Is the Expansion of the Universe Leading to Heat Death?

[shingetsunohimitsu]

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]

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]

... 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.

 

[SpaceTiger]

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.

 

[Chronos]

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.

 

[SpaceTiger]

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.

 

[Mike2]

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?

 

[SpaceTiger]

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.

 

[Mike2]

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]

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?

 

[Mike2]

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.

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.

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.

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?

 

[SpaceTiger]

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.

 

[Chronos]

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.

 

[Mike2]

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]

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]

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.

 

[SpaceTiger]

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]

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?

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.

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.

 

[SpaceTiger]

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]

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]

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.

 

[SpaceTiger]

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]

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.

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...

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.

 

[SpaceTiger]

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.

 

[Chronos]

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.

I think you're approaching crackpot territory here.

No disagreement there. I try to suppress my inner crackpot, but not always with complete success

 

[SpaceTiger]

No disagreement there. I try to suppress my inner crackpot, but not always with complete success

I'm sure there's a little crackpot in all of us.

 

[Mike2]

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.

Actually, I strongly suspect that the existence of particles themselves are consequence of a conservation of information law at work in the universe. With the expansion of the universe, the highly concentrated structure of the universe at first has entropy associated with it. For example, this could be the structure of a very tight curvature in a very small region. Then as it expands it dissipates and entropy increases. I suspect particles arose to form pockets of information to compensate for the dissipation of expansion of space. I can't prove it yet. But there is an intuitive appeal to it, at least for me. I can't imagine how the universe as a whole could gain or lose information, where would it go? That would be like writing a book and throwing it out of existence, you can't do that. Whereever it goes is part of the universe. Nor are books thrown into the universe from outside. So if the universe as a whole cannot lose information, or gain information for that matter, then there is a conservation of information/entropy law at work in the universe. And structures MUST arise to compensate for dissipation.

If entropy/information is a description of the whole state, then it does not care how fast things are moving inside the system for which it is calculated. Chronos may be right and entropy may be a causal link between distant objects moving faster than light beyond the cosmological event horizon. Isn't entropy a "causal" link to know information about one particle that is quantum entangled with another moving faster than light with respect to the first?

 

[SpaceTiger]

But there is an intuitive appeal to it, at least for me. I can't imagine how the universe as a whole could gain or lose information, where would it go?
That would be like writing a book and throwing it out of existence, you can't do that. Whereever it goes is part of the universe. Nor are books thrown into the universe from outside.

That's a pretty silly proof, but I'm curious how you're defining "universe". Is it everything we can see at a given moment in cosmic time?

So if the universe as a whole cannot lose information, or gain information for that matter, then there is a conservation of information/entropy law at work in the universe. And structures MUST arise to compensate for dissipation.

This requires you changing the laws of physics, as I said. We can't say for sure that the laws of physics are the same everywhere in the universe and at every time, but this seems pretty ad hoc and too speculative to be of much scientific value at this point.

Isn't entropy a "causal" link to know information about one particle that is quantum entangled with another moving faster than light with respect to the first?

Ugh, let's not get started on quantum entanglement again. I'm sure that has been beaten to death many times on PF. Let's just say I don't think that there's a violation of relativistic causality and, therefore, I don't think it makes sense to think of entropy in that way.

 

[Mike2]

But there is an intuitive appeal to it, at least for me. I can't imagine how the universe as a whole could gain or lose information, where would it go?
That would be like writing a book and throwing it out of existence, you can't do that. Whereever it goes is part of the universe. Nor are books thrown into the universe from outside.

That's a pretty silly proof, but I'm curious how you're defining "universe". Is it everything we can see at a given moment in cosmic time?

I'm not sure that postulating a conservation of information law is "silly" at all. That's saying nothing more than that the existence of the universe as a whole is an absolute certainty. And a 100% probability results in no information at all. So at what point in time, or at what size of the universe did the existence of the universe as a whole ever become questionable? At what point in the evolution of the universe were there ever alternatives to its existence to consider the probability of? I think the obvious answer is never. The existence of the universe as a whole has always been, and always will be, an absolute certainty. This means exactly that there is a conservation of information law stating that the information content of the universe will be zero by definition always.

This means exactly that whatever structure emerges in the universe must be balanced by dissipative effects and visa versa. And it is fair to say that the dissipative effect (entropy) of expansion gave rise to particles and people. For there has to be balance.

You object because you don't see how global properties can cause local effects. But I'm sure you can imagine how the gobal effects of a very small initial universe influenced the course of particles at that time, right? Just think of a universe at the size of a particle and I'm sure you will agree that overall topology played a vital role in shaping the properties of particles.

Even by today's standards, the mere existence of quantum mechanics connects the motion of particles, by the probabilities involved, to the constraints of a greater environment. Entropy is connected to particles through the probabilites of quantum mechanics. For if the particles were not quantum mechanical and their interaction was absolutely deterministic, then there would be no possible alternative to their course. And there would be no talk of evolving to a more probable state (entropy)

So if the universe as a whole cannot lose information, or gain information for that matter, then there is a conservation of information/entropy law at work in the universe. And structures MUST arise to compensate for dissipation.

This requires you changing the laws of physics, as I said. We can't say for sure that the laws of physics are the same everywhere in the universe and at every time, but this seems pretty ad hoc and too speculative to be of much scientific value at this point.

I don't see how this requires changing the laws of physics. It just becomes more probable that complex structures would arise.

What I think is going on (my speculation, agian) is that the overall expansion of the universe gives rise to particle creation, the zero point energy = the cosmological constant, etc. Then the existence of a cosmological event horizon is giving rise to gravity that creates planets, stars, and galaxies. Then the shrinking of the cosmological event horizon gives rise to life, etc.

 

[SpaceTiger]

I'm not sure that postulating a conservation of information law is "silly" at all.

What was silly was that your argument was based entirely on popular analogies to real science.

That's saying nothing more than that the existence of the universe as a whole is an absolute certainty. And a 100% probability results in no information at all. So at what point in time, or at what size of the universe did the existence of the universe as a whole ever become questionable? At what point in the evolution of the universe were there ever alternatives to its existence to consider the probability of? I think the obvious answer is never. The existence of the universe as a whole has always been, and always will be, an absolute certainty. This means exactly that there is a conservation of information law stating that the information content of the universe will be zero by definition always.

I noticed that you didn't answer my question, so I'll assume you're not familiar with the different possible definitions of "universe":

1. All that we can observe at this moment in time.
2. All that has had a causal influence on us since the beginning of time.
3. All that has or will have a causal influence on us.
4. All that could have a causal influence on us.

This may not be all-inclusive, but it communicates the problem. As we go down the list, the definitions become more difficult for science to deal with, because they depend on philosophical assumptions that science cannot demonstrate by experiment. The problem is that, in order to make a useful theory of the universe, we need to invoke, at the very least, option #2; that is, we have to assume the existence of something that cannot be observed.

The reason I bring it up is that, In order for any what was quoted above to be consistent with what you said in the beginning (that the event horizon determines the entropy), you must select option 1 and you must reject general relativity's validity on cosmic scales. In the mainstream model of the universe, the size of the event horizon is changing with time, so the total amount of information contained within it would also be changing.

You object because you don't see how global properties can cause local effects. But I'm sure you can imagine how the gobal effects of a very small initial universe influenced the course of particles at that time, right? Just think of a universe at the size of a particle and I'm sure you will agree that overall topology played a vital role in shaping the properties of particles.

General relativity is a local theory (Einstein would not have had it any other way), so the overall topology of the universe will only be detectable (or, to put it another way, cause changes locally) if it has a curvature scale comparable to the observable universe.

I don't see how this requires changing the laws of physics. It just becomes more probable that complex structures would arise.

Which is exactly why I'm saying your theory requires changing the laws of physics. Given a set of initial conditions, the laws of quantum mechanics will give the probability of the system evolving to various states. If you wish to change these probabilities at different epochs, you must either change the laws of quantum mechanics or change the initial conditions. The latter, however, are set by those same laws.

 

[Chronos]

I vote for option 3. After the initial inflationary period [which appears to have preceded the current observable universe], the boundaries of the observable universe appear fixed.

 

[SpaceTiger]

I vote for option 3. After the initial inflationary period [which appears to have preceded the current observable universe], the boundaries of the observable universe appear fixed.

So you're saying you don't believe the standard model?

 

[Chronos]

3. All that has or will have a causal influence on us.

Is that option excluded by the standard model?

 

[SpaceTiger]

Is that option excluded by the standard model?

No, the option isn't, but your interpretation is:

"After the initial inflationary period [which appears to have preceded the current observable universe], the boundaries of the observable universe appear fixed."

Unless I'm misunderstanding you, that's not in accordance with standard LCDM.

 

[Chronos]

My petticoat appears to be showing This is slippery territory and it would not be the first time I've left skid marks attempting to traverse it. My grasp of the material may be flawed, but, this is what I have in mind:

Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe
http://arxiv.org/abs/astro-ph/0310808

Two quotes, in particular:

The particle horizon, not the Hubble sphere, marks the size of our observable universe because we cannot have received light from, or sent light to, anything beyond the particle horizon. Our effective particle horizon horizon is the cosmic microwave background (CMB), at redshift z ~ 1100, because we cannot see beyond the surface of last scattering.

The proper distance to the particle horizon is not DPH = ct0. Rather, it is the proper distance to the most distant object we can observe, and is therefore related to how much the universe has expanded, i.e. how far away the emitting object has become, since the beginning of time. In general this is ~ 3ct0. The relationship between the particle horizon and light travel time arises because the comoving coordinate of the most distant object we can see is determined by the comoving distance light has traveled during the lifetime of the universe.

 

[SpaceTiger]

The proper distance to the particle horizon is not DPH = ct0. Rather, it is the proper distance to the most distant object we can observe, and is therefore related to how much the universe has expanded, i.e. how far away the emitting object has become, since the beginning of time. In general this is ~ 3ct0. The relationship between the particle horizon and light travel time arises because the comoving coordinate of the most distant object we can see is determined by the comoving distance light has traveled during the lifetime of the universe.

The important thing to note is in that last sentence: "...the comoving coordinate of the most distant object we can see is determined by the comoving distance light has traveled during the lifetime of the universe." It implies that the comoving distance to the most distant object we can see depends on how old the universe is (i.e. changes with time). This is shown more explicitly in the bottom panel of Figure 1, where the dashed line shows how the particle horizon has changed throughout cosmic history.

 

[Chronos]

I interpretted [misinterpretted?] that to mean we have always been able to observe light emitted by any object that has ever, or will ever, be within our particle horizon since the beginning of time. I thought figure 1 depicted the spatial displacement of the particle horizon over time. The temporal displacement was always T[now] minus T0. Your patience is appreciated.

 

[SpaceTiger]

I interpretted [misinterpretted?] that to mean we have always been able to observe light emitted by any object that has ever, or will ever, be within our particle horizon since the beginning of time. I thought figure 1 depicted the spatial displacement of the particle horizon over time.

Actually, that section from which you quoted is trying to make exactly that distinction. It's saying that the plot depicts a changing particle horizon with time instead of the worldline of a single particle horizon. The plot is in comoving coordinates, so it follows the expansion, in a manner of speaking. If the horizon moves from one set of comoving coordinates to another, then it will be surrounded by a different set of galaxies, clusters, etc. Likewise, if the comoving radius of our particle horizon is increasing, then that means it encloses more objects with time.

Does that make sense? If comoving coordinates are a point of confusion then I will happily elaborate.

 

[Mike2]

I noticed that you didn't answer my question, so I'll assume you're not familiar with the different possible definitions of "universe":

1. All that we can observe at this moment in time.
2. All that has had a causal influence on us since the beginning of time.
3. All that has or will have a causal influence on us.
4. All that could have a causal influence on us.

I was suggesting that the cosmological event horizon was restricting and reducing entropy so that complex forms such as life came into existence. Since entropy is a description of the whole state, it does not matter how fast the particles are or how heavy they are. This means that it must be the size of the whole universe itself, everything that now exists whether observable or not, that would cause complexity to emerge to compensate for dissipation. If it exists, this would be a very strong restriction and would be implemented with high probability since there would be no alternative but that this balance be maintained. So I suppose that this kind of balance to entropy would give rise to more solid objects such as particles themselves. It may be that as the universe as a whole expands and the curvature of space decreases, that this dissipation is compensated for by the curvature involved with dense energy of particles at those points.

But the cosmological horizon is much smaller than the size of the entire universe. And since objects there redshift and slow just as with a black hole event horizon, I also speculated that the calculation for the entropy of a black hole is applicable to the entropy inside the cosmological event horizon. Thus, if the cosmological event horizon is shrinking, then the restriction of entropy inside become more restricted. As I recall from the paper I read that it may be that the restriction on entropy inside the event horizon has not yet become smaller than the entropy inside. But they may not have taken into account the entropy of space itself or of dark matter or dark energy, etc. But if the horizon's restriction of entropy inside does not actually cause complexity to start to arise, then perhaps the expansion of the universe may be limited so that the entropy of the horizon never becomes smaller than the entropy inside. Or since the cosmological event horizon is not a topological property, its entropy may not require a topological compensation, such as a particle, but my require only a softer response of just the configuration of particles on the average with possibly some delay.

 

[Chronos]

Bear with me a bit longer, ST, I'm trying to wrap my head around this. From page 9-10 of the Lineweaver paper:

The particle horizon has traditionally been depicted as the worldline or comoving coordinate of the most distant particle that we have ever been able to see (Rindler, 1956; Ellis & Rothman, 1993). The only information this gives is contained in a single point: the current distance of the particle horizon, and this indicates the current radius of the observable universe. The rest of the worldline can be misleading as it does not represent a boundary between events we can see and events we cannot see, nor does it represent the distance to the particle horizon at different times.

I'm reading this to mean the observable universe only changes in size, not observable content over time. The paragraph that follows appears to support this interpretation:

An alternative way to represent the particle horizon is to plot the distance to the particle horizon as a function of time (Kiang, 1991). The particle horizon at any particular time defines a unique distance which appears as a single point on a spacetime diagram. Connecting the points gives the distance to the particle horizon vs time. It is this time dependent series of particle horizons that we plot in Fig. 1. (Rindler (1956) calls this the boundary of our creation light cone – a future light cone starting at the big bang.) Drawn this way, one can read from the spacetime diagram the distance to the particle horizon at any time. There is no need to draw another worldline.

Thanks again for your indulgence [amateurs can be thick skulled].

 

[Garth]

I was suggesting that the cosmological event horizon was restricting and reducing entropy so that complex forms such as life came into existence.

There are two discussions going on here, one about various horizons and the other about entropy and 'information'.

May I 'fly a kite' about entropy?
The concept of entropy arose from the Second Law of Thermodynamics which itself arose from the study of heat engines and the behaviour of hot gas under pressure in a closed system. Molecules of such a pressurized gas tended to 'fly apart' and thus increase the disorder of that system.

This vague concept was given mathematical precision in the definition of entropy S:

dS=\frac{dQ}{T}
where dQ is the change in heat absorbed/lost by a system at temperature T.

However when considering the entropy of the universe, and the problem of how order arose from an original disordered state, there are two recognised questions and a third one that I have always pondered about but never resolved.

Perhaps you may enlighten me.

The first question in cosmological entropy is whether the universe can be considered as a closed system, if not the 2nd Law does not apply.

The second is whether the very fact of the expansion of the universe increases the number of possible states available for physical systems within it and that itself reduces the entropy.

But my question is whether the 2nd Law applies in the first place to a gravitating system, such as the universe, in which particles tend to 'fly together', rather than apart. In this case, when gravitation is the dominant force, may it be seen as a natural entropy-reducing and order-producing agency working in opposition to the Second Law of Thermodynamics?

Just a thought.

Garth

 

[SpaceTiger]

But my question is whether the 2nd Law applies in the first place to a gravitating system, such as the universe, in which particles tend to 'fly together', rather than apart. In this case, when gravitation is the dominant force, may it be seen as a natural entropy-reducing and order-producing agency working in opposition to the Second Law of Thermodynamics?

There's an interesting discussion of this here. In short, a system collapsing under the influence of gravity will experience a decrease in entropy, as one might intuitively expect, but it also loses energy. If it loses energy, then that means that something is leaving the system, "carrying away" entropy with it. Most of the time, this something will be light.

 

[SpaceTiger]

The particle horizon has traditionally been depicted as the worldline or comoving coordinate of the most distant particle that we have ever been able to see (Rindler, 1956; Ellis & Rothman, 1993).

Yes, this is our current particle horizon. The "worldline" of an object at this distance will bring it, in physical coordinates, further and further from us with time, but if viewed in comoving coordinates the distance is a constant. However, this is only for the current particle horizon, as is described in the next few sentences:

The only information this gives is contained in a single point: the current distance of the particle horizon, and this indicates the current radius of the observable universe. The rest of the worldline can be misleading as it does not represent a boundary between events we can see and events we cannot see, nor does it represent the distance to the particle horizon at different times.

That last sentence is key. It says that the worldline of the current particle horizon does not represent the particle horizon at different times. This is another way of saying that the comoving radius of the observable universe changes with time, which is another way of saying that the contents of the observable universe change with time.

 

[Garth]

There's an interesting discussion of this here. In short, a system collapsing under the influence of gravity will experience a decrease in entropy, as one might intuitively expect, but it also loses energy. If it loses energy, then that means that something is leaving the system, "carrying away" entropy with it. Most of the time, this something will be light.

Yes thank you - the system is radiating away energy.

I was actually thinking about a dust cloud collapsing under its own gravity - a cloud of non-interacting particles. (sounds familiar?)

BTW I'm interested that Baez recommended the book "F. Reif, Fundamentals of Statistical and Thermal Physics, McGraw-Hill, New York, 1965", it's sitting on my bookshelf. It was our textbook at BSc level and I bought it at huge expense, but then at MSc level we were told not to use it because it is basically mistaken! I never got to the bottom of that!

Garth

 

[SpaceTiger]

I was actually thinking about a dust cloud collapsing under its own gravity - a cloud of non-interacting particles. (sounds familiar?)

That's a bit trickier, since non-interacting particles cannot reach eqilibrium, but I assure you the second law still applies. The gravitational force is time-reversible, meaning the fluctuation theorem would apply to it as well as to the other forces.

 

[Mike2]

That's a bit trickier, since non-interacting particles cannot reach eqilibrium, but I assure you the second law still applies. The gravitational force is time-reversible, meaning the fluctuation theorem would apply to it as well as to the other forces.

Do you have a link to a more mathematically complete explanation of the Fluctuation theorem. Thanks.

Something I don't understand. If time reversible processes mathematically lead to entropy, then doesn't the mathematics equally say that entropy leads to reversible processes, in otherwords, entropy influences the particle physics? What I don't understand is how math can prove one thing, but that thing does not prove the one. In logic one has material implication where one thing can prove the second but the second does not prove the first. But in math we're dealing with equivalences where if one thing equals another, than that means the other thing equals the first. So how did material implication enter the process of proving the Fluctuation theorem?

 

[SpaceTiger]

Do you have a link to a more mathematically complete explanation of the Fluctuation theorem. Thanks.

http://prola.aps.org/abstract/PRL/v71/i15/p2401_1?qid=57a56940f9ccff67&qseq=2&show=10

 

[Gold Barz]

Sorry ST, but could you reply to the question I PM'd you about this specific topic please?

Thanks.

 

[SpaceTiger]

Sorry ST, but could you reply to the question I PM'd you about this specific topic please?

Perhaps you should start asking your questions on the forum. After all, that was its original intent.

 

[Gold Barz]

What do you guys think of quantum fluctuations/virtual particles being able to inflate as universes during/after heat death?...maybe that is how universes are born? maybe that's how inflation happens...is it a cuckoo theory or a pretty reasonable one?