Abstract
It is shown that the existing formulations of stochastic mechanics are not equivalent to the Schrödinger equation, as had previously been believed. It is argued that this is a reflection of fundamental inadequacies in the physical foundations of stochastic mechanics.
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References
Edward Nelson, “Derivation of the Schrödinger equation from Newtonian mechanics,”Phys. Rev. 150, 1079–1085 (1966).
Mark Davidson, “A generalization of the Fényes-Nelson stochastic model of quantum mechanics,”Lett. Math. Phys. 3, 271–277 (1979).
Kunio Yasue, “Stochastic calculus of variations,”J. Funct. Anal.,41, 327–340 (1981).
Francesco Guerra and Laura M. Morato, “Quantization of dynamical systems and stochastic control theory,”Phys. Rev. D 27, 1774–1786 (1983).
Laura M. Morato, “Path-wise stochastic calculus of variations with the classical action and quantum systems,”Phys. Rev. D 32, 1982–1987 (1985).
Rossana Marra, “Variational principles for conservative and dissipative diffusions,”Phys. Rev. D 36, 1724–1730 (1987).
John D. Lafferty, “The density manifold and configuration space quantization,”Trans. Am. Math. Soc. 633, 699–741 (1988).
Eric A. Carlen, “Conservative diffusions,”Commun. Math. Phys. 94, 293–315 (1984).
Imre Fényes, “Eine wahrscheinlichkeitstheoretische Begründung und Interpretation der Quantenmechanik,”Z. Phys. 132, 81–106 (1952).
Edward Nelson,Dynamical Theories of Brownian Motion (Princeton University Press, Princeton, 1967).
Sergio Albeverrio and Raphael Høegh-Krohn, “A remark on the connection between stochastic mechanics and the heat equation,”J. Math. Phys. 15, 1745–1747 (1974).
Sheldon Goldstein, “Stochastic mechanics and quantum theory,”J. Stat. Phys. 47(5/6), 645–667 (1987); see especially the discussion of the Aharonov-Bohm effect, §10.1.
Edward Nelson, “Stochastic mechanics and random fields,” to appear.
Edward Nelson,Quantum Fluctuations (Princeton University Press, Princeton, NJ, 1985).
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Some relatively minor difficulties with the demonstration of equivalence are already known for the special case in which the nodal surface separates the manifold of the diffusion into disjoint components.(1,11) The problems described in this paper are much more general and quite unrelated.
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Wallstrom, T.C. On the derivation of the Schrödinger equation from stochastic mechanics. Found Phys Lett 2, 113–126 (1989). https://doi.org/10.1007/BF00696108
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DOI: https://doi.org/10.1007/BF00696108