Here is a simplification of the paradox.

In the left hand diagram above, a ray of light enters the chamber
from the left, reflects off of a flat mirror, which is set at a
45^{o} angle so the beam is reflected at a
right angle, where it hits the ceiling directly above it's point of
reflection.

The diagram on the right represents the same chamber accelerated to 0.87 C.
Now everything is Lorentz contracted to half of it's original size in the
direction of motion (green arrows). The mirror is no longer at a 45 degree
angle. It's a 26.56^{o} angle. so the light no longer
hits the ceiling directly above the mirror. Or does it?

-or-

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