puzzle on time\'s arrow
 

Suppose, someplace deep in space, we have a spaceship. The ship is divided into two halves, each half containing some people, plants, nuclear reactors, lights, computers, etc. and each half is completely, perfectly sealed off from the other half (and from the rest of the universe). Now, this ship has a very strange thermodynamic property:

In one half of the ship, the thermodynamic arrow of time points in one direction, and in the other half of the ship, it points in the opposite direction. In other words, the people in each half of the ship are familiar with the fact that their entropy only increases with time (2nd law of thermo), but due to the fact that each side is completely isolated from the other, the direction of time in which entropy increases is arbitrary -- they need not agree, and in fact they don't agree in this thought experiment. Their life functions depend on the 2nd law (turning food, air, water into poop), their energy generation depends on it (turning uranium into lighter elements + energy), and their senses depend on it (their eyes gather a tiny bit of light from the lightbulb, and then an image is formed in their brains, and then memories).

Now, to each half's occupants, the goings on in the opposite half must seem extremely bizarre (though they are isolated from each other so they don't get to directly observe what is happening). For example, the memory of an image of a lightbulb in the brain of an occupant forms, creates an image in the visual cortex, which in turn excites the rods and cones of the eye to emit a bit of light, which then miraculously combines with the rest of the light in the room in just a perfect way to converge on the heating element of an incadescent light bulb, which then produces an electric current which goes back to the nuclear reactor and uses all its energy to fuse lighter nuclei into Uranium.

To occupants in half A, it must seem that all the life happening in half B must depend on a stupendous series of perfectly orchestrated events which, if interrupted in the slightest way, would destroy the entire process. The occupants of half B feel the same way about the goings on in half A.

(a note -- since physics is time-reversal invariant, such a spaceship could actually "in principle" be built without violating any fundamental physical laws -- it would merely be insanely difficult)

Now, the puzzle: What happens if, at some not-particularly-special time t=T, the partition (a force field, or whatever) is removed between the two halves of the spaceship and both sides are directly exposed to each other (we close it again at t=T' to keep this event time-symmetrical)? Which side's arrow of time wins out (or can one possibly win out if both sides are about the same size)? Can anyone possibly survive this event? What would side A see as they look into side B, and vice-versa? Basically, what happens? Note: both sides are made of perfectly ordinary matter -- no antimatter involved, so no enormous explosions. And the two sides need not be perfect mirror images of each other (side A is manned by Italians, side B is manned by Frenchmen, for example -- so whatever happens doesn't depend on perfect symmetry).

Re: puzzle on time\'s arrow
 

Hi Metric, thanks for this question. I can’t wait to hear knowing peoples responses. I’m guessing that the side with the most particles wins out. Also, I’m wondering about the anti - matter issue. If the laws of thermodynamics are reversed in both sides of the spaceship, are you sure that matter is not also reversed? Or that there is no anti- matter?

Sorry man, I got all my physics from Star Trek.

Re: puzzle on time\'s arrow
 

[ QUOTE ]
Hi Metric, thanks for this question. I can’t wait to hear knowing peoples responses. I’m guessing that the side with the most particles wins out. Also, I’m wondering about the anti - matter issue. If the laws of thermodynamics are reversed in both sides of the spaceship, are you sure that matter is not also reversed? Or that there is no anti- matter?

Sorry man, I got all my physics from Star Trek.

[/ QUOTE ]

Yes, there is a way in which anti-matter is related to ordinary matter through time reversal, which is why I mentiond that little proviso. But that is seperate from thermodynamics -- you could have a planet made of anti-matter and thermodynamics could work just the same as it does here (and antimatter doesn't violate the 2nd law in particle colliders, for example). Likewise, you could have the situation I describe -- a collection of ordinary matter for whom the thermodynamic arrow of time is reversed.

Re: puzzle on time\'s arrow
 

Well interesting. Suppose our universe with one arrow of time collided with another universe with another arrow of time. If the two universes didn’t blow each other up, I’d reckon that they’d slip on by each other without the one knowing anything about the other. How can we now detect particles that always travel from the future to the past?

Re: puzzle on time\'s arrow
 

[ QUOTE ]
In one half of the ship, the thermodynamic arrow of time points in one direction, and in the other half of the ship, it points in the opposite direction.

[/ QUOTE ]

According to the Brian Greene book , the reason for the particular direction of the time arrow is the extreme order that was present early in the universe. Otherwise the physics is symmetrical.

There is not some physical law "switch" to throw for each side of the ship.


D.

Re: puzzle on time\'s arrow
 

This is definitely an interesting hypothetical, but I had a little trouble trying to get a meaningful answer.

[ QUOTE ]
In one half of the ship, the thermodynamic arrow of time points in one direction, and in the other half of the ship, it points in the opposite direction.

[/ QUOTE ]

I realize this is a thought experiment, but we call the second law a 'law' for a reason. As in, this is a rule that must be symmetric and invariant for the entire universe. Therefore I think you inherently must be describing two different universes, because their laws are different. How can two universes with two different sets of laws interact? That's a damn good question that no one will claim to have the answer to. I personally think, however, that no meaninful information exchange can take place between two universes because the asymmetry of their 'laws' _must_ destroy the context of all information.

Now, it's possible that all the processes on both sides are isentropic (adiabatic with respect to the 'barrier' and fully reversible). If this is the case, both sides would see the other side in a state of rest. In other words there would be no apparent 'time evolution'.

Re: puzzle on time\'s arrow
 

I'll be honest, I haven't the slightlest clue what would happen, but [ QUOTE ]
poop

[/ QUOTE ] is definitely the key to finding an answer.

In seriousness, could you elaborate on what you mean by "which side's arrow of time wins out"? I don't understand how you could mix and match thermodynamic principles hypothetically by removing some barrier between universes. Do you mean, roughly, that when the two universes/compartments mix, that one direction should be more "powerful" (I don't know what word to use here) and should force both compartments to behave in the same way?
I guess I just don't see how the hypothetical is logically consistent given that we have no empirical evidence to what would happen when two universes with separate laws "mix" (since as far as we know this isn't possible). There may be something more fundamental than the laws of thermodynamics that I'm missing, though.

Re: puzzle on time\'s arrow
 

Metric,

Have you read Martin Amis's Time's Arrow? Awesome good book.

Re: puzzle on time\'s arrow
 

[ QUOTE ]
I realize this is a thought experiment, but we call the second law a 'law' for a reason. As in, this is a rule that must be symmetric and invariant for the entire universe. Therefore I think you inherently must be describing two different universes, because their laws are different.

[/ QUOTE ]
Some people seem to be gravitating to this point, so let me say a couple things about the 2nd law.

Typical derivations of the 2nd law come from "course-graining" arguments. That is, you lump all states together that look more or less the same, and those correspond to the same "thermodynamic" state. The entropy then involves counting just how much wiggle room there is in each thermodynamic state -- how much could things be different, but still be the same thermodynamic state. And the 2nd law basically says things will tend to move randomly into thermodynamic states with more and more wiggle room (entropy). Thermodynamic equilibrium has by far the most wiggle room of any state -- once you get there, it's very improbable that you'll ever get out.

The problem is this: This argument works exactly the same if you evolve things backward in time. This comes from the fact that for EVERY solution that obeys the 2nd law, there is another one that violates it -- just time-reverse the solution (replace t by -t in the equations), and you get another perfectly good solution that solves the equations of motion.

So, from a fundamental statistical point of view, the 2nd law is just our universe moving toward higher entropy because it started in a state of very low entropy (perfectly reasonable and what the above argument predicts). 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 by a corresponding amount because it would take so much work to get everything "just right." (this happens in your computer, for example -- you order the hard drive and thus decrease it's entropy, but in doing so you increase the thermodynamic entropy of the universe by a corresponding amount -- this is why your computer gets hot)

So hopefully I've convinced everyone that this situation is not physically unthinkable -- merely insanely difficult or improbable. But once you have these systems (the hard part), it is amazing to me how difficult it is to describe what would happen when they are brought into contact -- even in the most rough, hand-waving sort of way (which should be the easy part). After thinking about this for way too long, I think I have most of it more or less sorted out -- still, it's amazing how fast it forces you confront fundamental issues in thermodynamics/stat mech.

Re: puzzle on time\'s arrow
 

[ QUOTE ]
Metric,

Have you read Martin Amis's Time's Arrow? Awesome good book.

[/ QUOTE ]
No, but it sounds fascinating from some of the online reviews -- I'll have to check it out.

Re: puzzle on time\'s arrow
 

[ QUOTE ]
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

[/ QUOTE ]

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.

Re: puzzle on time\'s arrow
 

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.

Re: puzzle on time\'s arrow
 

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.

Re: puzzle on time\'s arrow
 

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.

Re: puzzle on time\'s arrow
 

Metric,

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

Re: puzzle on time\'s arrow
 

[ QUOTE ]
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.

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

[ QUOTE ]
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).

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

[ QUOTE ]
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.

[/ QUOTE ]
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.

[ QUOTE ]
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.

[/ QUOTE ]
This is precisely why this is an interesting problem.

Re: puzzle on time\'s arrow
 

[ QUOTE ]
Metric,

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

[/ QUOTE ]
Yep.

Re: puzzle on time\'s arrow
 

[ QUOTE ]
[ QUOTE ]
Metric,

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

[/ QUOTE ]
Yep.

[/ QUOTE ]

Glad we settled that!

Re: puzzle on time\'s arrow
 

[ QUOTE ]
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.

[/ QUOTE ]

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?

Re: puzzle on time\'s arrow
 

[ QUOTE ]
[ QUOTE ]
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.

[/ QUOTE ]

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.

[/ QUOTE ]
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.

[ QUOTE ]
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?

[/ QUOTE ]
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.

[ QUOTE ]
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.

[/ QUOTE ]
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.

[ QUOTE ]
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?

[/ QUOTE ]
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.