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 |
Bell Inequalities, Non-Metric Space, Projective Geometry, Bohmian Mechanics, Quantum Lorentz Transformations, Measurability
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APA Style
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
ACS Style
Fosco Ruzzene. Quantum Mechanics in Space and Time. Am. J. Mod. Phys. 2015, 4(5), 221-231. doi: 10.11648/j.ajmp.20150405.12
AMA Style
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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Download@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}
}
TY - JOUR T1 - Quantum Mechanics in Space and Time AU - Fosco Ruzzene Y1 - 2015/08/29 PY - 2015 N1 - https://doi.org/10.11648/j.ajmp.20150405.12 DO - 10.11648/j.ajmp.20150405.12 T2 - American Journal of Modern Physics JF - American Journal of Modern Physics JO - American Journal of Modern Physics SP - 221 EP - 231 PB - Science Publishing Group SN - 2326-8891 UR - https://doi.org/10.11648/j.ajmp.20150405.12 AB - 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. VL - 4 IS - 5 ER -
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