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arXiv:hep-ph/0201064 · CPT and Lorentz Symmetry

CLASSICAL ANALOGUE MODELS FOR T AND CPT VIOLATION

Ágnes Roberts

Published Feb 1, 2002• 1 citation
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Abstract

Classical-mechanical oscillating systems are analyzed to model CP violating neutral kaon oscillations. Through the identification of the key features of the quantum effective hamiltonian we search for similarities in the characteristic matrix of the classical systems. Some no-go results are found for undamped systems and for systems using two one-dimensional coupled oscillators. A model is presented emulating both T and spontaneous CPT violation.

DOI
10.1142/9789812778123_0041

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Classical-mechanical oscillating systems are analyzed to model CP violating neutral kaon oscillations. Through the identification of the key features of the quantum effective hamiltonian we search for similarities in the characteristic matrix of the classical systems. Some no-go results are found for undamped systems and for systems using two one-dimensional coupled oscillators. A model is presented emulating both T and spontaneous CPT violation.
Analogue models for CP\mathrm{CP}CP violation in neutral-meson systems are studied in a general framework. No-go results are obtained for models in classical mechanics that are nondissipative or that involve one-dimensional oscillators. A complete emulation is shown to be possible for a two-dimensional oscillator with rheonomic constraints, and an explicit example with spontaneous T and CPT\mathrm{CPT}CPT violation is presented. The results have implications for analogue models with electrical circuits.
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.
The neutral kaon system offers a unique possibility to perform fundamental tests of CPT invariance, as well as of the basic principles of quantum mechanics. The most recent limits on several kinds of possible CPT violation and decoherence mechanisms, which in some cases might be justified in a quantum gravity framework, are reviewed, including the latest results obtained by the KLOE experiment at the DAΦNE e + e - collider. No deviation from the expectations of quantum mechanics and CPT symmetry is observed, while the precision of the measurements, in some cases, reaches the interesting Planck scale region.
Neutral kaons provide one of the most sensitive systems to test quantum mechanics and CPT violation.In the first part of this report I review the results on CPT violation searches in the kaon system from the CPLEAR, KLOE and KTeV experiments.In the second part, I report tests of quantum coherence related to CPT violation, performed at CPLEAR and KLOE by studying the time evolution of the kaon system.The results show no deviations from the expectations of quantum mechanics and CPT symmetry, and the accuracy reaches the interesting region of the Planck's scale.
The equivalence between the Schrödinger dynamics of a quantum system with a finite number of basis states and a classical dynamics is realized in terms of electric networks. The isomorphism that connects in a univocal way both dynamical systems was applied to the case of neutral mesons, kaons in particular, and the class of electric networks univocally related to the quantum system was analysed. Moreover, under CPT invariance, the relevant ϵ parameter that measures CP violation in the kaon system is reinterpreted in terms of network parameters. All these results were explicitly shown by means of both a numerical simulation of the implied networks and by constructing the corresponding circuits.