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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… Click to show full abstract
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 Hamiltonian impels a causal evolution of probabilities, even in the presence of interactions, the relativistic-Schr\"odinger model is acausal. We quantify the causality breakdown in the latter model and argue that, in contrast to the popular viewpoint, it is not related to the localization properties of the states.
Journal Title: Physical Review A
Year Published: 2017
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