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Demonstration of K0K0, B0B0, and D0D0 Transitions with a Pair of Coupled Pendula

Klaus R. Schubert, Jürgen Stiewe

Published Aug 16, 2016• 0 citations
OpenAlex

Abstract

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.

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with a Pair of Coupled Pendula

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•Jan 1, 2011•0 citations

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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.

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Tabletop time-reversal violation

Jonathan L. Rosner

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arXiv:hep-ph/9508298•American Journal of Physics•Aug 1, 1996•18 citations
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.
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.
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.