Moving Unstable Particles and Special Relativity

Eugene V Stefanovich

doi:10.1155/2018/4657079

Abstract

In Poincaré-Wigner-Dirac theory of relativistic interactions, boosts are dynamical. This means that, just like time translations, boost transformations have a nontrivial effect on internal variables of interacting systems. In this respect, boosts are different from space translations and rotations, whose actions are always universal, trivial, and interaction-independent. Applying this theory to unstable particles viewed from a moving reference frame, we prove that the decay probability cannot be invariant with respect to boosts. Different moving observers may see different internal compositions of the same unstable particle. Unfortunately, this effect is too small to be noticeable in modern experiments.

Highlights

Time dilation is one of the most spectacular predictions of special relativity
In special relativity boosts are kinematical. This hypothesis is known as the condition of “invariant trajectories” or “manifest covariance.”
The well-known Currie-Jordan-Sudarshan theorem [29] states that this condition is not compatible with the Hamiltonian description of dynamics presented in the previous section

Summary

Introduction

Time dilation is one of the most spectacular predictions of special relativity. This theory predicts that any timedependent process slows down by the universal factor of 1/√1 − V2/c2 ≡ cosh θ when viewed from a reference frame moving with the speed V (and rapidity θ). According to special relativity, the decay law of a moving particle should be exactly cosh θ times slower: ΥSR (θ, t) = Υ (0, t cosh θ ) (1). This prediction was confirmed in numerous measurements [1,2,3,4]. The best accuracy of 0.1% was achieved in experiments with relativistic muons [5, 6]

Methods

Results

Conclusion