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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Bell’s locality and ɛ′ /ɛ

Fabio Benatti, Roberto Floreanini B

Published Feb 1, 1998• 32 citations
Publisher

Abstract

We formulate a set of Bell's inequalities for the system of two correlated neutral kaons coming from the decay of a \ensuremath{\varphi} meson, without assuming $\mathrm{CP}$ and $\mathrm{CPT}$ invariance. We show that a nonvanishing value of the phenomenological parameter ${\mathrm{\ensuremath{\varepsilon}}}^{\ensuremath{'}}$ would violate such inequalities, ruling out Bell's locality.

DOI
10.1103/physrevd.57.r1332

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We formulate a set of Bell's inequalities for the system of two correlated neutral kaons coming from the decay of a \ensuremath{\varphi} meson, without assuming CP\mathrm{CP}CP and CPT\mathrm{CPT}CPT invariance. We show that a nonvanishing value of the phenomenological parameter \ensuremathε\ensuremath′{\mathrm{\ensuremath{\varepsilon}}}^{\ensuremath{'}}\ensuremathε\ensuremath′ would violate such inequalities, ruling out Bell's locality.
A local realistic theory of single neutral kaons and of correlated neutral kaon pairs is formulated by deducing the most general consequences of three assumptions: (i) the Einstein-Podolsky-Rosen (EPR) reality criterion, (ii) locality, and (iii) no retroactive causality. Variables must be introduced for every kaon determining the stable CP\mathrm{CP}CP value and the variable value of strangeness S.S.S. Instantaneous SSS jumps are shown to take place. If kaon pairs are produced in \ensuremath{\Phi} meson decays, the local realistic probability of observing K‾0K‾0{\overline{K}}^{0}{\overline{K}}^{0}K0K0 pairs at certain different proper times necessarily differs by 30% from the quantum-mechanical predictions. The size of this difference justifies our systematic neglect of CP\mathrm{CP}CP violation. A \ensuremath{\Phi} factory is thus shown to provide a unique tool for the study of the EPR problem
A local realistic theory of single neutral kaons and of correlated neutral kaon pairs was formulated [F. Selleri, Phys. Rev. A 56, 3493 (1997)] by deducing the consequences of three assumptions: (i) Einstein-Podolsky-Rosen reality criterion; (ii) locality; (iii) lack of retroactive causality. Variables were introduced for every kaon determining the stable CP\mathrm{CP}CP value and the changing value of strangeness S. That theory is here generalized by taking into full account the history-dependent nature of kaons. If kaon pairs are produced in $\ensuremath{\varphi}$ meson decays, the local realistic probability of observing K0K0{K}^{0}{K}^{0}K0K0 pairs at certain different proper times turns out to differ considerably from the quantum-mechanical predictions.
We extend the use of Bell inequalities to $\ensuremath{\Phi}\ensuremath{\rightarrow}{K}^{0}{\overline{K}}^{0}$ decays by exploiting analogies and differences to the well-known and experimentally verified singlet-spin case. Contrasting with other analyses, our Bell inequalities are violated by quantum mechanics and can strictly be derived from local realistic theories. In principle, quantum mechanics could then be tested using unstable, oscillating states governed by a $\mathrm{CP}\ensuremath{-}\mathrm{violating}$ Hamiltonian.