Abstract
Stochastic mechanics may be regarded as both generalizing classical mechanics to processes with intrinsic randomness, as well as providing the sort of detailed description of microscopic events declared impossible under the traditional interpretation of quantum mechanics. It avoids the many conceptual difficulties which arise from the assumption that quantum mechanics, i.e., the wave function, provides a complete description of (microscopic) physical reality. Stochastic mechanics presents a unified treatment of the microscopic and macroscopic domains, in which the process of measurement plays no special physical role and which reduces to Newtonian mechanics in the macroscopic limit.
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References
N. Bohr,Phys. Rev. 48:696 (1935).
B. De Witt and N. Graham, eds.,The Many-Worlds Interpretation of Quantum Mechanics (Princeton University Press, Princeton, New Jersey, 1973).
I. Fényes,Z. Physik 132:81 (1952).
E. Nelson,Phys. Rev. 150:1079 (1966).
E. Nelson,Dynamical Theories of Brownian Motion (Princeton University Press, Princeton, New Jersey, 1967).
E. Nelson,Quantum Fluctuations (Princeton University Press, Princeton, New Jersey, 1985).
E. P. Wigner, Remarks on the mind-body question, inThe Scientist Speculates, I. J. Good, ed. (Basic Books, New York, 1962); repinted in E. P. Wigner,Symmetries and Reflections (Indiana University Press, Bloomington, Indiana, 1967).
E. Schrödinger,Proc. Am. Phil. Soc. 124:323 (1980).
E. P. Wigner,Am. J. Phys. 31:6 (1963).
A. Daneri, A. Loinger, and G. M. Prosperi,Nucl. Phys. 33:297 (1962).
K. Hepp,Helv. Phys. Acta 45:237 (1972).
K. Yasue,J. Funct. Anal. 41:327 (1981).
F. Guerra and L. M. Morato,Phys. Rev. D 27:1774 (1983).
K. Gottfried,Quantum Mechanics I (Benjamin, New York, 1966).
D. S. Shucker,J. Funct. Anal. 38:146 (1980).
A. Einstein, B. Podolsky, and W. Rosen,Phys. Rev. 47:777 (1935).
D. Bohm,Quantum Theory (Prentice-Hall, Englewood Cliffs, New Jersey, 1951).
J. S. Bell,Rev. Mod. Phys. 38:447 (1966).
A. Aspect, J. Dalibard, and G. Roger,Phys. Rev. Lett. 49:1804 (1982).
T. G. Dankel, Jr.,Arch. Rat. Mech. Anal. 37:192 (1970).
Y. Aharanov and D. Bohm,Phys. Rev. 115:485 (1959).
A. Grünbaum,Modern Science and Zeno's Paradoxes (Middletown, Connecticut, 1967).
D. Dürr and S. Goldstein, Stochastic mechanics and macroscopic reality, in preparation.
D. Bohm,Phys. Rev. 85:166 (1952).
D. Bohm,Phys. Rev. 89:458 (1953).
R. Haag, D. Kastler, and E. Trych-Pohlymeyer,Commun. Math. Phys. 38:173 (1974).
M. Aizenman, S. Goldstein, and J. L. Lebowitz,J. Math. Phys. 16:1284 (1975).
F. Guerra and P. Ruggerio,Phys. Rev. Lett. 31:1022 (1973).
A. S. Wightman, Statistical mechanics and ergodic theory—An expository lecture, inStatistical Mechanics at the Turn of the Decade, E. G. D. Cohen, eds. (Marcel Dekker, New York, 1971).
H. Pagels,The Cosmic Code (Simon and Schuster, New York, 1982).
A. Pais,Subtle Is the Lord (Oxford University Press, New York, 1982).
G. F. DeAngelis, A route to stochastic mechanics, inStochastic Processes in Classical and Quantum Systems, S. Albeverio, G. Casati, and D. Merlini, eds.
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Goldstein, S. Stochastic mechanics and quantum theory. J Stat Phys 47, 645–667 (1987). https://doi.org/10.1007/BF01206150
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DOI: https://doi.org/10.1007/BF01206150