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EVENTS AND PIECEWISE DETERMINISTIC DYNAMICS IN EVENT-ENHANCED QUANTUM-THEORY

Ph. Blanchard, Arkadiusz Jadczyk

Published Jan 1, 1995• 24 citations
OpenAlex

Abstract

We enhance the standard formalism of quantum theory to enable events. The concepts of experiment and of measurement are defined. Dynamics is given by Liouville's equation that couples quantum system to a classical one. It implies a unique Markov process involving quantum jumps, classical events and describing sample histories of individual systems.

Related papers

EVENT-ENHANCED QUANTUM-THEORY AND PIECEWISE DETERMINISTIC DYNAMICS

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Theory of Events

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We review what we call \event-enhanced formalismof quantum theory. In this approach we explicitly assume classical nature of events. Given a quantum system, that is coupled to a classical one by a suitable coupling, classical events are being triggered. The trigerring process is partly random and partly deterministic. Within this new approach one can modelize real experimental events, including pointer readings of measuring devices. Our theory gives, for the rst time, a unique algorithm that can be used for computer generation of experimental runs with individual quantum objects.

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Topics in Quantum Dynamics

Arkadiusz Jadczyk

The paper consists of two parts. In the first part Schroedinger's equation for a charged quantum particle in a Galilei-Newton curved space-time is derived in a fully geometrical way. Gravitational and electromagnetic fields are coded into space metric and space-time connection. The fundamental geometrical object is a quantum connection in a Hermitian line bundle over the 7-dimensional jet space of 3-velocities. The secondary object is the bundle of Hilbert spaces over absolute time. Time appears as a superselection quantity while Shroedinger equation is interpreted as parallel transport in this bundle. In the second part the problem of measurement in quantum theory is discussed as a part of a more general problem of coupling between quantum and classical systems. The standard framework of quantum theory is extended so as to allow for dynamical central observables within dissipative dynamics. It is shown that within this approach one obtains not only Liouville equation that describes statistical ensembles, but also a piecewise-deterministic random process describing sequences of "events" that can be monitored by a continuous observation of the single, coupled classical system. It also describes "quantum jumps" or "wave packet reductions" that accompany these events. Two example are worked out in some details. The last one deals with the problem oof "how to determine the wave function ?".

arXiv:hep-th/9406204•Jun 30, 1994•19 citations
We enhance the standard formalism of quantum theory to enable events. The concepts of experiment and of measurement are defined. Dynamics is given by Liouville's equation that couples quantum system to a classical one. It implies a unique Markov process involving quantum jumps, classical events and describing sample histories of individual systems.
The standard formalism of quantum theory is enhanced and definite meaning is given to the concepts of experiment, measurement and event. Within this approach one obtains a uniquely defined piecewise deterministic algorithm generating quantum jumps, classical events and histories of single quantum objects. The wave-function Monte Carlo method of Quantum Optics is generalized and promoted to the level of a fundamental process generating all the real events in Nature. The already worked out applications include SQUID-tank model and generalized cloud chamber model with GRW spontaneous localization as a particular case. Differences between the present approach and quantum measurement theories based on environment-induced master equations are stressed. Questions: what is classical, what is time, and what observers are addressed. Possible applications of the new approach are suggested, among them connection between the stochastic commutative geometry and Connes' noncommutative formulation of the Standard Model, as well as potential applications to the theory and practice of quantum computers.
Abstract The standard formalism of quantum theory is enhanced and definite meaning is given to the concepts of experiment, measurement and event. Within this approach one obtains a uniquely defined piecewise deterministic algorithm generating quantum jumps, classical events and histories of single quantum objects. The wave‐function Monte Carlo method of Quantum Optics is generalized and promoted to the level of a fundamental process generating all the real events in Nature. The already worked out applications include SQUID‐tank model and generalized cloud chamber model with GRW spontaneous localization as a particular case. Differences between the present approach and quantum measurement theories based on environment‐induced master equations are stressed. Questions: what is classical, what is time, and what observers are addressed. Possible applications of the new approach are suggested, among them connection between the stochastic commutative geometry and Connes' noncommutative formulation of the Standard Model, as well as potential applications to the theory and practice of quantum computers.
We review what we call \event-enhanced formalismof quantum theory. In this approach we explicitly assume classical nature of events. Given a quantum system, that is coupled to a classical one by a suitable coupling, classical events are being triggered. The trigerring process is partly random and partly deterministic. Within this new approach one can modelize real experimental events, including pointer readings of measuring devices. Our theory gives, for the rst time, a unique algorithm that can be used for computer generation of experimental runs with individual quantum objects.
The paper consists of two parts. In the first part Schroedinger's equation for a charged quantum particle in a Galilei-Newton curved space-time is derived in a fully geometrical way. Gravitational and electromagnetic fields are coded into space metric and space-time connection. The fundamental geometrical object is a quantum connection in a Hermitian line bundle over the 7-dimensional jet space of 3-velocities. The secondary object is the bundle of Hilbert spaces over absolute time. Time appears as a superselection quantity while Shroedinger equation is interpreted as parallel transport in this bundle. In the second part the problem of measurement in quantum theory is discussed as a part of a more general problem of coupling between quantum and classical systems. The standard framework of quantum theory is extended so as to allow for dynamical central observables within dissipative dynamics. It is shown that within this approach one obtains not only Liouville equation that describes statistical ensembles, but also a piecewise-deterministic random process describing sequences of "events" that can be monitored by a continuous observation of the single, coupled classical system. It also describes "quantum jumps" or "wave packet reductions" that accompany these events. Two example are worked out in some details. The last one deals with the problem oof "how to determine the wave function ?".