Abstract
We extend the constructions of previous papers, showing the equivalence of quantum mechanics and a classical probability formalism with constraints assuring differentiable probability densities without contradictions, to show that these constructions also yield Maxwell's equations and the Lorentz force. These constructions have already yielded Schroedinger's equation for a charged particle in an electromagnetic field, but here it is shown that this statistical construction provides the basis for gauge conditions and defines a specific gauge for this non-relativistic formalism. These constructions also provide new insight into the relationship of Schroedinger quantum mechanics and a classical diffusion process.
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References
Collins, R. Eugene, “Quantum theory: A Hilbert space formalism for probability theory,”Found. Phys. 7 (7/8) (1977).
Collins, R. Eugene, “The mathematical basis of quantum mechanics,”Lett. Nuovo Cimento 18 (18) (1977).
Collins, R. Eugene, “The mathematical basis of quantum mechanics, II,”Lett. Nuovo Cimento 25 (15) (1979).
Collins, R.E., and J.R. Fanchi, “Relativistic quantum mechanics: A space-time formalism for spin-zero particles,”Nuovo Cimento 48A (3) (1978).
Fanchi, J.R., and R.E. Collins, “Quantum mechanics of relativistic spinless particles,”Found. Phys. 8 (11/12) (1978).
Collins, R. Eugene, “On non-electromagnetic interactions in quantum mechanics,” unpublished (1980).
Collins, R. Eugene, “On some features of differentiable probabilities: A new viewpoint in physics,”J. Math Phys. 34 (7) (1993).
Fanchi, J.R.,Parametrized Relativistic Quantum Theory (Kluwer Academic, Netherlands, 1993)
Collins, R. Eugene,“Quantum mchanics as a classical diffusion process,”Found. Phys. Lett. 5 (1) (1992).
Nelson, Edward,Quantum Fluctuations (Princeton University Press, Princeton, 1985).
Collins. R. Eugene, “The mathematical basis of physical laws: Relativistic mechanics, quantum mechanics, the Lorentz force, Maxwell's equations, and non-electromagnetic forces for spin-zero particles,”Found. Phys., to be published.
Feller, W.,An Introduction to Probability Theory and its Applications, Vol. II (Wiley, New York, 1966); see p. 321.
Riesz, F. and B. Sz-Nagy,Functional Analysis, translated by L.F. Boron Ungar, New York, 1955). Also see T.F. Jordan,Linear Operators for Quantum Mechanics (John Wiley, New York, 1969), p. 10.
Stone, M.H.,Linear Transformations in Hilbert Space (American Mathematical Society, New York 1932). Also see T.F. Jordan,ibid., p. 52.
Bohm, David,Causality and Chance in Modern Physics (Routledge & Kegan Paul, London, 1958).
Amiet, J.P. and P. Huguenin,Helv. Phys. Act. 52 (621) (1980).
Jauch, J.M.,Foundations of Quantum Mechanics (Addison-Wesley, Reading, Mass. 1968), pp. 235 - 239.
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Collins, R.E. Statistical basis for physical laws; non-relativistic theory. Found Phys Lett 6, 429–449 (1993). https://doi.org/10.1007/BF00682791
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DOI: https://doi.org/10.1007/BF00682791