Related papers: Quantum spacetime from constraints: wave equations and fields

Quantum spacetime from constraints: wave equations and fields

URL: http://arxiv.org/abs/2508.12698v3
Date: Mon, 29 Sep 2025 08:44:20 GMT
Title: Quantum spacetime from constraints: wave equations and fields
Authors: Tommaso Favalli,
Abstract summary: We extend the Page and Wootters quantum time formalism to include both quantum clocks and rods.<n>We show that the standard wave equations governing quantum particles emerge naturally from this framework.<n>Our results provide further support for the idea that quantum dynamics in spacetime may emerge from entanglement and constraints.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: In previous works, we showed that both time and space can emerge from entanglement within a globally constrained quantum Universe, with no background coordinates. By extending the Page and Wootters quantum time formalism to include both quantum clocks and rods, and imposing global constraints on total energy and momentum, we constructed a fully relational model of quantum spacetime. Here we take a further step: working in 1+1 dimensions, we show that the standard wave equations governing quantum particles (the Schr\"odinger, Klein-Gordon and Dirac equations) emerge naturally from this framework. The solutions of the equations are derived directly from the constraints, without assuming any external spacetime structure. The second quantization formalism is also implemented and discussed. Our results provide further support for the idea that quantum dynamics in spacetime may emerge from entanglement and constraints.

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