Quantum Reference Frames for Lorentz Symmetry

TL;DR

This paper develops a framework for quantum reference frame transformations that incorporate Lorentz symmetry, enabling the analysis of relativistic quantum effects like superpositions of time dilation and length contraction.

Contribution

It introduces a formulation of relativistic quantum mechanics independent of preferred time slices and defines quantum Lorentz transformations and superpositions of boosts.

Findings

Superposition of time dilations demonstrated

Superposition of length contractions analyzed

Potential experimental observations discussed

Abstract

Since their first introduction, Quantum Reference Frame (QRF) transformations have been extensively discussed, generalising the covariance of physical laws to the quantum domain. Despite important progress, a formulation of QRF transformations for Lorentz symmetry is still lacking. The present work aims to fill this gap. We first introduce a reformulation of relativistic quantum mechanics independent of any notion of preferred temporal slicing. Based on this, we define transformations that switch between the perspectives of different relativistic QRFs. We introduce a notion of ''quantum Lorentz transformations'' and ''superposition of Lorentz boosts'', acting on the external degrees of freedom of a quantum particle. We analyse two effects, superposition of time dilations and superposition of length contractions, that arise only if the reference frames exhibit both relativistic and quantum-mechanical features. Finally, we discuss how the effects could be observed by measuring the wave-packet extensions from relativistic QRFs.