puzzle on time's arrow

[Metric]

[ 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.

[m_the0ry]

[ 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.

[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.

[Borodog]

Metric,

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

[Metric]

[ QUOTE ]
Metric,

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

[/ QUOTE ]
Yep.

[Borodog]

[ 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!