Please enter verification code
Confirm
Quantum Mechanics in Space and Time
American Journal of Modern Physics
Volume 4, Issue 5, September 2015, Pages: 221-231
Received: Aug. 1, 2015; Accepted: Aug. 17, 2015; Published: Aug. 29, 2015
Views 4333      Downloads 144
Author
Fosco Ruzzene, Department of Econometrics and Business Statistics, Monash University (Retired), Caulfield East, Australia
Article Tools
Follow on us
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.
Keywords
Bell Inequalities, Non-Metric Space, Projective Geometry, Bohmian Mechanics, Quantum Lorentz Transformations, Measurability
To cite this article
Fosco Ruzzene, Quantum Mechanics in Space and Time, American Journal of Modern Physics. Vol. 4, No. 5, 2015, pp. 221-231. doi: 10.11648/j.ajmp.20150405.12
References
[1]
J. S. Bell, Speaking and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, UK 1987)
[2]
A. Aspect, P. Granger and G. Roger, Phys. Rev. Lett. 49 n. 2, p. 91 (1982)
[3]
T. M. Nieuwenhuizen, Found. Phys. (2011) 41: 580-591
[4]
Travis Norsen, Found. Phys. (2007) 37: 311-339; T. Norsen, American Journal of Physics 79, 1261 (2011)
[5]
H. M. Wiseman, J. Phys. A. Math. Theor. 47 (2014) 424001at http://arXiv.org/abs/1402.0351 (2014) Howard M. Wiseman and Eric G. Cavalcanti, at http://arXiv.org/abs/1503.06413v1 (2015) Travis Norsen International Journal of Quantum Foundations 1: 65 – 84, 2015
[6]
Marek Zukowski, at http://arXiv.org/abs/1501.05640v1 (2015), http://arXiv.org/abs/1501.04618v1 (2015)
[7]
A. Aspect, Nature 438, 745 (2005) Nicolas Gisen, Found. Phys. Vol. 42, no. 1, 80-85 (2010)
[8]
G. Ghirardi, Journal of Physics: Conf. Ser. 174 (2009) 012013
[9]
S. Goldstein, T. Norsen, D. Tausk, N. Zanghi, Scholarpedia, 6 (10): 8378
[10]
M. Ozawa, Phys. Lett. A. 318 (2003) 21; Masanao Ozawa, at http://arXiv.org/abs/1308.3540v1 (2013)
[11]
J. Erhart, S. Sponar, G. Sulyok, G. Badurek, M. Ozawa, and Y. Hasegaw, Nature Physics vol 8, 185 (2012)
[12]
Paul Busch, Pekka Lahti, Reinhard F. Werner, at http://arXiv.org/abs/1312.4392v2 (2014)
[13]
H. M. Wiseman, 2007 New J. Phys. 9, 165 doi:10.1088/1367-2630/9/6/165
[14]
S. Kocsis, B. Braverman, S. Ravets, M. J. Stevens, R. P. Mirin, L. Krister Shalm, A. M. Steinberg, Science, vol 332 1170 (2011)
[15]
J. S. Lundeen, A. M. Steinberg, Phys. Rev. Lett. 102, 020404 (2009)
[16]
Fosco Ruzzene, American Journal of Modern Physics, Vol. 2, No. 6, 2013 pp. 350-356
[17]
David Hilbert, The Foundations of Geometry 2005 eBook 17384
[18]
Gilbert De B. Robibson, The Foundations of Geometry, fourth Edition, University of Toronto Press
[19]
C. R. Wylie, Introduction to Projective Geometry, Dover Publications, Inc. New York
[20]
C. R. Wylie, Foundations of Geometry, Dover Publications, Inc. New York
[21]
Matthew F. Pusey, Jonathan Barrett and Terry Rudolph, Nature Physics, 8, 475 – 478, (2012), doi:10.1038/nphys2309
[22]
Roger Colbeck and Renato Renner, at http://arXiv.org/abs/1111.6597v2, http://arXiv.org/abs/1312.7353v1
[23]
D. Bohm, Physical Review, 85, 166-193 (1952)
[24]
Bohmian Mechanics, Stanford Encyclopedia of Philosophy
[25]
J. S. Bell, Ann. (N. Y.) Acad. Sci. 480, 263 (1986)
[26]
A. M. Cetto, L. La Pena and E. Santos, Phys. Lett. 113A, 304 (1985)
[27]
O. Cohan, Phys. Rev. A. vol. 56. No. 5, 3484 (1997)
[28]
J. Kiukas, R. F. Werner, J. of Math. Phys. vol 51, no. 7, 072105 (2010)
[29]
Abner Shimony, Bell’s Theorem, Stanford Encyclopedia of Philosophy
[30]
M. Revzen, P. A. Mello, A. Mann, L. M. Johansen, Phys. Rev. A. 71 022103 (2005)
[31]
Luigi Maxmilian Caligiuri, Amrit Sorli, American Journal of Modern Physics. Vol. 2, No. 6, 2013, pp. 375-382
[32]
Palash B. Pal, Eur. J. Phys. 24, 315-319 (2003)
[33]
Alon Drory, at http://arXiv.org/abs/1412.4018v1
[34]
James D. Edmonds, Jr. International Journal of Theoretical Physics, vol. 6, no. 3, 205 (1972).
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186