Zitterbewegung of a Model Universe

TL;DR

This paper explores the quantum dynamics of Bianchi-Type I universe models, analyzing metric operator evolution to understand singularity behavior and curvature invariants without relying on wave functions.

Contribution

It introduces a Heisenberg picture approach to quantum cosmology, focusing on metric operators and their Zitterbewegung analogy, providing new insights into singularity analysis.

Findings

Quantum evolution does not remove the classical curvature divergence.

The metric exhibits Zitterbewegung-like behavior near singularities.

Classical $t^{-4}$ divergence of the Kretschmann scalar persists after quantization.

Abstract

We investigate the quantum evolution of the metric operators for Bianchi-Type I model universes in the Heisenberg picture in order to remove the need to consider the wave function of the universe and interpret its "spin" variables. The calculation is analogous to that of the Zitterbewegung of the Dirac electron. We consider the behavior of the metric near the classical singularity, and consider the curvature there. Although factor ordering questions preclude the presentation of an unambiguous result for the curvature invariants, it does seem that the classical $t^{-4}$ divergence of the Kretschmann scalar is not removed by quantization.