Causal evolution of wave packets

Drawing from the optimal transport theory adapted to the relativistic setting we formulate the principle of a causal flow of probability and apply it in the wave packet formalism. We demonstrate that whereas the Dirac system is causal, the relativistic-Schr\"odinger Hamiltonian impels a superlu...

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Bibliographic Details
Published in:arXiv.org 2016-10
Main Authors: Eckstein, Michał, Miller, Tomasz
Format: Article
Language:English
Subjects:
Evolution
Relativism
Relativistic effects
Transport theory
Wave packets
Online Access:Get full text
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Summary:Drawing from the optimal transport theory adapted to the relativistic setting we formulate the principle of a causal flow of probability and apply it in the wave packet formalism. We demonstrate that whereas the Dirac system is causal, the relativistic-Schr\"odinger Hamiltonian impels a superluminal evolution of probabilities. We quantify the causality breakdown in the latter system and argue that, in contrast to the popular viewpoint, it is not related to the localisation properties of the states.
ISSN:2331-8422
DOI:10.48550/arxiv.1610.00764