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Old 08-22-2007, 06:00 AM
Metric Metric is offline
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Join Date: Oct 2005
Posts: 1,178
Default 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).
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