Abstract
A local interpretation of quantum mechanics is presented. Its main ingredients are: first, a label attached to one of the “virtual” paths in the path integral formalism, determining the output for measurement of position or momentum; second, a mathematical model for spin states, equivalent to the path integral formalism for point particles in space time, with the corresponding label. The mathematical machinery of orthodox quantum mechanics is maintained, in particular amplitudes of probability and Born’s rule; therefore, Bell’s type inequalities theorems do not apply. It is shown that statistical correlations for pairs of particles with entangled spins have a description completely equivalent to the two slit experiment, that is, interference (wave like behaviour) instead of non locality gives account of the process. The interpretation is grounded in the experimental evidence of a point like character of electrons, and in the hypothetical existence of a wave like, the de Broglie, companion system. A correspondence between the extended Hilbert spaces of hidden physical states and the orthodox quantum mechanical Hilbert space shows the mathematical equivalence of both theories. Paradoxical behaviour with respect to the action reaction principle is analysed, and an experimental set up, modified two slit experiment, proposed to look for the companion system.
Similar content being viewed by others
Notes
Of course, when we look we disturb the state of the system. The point is if its corpuscular character is preserved or not.
In [34] the Wigner function is interpreted (and measured) as a difference of probabilities.
References
Born, M.: On the quantum mechanics of collisions. Z. Phys. 37, 863–867 (1926)
Heisenberg, W.: The Physical Principles of the Quantum Theory. University of Chicago Press, Chicago (1930)
von Newmann, J.: Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton (1955)
Feynman, R.P., Hibbs, A.R.: Quantum Mechanics and Path Integrals. McGraw–Hill, New York (1965)
Einstein, A.: Physics and reality. J. Franklin Inst. 221, 349–382 (1936)
Bohm, D.: A suggested interpretation of the quantum theory in terms of “Hidden” variables. I and II. Phys. Rev. 85, 166–192 (1952)
Everett, H.: “Relative State” formulation of quantum mechanics. Rev. Mod. Phys. 29, 454–462 (1957)
Bunge, M. (ed.): Quantum Theory and Reality. Springer, Berlin (1967)
Hartle, J.B.: Quantum mechanics of individual systems. Am. J. Phys. 36(8), 704–712 (1968)
Ballentine, L.E.: The statistical interpretation of quantum mechanics. Rev. Mod. Phys. 42, 380–385 (1970)
d’Espagnat, B.: Conceptual Foundations of Quantum Mechanics, 2nd edn, Addison Wesley, New York, ISBN 0-8133-4087-X (1976)
Gell-Mann, M.: The Nature of the Physical Universe: The (1976) Nobel Conference, p. 29. Wiley, New York (1979)
Wheller, J.A., Zurek, W.H. (eds.): Quantum Theory and Measurement. Princeton University Press, Princeton (1983)
Ballentine, L.E.: In: Roth, L.M., Inomata, A. (eds.) Fundamental Questions in Quantum Physics, pp. 65–75. Gordon and Breach, New York (1986)
Home, D., Whitaker, M.A.B.: The ensemble interpretation and context-dependence in quantum systems. Phys. Lett. A 115, 81–83 (1986)
Gibbons, P.: Particles and Paradoxes: The Limits of Quantum Logic. Cambridge University Press, Cambridge (1987)
Bell, J.S.: Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy, 2nd edn. Cambridge University Press, Cambridge (2004) ISBN 9780521523387
Penrose, R.: The Emperor’s New Mind. Oxford University Press, Oxford (1989) ISBN 0-19-851973-7
Omnes, R.: The Interpretation of Quantum Mechanics. Princeton University Press, Princeton (1994) ISBN 9780691036694
Pavon, M.: Stochastic mechanics and the Feynman integral. J. Math. Phys. 41, 6060–6078 (2000)
Belifante, J.: A Survey of Hidden Variables Theories. Pergamon, Oxford (1973)
Ballentine, L.E.: Foundations of quantum mechanics since the Bell inequalities. Am. J. Phys. 55, 785–792 (1987)
Bell, J.S.: In: Miller, A.I. (ed.) Sixty-two Years of Uncertainty, pp. 17–31. Plenum press, New York (1990)
Home, D., Whitaker, M.A.B.: Ensemble interpretations of quantum mechanics: a modern perspective. Phys. Rep. 210(4), 223–317 (1992)
Cabello, A.: Bibliographic guide to the foundations of quantum mechanics and quantum information. arXiv:quant-ph/0012089 (2004)
Bell, J.S.: On the Einstein Podolsky Rosen paradox. Physics 1(3), 195–200 (1964)
Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880–883 (1969)
Greenberger, D.M., Horne, M.A., Shimony, A., Zeilinger, A.: Bells theorem without inequalities. Am. J. Phys. 58(12), 1131–1142 (1990)
Mermin, N.D.: Hidden variables and the two theorems of John Bell. Rev. Mod. Phys. 65(3), 803–816 (1993)
Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935)
Aspect, A., Grangier, P., Roger, G.: Experimental test of bell’s inequalities using time-varying analyzers. Phys. Rev. Lett. 49(25), 1804–1807 (1982)
Popper, K.: In: Korner, Price, (eds.) Thepo Propensity Interpretation of the Calculus of Probability and of the Quantum Theory: Observations and interpretations, pp. 65–70. Butters Worth Scientific Publications, New York (1957)
Lopez, C.:Vacuum, S3: International Workshop on Symmetries, Special functions and Superintegrability (Meeting to Honour Professor Mariano del Olmo in his 60th Birthday), Valladolid (Spain), July 10–11, 2014
Banaszek, K., Radzewicz, C., Wodkiewicz, K., Krasinski, J.S.: Direct measurement of the Wigner function by photon counting. Phys. Rev. A 60, 674–677 (1999)
Wigner, E.P.: On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40, 749–759 (1932)
Groenewold, H.J.: On the principles of elementary quantum mechanics. Physica 12(7), 405–460 (1946)
Moyal, J.E.: Quantum mechanics as a statistical theory. Proc. Camb. Philos. Soc. 45(01), 99–124 (1949)
Braffort, P., Spighel, M., Tzara, C.: Quelques consequences de la theorie de l’action a distance en electrodynamique classique. C. R. Acad. Sci., Paris. 239, 157–160, 925 (1954)
Sokolov, A.A., Tumanov, V.: The uncertainty relation and fluctuation theory. Sov. Phys.- JETP 3(6), 958–959 (1956)
de Broglie, L.: Interpretation of quantum mechanics by the double solution theory. Ann. Fond. Louis Broglie 12(4), 1–23 (1987)
Nelson, E.: Derivation of the Schroedinger Equation from Newtonian Mechanics. Phys. Rev. 150, 1079–1085 (1966)
Grossing, G.: Sub-quantum thermodynamics as a basis of emergent quantum mechanics. Entropy 12(9), 1975–2044 (2010)
V. I. Sbitnev : Physical vacuum is a special superfluid medium. arXiv:1501.06763 (2015)
Bohr, N., Kramers, H.A., Slater, J.C.: The quantum theory of radiation. Philos. Mag. 47, 785–802 (1924)
Acknowledgments
Financial support from research Project MAT2011-22719 is acknowledged.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lopez, C. A Local Interpretation of Quantum Mechanics. Found Phys 46, 484–504 (2016). https://doi.org/10.1007/s10701-015-9976-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-015-9976-4