Physical and unphysical phases of uniformly accelerated particles

The motion of an electron in a uniform electric field, as in free fall, is characterized by the existence of pairs of trajectories that rejoin on the same final point. The corresponding interference pattern was first observed in 1996, and explained by the elementary model of uniform acceleration starting from a motionless electron source. In the experiment, however, the electron source is a fast-moving negative ion, which makes direct application of the model questionable. Relativistic arguments can be used to ascertain that no phase changes are actually produced by the motion of the source. The quantum phase of the electron can also be checked all along its two interfering trajectories. This method, which produces the same reassuring result as relativity, gives us the opportunity to revisit the relativistic transformation of the Schrödinger phase. It also makes it possible to calculate the effect of an acceleration of both the free electron and the electron emitter. Only in this case is a change of the interference pattern expected, but it is quantitatively negligible in the actual experiment.