Causal evolution of wave packets

Michał Eckstein and Tomasz Miller
Phys. Rev. A 95, 032106 – Published 8 March 2017

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-Schrödinger 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.

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  • Received 16 October 2016

DOI:https://doi.org/10.1103/PhysRevA.95.032106

©2017 American Physical Society

Physics Subject Headings (PhySH)

General PhysicsGravitation, Cosmology & AstrophysicsQuantum Information, Science & TechnologyInterdisciplinary PhysicsParticles & Fields

Authors & Affiliations

Michał Eckstein*

  • Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, ulica prof. Stanisława Łojasiewicza 11, 30-348 Kraków, Poland and Copernicus Center for Interdisciplinary Studies, ulica Szczepańska 1/5, 31-011 Kraków, Poland

Tomasz Miller

  • Faculty of Mathematics and Information Science, Warsaw University of Technology, ulica Koszykowa 75, 00-662 Warsaw, Poland and Copernicus Center for Interdisciplinary Studies, ulica Szczepańska 1/5, 31-011 Kraków, Poland

  • *michal.eckstein@uj.edu.pl
  • t.miller@mini.pw.edu.pl

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Issue

Vol. 95, Iss. 3 — March 2017

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