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arXiv:quant-ph/0608248

Particle decay processes, the quantum Zeno effect and the continuity of time

George Jaroszkiewicz, Jon Eakins

Published Aug 31, 2006• 1 citation
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Abstract

Signal-state quantum mechanics is used to discuss quantum mechanical particle decay probabilities and the quantum Zeno effect. This approach avoids the assumption of continuous time, conserves total probability and requires neither non-Hermitian Hamiltonians nor the ad-hoc introduction of complex energies. The formalism is applied to single channel decays, the ammonium molecule, and neutral Kaon decay processes.

DOI
10.48550/arxiv.quant-ph/0608248

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Signal-state quantum mechanics is used to discuss quantum mechanical particle decay probabilities and the quantum Zeno effect. This approach avoids the assumption of continuous time, conserves total probability and requires neither non-Hermitian Hamiltonians nor the ad-hoc introduction of complex energies. The formalism is applied to single channel decays, the ammonium molecule, and neutral Kaon decay processes.
Introduction In this chapter we discuss experiments where the run architecture is significantly different from that of standard in-out experiments such as particle scattering. We apply the quantized detector network (QDN) formalism to particle decays, the ammonium molecular system, Kaon-type regeneration decay experiments, and quantum Zeno experiments. In all of these experiments, the problem is the modeling of time, which conventionally is taken to be continuous. In QDN, time is treated in terms of stages, which are discrete.We show how the QDN formalism deals with such experiments. In standard quantum mechanics (QM), time is assumed to be continuous. That is a legacy from classical mechanics (CM), which does not concern itself in general with the processes of observation. CMassumes systems under observation (SUOs) “have” physical properties that are independent of how they are observed. In contrast, QM cannot be considered without a discussion of the processes of observation. On close inspection of any process of observation, as it is actually carried out in the laboratory and not how it is modeled theoretically , the continuity of time does not look quite so obvious. The problem is that there are two mutually exclusive views about the nature of observation in physics. These were discussed in detail by Misra and Sudarshan (MS) in an influential paper on the quantum Zeno effect (Misra and Sudarshan, 1977). On the one hand, no known principle forbids the continuity of time, so the axioms of QM are stated implicitly in terms of continuous time. When the Schrödinger equation is postulated to be one of them (Peres, 1995), temporal continuity is assumed explicitly. On the other hand, it is an empirical fact that no experiment can actually monitor any SUO in a truly continuous way. All references to continuous time measurements are invariably based on statistical modeling of complex processes, with the continuity of time having much the same status as that of temperature. Such effective parameters are extremely useful in physics, but their status as model-dependent, emergent attributes of SUOs, and the apparatus used to observe them, should always be kept in mind. The best that could be done toward simulating temporal continuity in physics would be to perform a sequence of experiments with a carefully prescribed decreasing measurement time scale, such as occurs in experiments investigating the phenomenon known as the quantum Zeno effect (Itano et al., 1990).
Particle Decays IntroductionIn this chapter we discuss experiments where the run architecture is significantly different from that of standard in-out experiments such as particle scattering.We apply the quantized detector network (QDN) formalism to particle decays, the ammonium molecular system, Kaon-type regeneration decay experiments, and quantum Zeno experiments.In all of these experiments, the problem is the modeling of time, which conventionally is taken to be continuous.In QDN, time is treated in terms of stages, which are discrete.We show how the QDN formalism deals with such experiments.In standard quantum mechanics (QM), time is assumed to be continuous.That is a legacy from classical mechanics (CM), which does not concern itself in general with the processes of observation.CM assumes systems under observation (SUOs) "have" physical properties that are independent of how they are observed.In contrast, QM cannot be considered without a discussion of the processes of observation.On close inspection of any process of observation, as it is actually carried out in the laboratory and not how it is modeled theoretically, the continuity of time does not look quite so obvious.The problem is that there are two mutually exclusive views about the nature of observation in physics.These were discussed in detail by Misra and Sudarshan (MS) in an influential paper on the quantum Zeno effect (Misra and Sudarshan, 1977).On the one hand, no known principle forbids the continuity of time, so the axioms of QM are stated implicitly in terms of continuous time.When the Schrödinger equation is postulated to be one of them (Peres, 1995), temporal continuity is assumed explicitly.On the other hand, it is an empirical fact that no experiment can actually monitor any SUO in a truly continuous way.All references to continuous time measurements are invariably based on statistical modeling of complex processes, with the continuity of time having much the same status as that of temperature.Such effective parameters are extremely useful in
Quantum mechanics enables the calculation of the time evolution of a dynamical system provided the Hamiltonian is defined and the initial state is specified. Due to the time reversal invariance, the time evolution of a given initial state at t=0 does not have a time-arrow. These problems have been extensively studied by E. C. G. Sudarshan and collaborators, including myself. Here the survival probability, which is the square of the survival amplitude, is an even function of t. Using the survival amplitude as a common framework, we discuss Zeno effects in several processes: the decay of an unstable particle, pion productions in proton-nucleus collisions and the Aharonov-Vardi effect which is another manifestation of the Zeno effect.