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Translation of Time-Reversal Violation in the Neutral K-Meson System into a Table-Top Mechanical System

Andreas Reiser, Klaus R. Schubert

Published Aug 16, 2016• 13 citations
OpenAlex

Abstract

Weak interactions break time-reversal (T) symmetry in the two-state system of neutral K mesons. We present and discuss a two-state mechanical system, a Foucault-type pendulum on a rotating table, for a full representation of K0 K0bar transitions by the pendulum motions including T violation. The pendulum moves with two different oscillation frequencies and two different magnetic dampings. Its equation of motion is identical with the differential equation for the real part of the CPT-symmetric K-meson wave function. The pendulum is able to represent microscopic CP and T violation with CPT symmetry owing to the macroscopic Coriolis force which breaks the symmetry under reversal-of-motion. Video clips of the pendulum motions are shown as supplementary material.

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Weak interactions break time-reversal (T) symmetry in the two-state system of neutral K mesons. We present and discuss a two-state mechanical system, a Foucault-type pendulum on a rotating table, for a full representation of K0 K0bar transitions by the pendulum motions including T violation. The pendulum moves with two different oscillation frequencies and two different magnetic dampings. Its equation of motion is identical with the differential equation for the real part of the CPT-symmetric K-meson wave function. The pendulum is able to represent microscopic CP and T violation with CPT symmetry owing to the macroscopic Coriolis force which breaks the symmetry under reversal-of-motion. Video clips of the pendulum motions are shown as supplementary material.
Weak interactions break time-reversal (T) symmetry in the two-state system of neutral K mesons. We present and discuss a two-state mechanical system, a Foucault-type pendulum on a rotating table, for a full representation of K0 K0bar transitions by the pendulum motions including T violation. The pendulum moves with two different oscillation frequencies and two different magnetic dampings. Its equation of motion is identical with the differential equation for the real part of the CPT-symmetric K-meson wave function. The pendulum is able to represent microscopic CP and T violation with CPT symmetry owing to the macroscopic Coriolis force which breaks the symmetry under reversal-of-motion. Video clips of the pendulum motions are shown as supplementary material.
A setup of two coupled and damped pendula is used to demonstrate the main features of transitions between the neutral mesons K 0 , D 0 , B 0 and their antiparticles, including CP violation in the K 0 system. The transitions are described by two-state Schrodinger equations. Since the real parts of their solutions obey the same differential equations as the pendula coordinates, the pendulum motions can be used to represent the meson transitions. Video clips of the motions are attached as supplementary material.
A setup of two coupled and damped pendula is used to demonstrate the main features of transitions between the neutral mesons K 0 ,D 0 ,B 0 and their antiparticles, including CP violation in the K 0 system. The transitions are described by two-state Schr¨ odinger equations. Since the real parts of their solutions obey the same differential equations as the pendula coordinates, the pendulum motions can be used to represent the meson transitions. Movie clips of the motions are available as supplementary material.
It is easy to construct classical 2-state systems illustrating the behavior of the short-lived and long-lived neutral KKK mesons in the limit of CP conservation. The emulation of CP violation is more tricky, but is provided by the two-dimensional motion of a Foucault pendulum. Analogies are drawn between the pendulum and observables in neutral kaon decays. An emulation of CP- and CPT-violation using electric circuits is also discussed.
Genuine tests of an asymmetry under T and/or CPT transformations imply the interchange between in-states and out-states. I explain a methodology to perform model-independent separate measurements of the three CP, T and CPT symmetry violations for transitions involving the decay of the neutral meson systems in B- and Φ-factories. It makes use of the quantum-mechanical entanglement only, for which the individual state of each neutral meson is not defined before the decay of its orthogonal partner. The final proof of the independence of the three asymmetries is that no other theoretical ingredient is involved and that the event sample corresponding to each case is different from the other two. The experimental analysis for the measurements of these three asymmetries as function of the time interval Δt > 0 between the first and second decays is discussed, as well as the significance of the expected results. In particular, one may advance a first observation of true, direct, evidence of Time-Reserval-Violation in B-factories by many standard deviations from zero, without any reference to, and independent of, CP-Violation. In some quantum gravity framework the CPT-transformation is ill-defined, so there is a resulting loss of particle-antiparticle identity. This mechanism induces a breaking of the EPR correlation in the entanglement imposed by Bose statistics to the neutral meson system, the so-called ω -effect. I present results and prospects for the ω -parameter in the correlated neutral meson-antimeson states.