Boosting unstable particles

TL;DR

This paper investigates how Lorentz boosts affect the quantum state of unstable particles, revealing that decay probabilities are frame-dependent due to relativistic effects on wavefunctions, challenging classical notions of invariance.

Contribution

It demonstrates that Lorentz boosts cause superpositions of decayed and non-decayed states, showing decay probabilities are inherently non-Lorentz-invariant in quantum theory.

Findings

Decay probabilities depend on the frame of reference.

Wavefunction tails travel to past and future under boosts.

A fundamental lower bound on localization affects the effect.

Abstract

In relativity, there is no absolute notion of simultaneity, because two clocks that are in different places can always be desynchronized by a Lorentz boost. Here, we explore the implications of this effect for the quantum theory of unstable particles. We show that, when a wavefunction is boosted, its tails travel one to the past and the other to the future. As a consequence, in the new frame of reference, the particle is in a quantum superposition "decayed + non decayed", where the property "decayed-ness" is entangled with the position. Since a particle cannot be localised in a region smaller than the Compton wavelength, there is a non-zero lower bound on this effect, which is fundamental in nature. The surprising implication is that, in a quantum world, decay probabilities can never be Lorentz-invariant. We show that this insight was the missing ingredient to reconcile the seemingly conflicting views about time dilation in relativistic quantum mechanics and quantum field theory.