Packet Spreading and Einstein Retardation

TL;DR

This paper investigates Einstein retardation in quantum mechanics, demonstrating that the classical slowing of nonstationary systems does not universally apply to quantum systems like a spreading wave packet.

Contribution

It reveals that Einstein retardation is not a universal law in quantum mechanics by analyzing a free spinless particle's wave packet evolution.

Findings

ER does not hold for a free spreading wave packet

ER is not a universal kinematic law in quantum systems

Previous exceptions to ER are confirmed

Abstract

According to the classical special theory of relativity any nonstationary system moving with velocity $v$ must evolve (e.g., decay) $1/\gamma$ times slower than the system at rest, $\gamma =(1-v^2)^{-1/2}$ (the Einstein retardation ER). Quantum mechanics allows one to calculate the evolution of both systems separately and to compare them thus verifying ER. It is shown here that ER is not valid for a simple system: the spreading packet of the free spinless particle. Earlier it was shown that ER does not hold for some other systems. So one may state that ER is not a universal kinematic law in quantum mechanics.