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Physical Review A

Incompatibility between local realism and quantum mechanics for pairs of neutral kaons

F. Selleri

Published Nov 1, 1997• 60 citations
Publisher

Abstract

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 $\mathrm{CP}$ value and the variable value of strangeness $S.$ Instantaneous $S$ jumps are shown to take place. If kaon pairs are produced in \ensuremath{\Phi} meson decays, the local realistic probability of observing ${\overline{K}}^{0}{\overline{K}}^{0}$ 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 $\mathrm{CP}$ violation. A \ensuremath{\Phi} factory is thus shown to provide a unique tool for the study of the EPR problem

DOI
10.1103/physreva.56.3493

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arXiv:2111.04328•Nov 8, 2021•2 citations
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.
The Einstein-Podolsky-Rosen (EPR) entanglement of a neutral K-meson (kaon) pair enjoys the peculiar quantum behaviour of mixing, charge-parity CP{\cal CP}CP violation (C{\cal C}C - charge conjugation, P{\cal P}P - parity) and two non-orthogonal eigenstates of definite time evolution KLK_LKL​ and KSK_SKS​ with very different lifetimes. The dynamics of this strange entanglement, experimentally accessible at the ϕ\phiϕ-factory, makes possible the search for novel phenomena not accessible in any other system, i.e. at interference times and at decoherence times of the single partners after their disentanglement, in order to unveil the nature of the correlation between the two neutral kaons. Until now, the studies have been concentrated on the single kaon intensity distribution between the two decay times t1t_1t1​ and t2t_2t2​ with Δt=t2−t1>0\Delta t = t_2 - t_1 > 0Δt=t2​−t1​>0. Here we show that the entire two single time distributions, before each decay, are physical in both senses: past to future, leading to the state of the living partner at time t2t_2t2​ from the observation of the first decay channel at t1t_1t1​, and future to past, leading to the past state of the decayed kaon at time t1t_1t1​ from the observation of the second decay channel at t2t_2t2​. Our results thus demonstrate an affirmative answer to the title: it does, the past decayed state depends on the result of the future measurement for the living partner. This novel effect is truly observable through the first decay time distributions. Besides the implications for quantum physics for all Δt\Delta tΔt, at large decoherence times the resulting first decayed state is always KSK_SKS​, providing a genuine tag of this kaon state in the decoherence region, and a unique and important experimental tool to prepare a pure KSK_SKS​ beam.
We shortly review a couple of proposals of Bell inequality tests with entangled pairs of neutral kaons from φ resonance decays.The suggested experiments are discussed in the light of the essential requirements for a genuine discrimination between local hidden-variable theories (i.e., local realism) and quantum mechanics.We clarify the logical limitations of these tests in refuting the whole class of local realistic models.Detailed analyses imply that a Bell-type test with neutral kaons free from the detection loophole requires a few % strangeness detection efficiencies and very high efficiencies for the detection of the kaon decay products.
In this talk we discuss the predictions of local realistic theories for the evolution of a K0-K0bar quantum entangled pair created in the decay of the phi-meson. It is shown, in agreement with Bell's theorem, that the most general local hidden-variable model fails in reproducing the whole set of quantum-mechanical observables. We achieve this conclusion by employing two different approaches. In the first approach, the local realistic observables are deduced from the most general premises concerning locality and realism, and Bell-like inequalities are not employed. The other approach makes use of Bell's inequalities. Under particular conditions for the detection times, within the first approach the discrepancy between quantum mechanics and local realism for the asymmetry parameter turns out to be not less than 20%. A similar incompatibility can be made evident by means of a Bell-type test, by employing a Clauser-Horne-Shimony-Holt's inequality written in terms of properly normalized observables. Because of its relatively low experimental accuracy, the data obtained by the CPLEAR collaboration do not yet allow a decisive test of local realism. Such a test, both with and without the use of Bell's inequalities, should be feasible in the future at the Frascati Phi-factory.
Precision tests of quantum mechanics and CPT \mathcal{CPT} CPT symmetry with entangled neutral kaons at KLOE
Abstract The quantum interference between the decays of entangled neutral kaons is studied in the process ϕ → KSKL → π+π−π+π−, which exhibits the characteristic Einstein-Podolsky-Rosen correlations that prevent both kaons to decay into π+π− at the same time. This constitutes a very powerful tool for testing at the utmost precision the quantum coherence of the entangled kaon pair state, and to search for tiny decoherence and CPT \mathcal{CPT} CPT CPT violation effects, which may be justified in a quantum gravity framework. The analysed data sample was collected with the KLOE detector at DAΦNE, the Frascati ϕ-factory, and corresponds to an integrated luminosity of about 1.7 fb−1, i.e. to about 1.7 × 109ϕ → KSKL decays produced. From the fit of the observed ∆t distribution, being ∆t the difference of the kaon decay times, the decoherence and CPT \mathcal{CPT} CPT CPT violation parameters of various phenomenological models are measured with a largely improved accuracy with respect to previous analyses. The results are consistent with no deviation from quantum mechanics and CPT \mathcal{CPT} CPT CPT symmetry, while for some parameters the precision reaches the interesting level at which — in the most optimistic scenarios — quantum gravity effects might show up. They provide the most stringent limits up to date on the considered models.
The quantum interference between the decays of entangled neutral kaons is studied in the process ϕ→KSKL→π+π−π+π−ϕ\rightarrow K_S K_L \rightarrowπ^+π^-π^+π^-ϕ→KS​KL​→π+π−π+π−, which exhibits the characteristic Einstein--Podolsky--Rosen correlations that prevent both kaons to decay into π+π−π^+π^-π+π− at the same time. This constitutes a very powerful tool for testing at the utmost precision the quantum coherence of the entangled kaon pair state, and to search for tiny decoherence and CPT violation effects, which may be justified in a quantum gravity framework. The analysed data sample was collected with the KLOE detector at DAΦΦΦNE, the Frascati ϕϕϕ-factory, and corresponds to an integrated luminosity of about 1.7 fb−1^{-1}−1, i.e. to about 1.7×1091.7 \times 10^91.7×109 ϕ→KSKLϕ\rightarrow K_S K_Lϕ→KS​KL​ decays produced. From the fit of the observed ΔtΔtΔt distribution, being ΔtΔtΔt the difference of the kaon decay times, the decoherence and CPT violation parameters of various phenomenological models are measured with a largely improved accuracy with respect to previous analyses. The results are consistent with no deviation from quantum mechanics and CPT symmetry, while for some parameters the precision reaches the interesting level at which -- in the most optimistic scenarios -- quantum gravity effects might show up. They provide the most stringent limits up to date on the considered models.