Theory of Quantum Space-Time

TL;DR

This paper proposes a quantum mechanical extension of space-time based on a generalized equivalence principle, exploring its symmetries, hierarchical causal structure, and the emergence of classical space-time as a density matrix map.

Contribution

It introduces a higher-dimensional quantum space-time framework with a novel symmetry group and describes how classical space-time emerges from quantum operators.

Findings

Quantum space-time has a rich hierarchical causal structure.

Symmetry group generated by irreducible Killing tensors.

Classical space-time emerges as a density matrix map from quantum space-time.

Abstract

A generalised equivalence principle is put forward according to which space-time symmetries and internal quantum symmetries are indistinguishable before symmetry breaking. Based on this principle, a higher-dimensional extension of Minkowski space is proposed and its properties examined. In this scheme the structure of space-time is intrinsically quantum mechanical. It is shown that the causal geometry of such a quantum space-time possesses a rich hierarchical structure. The natural extension of the Poincare group to quantum space-time is investigated. In particular, we prove that the symmetry group of a quantum space-time is generated in general by a system of irreducible Killing tensors. When the symmetries of a quantum space-time are spontaneously broken, then the points of the quantum space-time can be interpreted as space-time valued operators. The generic point of a quantum space-time in the broken symmetry phase thus becomes a Minkowski space-time valued operator. Classical space-time emerges as a map from quantum space-time to Minkowski space. It is shown that the general such map satisfying appropriate causality-preserving conditions ensuring linearity and Poincare invariance is necessarily a density matrix.