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Suppose I have two identical baseballs. I mark one with a black dot.
I use two ball launchers to put them on a collision course with each
other. The marked ball is in the left launcher, the unmarked ball in
the right launcher. I tell you everything about the launch speeds,
angles, positions, etc. They collide behind a barrier that I can't
see around. But then they reappear, one to the left and to the right
after the collision behind the barrier. The game is to predict which
baseball has the black dot on it and then go look at the two balls
and see if you're right.
Now repeat this experiment with two identical atoms. Under what
circumstances (if any) can I still win this game? No fair setting the
launchers so that the atoms don't actually collide and just pass each
other by a large distance.