puzzle on time's arrow

[m_the0ry]

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However, there is nothing *fundamentally* wrong with fine-tuning a solution in such a way that for some small piece of the universe (one half of my space ship), the entropy is decreasing rather than increasing. It would merely be extremely difficult. If you did this by ordering the system just perfectly, you would still be obeying the 2nd law of thermodynamics, because in creating this order in the spaceship, you would disorder the rest of the universe

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So the force field only isolates the two halves of the ship, it doesn't make both halves of the ship closed systems. Like you said, in order for the decreasing entropy side to evolve the way it does and simultaneously obey the 2nd law, we have to continuously 'inject order' into the system.

I was making a pretty critical misinterpretation of your problem.

So the answer the original question, I think the increasing entropy side wins. To see why we have to envision the interactions not as 'running in -t time' but rather as going in +t time with the right conditions For each fusion reaction on the 'normal side', we have a fission reaction on the other side consisting of a perfectly synchronized meeting of one neutron, one helium, X gamma photons, and K joules of thermal energy. Especially when we consider the stochastic nature of the quantum world, this situation falls under the umbrella of 'technically feasible, astronomically improbable'. A question that comes to mind is whether it's possible to engineer a photon to be incident at such a specific time (order of femtoseconds?) and space (picometers) keeping in mind the uncertainty principle constraint. Which would make the entire process one that could only happen with a purely random 'order pump'.

Because every interaction with the backwards running half of the spaceship and its outside 'order injecting' system must be perfectly synchronized like this, any non-perfectly synchronized interaction would lead to a sort of cascade effect. But this depends on the behavior of the order pump. If we assume it keeps running and engineering ('chance-ineering?' is that even a word?) things to run in backwards physics then the question of 'who wins' is simply a matter of quantifying the order flux in the second half of the spaceship.

[Metric]

This is close to my own interpretation, except that:

1) I do not think of it in terms of a "continuous order pump" -- merely a stupendously ordered set of initial conditions, which would only be required in one half of the ship. The other side could have generic initial conditions. The side with generic initial conditions then wins the "collision of time's arrows."

2) There is another way to phrase the problem, in terms of "generic initial conditions" in half A, and "generic final conditions" in half B (which, given the backward evolution in half B are really a kind of initial condition for B). This is the most time symmetric form of the problem, in which you can't really state which is the "correct" arrow of time by appealing to the outside. In this case, the thermodynamic future of both sides appears to me to pretty much be destroyed.

[hexag1]

the direction of time in which entropy increases is arbitrary


see this is where you lost me. in my view, times arrow, by definition goes in the direction of increasing entropy. if you redefine it, then you need a new term.

[m_the0ry]

Entropy defines the direction of time, and therein I think lies your misinterpretation.

We define the system as the backwards running half of the spaceship. The problem forces a tri-chotomy, we must either say:

1) "the 2nd law is still obeyed, the order just comes from somewhere else"

this is my interpretation but apparently I am presenting a different problem, as stated above.

2) "entropy is allowed to stay constant"

This is a legitimate thermodynamically, but then the backwards system must only consist of ideally reversible processes (which is isentropic and thus represents a system at thermodynamic rest thus there is no time evolution).

3) "the entropy increases in the system without outside interference"

This is a 'given' in your problem, and I have problems with it. I don't see how I can justify abandoning the 2nd law like this. The repurcussions are pretty nasty. We have to completely deny the directionality of spontaneous processes, which defies all empirical evidence.

Physical processes are explicable in both time directions, but you really have to be careful how you define your system. Saying entropy increases in a closed system is really not a trivial statement.

[Borodog]

Metric,

I think the direction of time's arrow is due to boundary conditions. What do you think?

[Metric]

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1) "the 2nd law is still obeyed, the order just comes from somewhere else"

this is my interpretation but apparently I am presenting a different problem, as stated above.

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No, this is certainly one possible scenario. In this scenario, the order comes from the specification of the initial conditions to (unimaginably) high precision.

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2) "entropy is allowed to stay constant"

This is a legitimate thermodynamically, but then the backwards system must only consist of ideally reversible processes (which is isentropic and thus represents a system at thermodynamic rest thus there is no time evolution).

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I am not describing this scenario, as I specifically want a system with interesting things happening -- not simple thermodynamic equilibrium.

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3) "the entropy increases in the system without outside interference"

This is a 'given' in your problem, and I have problems with it. I don't see how I can justify abandoning the 2nd law like this. The repurcussions are pretty nasty. We have to completely deny the directionality of spontaneous processes, which defies all empirical evidence.

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If the initial conditions (at time T) are specified to high precision, then nothing can be regarded as "spontaneous." We simply have a system evolving deterministically through phase space, from regions of high entropy (at time T) to regions of low entropy (at time T') -- the essential point is that this is fundamentally allowed. Statistically, there are an equal number of "thermodynamically backward evolving" solutions as there forward evolving solutions.

We could also specify the solution not by specifying "special initial conditions" (at time T) but by specifying "generic final condtions" (at time T'). Every statistical derivation of the 2nd law then predicts that entropy will increase as you evolve the state back from final time T' back to the initial time T.

Basically, this whole scenario was dreamed up as a tangent to my ponderings of how time asymmetric laws (the 2nd law) can emerge from time-symmetrical underlying physics.

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Physical processes are explicable in both time directions, but you really have to be careful how you define your system. Saying entropy increases in a closed system is really not a trivial statement.

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This is precisely why this is an interesting problem.

[Metric]

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Metric,

I think the direction of time's arrow is due to boundary conditions. What do you think?

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Yep.

[Borodog]

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Metric,

I think the direction of time's arrow is due to boundary conditions. What do you think?

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Yep.

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Glad we settled that!

[m_the0ry]

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If the initial conditions (at time T) are specified to high precision, then nothing can be regarded as "spontaneous." We simply have a system evolving deterministically through phase space, from regions of high entropy (at time T) to regions of low entropy (at time T') -- the essential point is that this is fundamentally allowed. Statistically, there are an equal number of "thermodynamically backward evolving" solutions as there forward evolving solutions.

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I see what you're saying and I'm feeling pretty betrayed by classical thermo at this point, but that's what I get for being an engineer. My next question, in retrospect, is why you feel it's necessary that the initial conditions are 'highly ordered'? Doesn't the phase space of a highly disordered system include evolutions that increase entropy?

Intuitively I want to say that the forward facing system wins out because the reversed one is more 'fragile.' But I cannot substantiate that in the framework of statistical mechanics - without fabricating some asymmetry to help out my argument.

I was digging around and found quite a few papers on CPT violations, some of them in subatomic particles, others in atoms. Are we really confident enough to say that it's a result of boundary conditions, and not just an incomplete picture of physics?

[Metric]

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If the initial conditions (at time T) are specified to high precision, then nothing can be regarded as "spontaneous." We simply have a system evolving deterministically through phase space, from regions of high entropy (at time T) to regions of low entropy (at time T') -- the essential point is that this is fundamentally allowed. Statistically, there are an equal number of "thermodynamically backward evolving" solutions as there forward evolving solutions.

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I see what you're saying and I'm feeling pretty betrayed by classical thermo at this point, but that's what I get for being an engineer.

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Don't feel too bad -- this has been driving people crazy for over a century. See, for example, the first page of:
http://arxiv.org/PS_cache/quant-ph/p.../0101140v1.pdf
for a brief historical sketch of how people have tried to deal with this.

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My next question, in retrospect, is why you feel it's necessary that the initial conditions are 'highly ordered'? Doesn't the phase space of a highly disordered system include evolutions that increase entropy?

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If you pick generic initial conditions at time T, then the most probable evolution is into states of higher entropy both into the future and into the past. In building "side B" of our spaceship, we want the thing to evolve into states of lower entropy into the future -- thus, we are forced to pick the initial state VERY CAREFULLY (in reality it would be incredibly hard) to avoid getting one of the standard ones that evolves to a state of higher entropy into the future.

By contrast, we don't need to specify the initial conditions of "side A" with high precision at all. We just throw the contents in there any old way, and statistically it is almost a certainty that it will move to a state of higher entropy as we evolve it into the future.

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Intuitively I want to say that the forward facing system wins out because the reversed one is more 'fragile.' But I cannot substantiate that in the framework of statistical mechanics - without fabricating some asymmetry to help out my argument.

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The solution, I think, is that the thermodynamic behavior of "side B" is dependent on our precise initial conditions and the assumption of no outside influences. I.E. it is more fragile. Side A's thermodynamic behavior does not depend on any such precisely controlled initial conditions -- we picked the state more or less randomly. Thus, the combined state of the two systems has randomness associated with it due to side A -- when we expose the two sides to each other, any fine tuning we did to carefully select side B's evolution goes straight out the window -- it gets randomized again due to side A. And a randomly chosen state is going to evolve to higher entropy -- thus side A wins, if we formulate the problem in this particular way.

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I was digging around and found quite a few papers on CPT violations, some of them in subatomic particles, others in atoms. Are we really confident enough to say that it's a result of boundary conditions, and not just an incomplete picture of physics?

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It's possible, but doesn't seem very likely. The standard view is that CP violation is way too tiny to result in something as dramatic and obvious as the 2nd law.