Two spacecraft,
coasting past each other in deep
space, suffer a grazing collision.
Light from the resulting (minor) explosion enters both ships through partially-reflective
windows. A small amount of the entering light travels at just the right
angles to be trapped between the reflective
surfaces of windows and mirrors
on opposite sides of the ships'
hulls.
From the perspective of observers on the Nostromo, the Nostromo "light clock" beam bounces up and down. However, the Sulaco's light clock beam travels along a diagonal path since the Sulaco is moving to the right. According to Nostromo's crew, the distance traveled by their own light beam during a mirror-to-mirror "roundtrip" is shorter than the corresponding roundtrip distance traveled by the moving Sulaco's beam.
From the perspective of observers on the Sulaco, the Sulaco "light clock" beam bounces up and down. However, the Nostromo's light clock beam travels along a diagonal path since the Nostromo is moving to the left. According to Sulaco's crew, the distance traveled by their own light beam during a mirror-to-mirror "roundtrip" is shorter than the corresponding roundtrip distance traveled by the moving Nostromo's beam.
Here's a cool 173kb Quicktime movie, made by physicists at the Australian National University. (They have produced a few other animations.) It shows five stationary light clocks and one moving light clock. Notice how much further the light beam travels between bounces in the moving light clock.
