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arXiv:1003.2781

Crucial tests of the existence of a Time Operator

Thomas Durt

Published Mar 14, 2010• 3 citations
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Abstract

In the present paper we show that the Temporal Wave Function approach of the decay process, which is a multicomponent version of the Time Operator approach leads to new, non-standard, predictions concerning the statistical properties of decay time distributions of single kaons and entangled pairs of mesons. These results suggest crucial experimental tests for the existence of a Time Operator for the decay process to be realized in High Energy Physics or Quantum Optics.

DOI
10.48550/arxiv.1003.2781

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•Dec 10, 2019•1 citation
In the present paper we show that the Temporal Wave Function approach of the decay process, which is a multicomponent version of the Time Operator approach leads to new, non-standard, predictions concerning the statistical properties of decay time distributions of single kaons and entangled pairs of mesons. These results suggest crucial experimental tests for the existence of a Time Operator for the decay process to be realized in High Energy Physics or Quantum Optics.
The status of Time in the Quantum Theory remains even today a largely open question. In particular, the existence of a Quantum Time Operator that would describe the distribution of decay times of an unstable quantum system (in analogy with the Position operator that is associated to the position distribution) remained a polemichal question during several decades. Recently, we conceived experimental proposals involving CP violating processes (of single mesons and entangled pairs of mesons) that can be considered as crucial experiments aimed at testing the existence of a Quantum Time Operator. In the present paper, we shall present a similar proposal that can be realized with a single trapped ion. These proposals aim at bringing fundamental problems related to the status of Time in the Quantum Theory to the realm of experimental physics.
The role played by time in the quantum theory is still mysterious by many aspects. In particular it is not clear today whether the distribution of decay times of unstable particles could be described by a time operator (TO). As we shall discuss, different approaches to this problem (one could say interpretations) can be found in the literature on the subject. As we shall show, it is possible to conceive crucial experiments aimed at distinguishing the different approaches, by measuring with accuracy the statistical distribution of decay times of entangled particles. Such experiments can be realized in principle with entangled kaon pairs.
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 the system of a pair of quantum-entangled neutral kaons from meson decays, when one kaon collapses into the [Formula: see text] state, the other will collapse instantaneously into the [Formula: see text] state, due to entanglement and nonlocality. However, if the alternative hypothesis is correct and there is a time window during which one kaon is unaware that the other has decayed, some quantum mechanically prohibited [Formula: see text] decays may occur. We calculate the branching ratios of [Formula: see text] in vector meson decays under locality hypothesis and compare them with experimental results. We show that the branching ratio of [Formula: see text] under locality assumption is already excluded by the BESIII experimental upper limit. Additional experimental results are proposed to perform this test in the future.
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.