On alternative approaches to Lorentz violation in loop quantum gravity inspired models

TL;DR

This paper examines the possibility of removing Lorentz violations in loop quantum gravity models through variable redefinitions, concluding that such alternatives are inconsistent with the quantum theory and that Lorentz invariance must be broken or extended.

Contribution

It demonstrates the inconsistency of alternative variable choices with the underlying quantum theory, emphasizing the necessity of Lorentz symmetry extension or supersession.

Findings

Alternative variable choices conflict with quantum theory constraints

Lorentz invariance cannot be preserved with standard variables in this framework

Relativity principle requires extending or superseding Lorentz symmetry

Abstract

Recent claims point out that possible violations of Lorentz symmetry appearing in some semiclassical models of extended matter dynamics motivated by loop quantum gravity can be removed by a different choice of canonically conjugated variables. In this note we show that such alternative is inconsistent with the choice of variables in the underlying quantum theory together with the semiclassical approximation, as long as the correspondence principle is maintained. A consistent choice will violate standard Lorentz invariance. Thus, to preserve a relativity principle in this framework, the linear realization of Lorentz symmetry should be extended or superseded.