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Stochastic Quantum Mechanics and Quantum Spacetime

A Consistent Unification of Relativity and Quantum Theory Based on Stochastic Spaces

  • Book
  • © 1984

Overview

Authors:
  1. Eduard Prugovečki

    1. Department of Mathematics, University of Toronto, Canada

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Part of the book series: Fundamental Theories of Physics (FTPH, volume 4)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xxi
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  2. Stochastic Quantum Mechanics

    1. Front Matter

      Pages 1-1
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    2. Nonrelativistic Stochastic Quantum Mechanics

      • Eduard Prugovečki
      Pages 3-68

    3. Relativistic Stochastic Quantum Mechanics

      • Eduard Prugovečki
      Pages 69-133

    4. Statistical Mechanics on Stochastic Phase Spaces

      • Eduard Prugovečki
      Pages 134-176

  3. Quantum Spacetime

    1. Front Matter

      Pages 177-177
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    2. Reciprocity Theory and the Geometrization of Stochastic Quantum Mechanics

      • Eduard Prugovečki
      Pages 179-213

    3. Field Theory on Quantum Spacetime

      • Eduard Prugovečki
      Pages 214-258

  4. Back Matter

    Pages 259-302
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Keywords

About this book

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.

Reviews

`It is a book which should certainly be included in any library collection on quantum mechanics, and perhaps in the personal libraries of those who are interested in more than standard presentations.' The Australian Physicist (July 1985)

Authors and Affiliations

  • Department of Mathematics, University of Toronto, Canada

    Eduard Prugovečki

Bibliographic Information

  • Book Title: Stochastic Quantum Mechanics and Quantum Spacetime

  • Book Subtitle: A Consistent Unification of Relativity and Quantum Theory Based on Stochastic Spaces

  • Authors: Eduard Prugovečki

  • Series Title: Fundamental Theories of Physics

  • DOI: https://doi.org/10.1007/978-94-009-4492-3

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: D. Reidel Publishing Company, Dordrecht, Holland 1984

  • Hardcover ISBN: 978-90-277-1617-0Due: 31 January 1984

  • Softcover ISBN: 978-94-010-8501-4Published: 06 October 2011

  • eBook ISBN: 978-94-009-4492-3Published: 06 December 2012

  • Series ISSN: 0168-1222

  • Series E-ISSN: 2365-6425

  • Edition Number: 1

  • Number of Pages: 328

  • Topics: Theoretical, Mathematical and Computational Physics

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