Does quantum mechanics tell an atomistic spacetime?

TL;DR

This paper explores the possibility that quantum mechanics may emerge from an underlying atomistic structure of spacetime, proposing a model that links discreteness to quantum phenomena and localization.

Contribution

It introduces a theoretical framework suggesting quantum mechanics could be a coarse-grained reflection of spacetime's atomistic nature, incorporating anharmonic interactions and localization mechanisms.

Findings

Classical and quantum evolution equations are similar under certain conditions.

The model provides a decoherence and localization mechanism.

Relation to primordial degrees of freedom is nonlocal.

Abstract

The canonical answer to the question posed is "Yes." -- tacitly assuming that quantum theory and the concept of spacetime are to be unified by `quantizing' a theory of gravitation. Yet, instead, one may ponder: Could quantum mechanics arise as a coarse-grained reflection of the atomistic nature of spacetime? -- We speculate that this may indeed be the case. We recall the similarity between evolution of classical and quantum mechanical ensembles, according to Liouville and von Neumann equation, respectively. The classical and quantum mechanical equations are indistinguishable for objects which are free or subject to spatially constant but possibly time dependent, or harmonic forces, if represented appropriately. This result suggests a way to incorporate anharmonic interactions, including fluctuations which are tentatively related to the underlying discreteness of spacetime. Being linear and local at the quantum mechanical level, the model offers a decoherence and natural localization mechanism. However, the relation to primordial deterministic degrees of freedom is nonlocal.