Abstract
On Bohm's formulation of quantum mechanics particles always have determinate positions and follow continuous trajectories. Bohm's theory, however, requires a postulate that says that particles are initially distributed in a special way: particles are randomly distributed so that the probability of their positions being represented by a point in any regionR in configuration space is equal to the square of the wave-function integrated overR. If the distribution postulate were false, then the theory would generally fail to make the right statistical predictions. Further, if it were false, then there would at least in principle be situations where a particle would approach an eigenstate of having one position but in fact always be somewhere very different. Indeed, we will see how this might happen even if the distribution postulate were true. This will help to show how loose the connection is between the wave-function and the positions of particles in Bohm's theory and what the precise role of the distribution postulate is. Finally, we will briefly consider two attempts to formulate a version of Bohm's theory without the distribution postulate.
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References
Albert, D. Z.: 1992,Quantum Mechanics and Experience, Harvard University Press, Cambridge, MA.
Bell, J. S.: 1981, ‘Quantum mechanics for cosmologists’, reprinted in Bell, J. S. (1987, pp. 117–38).
Bell, J. S.: 1980, ‘De Broglie-Bohm, delayed-choice double-slit experiment, and density matrix’, reprinted in Bell, J. S. (1987, pp. 111–6).
Bell, J. S.: 1987,Speakable and Unspeakable in Quantum Theory, Cambridge University Press, Cambridge.
Bohm, D.: 1952, ‘A suggested interpretation of the quantum theory in terms of “hidden” variables, I and II’,Physical Review 85, 166–79 and 180–93.
Bohm, D. and Hiley, B. J.: 1993,The Divided Universe: An Ontological Interpretation of Quantum Theory, Routledge, London.
de Broglie, L.: 1930,An Introduction to the Study of Wave Mechanics, E. P. Dutton and Co., New York.
DeWitt, B. S. and Graham, Neill (eds.): 1973,The Many-Worlds Interpretation of Quantum Mechanics, Princeton University Press, Princeton.
Everett, H. III.: 1957, ‘“Relative state” formulation of quantum mechanics’,Reviews of Modern Physics 29, 454–62, reprinted in DeWitt and Graham (eds.) (1973).
Everett, H. III.: 1973, ‘Theory of the universal wave-function’, in DeWitt and Graham (eds.) (1973).
Hartle, J.: 1968, ‘Quantum mechanics of individual systems’,American Journal of Physics 36, 704–12.
von Neumann, J.: 1932,Mathematische Grundlagen der Quantenmechanik, Springer, Berlin; reprinted and translated asMathematical Foundations of Quantum Mechanics, in R. Beyer (trans.) Princeton University Press, Princeton, 1955.
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Barrett, J.A. The distribution postulate in Bohm's theory. Topoi 14, 45–54 (1995). https://doi.org/10.1007/BF00763478
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DOI: https://doi.org/10.1007/BF00763478