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ON THE MEASUREMENT OF TIME CORRELATIONS FOR QUANTUM-MECHANICAL SYSTEMS

M. L. Goldberger, Kenneth Watson

Published Nov 19, 1963• 0 citations
OpenAlex

Abstract

It is cu~tomary in the pedagogica.ldevelopment of quantum mechanics • ...and field theory to mention'the limitations on correlated measurements of observables at different space-time points.Little attention has .•8been given, however, to actual experiments for making such observations, or their usefulness.In this paper and in a subsequent one, we shall •,• discuss both of these subjects from a general point of view and w1 th •.particular applications to scattering processes. :! .This work is an outgrowth from a recent paper on the correlated :1 .counting rate of two detectors recording particles scattered from a 1 . .

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Particle Decays

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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

Cambridge University Press eBooks•Jul 13, 2023•1 citation

Particle Decays

George Jaroszkiewicz

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).

Cambridge University Press eBooks•Nov 28, 2017•0 citations
It is cu~tomary in the pedagogica.ldevelopment of quantum mechanics • ...and field theory to mention'the limitations on correlated measurements of observables at different space-time points.Little attention has .•8been given, however, to actual experiments for making such observations, or their usefulness.In this paper and in a subsequent one, we shall •,• discuss both of these subjects from a general point of view and w1 th •.particular applications to scattering processes. :! .This work is an outgrowth from a recent paper on the correlated :1 .counting rate of two detectors recording particles scattered from a 1 . .
The role played by time in the quantum theory is still mysterious by many aspects. In particular it is not clear today whether the distribution of decay times of unstable particles could be described by a time operator (TO). As we shall discuss, different approaches to this problem (one could say interpretations) can be found in the literature on the subject. As we shall show, it is possible to conceive crucial experiments aimed at distinguishing the different approaches, by measuring with accuracy the statistical distribution of decay times of entangled particles. Such experiments can be realized in principle with entangled kaon pairs.
In recent decades it was established that the quantum measurements of physical quantities in space-time points divided by space-like intervals may be correlated. Though such correlation follows from the formulas of quantum mechanics its physics so far remains unclear and there is a number of different and rather contradictory interpretations. They concern particularly the so-called Einstein-Podolsky-Rosen paradox where the momentary action at a distance together with non-local entangled states is used for the interpretation. We assume that the quantum theory can be formulated as local and look for the consequences of this assumption. Accordingly we try to explain the correlation phenomena in a local way looking for the origin of correlation. To exclude a presupposed correlation of participating quantum particles we consider two independent particle sources and two detectors that are independent as well. We show that the origin of the correlation is the feature that the occupation number of a particle (and other its measurable quantities) is formed by a pair of complex conjugated wave functions with in general arbitrary phases. We consider this point as crucial as it provides interpretation of the observed correlation phenomena that may otherwise look puzzling. We briefly discuss a special type of noise that is typical for the quantum correlation phenomena.
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
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).