The Entropic Uncertainty Principle for Decaying Systems and CP violation

TL;DR

This paper explores how the entropic uncertainty principle applies to decaying systems like neutral K-mesons, linking CP violation to fundamental measurement uncertainties in quantum mechanics.

Contribution

It introduces an effective formalism to analyze uncertainty relations in decaying systems and connects CP violation with inherent measurement uncertainties.

Findings

Uncertainty between strangeness measurements at different times due to decay.

CP violation causes an intrinsic uncertainty in the evolution of eigenstates.

The formalism reveals fundamental limits on predicting outcomes in decaying quantum systems.

Abstract

Employing an effective formalism for decaying system we are able to investigate Heisenberg's uncertainty relation for observables measured at accelerator facilities. In particular we investigate the neutral K--meson system and show that, firstly, due to the time evolution an uncertainty between strangeness measurements at different times is introduced and, secondly, due to the imbalance of matter and antimatter (CP violation) an uncertainty in the evolution of the eigenstates of the effective Hamiltonian of the system. Consequently, the existence of CP violation is linked to uncertainties of observables, i.e. the outcomes cannot be predicted even in principle to arbitrary precisions.