Standard Model of Particle Physics Violating Crypto-Nonlocal Realism

TL;DR

This paper demonstrates that the Standard Model of particle physics violates crypto-nonlocal realism by deriving a new Leggett inequality and showing its violation in entangled mesons, with potential tests in other quantum systems.

Contribution

It extends Leggett inequalities to include hidden variable-determined measurement settings and shows their violation within the Standard Model, revealing nonlocal realism violations.

Findings

Violation of the new Leggett inequality by entangled $B_d$ mesons.

Maximum violation estimated at about 2.7%.

Implication that the Standard Model violates crypto-nonlocal realism.

Abstract

It has been well established that quantum mechanics (QM) violates Bell inequalities (BI), which are consequences of local realism (LR). Remarkably QM also violates Leggett inequalities (LI), which are consequences of a class of nonlocal realism called crypto-nonlocal realism (CNR). Both LR and CNR assume that measurement outcomes are determined by preexisting objective properties, as well as hidden variables (HV) not considered in QM. We extend CNR and LI to include the case that the measurement settings are not externally fixed, but determined by hidden variables (HV). We derive a new version of LI, which is then shown to be violated by entangled $B_d$ mesons, if charge-conjugation-parity (CP) symmetry is indirectly violated, as indeed established. The experimental result is quantitatively estimated by using the indirect CP violation parameter, and the maximum of a suitably defined relative violation is about $2.7\%$. Our work implies that standard model (SM) of particle physics violates CNR. Our LI can also be tested in other systems such as photon polarizations.