Which is the quantum decay law of relativistic particles?

¹ Department of Physics, Hakim Sabzevari University - P. O. Box, 397, Sabzevar, Iran
² Department of Physics, University of Torino - Via P. Giuria 1, I-10125 Torino, Italy
³ INFN, Sezione di Torino - Via P. Giuria 1, I-10125 Torino, Italy

Received: 14 January 2015
Accepted: 3 March 2015

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.