Quantum Future Abstracts

**QF ABSTACTS**
[blaja95d]: Events and Piecewise Deterministic Dynamics in Event Enhanced Quantum Theory
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.
[blaja95c]:
Event generating algorithm corresponding to a linear master equation of Lindblad's type is described and illustrated on two examples: that of a particle detector and of a fuzzy clock. Relation to other approaches to the foundations of quantum theory and to the description of quantum measurements is briefly discussed
[blaja95b]:
We review what we call event-enhanced formalism of 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 first time, a unique algorithm that can be used for computer generation of experimental runs with individual quantum objects.
[blaja95a]:
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 are 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.
[blaja94c]:
The standard formalism of quantum theory is enhanced to allow for a definite meaning to the concepts of measurement and events. Within this approach one obtains not only Liouville equation that describes statistical ensembles but also a piecewise deterministic Markov process that can be used for a computer simulation of real time series of experiments on single quantum objects. Events follow laws of probabilities but probabilities obey a causal law. A generalized cloud chamber model is discussed. The classical events account for particle tracks while the quantum jumps are shown to be identical to the spontaneous localization model of Ghirardi, Rimini and Weber. Moreover we show that the Born's postulate is automatically satisfied. Bohm's version of the EPR experiment is also discussed within the enhanced
[blaja94b]:
Model interactions between classical and quantum systems are briefly reviewed. These include: general measurement - like couplings, Stern-Gerlach experiment, model of a counter, quantum Zeno effect, piecewise deterministic Markov processes and meaning of the wave function.
[jad94c]:
We propose a precise meaning to the concepts of experiment, measurement, and event, in the event-enhanced formalism of quantum theory. A minimal piecewise deterministic process is given that can be used for a computer simulation of real time series of experiments on single quantum objects. As an example a generalized cloud chamber is described, including multiparticle case. Relation to the GRW spontaneous localization model is discussed.
[jad94b]:
The law of track formation in cloud chambers is derived from the Liouville equation with a simple Lindblad's type generator that describes coupling between a quantum particle and a classical, continuous, medium of two--state detectors. Piecewise deterministic random process (PDP) corresponding to the Liouville equation is derived. The process consists of pairs (classical event, quantum jump), interspersed with random periods of continuous (in general, non--linear) Schroedinger's--type evolution. The classical events are flips of the detectors -- they account for tracks. Quantum jumps are shown, in the simplest, homogeneous case, to be identical to those in the early spontaneous localization model of Ghirardi, Rimini and Weber (GRW). The methods and results of the present paper allow for an elementary derivation and numerical simulation of particle track formation and provide an additional perspective on GRW's proposal.
[jad94a]:
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 of how to determine the wave function ?.
[blaja93d]:
Model interactions between classical and quantum systems are briefly discussed. These include: general measurement-like couplings, Stern-Gerlach experiment, model of a counter, quantum Zeno effect, SQUID--tank model
[blaja93b]:
A model interaction between a two-state quantum system and a classical switching device is analysed and shown to lead to the quantum Zeno effect for large values of the coupling costant kappa. A minimal piecewise deterministic random process compatible with the Liouville equation is described, and it is shown that 1/kappa can be interpreted as the jump frequency of the classical device.
[blaja93a]: On interaction between classical and quantum systems
We propose a mathematically consistent model of interaction between classical and quantum systems
[jad90]: Bioelectronics as seen by a theoretical physicist
A subjective view of the author on the present status of theoretical physics and bioelectronics is presented. A believe is expressed that nearly all essential life processes can be explained by a joint effort of mathematics, physics, chemistry and biology in the framework of the actual paradigm. It is also pointed out that, in the author's opinion, in order to explain the phenomenon of life itself as well as that of consciousness, we need a new theory of complex and selforganized systems, and also a new theory uniting quantum matter with information fields. While the first theory is developing rapidly in recent years, the second one needs a radical change in the foundations of quantum theory. One may need to this end to implement Wigner's ideas of nonlinear quantum evolution equations, and to take into account the essential role of light in mediating between classical and quantum universes and in quantum-theoretical description of "events" and "measurements".

Last modified on: June 27, 2005.