Wigner rotations and an apparent paradox in relativistic quantum information

TL;DR

The paper reveals a paradox in relativistic quantum information where applying Wigner rotations linearly to superposed states causes frame-dependent detection probabilities, resolved by considering the physical state construction.

Contribution

It demonstrates that linear application of Wigner rotations to superposed states leads to paradoxes, emphasizing the importance of physical interpretation in relativistic quantum states.

Findings

Linear Wigner rotations cause frame-dependent detection probabilities.

Resolving the paradox requires considering the physical state construction.

The study highlights the need for careful interpretation of relativistic quantum transformations.

Abstract

It is shown that a general model for particle detection in combination with a linear application of the Wigner rotations, which correspond to momentum-dependent changes of the particle spin under Lorentz transformations, to the state of a massive relativistic particle in a superposition of two counter-propagating momentum states leads to a paradox. The paradoxical behavior is that the probability of finding the particle at different positions would depend on the reference frame. A solution to the paradox is given when the physical construction of the corresponding state is taken into account, suggesting that we cannot in general linearly apply the Wigner rotations to a quantum state without considering the appropriate physical interpretation.