Quantum Mechanics, Gravity and Modified Quantization Relations

TL;DR

This paper explores how quantum rules might vary with energy scale, proposing an energy-dependent effective Planck constant and setting bounds based on muon magnetic moment measurements, implying quantum mechanics holds up to very high energies.

Contribution

It introduces a phenomenological model of energy-dependent quantization and constrains it using experimental muon data, extending the understanding of quantum mechanics at high energies.

Findings

Bound on deviation of effective  from standard value at muon scale

Quantum theory remains valid up to  GeV energy scale

Supports the consistency of quantum mechanics during inflation

Abstract

In this paper we investigate a possible energy scale dependence of the quantization rules and in particular, from a phenomenological point of view, an energy scale dependence of an effective $\hbar$. We set a bound on the deviation from the value of $\hbar$ at the muon scale from its usual value using measurements of the anomalous magnetic moment of the muon. Assuming that inflation took place, we can conclude that nature is described by a quantum theory at least up to an energy scale of about $10^{16}$ GeV.