Lorentz Transformation in Quantum Mechanics

TL;DR

This paper investigates how Lorentz transformations affect quantum wave functions and examines the relativistic invariance of a stochastic measurement model in quantum mechanics, highlighting potential points of non-invariance.

Contribution

It introduces a relativistic version of a stochastic quantum measurement model and analyzes its invariance under Lorentz transformations through thought experiments.

Findings

Identifies critical points where non-invariance may occur

Provides insights into the compatibility of quantum mechanics with relativity

Shades light on experimental observations related to relativistic quantum effects

Abstract

The compatibility of special relativity and Quantum Mechanics has been questioned by several authors. The origin of this tension can be traced back mainly to the introduction of the measurement processes and the corresponding wave function reduction, which play a crucial role in Quantum Mechanics. We approach this problem with the help of a recent proposal for a model of Quantum Mechanics, where the measurement is explicitly described as a specific stochastic process. This implements ordinary Quantum Mechanics, where measurement and reduction are treated as phenomenological events of unknown origin without any physical justification. To state clearly the question in general, we first discuss and establish the effect of a Lorentz transformation on a generic wave function in space-time. Alongside the analysis we formulate the relativistic version of the model. We then consider few thought experiments in order to analyze to what extent Quantum Mechanics follows relativistic invariance and find the specific critical points where non invariance possibly occurs. The analysis can shade light to the interpretation of the existing experimental observations.