Quantum Mechanics at the Planck Scale

TL;DR

This paper proposes a generalized quantum theory that removes the need for a fixed causal structure, making it suitable for quantum gravity at the Planck scale where spacetime geometry is quantum in nature.

Contribution

It introduces a fully four-dimensional, background-independent quantum framework for cosmological spacetime, extending usual quantum mechanics to incorporate quantum spacetime geometry.

Findings

Generalized quantum theory incorporates spacetime alternatives and histories.

Recovers usual quantum mechanics as an approximation.

Framework is suitable for quantum gravity at the Planck scale.

Abstract

Usual quantum mechanics requires a fixed, background, spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which spacetime geometry is a quantum variable. The elements of generalized quantum theory are briefly reviewed and illustrated by generalizations of usual quantum theory that incorporate spacetime alternatives, gauge degrees of freedom, and histories that move forward and backward in time. A generalized quantum framework for cosmological spacetime geometry is sketched. This theory is in fully four-dimensional form and free from the need for a fixed causal structure. Usual quantum mechanics is recovered as an approximation to this more general framework that is appropriate in those situations where spacetime geometry behaves classically. (Talk given at the Workshop on Physics at the Planck Scale, Puri, India, December12-21, 1994. This talk is a precis of the author's 1992 Les Houches Lectures: Spacetime Quantum Mechanics and the Quantum Mechanics of Spacetime, gr-qc/9304006).