The interaction of propagating space-time fluctuations with wave packets

Abstract

It has been suggested by Percival and Strunz that fluctuations in spacetime on the Planck scale might be detected by atom interferometers. Thus far, the models used to predict the impact of these fluctuations have been limited to a description of the atoms in terms of two states corresponding to the two arms of an interferometer. In this paper we generalise this model to include the effects of spacetime fluctuations on atomic wavepackets. When the fluctuations are assumed to have simple non–commutative properties, the density matrix of a wave packet is shown to evolve according to an equation of the same general form as that hypothesised by Ghirardi, Rimini and Weber, as a way of dealing with the measurement problem in quantum mechanics.