The Universe as a Detector: A Quantum Filtering Formulation of the Di\'osi-Penrose Model

Abstract

We consider the Di\'osi-Penrose problem but rather than postulating background gravitational fluctuations, we instead consider the quantum filter that arises from space-time homodyning the continuum of output quadrature described in the open quantum stochastic model presented here. This is described by a quantum Kushner-Stratonovich equation, typical of the form appearing in continuous-time collapse of the wave-function models in Quantum Decoherence Theory