  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 bi-chromatic 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.
