On the Quantum Deviations from Einstein Dilation of Unstable Quanton Decay Evolution and Lifetimes

TL;DR

This paper unifies previous incomplete and misleading discussions on quantum deviations from Einstein dilation in unstable particles, clarifying the role of velocity eigenstates and analyzing decay lifetimes to reveal deviations from classical predictions.

Contribution

It provides a unified theoretical framework that incorporates all previous approaches, clarifies misconceptions, and emphasizes the importance of velocity eigenstates in decay evolution analysis.

Findings

Unified treatment of decay evolution under boosts.

Reinstates velocity eigenstates as essential.

Shows deviations from Einstein dilation in lifetimes.

Abstract

For over a decade several workers have argued for the existence of quantum deviations from the classical, Einstein dilation of the decay evolution of moving or Lorentz boosted unstable particles. While the general claim is correct, the discussions have been incomplete and, sometimes, misleading. The discussions have been of three kinds. Type 1 examines the time dependence of the survival probability for 3-momentum eigenstates of the unstable quanton (Khalfin). Type 2 does the same for velocity eigenstates, obtaining an outrageous result which then discredits velocity eigenstates (Shirokov / Hegerfeldt). Type 3 examines arbitrary boosts of 3-momentum eigenstates (Stefanovich). Type 1 is incomplete since the momentum eigenstates are not the boosts of one another. Type 2 is misleading since the outrageous result is due to misinterpreting the initial conditions of the velocity eigenstates (as I have previously argued). Type 3 is the most satisfactory, but has failed to recognize and implement the unification of all three types of discussion that can be achieved. In this paper I will provide that unified treatment, beginning with a recapitulation of Type 1 and offering further clarification of Type 2 in the process. The unified treatment fully reinstates velocity eigenstates as essential contributors to unstable quanton states. Besides discussing the time evolution of survival probabilities I also focus on the concept of lifetime defined as the average time of decay. This quantity is helpful in order to display the inequivalent dependence of dilation on momentum and boosts most sharply and the deviation from Einstein dilation most cleanly.