Spacetime as a Tightly Bound Quantum Crystal

TL;DR

This paper proposes a novel formulation of quantum physics using reparametrized spacetime as a quantum crystal, linking quantum dynamics with solid state physics concepts and exploring implications for relativity and the universe's wavefunction.

Contribution

It introduces a second quantized spacetime mode framework and suggests modeling spacetime dynamics akin to electron propagation in a crystal lattice.

Findings

Spacetime can be modeled as a quantum crystal with modes.

The formulation connects quantum dynamics to solid state physics.

Implications for mode entanglement and the wavefunction of the universe.

Abstract

We review how reparametrization of space and time, namely the procedure where both are made to depend on yet another parameter, can be used to formulate quantum physics in a way that is naturally conducive to relativity. This leads us to a second quantised formulation of quantum dynamics in which different points of spacetime represent different modes. We speculate on the fact that our formulation can be used to model dynamics in spacetime the same way that one models propagation of an electron through a crystal lattice in solid state physics. We comment on the implications of this for the notion of mode entanglement as well as for the fully relativistic Page-Wootters formulation of the wavefunction of the Universe.