Space and time as a consequence of GRW quantum jumps

Abstract

The Ghirardi-Rimini-Weber (GRW) theory of spontaneous collapse offers a possible resolution of the quantum measurement problem. In this theory, the wave function of a particle spontaneously and repeatedly localises to one or the other random position in space, as a consequence of the hypothesised quantum jumps. In between jumps the wave function undergoes the usual Schr\"{o}dinger evolution. In the present paper we suggest that these jumps take place in Hilbert space, with no reference to physical space, and physical three-dimensional space arises as a consequence of localisation of macroscopic objects in the universe. That is, collapse of the wave-function is responsible for the origin of space. We then suggest that similar jumps take place for a hypothetical time operator in Hilbert space, and classical time as we know it emerges from localisation of this time operator for macroscopic objects. More generally, the jumps are suggested to take place in an operator space-time in Hilbert space, leading to an emergent classical space-time.