Causal evolution of wave packets

TL;DR

This paper explores the causal properties of wave packet evolution in relativistic quantum systems, showing that Dirac systems are causal while relativistic Schrödinger systems exhibit superluminal probability evolution, challenging common beliefs.

Contribution

It introduces a causal flow principle based on optimal transport theory in a relativistic context and compares causality in Dirac and relativistic Schrödinger systems.

Findings

Dirac systems are causal in wave packet evolution.

Relativistic Schrödinger Hamiltonian causes superluminal probability evolution.

Causality breakdown is not due to state localization.

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-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.