Superluminal matter waves

TL;DR

This paper demonstrates that solutions to the Dirac equation can have wavefunction peaks traveling faster than light, challenging traditional interpretations while maintaining subluminal expectation velocities.

Contribution

It introduces superluminal matter wave solutions to the Dirac equation, constructed via superpositions in momentum space, revealing new possibilities for wavefunction behavior.

Findings

Wavefunction peaks can travel faster than light.

Solutions maintain a near-constant profile during superluminal motion.

Implications for quantum processes sensitive to local probability density.

Abstract

The Dirac equation has resided among the greatest successes of modern physics since its emergence as the first quantum mechanical theory fully compatible with special relativity. This compatibility ensures that the expectation value of the velocity is less than the vacuum speed of light. Here, we show that the Dirac equation admits free-particle solutions where the peak amplitude of the wavefunction can travel at any velocity, including those exceeding the vacuum speed of light, despite having a subluminal velocity expectation value. The solutions are constructed by superposing basis functions with correlations in momentum space. These arbitrary velocity wavefunctions feature a near-constant profile and may impact quantum mechanical processes that are sensitive to the local value of the probability density as opposed to expectation values.