Quantum Matter Makes Lightcones Quantum

Abstract:In gravitational physics, matter does not merely move within spacetime; it also determines the light cones that define causal relations. What happens when the matter that determines these light cones is itself in a quantum state? We address this question in a controlled low-energy setting: a massless scalar field propagating in the spacetime with the Newtonian gravitational potential sourced by a non-relativistic quantum particle. We show that the light cones are affected by an operator-valued Shapiro delay, with the three consequences: (i) causal-boundary shifts are promoted to noncommuting observables, giving the causal structure an irreducible quantum uncertainty; (ii) the causal relation between two fixed spacetime points can become a superposition of timelike and spacelike configurations; and (iii) tracing out the source smears the Wightman light-cone singularity, producing an effective UV cutoff. Thus, quantum matter does not merely fluctuate within spacetime; it makes the causal structure itself quantum, even without including propagating graviton modes.

arXiv:2606.03671 [gr-qc]

(or arXiv:2606.03671v2 [gr-qc] for this version)

https://doi.org/10.48550/arXiv.2606.03671 Focus to learn more arXiv-issued DOI via DataCite

Phys.Rev.D 114 (2026) 4, 044047

https://doi.org/10.1103/rg3n-98lr Focus to learn more DOI(s) linking to related resources

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