Spacetime as a Tightly Bound Quantum Crystal

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.