow of time, I was agreeing with you. I'm invoking it only to show that it does not make sense to use the "total entropy of the universe" as an additional causal agent in the behavior of physical systems.
Well, again, I'm curious to know where you read about this axiom. Certainly I've seen physicists talk about causality, but only in the context of ruling out FTL or time travel, I've never seen it in a purely thermodynamic context. Again, all the physicists I've seen discuss the arrow of time in books (Hawking, Penrose, and Greene are the three examples that come to mind) suggest it should be explained in terms of the low entropy of the universe at or near the big bang, although they may have different ideas about why the big bang started the universe off in such a low-entropy state in the first place.
SpaceTiger said:
If we're talking about macroscopic systems here, then as I understand it, yes, it would be a violation of the second law of thermodynamics, which rests on the assumption of a specific arrow of time (to use your preferred terminology).
I agree it's a violation of the 2nd law, but is it a violation of the "axiom of causality" as you understand the term? I don't think most physicists would refer to this sort of thing as a "causality violation", but maybe that's different...
SpaceTiger said:
I suppose that a universe with no thermodynamic arrow of time is possible, in principle, but again, I don't think that's relevant here and it seems a bit picky.
I wasn't talking about a whole universe, just an isolated system at equilibrium.

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JesseM said:
Well, again, I'm curious to know where you read about this axiom. Certainly I've seen physicists talk about causality, but only in the context of ruling out FTL or time travel, I've never seen it in a purely thermodynamic context.

To be honest, I don't remember where I first heard it, and I'm away from my office, so I can't check my books. Keep in mind that I'm an astrophysicist, so my exposure would likely be different from that of a pure physicist. That aside, though, I'm surprised you've never heard anyone talk about the second law of thermodynamics in terms of cause and effect. I'm sure I've heard the shattering glass example given in my physics classes.

Again, all the physicists I've seen discuss the arrow of time in books (Hawking, Penrose, and Greene are the three examples that come to mind) suggest it should be explained in terms of the low entropy of the universe at or near the big bang, although they may have different ideas about why the big bang started the universe off in such a low-entropy state in the first place.

I just want to make sure it's clear that my posts aren't attempting to dispute any of those ideas.

I agree it's a violation of the 2nd law, but is it a violation of the "axiom of causality" as you understand the term? I don't think most physicists would refer to this sort of thing as a "causality violation", but maybe that's different...

Ok, now I see why you're so strongly objecting to the terminology. Yes, you're exactly right, "causality violation" is usually used in the context of relativity. Yes, I would consider it a violation of the "axiom", but should have said it in another way.

I wasn't talking about a whole universe, just an isolated system at equilibrium.

Ok, but again, I don't really see why this is such an important point. The distinction between $$\Delta S>0$$ and $$\Delta S \geq 0$$ doesn't seem worth considering in real systems, since the second law is statistical in nature to start with.

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Chronos