The principal intent of this monograph is to present in a systematic and self-con tained fashion the basic tenets, ideas and results of a framework for the consistent unification of relativity and quantum theory based on a quantum concept of spacetime, and incorporating the basic principles of the theory of stochastic spaces in combination with those of Born's reciprocity theory. In this context, by the physicial consistency of the present framework we mean that the advocated approach to relativistic quantum theory relies on a consistent probabilistic interpretation, which is proven to be a direct extrapolation of the conventional interpretation of nonrelativistic quantum mechanics. The central issue here is that we can derive conserved and relativistically convariant probability currents, which are shown to merge into their nonrelativistic counterparts in the nonrelativistic limit, and which at the same time explain the physical and mathe matical reasons behind the basic fact that no probability currents that consistently describe pointlike particle localizability exist in conventional relativistic quantum mechanics. Thus, it is not that we dispense with the concept oflocality, but rather the advanced central thesis is that the classical concept of locality based on point like localizability is inconsistent in the realm of relativistic quantum theory, and should be replaced by a concept of quantum locality based on stochastically formulated systems of covariance and related to the aforementioned currents.

The principal intent of this monograph is to present in a systematic and self-con tained fashion the basic tenets, ideas and results of a framework for the consistent unification of relativity and quantum theory based on a quantum concept of spacetime, and incorporating the basic principles of the theory of stochastic spaces in combination with those of Born's reciprocity theory. In this context, by the physicial consistency of the present framework we mean that the advocated approach to relativistic quantum theory relies on a consistent probabilistic interpretation, which is proven to be a direct extrapolation of the conventional interpretation of nonrelativistic quantum mechanics. The central issue here is that we can derive conserved and relativistically convariant probability currents, which are shown to merge into their nonrelativistic counterparts in the nonrelativistic limit, and which at the same time explain the physical and mathe matical reasons behind the basic fact that no probability currents that consistently describe pointlike particle localizability exist in conventional relativistic quantum mechanics. Thus, it is not that we dispense with the concept oflocality, but rather the advanced central thesis is that the classical concept of locality based on point like localizability is inconsistent in the realm of relativistic quantum theory, and should be replaced by a concept of quantum locality based on stochastically formulated systems of covariance and related to the aforementioned currents.

Offers a new mathematical formulation of quantum theory, clarifies a number of discrepancies within the prior formulation, describes new applications to experiments in physics, and extends the realm of application beyond physics to such fields as signal processing and neuroscience. The approach is based on new extensions of the theory of group representations, which are developed and illustrated in the text, and connects quantum theory with quantum logic, philosophy, and the history of science. Assumes a knowledge of basic topology and analysis, some modern abstract algebra, and at least rudimentary quantum mechanics. Annotation copyright by Book News, Inc., Portland, OR

Quantum theory is one of the most fascinating and successful constructs in the intellectual history of mankind. Nonetheless, the theory has very shaky philosophical foundations. This book contains thoughtful discussions by eminent researchers of a spate of experimental techniques newly developed to test some of the stranger predictions of quantum physics. The advances considered include recent experiments in quantum optics, electron and ion interferometry, photon down conversion in nonlinear crystals, single trapped ions interacting with laser beams, atom-field coupling in micromaser cavities, quantum computation, quantum cryptography, decoherence and macroscopic quantum effects, the quantum state diffusion model, quantum gravity, the quantum mechanics of cosmology and quantum non-locality along with the continuing debate surrounding the interpretation of quantum mechanics. Audience: The book is intended for physicists, philosophers of science, mathematicians, graduate students and those interested in the foundations of quantum theory.

Proceedings of the August 1995 symposium, held in honor of Professor Jean-Pierre Vigier. Fifty papers address ideas about the nature of light and photons, electrodynamics, the formulation and interpretation of quantum mechanics, and aspects of relativity theory. Some deal with alternative interpretations of quantum phenomena in the tradition of Vigier and Bohm. As stressed by Vigier at the symposium, the current experimental situation now allows for individual quantum events to be studied using parametric down converters, meaning that experimental challenges to the orthodox interpretation may actually be realized. Annotation copyrighted by Book News, Inc., Portland, OR