Wavepackets for particles of indefinite mass

Abstract

Using a formalism that includes particles with indefinite and variable masses, we can create a much richer set of states than in conventional quantum mechanics. For example, in a gravitational field the equivalence principle implies that the motion of a particle is independent of the mass. Thus it is possible to create physical states with large Δm but very small Δν and Δx, so that the trajectory of a particle is well determined, while the Δp · Δx uncertainty relation is satisfied. We also provide a quantitative description of wavepackets with arbitrary distributions in momentum and mass (or alternatively velocity and mass) and discuss a simple diffraction slit experiment as an example of their physical propagation. The Schrödinger equation is solved for a decaying particle at rest. It is also shown that Galilean invariance plays a natural and cohesive role within the variable mass formalism, unlike the case in conventional quantum mechanics where the existence of multiple mass states would violate Galilean invariance.