Quantum gravity inspired nonlocal quantum dynamics preserving the classical limit

TL;DR

This paper investigates nonlocal modifications to quantum mechanics inspired by quantum gravity, showing that such modifications can be consistent with classical physics at high energies and proposing experiments with massive objects for testing these effects.

Contribution

It analyzes nonlocal Schrödinger dynamics for a quantum harmonic oscillator without perturbation theory, revealing conditions where classical limits are preserved despite quantum deviations.

Findings

Deviations from standard quantum mechanics occur at low occupation numbers.

Classical probability densities and free energy remain unaffected up to the nonlocality scale.

Massive quantum objects are promising for testing quantum gravity phenomenology.

Abstract

Several approaches to quantum gravity lead to nonlocal modifications of fields' dynamics. This, in turn, can give rise to nonlocal modifications of quantum mechanics at non-relativistic energies. Here, we analyze the nonlocal Schr\"{o}dinger evolution of a quantum harmonic oscillator in one such scenario, where the problem can be addressed without the use of perturbation theory. We demonstrate that although deviations from standard quantum predictions occur at low occupation numbers, where they could potentially be detected or constrained by high-precision experiments, the classical limits of quantum probability densities and free energy remain unaffected up to energies comparable with the nonlocality scale. These results provide an example of nonlocal quantum dynamics compatible with classical predictions, suggesting massive quantum objects as a promising avenue for testing some phenomenological aspects of quantum gravity.