The alternative pilot-wave
theory of quantum phenomena—associated especially with Louis de Broglie, David Bohm, and John Bell—reproduces the statistical predictions of ordinary quantum mechanics but without recourse to special ad hoc axioms pertaining to measurement. That (and how) it does so is relatively straightforward to understand in the case of position measurements and, more generally, measurements, whose outcome is ultimately registered by the position of a pointer. Despite a widespread belief to the contrary among physicists, the theory can also account successfully for phenomena involving spin. The main goal of this paper is to explain how the pilot-wave theory's account of spin works. Along the way, we provide illuminating comparisons between the orthodox and pilot-wave accounts of spin and address some puzzles about how the pilot-wave theory relates to the important theorems of Kochen and Specker and Bell.
Thanks to George Greenstein for organizing the wonderful series of meetings at which I had the opportunity to first try out some of this material on a live audience. Philip Pearle, John Townsend, Roderich Tumulka, and two anonymous referees provided helpful comments on an earlier draft.
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And later: “ Since every electron constitutes a magnetic dipole (picture it, if you wish, as a tiny spinning sphere of charge), you might expect paramagnetism to be a universal phenomenon.” Interestingly, Griffiths is more carefully orthodox about spin in his Introduction to Quantum Mechanics, 2nd ed. (Pearson Prentice Hall, Upper Saddle River, NJ, 2004). Google Scholar
- 33. In this respect it is somewhat telling that the worst offenses against the official orthodox view tend to occur in figures and illustrations. Almost all quantum mechanics textbooks, for example, include diagrams depicting the precession, induced by the presence of a magnetic field, of a particle's spin vector about some axis. Townsend's text (Ref. 3131. J. S. Townsend, A Modern Approach to Quantum Mechanics, 2nd ed. (University Science Books, Mill Valley, CA, 2012). All quotes are from Chaps. 3 and 4. ) avoids that particular misleading suggestion of a classical picture. But his front cover art—depicting a Stern-Gerlach spin measurement much like our Fig. 1—includes little circles with arrows (pointing, respectively, up and down) in the downstream sub-beams. The circles are even yellow, inviting us to recall Bell's warning, quoted earlier in Ref. 2626. The authors of Ref. 25 describe themselves as following Bell in concluding that, for the pilot-wave theory, “spin is not real.” Bell, for example, writes (in the first essay of Ref. 10): “We have here a picture in which although the wave has two components, the particle has only position. The particle does not ‘spin,’ although the experimental phenomena associated with spin are reproduced. Thus the picture resulting from a hidden-variable account of quantum mechanics need not very much resemble the traditional classical picture that the researcher may, secretly, have been keeping in mind. The electron need not turn out to be a small spinning yellow sphere.” Gestures in the direction of this same point were made even earlier by M. Renninger, “ Zum Wellen-Korpuskel-Dualismus,” Z. Phys. 136, 251–261 (1953), https://doi.org/10.1007/BF01325679 translated by W. De Baere as “ On Wave-Particle Duality,” <http://arxiv.org/abs/physics/0504043>; and still earlier by Lorentz, who discussed in 1922 a pilot-wave theory of photons, previously suggested by Einstein; see H. A. Lorentz, Problems of Modern Physics (Dover, New York, 1967), p. 157. note.
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