Causal evolution of wave packets

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 system is causal, the relativistic-Schrödinger 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.

32 pages, 5 figures, 2 tables

References in corpus (5)

• An experimental test of non-local realism
• Energy-dependent effective interactions for dilute many-body systems
• A simple model for interactions and corrections to the Gross-Pitaevskii Equation
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• Some remarks on the continuity equation

Cited by in corpus (1)

• The noncommutative geometry of Zitterbewegung