Thermodynamics and the Arrow of Time

[GleefulNihilism]

Here's a discussion I'm hoping to start.

As you may be aware, time goes forward. A shocking thing to say I know- but the universe clearly prefers time going from past to future, some relativity implications non-withstanding. The interesting thing about it is that the laws of physics seem to not have this preference for the most part. Have time progress backwards in your equations and some interesting things happen but overall most of the laws still work just fine.

The only really big exception seems to be the Second Law of Thermodynamics. The famous "in a closed system, entropy tends to increase with time".

My thought is, what if this interpretation isn't the correct one? Or at least isn't the only valid one?

Picture if the proper interpretation is "systems are found either in or moving towards their most probable state". What qualifies as the most probable state may change depending on the direction time is progressing, but we certainly see the previous interpretation within that considering disorder is more probable then order- and with particle velocity vectors perfectly reversed if time's direction is reversed the previous state becomes the most probable- right?

Anyway- an admitted weakness with this idea is my equations use. The Boltzmann Equation of S = k ln W would hold, and if we differentiate both sides by energy we see.

dS / dE = k d[ln W] / dE
1/kT = d[ln W] / dE​

Which admittedly I'm kind of stuck. It looks time independent too me, as W is the degeneracy of the micro-state within a macro-state.

Anyway, what I'm hoping to achieve is discussion. Ideally, with equations for or against depending on your view.

So, thoughts?

 

[kcdodd]

Statistically the past is not determined anymore then the future is. Given some system which is governed by statistical processes, how does one tell which state preceded the current state anymore then which state it will go to?

The problem comes from the perception that the past is determined while the future is not. If one observes a system evolve during some period of time, they have a record which can be "played" forward and backward in time within the observed time period. However, if the system is statistical in nature, the state of the system cannot be completely determined after the observation period, nor before it. By itself this still seems to preserve the symmetry of time, because the time before observation is of equal footing as the time after observation.

One might argue that the symmetry is broken because one is free to extend an observation period in only one direction, namely at the "present". One can take a measurement, and then take another measurement at a later time, but not a previous time. How would one tell if this was because time is asymmetric, or because they are not an "external" observer?

 

[Andy Resnick]

The origin of irreversibility, given the reversible nature of SM and QM, is not a simple topic- many books have been written about it (I'm currently skimming through 'physical origins of time asymmetry', by halliwell, perez-mercader, and zurek).

Davies, in his talk, claims that the resolution is 'well known' (maybe to him...), but provides a couple of references: Davies (1974) and Zeh (1989) which are also books. Anyhow, he claims that a permanently isolated system has no 'inbuilt arrow of time'.

One way time/irreversibility is recovered in QM is decoherence; and specifically the interaction of a system with the environment is considered as a measurement: Zurek is big on that, and it's appealing to me as well.

Cover's talk is entitled "Which processes satisfy the second law?", but I need to carefully read it before presenting it here.

Interested?

 

[Gerenuk]

There is no time dependence in your equations for a reason, because such thing as an arrow of time doesn't exist. Here is an analogy:
Imagine you have a wild fox in a cage, you put the cage in the forest and open the door. Now you come back one week later. Where do you think you will the fox be - in the cage or in the forest? One macrostate is "being in the cage" and the other macrostate is "being somewhere in the forest". Obviously the latter has a lot more microscopic realizations. So it's kind of obvious than any time you set free a fox in an open cage, one week later he will most likely end up somewhere in the forest. It's not impossible that he returns, but it would be foolish to assume that.
In thermodynamic terms that are two states. The particular cage with low entropy and the forest with high entropy. And you see entropy tends to increase.
That's exactly how the second law works. It knows absolutely nothing about the dynamics of the system (i.e. where the fox likes to go). It only knows that there are a lot more states at higher entropy possible. Of course a key assumption is that the fox has no preferance for any spot. That's the reason why the second law only works for completely random processes and not something like social dynamics.

If you tell the fox to go back exactly the way he came, he would do so. But that has nothing to do with most probable state. For a deterministic world there is a 100% defined state for either direction of time. However if you have incompletely information, and all you know is that the fox is "somewhere" in the forest, then the most probable state is certainly not a single specified spot you have in mind.

 

[Studiot]

As you may be aware, time goes forward. A shocking thing to say I know- but the universe clearly prefers time going from past to future, some relativity implications non-withstanding.

Some subscribe to the view that the passage of time is like the terminator on the surface of the earth.
Both the past and future are already there, and the present is a focus which sweeps past.
Just as both the land in day and the land in night are already there and the terminator constantly sweeps over them, changing the boundary between.
In this view the present is just like the terminator in some multidimensional universe turning on its axis.

Just as many of the laws of thermodynamics have no mention of Time, so they have no mention of spatial distance either.
So you equally make the same comments about the first or second laws saying that they have no preference for direction along the x, y or z axes either.

 

[Andy Resnick]

It's an interesting problem. There is no real connection between an 'arrow of time', and a requirement that the laws of physics be asymmetric with respect to time. Time itself is not treated any differently than any other coordinate (or continuous parameter), and one does not associate asymmetry between 'forward' and 'backward' distance measurements.

The 'direction' of time is a distinct concept from a 'flow' of time. Think of a compass needle: it is asymmetric, singles out a preferred direction, but does not imply flow or movement. Further, 'north' and 'south' are fixed, just like 'future' and 'past'.

Confusing the two concepts- direction and movement- is what leads to efforts to introduce an asymmetry in microscopic equations. However, it's not really required. All that's required (from a statistical perspective) is to specify an initial state with low entropy. And in fact, this is what we observe. This leads to the 'cosmological initial state problem'- how did the original low entropy state come to be?

An issue arises from QM: we can't have information about closed systems (since measurement is an interaction), so does time even *exist* in a closed system? This leads to the idea of 'consistent histories' and decoherence.

http://en.wikipedia.org/wiki/Consistent_histories

In the end, the perceived difference between future and past (i.e., we can't remember the future) is not really a 'problem'- while a definitive solution may not yet be known, there does not appear to be a fundamental flaw in the use of time-symmetric dynamical equations.

 

[Gerenuk]

In the end, the perceived difference between future and past (i.e., we can't remember the future) is not really a 'problem'- while a definitive solution may not yet be known, there does not appear to be a fundamental flaw in the use of time-symmetric dynamical equations.

There is no difference between time direction. If time direction went backwards, we would remember the "future" and not the "past".
And also there is no physical difference between future and past. If you wait long enough, low entropy states will be reached again. Unfortunately that could take an unimaginably long time.

 

[GleefulNihilism]

Well, there's some very smart people on this board. Currently I'm already readying "The Physical Basis of the Direction of Time" by Zeh and "The End of Time" by Barbour, might add another book to that for fun.

Heh, was hoping for a longer discussion- but something tells me we hit the bases of our understanding. Thank you ladies and gentlemen.

 

[Gerenuk]

I think I once looked at Zeh in search for an explanation of the arrow of time. I was hoping to find something which states that Markov processes converge.

But then I noticed the most simple idea which doesn't require magical laws and paradoxa is also consistent with all of physics. So there was no need to complicating derivations of the arrow of time.

The fox to forest picture is so trivial it's not even worth mentioning and yet it explains all of the second law.

 

[kcdodd]

I was also going to mention how the idea of causality enters into this. We take it for granted that we can only effect the future and not the past. If the future could determine the past in the same way the past determines the future, then paradoxical things happen. If we can only remember in one direction, it is only natural to take it as "the past".

 

[Andy Resnick]

<snip>

Heh, was hoping for a longer discussion- but something tells me we hit the bases of our understanding. Thank you ladies and gentlemen.

That's not a bad thing- 1) it means the people here are knowledgeable, and 2), an opportunity for a research project has been uncovered.

 

[GleefulNihilism]

That's not a bad thing- 1) it means the people here are knowledgeable, and 2), an opportunity for a research project has been uncovered.

Agreed. Didn't mean to infer this was a bad thing, just shorter then expected.