Interferometry with relativistic electrons

We propose an experiment to test the influence of Lorentz contraction on the interference pattern of a beam of electrons. The electron beam is split and recombined by two pairs of bichromatic laser pulses, using a variation of the Kapitza-Dirac effect. Between the pairs, the electrons are accelerated to relativistic speed. We show that Lorentz contraction of the distance between two partial beams will then lead to a reduction of fringe visibility. The connection of the proposal to Bell's spaceship paradox is discussed.