Which is the Quantum Decay Law of Relativistic Particles?

TL;DR

This paper clarifies the correct relativistic quantum decay law for unstable particles, showing that an appropriate definition of survival probability aligns with special relativity, resolving apparent contradictions in previous approaches.

Contribution

It introduces a relativistic definition of survival probability that accounts for space evolution, reconciling quantum decay laws with special relativity.

Findings

Standard decay law is recovered with the new definition.

Wave packet treatment provides a rigorous derivation.

Contradictions with previous non-standard effects are resolved.

Abstract

We discuss the relation between the quantum-mechanical survival probability of an unstable system in motion and that of the system at rest. The usual definition of the survival probability which takes into account only the time evolution of an unstable system leads to a relation between the survival probability of the system in motion and that of the system at rest which is different from the standard relation based on relativistic time dilation. This approach led other authors to claim non-standard quantum-mechanical effects which are in clear contradiction with Special Relativity. We show that an appropriate relativistic definition of the survival probability which takes into account also the space evolution of an unstable system leads to the standard relation between the survival probability of the system in motion and that of the system at rest, in agreement with Special Relativity. We present a rigorous derivation of this result based on a wave packet treatment.