Wigner rotations and an apparent paradox in relativistic quantum information
arXiv:1303.4367 · doi:10.1103/PhysRevA.87.042102
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.
5 pages, 2 figures. We changed the example used to show that the linear application of the Wigner rotations to the state of a massive relativistic particle in a superposition of two counter-propagating momentum states leads to a paradox. There was a problem with the example used in the previous version
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