The Hazy Spacetime of the Károlyházy Model of Quantum Mechanics

Abstract

A small amount of uncertainty, determined solely by constants of nature, is brought into the strucutre of classical, empty spacetime. It induces an uncertainty in the relative phases of the wave function of any isolated system. The Schrödinger evolution would then lead to the development of incoherent components (of components with completely uncertain relative phases) of the wave function. In order to prevent excessive deterioration of the coherence, random localizations of the wave function are introduced. The model gives realistic results, not only for the time evolution of microparticles and of solid bodies, but also for the decay of superpositions of traks in a cloud chamber. The formula for the spread of the relative phases is derived without the introduction of the family of auxiliary metrics used previously and without expansions in momentum space. This derivation shows clearly that the model does not contain adjustable cut-off parameters. The connection between the previous and the new derivation is given in the appendix.