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arXiv:hep-ph/9902427 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Quantum mechanics, Furry’s hypothesis, and a measure of decoherence in the K0K0 system

Reinhold A. Bertlmann, Walter Grimus, Beatrix C. Hiesmayr

Published Nov 12, 1999• 62 citations
arXivHTMLPDF

Abstract

We consider strangeness correlations of the Einstein-Podolski-Rosen type in ${K}^{0}{K}^{0}$ pairs created in a ${J}^{\mathrm{PC}}{=1}^{\ensuremath{-}\ensuremath{-}}$ state as a function of time under the hypothesis that spontaneous decoherence takes place. We parametrize the degree of decoherence by a factor $(1\ensuremath{-}\ensuremath{\zeta})$ which multiplies the quantum-mechanical interference terms occurring in the amplitudes for like and unlike strangeness events and discuss the dependence of this procedure on the basis chosen in ${K}^{0}\ensuremath{-}{K}^{0}$ space to which the interference terms correspond. Consequently, all statements about the ``decoherence parameter'' $\ensuremath{\zeta}$ inferred from experimental data are basis dependent as well. We illustrate this point by estimating the value of $\ensuremath{\zeta}$ for the two bases ${{K}_{L}{,K}_{S}}$ and ${{K}^{0},{K}^{0}}$ with the help of recent data of the CPLEAR experiment.

DOI
10.1103/physrevd.60.114032

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We consider strangeness correlations of the Einstein-Podolski-Rosen type in K0K0{K}^{0}{K}^{0}K0K0 pairs created in a JPC=1\ensuremath−\ensuremath−{J}^{\mathrm{PC}}{=1}^{\ensuremath{-}\ensuremath{-}}JPC=1\ensuremath−\ensuremath− state as a function of time under the hypothesis that spontaneous decoherence takes place. We parametrize the degree of decoherence by a factor (1\ensuremath−\ensuremathζ)(1\ensuremath{-}\ensuremath{\zeta})(1\ensuremath−\ensuremathζ) which multiplies the quantum-mechanical interference terms occurring in the amplitudes for like and unlike strangeness events and discuss the dependence of this procedure on the basis chosen in K0\ensuremath−K0{K}^{0}\ensuremath{-}{K}^{0}K0\ensuremath−K0 space to which the interference terms correspond. Consequently, all statements about the ``decoherence parameter'' \ensuremathζ\ensuremath{\zeta}\ensuremathζ inferred from experimental data are basis dependent as well. We illustrate this point by estimating the value of \ensuremathζ\ensuremath{\zeta}\ensuremathζ for the two bases KL,KS{{K}_{L}{,K}_{S}}KL​,KS​ and K0,K0{{K}^{0},{K}^{0}}K0,K0 with the help of recent data of the CPLEAR experiment.
Considering semileptonic decays of the entangled B0B0{B}^{0}{B}^{0}B0B0 state which is generated in the decay of $\ensuremath{\Upsilon}(4S),$ we simply multiply the quantum-mechanical interference term by a factor $(1\ensuremath{-}\ensuremath{\zeta})$ and use the ``decoherence parameter'' \ensuremath{\zeta} as a measure for deviations from quantum mechanics. We investigate several consequences of this modification of semileptonic B0B0{B}^{0}{B}^{0}B0B0 decays. In particular, we show that when confronted with the experimental values of the ratio R=(no. like-sign dilepton events)/(no. opposite-sign dilepton events) and of the ${B}_{H}\ensuremath{-}{B}_{L}$ mass difference, the ensuing one standard deviation range of the decoherence parameter depends strongly on the basis in the B0−−B0{B}^{0}--{B}^{0}B0−−B0 space used to build the entangled B0B0{B}^{0}{B}^{0}B0B0 state. On the other hand, in quantum mechanics physical quantities are, of course, independent of such arbitrary basis choices.
Much of the discussion of decoherence has been in terms of a particle moving in one dimension that is placed in an initial superposition state (a Schrödinger "cat" state) corresponding to two widely separated wave packets. Decoherence refers to the destruction of the interference term in the quantum probability function. Here, we stress that a quantitative measure of decoherence depends not only on the specific system being studied but also on whether one is considering coordinate, momentum or phase space. We show that this is best illustrated by considering Wigner phase space where the measure is again different. Analytic results for the time development of the Wigner distribution function for a two-Gaussian Schrodinger "cat" state have been obtained in the high-temperature limit (where decoherence can occur even for negligible dissipation) which facilitates a simple demonstration of our remarks.
We show that there is essentially only one way to construct a stochastic Schr\"odinger equation that gives a dynamical account of the transformation of entangled into factorized states and is consistent with both quantum mechanics and required symmetries. The noisy, nonlinear term is a unimodular scalar multiple of the time-reversal operator that must be present whenever a Hamiltonian term in the Schr\"odinger equation can distinguish the factorized constituents of an entangled state. The dynamical mechanism involved in the transformation of entangled into factorized states provides an explanation for the fact that Einstein-Podolsky-Rosen correlations appear in a time determined by the response of the measuring device and independent of the distance between the particles. The dependence on the response time of the measuring device may be testable through a delay in observing the collapse of mesoscopic ``Schr\"odinger cat'' states in ion traps. It is further shown that there are situations where a two-particle interaction can induce a nonlinear term by virtue of coupling to decay modes that distinguish factorized constituents of an entangled state. We show that this should happen in the neutral KKK-meson system where the entangled KL{K}_{L}KL​ state is pushed slightly in the direction of a factorized constituent (K0{(K}_{0}(K0​ or K0‾)\overline{{K}_{0}})K0​​) as a consequence of the fact that these can be distinguished via the sign of the charged lepton in a semileptonic decay mode. The result is a CP\mathrm{CP}CP violation that is within 20% of the experimental value.
First a generalized Bell-inequality for different times and for different quasi-spin states is developed. We focus on special quasi-spin eigenstates and times. The inequality based on a local realistic theory is violated by the CP-violating parameter, if the quantum theory is used to recalculate the probabilities. Next the quantum mechanical probabilities are modified by the decoherence approach which enables the initial state to factorize spontaneously. In this way we get a lower limit for the decoherence parameter ζ, which measures the degree of decoherence. This result is compared with the experimental value of the decoherence parameter ζdeduced from the data of the CPLEAR-experiment.
We show that it is possible to explain the quantum measurement process within the framework of quantum mechanics without any additional postulates. The key concept of the theory is decoherence, which appears as an inherent characteristic of quantum mechanics and results from the uncertainty relation. In contrast to environment-induced decoherence, this decoherence exists prior to a measurement being made. To clarify our idea, we examine three elemental experiments: a Stern-Gerlach-like experiment, the Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) experiment, and the double-slit experiment. By considering the first experiment, we explain how the uncertainty relation between position and momentum introduces decoherence prior to measurement. Consideration of the EPR-Bohm experiment leads us to conclude that the correlation of the EPR pair is not a consequence of what is known as the collapse of the wave function. Our theory of decoherence can also be applied to experiments with continuous eigenvalues, such as the double-slit experiment. Consideration of the double-slit experiment leads us to understand how pure quantum mechanics describes the fact that quanta behave as interfering particles.
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.