Sorry for the confusing title! I have a question that I cannot wrap my mind around... Suppose the universe attains its state of maximum entopy (assuming maximum here also involves quantum effects such that in the end even the atoms disintegrate into photons and leptons). I understand that in order to do work there needs to be a temperature gradient( which wont be avilable) but would'nt quantum fluctuations still persist (uncertainty principle)? So if you agree on the quantum effects(i hope you do) then would;nt 'we' in principle be able to measure time still? So doesn't that mean that the direction of time has nothing to do with the increase in entropy of the universe? i.e the thermodynamic arrow of time AND the cosmological arrow of time are distinct and unrelated entities??? Also...if the universe is still expanding after alls said and done...what exactly will be causing the expansion? Shouldnt it fade with the apparent dissapearance of gravitation and the dark stuff?? I' am sorry if I sound dumb but I sounded like a good idea to ask.
Re: Physical interpretation of entropy if expansion causes a state of maximum entropy Think of what happens when the air in a room reaches maximum entropy: the air is still, not moving, and with the same temperature and pressure everywhere. But if you look at the microscopic picture, you still have lots of air molecules zipping this way and that randomly. So on very very small scales, you get lots of temperature gradients. But once you go to larger scales, these tiny gradients all average out to zero. The same basic thing will eventually happen in our universe as a whole. Sure, there will still be quantum fluctuations, but they'll all average to zero. Quantum effects really don't change our understanding of time or entropy in this situation.
Re: Physical interpretation of entropy if expansion causes a state of maximum entropy Interpretation of entropy is done in thermodynamics and statistical mechanics, not in cosmology, which has very little to say about stuff outside its scope. Nobody has proved that the final state of the universe was one of maximum entropy. A temperature gradient is not a needed condition for doing work. The direction of time has nothing to do with the increase in entropy of the universe. Time continues to flow when entropy is constant. And the «thermodynamic arrow of time» has nothing to see with «the cosmological arrow of time». In fact the cosmological expansion is a consequence of the field equations of GR, which is a time-reversible theory that conserves entropy.
Re: Physical interpretation of entropy if expansion causes a state of maximum entropy There's a lot wrong with this post. 1. In the most simplistic view of thermodynamics, where we ignore, for instance, the chemical potential, you need either a gradient in temperature, density, or pressure in order to do work. The statement of requiring a temperature differential may not be technically correct, but the idea is more or less accurate. 2. The direction of time is exactly due to the increase in entropy of the universe. All of the microscopic laws of physics are time-symmetric, not just General Relativity. So you cannot possibly use the time-symmetric property of GR to claim it conserves entropy. Instead what happens is that the derivation of the second law of thermodynamics from statistical mechanics should be understood as stating that when you begin with a low-entropy initial condition, entropy then increases. The origin of the arrow of time, therefore, is fundamentally cosmological, because the arrow of time necessarily comes down to there being some low-entropy initial conditions for our universe.
Re: Physical interpretation of entropy if expansion causes a state of maximum entropy Answer above. This part is all wrong. Entropy has nothing to see with direction of time. Time flows the same for reversible processes. It is not true that all of the microscopic laws of physics are time-symmetric. There is well-known irreversible microscopic formulations. E.g. By Sudarshan, By Prigogine... GR is a time reversible theory that, of course, conserves thermodynamic entropy as is well-known. Irreversible extensions to the laws of GR are also well-known. The derivation of the second law of thermodynamics from statistical mechanics is possible if by statistical mechanics one means some of the irreversible statistical mechanics (sometimes named nonequilibrium statistical mechanics that postulate equations beyond mechanics). If by statistical mechanics one means reversible mechanics, then the derivation is that van Kampen calls «mathematical funambulism». The claim that irreversibility is due to a low-entropy initial condition is one of the most misleading statements done about the second law and entropy that I know, and the work about the origin of the arrow of time by cosmologists (e.g. that popular book «The Quest for the Ultimate Theory of Time...») is one of the ill-informed and nonsensical that I know {*}. {*} You would not be surprised that the work by this famous cosmologist has been considered pure crackpotery in well-known blogs.
Re: Physical interpretation of entropy if expansion causes a state of maximum entropy If the process is reversible, then there is no arrow of time for that process. It is certainly possible to make up potential new physics which is does not follow TCP symmetry microscopically. But this is irrelevant: all known laws of physics are exactly invariant with respect to the TCP symmetry. Yeah, you're going to have to back this up. Because this sounds like a load of bull to me. Time symmetry cannot produce conservation of entropy when all known laws of physics are symmetric in time. How can it be misleading when it is exactly correct?
Re: Physical interpretation of entropy if expansion causes a state of maximum entropy As many others you continue confounding the arrow of time with the arrow of entropy. I believe that even philosophers as Price start to distinguish both. There are known laws that are not, and extensions of QM and QFT are developed for the study of irreversible processes. Some names were given before, and can be verified that they are serious guys (including Nobel winners and quasi-winners) who have advanced the field of irreversibility really, not charlatans fantasizing about parallel universes and related stuff in ridiculous books. There is a well-known theorem that supports that I am saying. It can be «exactly correct» only in the mind of people who has never studied thermodynamics beyond a trivial undergrad course (e.g., the famous cosmologist cited before).
Re: Physical interpretation of entropy if expansion causes a state of maximum entropy I'm not confounding them. The two are one and the same. There is no difference. Which laws would those be, specifically? Which theorem would that be, specifically?
Re: Physical interpretation of entropy if expansion causes a state of maximum entropy There is. E.g. the laws that apply to unstable quantum systems. Already Dirac noticed that the description of that kind of systems could not be done within the scope of QFT and QM. Liouville.
Re: Physical interpretation of entropy if expansion causes a state of maximum entropy ...that you can't seem to explain. You still haven't explained yourself. The theorem which states that the phase space volume is constant along trajectories of a Hamiltonian system? This doesn't have anything whatsoever to do with entropy conservation. Again, if it did, it would also apply to classical systems based upon Newtonian mechanics, which would prevent any entropy changes in such systems, making thermodynamics completely worthless.
Re: Physical interpretation of entropy if expansion causes a state of maximum entropy Just to be sure, the consensus view is given by the scholarpedia article: http://www.scholarpedia.org/article/Time's_arrow_and_Boltzmann's_entropy There are still some theorists in the community that disagree with this interpretation, but it is safe to say they are in the minority.
Re: Physical interpretation of entropy if expansion causes a state of maximum entropy I just started a new thread the other day asking "Why do so many people claim cyclic models brake down due to entropy?" There might be come good points there to better understand the roll of entropy, but I an not an expert. I kept hearing about this arrow of time being linked to entropy from various popular sources. I vaguely remebreded doing some calculation that required entropy in a Chemical Engineering elective to pass an exam with out learning what it was, but I had an inkling that there something wasn't right about this arrow of time and entropy thing, so I simply read about entropy on wikipedia and quickly came to the conclusion that as juangra says, that entropy is incorrectly applied in this case. It didn't seem to require a post grad for me to see the problem quite quickly, but it is very interesting thinking about the reasons why you can't break the 2nd law. This is the exact kind of article that made me start my thread. If most theorist agree with this interpretation, is it, either, I miss-understand entropy? or do most theorist miss-understand entropy? or to most theorist actually have a different interpretation? Judging from this thread, I can take a guess at the answer. I just learnt about the "Poincaré recurrence theorem" which can be applied to some systems which entropy can also be applied to. It shows that actually, the future will again at some point, given enough time, look very similar to the past. Entropy is relative to the observer and just tells us it will be extremely difficult for an observer to survive to see a system return to something near its start state. Perhaps entropy tells us more about the entity that is observing it, then the system its self.
Re: Physical interpretation of entropy if expansion causes a state of maximum entropy You did incorrect claims that were just corrected. I have given you a kind of systems for the which your affirmations are not valid and I said that there exists well-known extensions of QM and QFT that try to model those systems. That the Liouville theorem implies dS=0 has been known since Gibbs epoch and even before. Of course, Newtonian mechanics predicts dS=0. This is also a well-known result.
Re: Physical interpretation of entropy if expansion causes a state of maximum entropy Fortunately science is not a democracy where facts are established in a poll. History is full of examples where the majority was plain wrong. Moreover, claiming «consensus view» to a misguided encyclopedia article by Lebowitz reviewed by Carroll (whose contributions to the field are still less important and even considered crackpot in public by several physicists) is rather funny
Re: Physical interpretation of entropy if expansion causes a state of maximum entropy My question was initially concerned with the measurement of time inside a universe where the entropy has run on to its maximum limit. I understand from your arguments (which were highly educational by the way) that entropy and the universal expansion may not be related with respect to time. So can 'we' at such a point be actually able to MEASURE time or not? Thats my question.. If everything looks and feels the same at every point in the universe (and when you talk about GR the only matter around would exist as ~photons~leptons) So unless we can apply GR to to quantum entities doesn't that argument loose 'weight' in such a system?? Would time still have a meaning in a state of maximum entropy of the universe???
Re: Physical interpretation of entropy if expansion causes a state of maximum entropy Right, once you've reached maximum entropy, there is no arrow of time any longer.
Re: Physical interpretation of entropy if expansion causes a state of maximum entropy So that would mean that entropy does have a relation to time and its measurement. So suppose this maximum entropy starts reversing itself (assuming that now the cosmic expansion reverts into cosmic compression) so would the arrow of time that had lost all meaning would now suddenly revert back to HAVING a logical meaning? If yes, then with the entropy reducing, would the arrow of time do the same? i.e run backwards in synchronization with entropy???
Re: Physical interpretation of entropy if expansion causes a state of maximum entropy Not really. Entropy has nothing to do with the dimension of time. Distances in time are measured the same way whether you have an arrow of time or not. The issue, rather, is that time has no direction if you have no change in entropy. That's not possible. What you are, in effect, supposing is that suddenly the universe will start to prefer lower-probability states more than high-probability states. The proposal doesn't even make sense. Instead, if there is recollapse, entropy will continue to increase all the way. Basically, a universe where entropy cycles back and forth just doesn't work when you look at it in detail. You have to have some sort of process that can, from a high-entropy state, produce a low-entropy state. One potential idea here is a quantum vacuum fluctuation: here we have a very large, high-entropy state that has a fluctuation that produces a teeny tiny region of very low entropy. This isn't so dramatically unlikely any longer, because the large, high-entropy state has a low entropy density, so it isn't a dramatic drop in entropy. Then, because the new state is low in entropy, it will evolve forward in time. But which direction is forward? That will be random.