Is There an Observable Limit to Lorentz Invariance at the Compton Wavelength Scale?

TL;DR

This paper investigates whether Lorentz invariance can be violated at the scale of the muon's Compton wavelength, using a scenario involving muons orbiting near a microscopic Kerr black hole, and finds a stabilization effect at that scale.

Contribution

It demonstrates that kinematic and curvature effects can stabilize muon decay at the Compton wavelength, providing a potential observable limit to Lorentz invariance violation.

Findings

Muon decay spectrum stabilizes at the Compton wavelength scale.

Lorentz invariance violation may be limited at microscopic scales.

Curvature effects influence particle decay near black holes.

Abstract

The possibility of a frame-induced violation of Lorentz invariance due to non-inertial spin-1/2 particle motion is explored in detail for muon decay while in orbit near the event horizon of a microscopic Kerr black hole. It is explicitly shown that kinematic and curvature contributions to the muon's decay spectrum--in the absence of any unforeseen processes due to quantum gravity--lead to its stabilization at the muon's Compton wavelength scale. This example is emblematic of the search for unambiguous indicators to critically assess current and future approaches to quantum gravity research.