Consider two very short light pulses emitted from the centre (C) of two mirrors A and B (as shown in the diagram). From the point of view of the lab frame, the apparatus is all moving to the left at velocity v. Imagine there is also an electron near the centre of the apparatus, which is stationary in the apparatus frame and therefore also moving with velocity v to the left according to the lab frame.
The short light pulses (much shorter than the apparatus length) bounce off mirrors A and B and return and strike the electron. This situation has similarities with the Michelson-Morley experiment.
According to the frame moving with the apparatus, the pulses take an equal time to bounce off the mirrors and arrive back at C. Therefore the EM waves cancel and there is no net radiation pressure exerted on the electron.
According to the lab frame, the light pulse emitted to the left has less distance to travel overall and so arrives at C before the pulse that was emitted to the right. Therefore the first pulse accelerates the electron by exerting a radiation pressure on it.
Does the electron accelerate or not? :)
(I'm looking for derivations/proofs showing both frames' interpretations)