An article I read recently stated that Einstein's views on
simultaneity (or the lack thereof) may have been motivated in part by
the measurement of stellar aberration due to the motion of the Earth
around the Sun. Supposedly both Lorentz and Einstein thought that the
situation was symmetric and depended only on the transverse part of
the relative velocity between Earth and a star. The angles in the two
reference frames were related by cos(earth angle) = (cos(star angle)
-v/c) /(1-cos(star angle)*v/c). For small v aberration is usually
given as sin(telescope tilt angle) = v/c.
Now image that "Einstein's cat" is in a cage on a spacecraft at rest
relative to the Sun. A telescope is pointed at a star and tilted to
correct for expected aberration due to motion of the star. If the
light gets through the scope it shines on a photocell to activate a
release mechanism. Does the cat get out or not?
Hint: Think what would happen if you looked at double stars whose
components would have different relative velocities.
PS There is an additional effect sometimes called planetary
aberration which is a time delay effect due to the finite speed of
light. This effect occurs in classical physics but is often ignored.