Decoherence of quantum wavepackets due to interaction with conformal spacetime fluctuations

Abstract

One of the biggest problems faced by those attempting to combine quantum theory and general relativity is the experimental inaccessibility of the unification scale. In this paper we show how incoherent conformal waves in the gravitational field, which may be produced by quantum mechanical zero-point fluctuations, interact with the wavepackets of massive particles. The result of this interaction is to produce decoherence within the wavepackets which could be accessible in experiments at the atomic scale. Using a simple model for the coherence properties of the gravitational field we derive an equation for the evolution of the density matrix of such a wavepacket. Following the primary state diffusion programme, the most promising source of spacetime fluctuations for detection are the above zero-point energy fluctuations. According to our model, the absence of intrinsic irremoveable decoherence in matter interferometry experiments puts bounds on some of the parameters of quantum gravity theories. Current experiments give λ> 18. , where λt_{Planck} is an effective cut-off for the validity of low-energy quantum gravity theories.