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Quantum Mechanics in Space and Time

Received: 1 August 2015     Accepted: 17 August 2015     Published: 29 August 2015
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Abstract

The possibility that quantum mechanics is foundationally the same as classical theories in explaining phenomena in space and time is postulated. Such a view is motivated by interpreting the experimental violation of Bell inequalities as resulting from questions of geometry and algebraic representation of variables, and thereby the structure of space, rather than realism or locality. While time remains Euclidean in the proposed new structure, space is described by Projective geometry. A dual geometry facilitates description of a physically real quantum particle trajectory. Implications for the physical basis of Bohmian mechanics is briefly examined, and found that the hidden variables pilot-wave model is local. Conceptually, the consequence of this proposal is that quantum mechanics has common ground with relativity as ultimately geometrical. This permits the derivation of physically meaningful quantum Lorentz transformations. Departure from classical notions of measurability is discussed.

Published in American Journal of Modern Physics (Volume 4, Issue 5)
DOI 10.11648/j.ajmp.20150405.12
Page(s) 221-231
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Bell Inequalities, Non-Metric Space, Projective Geometry, Bohmian Mechanics, Quantum Lorentz Transformations, Measurability

References
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    Fosco Ruzzene. (2015). Quantum Mechanics in Space and Time. American Journal of Modern Physics, 4(5), 221-231. https://doi.org/10.11648/j.ajmp.20150405.12

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    Fosco Ruzzene. Quantum Mechanics in Space and Time. Am. J. Mod. Phys. 2015, 4(5), 221-231. doi: 10.11648/j.ajmp.20150405.12

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  • @article{10.11648/j.ajmp.20150405.12,
      author = {Fosco Ruzzene},
      title = {Quantum Mechanics in Space and Time},
      journal = {American Journal of Modern Physics},
      volume = {4},
      number = {5},
      pages = {221-231},
      doi = {10.11648/j.ajmp.20150405.12},
      url = {https://doi.org/10.11648/j.ajmp.20150405.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20150405.12},
      abstract = {The possibility that quantum mechanics is foundationally the same as classical theories in explaining phenomena in space and time is postulated. Such a view is motivated by interpreting the experimental violation of Bell inequalities as resulting from questions of geometry and algebraic representation of variables, and thereby the structure of space, rather than realism or locality. While time remains Euclidean in the proposed new structure, space is described by Projective geometry. A dual geometry facilitates description of a physically real quantum particle trajectory. Implications for the physical basis of Bohmian mechanics is briefly examined, and found that the hidden variables pilot-wave model is local. Conceptually, the consequence of this proposal is that quantum mechanics has common ground with relativity as ultimately geometrical. This permits the derivation of physically meaningful quantum Lorentz transformations. Departure from classical notions of measurability is discussed.},
     year = {2015}
    }
    

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Author Information
  • Department of Econometrics and Business Statistics, Monash University (Retired), Caulfield East, Australia

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