Summary
The mathematical formalism of the «pilot wave» theory may be arrived at by adding specific assumptions, intended to overcome the fundamental problems of Everett’s theory. A Madelung fluid of possible configurations in 3N-space is suggested as a useful way of visualizing the relation between these two «noncollapse» versions of quantum mechanics.
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References
J. S. Bell:The measurement theory of Everett and de Broglie’s pilot wave, inQuantum Mechanics, Determinism, Causality and Particles, edited byM. Flato et al. (Reidel, Dordrecht, 1976), p. 11.
J. S. Bell:Quantum mechanics for cosmologists, inQuantum Gravity 2, edited byC. J. Isham, R. Penrose andD. Sciama (Clarendon Press, Oxford, 1981), p. 611.
J. S. Bell:Six possible worlds of quantum mechanics, inSpeakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987), p. 181.
H.-D. Zeh:Found. Phys.,18, 723 (1988).
H. Everett III:Rev. Mod. Phys.,29, 454 (1957).
H. Everett III:The theory of the universal wave function, inThe Many-Worlds Interpretation of Quantum Mechanics, edited byB. S. DeWitt andN. Graham (Princeton University Press, Princeton, N. J., 1973), p. 3.
J.-M. Lévy-Leblond:Towards a Proper Quantum Theory, inQuantum Mechanics, a Half Century Later, edited byJ. Leite Lopes andM. Paty (Reidel, Dordrecht, 1977), p. 171.
Y. Ben-Dov:Fundamenta Scientiae,8, 331 (1987).
Y. Ben-Dov:Everett’s Theory and the many-worlds interpretation, to appear inAm. J. Phys. (1990).
L. de Broglie:J. Phys. Rad., Serie VI,8, 225 (1927).
D. Bohm:Phys. Rev.,85, 166, 180 (1952).
J. S. Bell:Found. Phys.,12, 989 (1982).
J. S. Bell:Beables for Quantum Field Theory, inSpeakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987), p. 173.
J. Von Neumann:Mathematische Grundlagen der Quantenmechanik (Springer-Verlag, Berlin, 1932); English Translation:Mathematical Foundation of Quantum Mechanics (Princeton University Press, Princeton, N. J., 1955).
B. D’Espagnat:Conceptual Foundations of Quantum Mechanics (Benjamin, Ca., 1971).
L. E. Ballentine:Found. Phys.,3, 229 (1973).
L. N. Cooper:Wavefunction and observer in the quantum theory, inThe Physicist’s Conception of Nature, edited byJ. Mehra (Reidel, Dordrecht, 1973), p. 668.
B. S. DeWitt:Phys. Today,23, 30 (1970).
D. Deutsch:Int. J. Theor. Phys.,24, 1 (1985).
H. P. Stapp:Found. Phys.,10, 767 (1980).
E. J. Squires:Eur. J. Phys.,8, 171 (1987).
H.-D. Zeh:Found. Phys.,3, 109 (1973).
D. Bohm andJ. P. Vigier:Phys. Rev.,96, 208 (1954).
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Ben-Dov, Y. Everett’s theory and the «pilot wave». Nuov Cim B 105, 1255–1262 (1990). https://doi.org/10.1007/BF02828978
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DOI: https://doi.org/10.1007/BF02828978