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arXiv:1512.08437

Falsification of a Time Operator Model based on Charge-Conjugation-Parity violation of neutral K-mesons

Thomas Durt, ANTONIO DI DOMENICO, Beatrix C. Hiesmayr

Published Dec 28, 2015• 3 citations
arXivHTMLPDF

Abstract

The founding fathers of the quantum theory already struggled with the different roles of space and time in quantum theory. Position is by default represented by an operator, whereas time is usually treated as a parameter. Time operator models exist, in particular a certain Time Operator model denoted the Temporal Wave Function (T.W.F.). This one extends the Born's rule to the time domain. The statistics of pure exponential decay does not allow to exclude this Born rule for time. However the tiny violation of the combined discrete symmetries $P$ (parity) and $C$ (charge conjugation) observed in the K-meson system allows us, as we prove in this paper, to discriminate between the standard predictions, made in the framework of the so-called mass-decay matrix formalism, and the T.W.F. predictions. We also present experimental data of a particular $CP$ violating decay channel, that is in contrast with the prediction of T.W.F. approach model, resulting in its falsification.

DOI
10.48550/arxiv.1512.08437

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The founding fathers of the quantum theory already struggled with the different roles of space and time in quantum theory. Position is by default represented by an operator, whereas time is usually treated as a parameter. Time operator models exist, in particular a certain Time Operator model denoted the Temporal Wave Function (T.W.F.). This one extends the Born's rule to the time domain. The statistics of pure exponential decay does not allow to exclude this Born rule for time. However the tiny violation of the combined discrete symmetries PPP (parity) and CCC (charge conjugation) observed in the K-meson system allows us, as we prove in this paper, to discriminate between the standard predictions, made in the framework of the so-called mass-decay matrix formalism, and the T.W.F. predictions. We also present experimental data of a particular CPCPCP violating decay channel, that is in contrast with the prediction of T.W.F. approach model, resulting in its falsification.
In this paper we propose to associate a temporal two-component wave-function to the decay process of meson particles. This simple quantum model provides a good estimation of the CP symmetry violation parameter. This result is based on our previous paper ("Two-Level Friedrichs model and Kaonic phenomenology", Physics Letters A 362, 100-104 (2007)) where we have shown that the two-level Friedrichs Hamiltonian model makes it possible to provide a qualitatively correct phenomenological model of kaons physics. In this previous paper, we derived a violation parameter that is 14 times larger than the measured quantity. In the present paper we improve our estimation of the violation and obtain the right order of magnitude. The improvement results from a renormalized superposition of the probability amplitudes describing short and long exponential decays. The renormalization occurs because the amplitudes that we are dealing with are associated to the decay rate, and not to the integrated decay rate or survival probability as is usually the case in standard approaches to CP-violation. We also compare with recent experimental data for the mesons D and B and also there the agreement between our model and experimental data is quite satisfying.
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.
Symmetries, and Symmetry Breakings, in the Laws of Physics play a crucial role in Fundamental Science. Parity and Charge Conjugation Violations prompted the consideration of Chiral Fields in the construction of the Standard Model, whereas CP-Violation needed at least three families of Quarks leading to Flavour Physics. In this Lecture I will discuss the Conceptual Basis and the present experimental results for a Direct Evidence of Separate Reversal-in-Time T, CP and CPT Genuine Asymmetries in Decaying Particles like Neutral Meson Transitions, using Quantum Entanglement and the Decay as a Filtering Measurement. The eight transitions associated to the Flavour-CP eigenstate decay products of entangled neutral mesons have demonstrated with impressive significance a separate evidence of TRV and CPV in B d -physics, whereas a CPTV asymmetry shows a 2-σ effect interpreted as an upper limit. Novel CPTV observables are discussed for K and B d transitions. Their observation would lead to a change of paradigm beyond Quantum Field Theory, however there is nothing in Quantum Mechanics forbidding CPTV. A clean methodology to disentangle CPTV effects in the Hamiltonian dynamics and the ω-effect weakening Entanglement in a given experiment is discussed.