Wednesday, 27 July 2011

de Broglie-Bohm interpretation of quantum theory

I am currently reading more about the de Broglie-Bohm interpretation of quantum theory. Robert A.J. Matthews in Facts versus Factions: The use and abuse of subjectivity in scientific research, writes:
During the 1950s, Pauli together with the charismatic and influential theorist Robert Oppenheimer succeeded in stifling discussion of the de Broglie-Bohm interpretation of quantum theory by a combination of spurious arguments and subjective criticism. After being told that supposedly knock-out arguments against the de Broglie-Bohm interpretation were invalid, Oppenheimer is alleged to have remarked that “Well...we’ll just have to ignore it” (quoted in Matthews 1992 p 146); ironically, Oppenheimer went on to write a book whose central thesis was the need for an open mind in science (Oppenheimer 1955).
The recent paper by Kocsis, et al. (2011) on Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer—highlighted as the secret life of photons revealed in Physics World (see also Catching sight of the elusive wave function)—is most interesting (and not to be confused with Abstruse Goose's The Secret Lives of Photons).

The correspondence between the single-particle two-slit trajectories to those in Philippidis et al. (1979) and Holland and Philippidis (2003) appear to be striking confirmation of the de Broglie-Bohm interpretation of quantum mechanics (even though they are dismissed by Mohrhoff). See also the bio of Basil Hiley in wikipedia.

A brief literature search led me to Dipole Moment Noise in the Hydrogen Atom in the Bohm Quantum-Mechanical Theory by Redington, Widom and Srivastava who write:
In the Bohm theory of quantum mechanics, particles move in well-defined paths. The probability distribution (at a single time) is exactly what would be computed from the Schrödinger equation. Here we consider two-time probabilities in the Bohm theory, and compute dipole moment fluctuation spectra for the hydrogen atom. The resulting dipole fluctuations differ from those which can be obtained from conventional quantum mechanics.
My view of de Broglie-Bohm was that it was “equivalent” to the Schrödinger equation. However, my thinking changed after reading the following section of On the Interpretation of Quantum Mechanics, Fock (1957) (my emphasis added):
What are the features of quantum mechanics that do not allow us to interpret them in a classical spirit and consider the wave function as a distributed field similar to the classical one? Discarding for a while some more deep epistemological arguments one can indicate some formal reasons contradicting this interpretation. First, in the case of a complex system consisting of several particles the wave function depends not only on three coordinates, but on all degrees of freedom of the system. It is a function of a point of a multidimensional configuration space and not of a real physical space. Second, in quantum mechanics the canonical transformations analogous to the Fourier transformation are allowed and all transformed functions obtained in this way describe the same state and are equivalent to the original wave function expressed in terms of the coordinates. And it is not only the absolute value squared of the original function that has a physical meaning, but the squared absolute values of the transformed functions as well. Third, the many body problem (in particular the problem of several identical particles) has in quantum mechanics some features that do not allow us to reduce this problem either to the problem of several disjoint particles or to formulate it as a field problem in the ordinary three-dimensional space. Hence if a complex system possesses a wave function then it is impossible to assign wave functions to single particles. Moreover, in the case of identical particles satisfying the Pauli principle there exists a quantum interaction of a special kind irreducible to a force interaction in the ordinary three-dimensional space. Another kind of interaction that is also irreducible to the classical one exists between particles described by symmetric wave functions. Finally, not only for the case of identical particles but for a single particle as well the wave function does not always exist and does not always change according to the Schrödinger equation; under certain conditions it simply disappears or gets replaced by another one (the so-called reduction of a wavelet, see §11). It is obvious that such “momentary change” does not agree with the notion of a field. 
The described features of quantum mechanics make in advance inconsistent all attempts to interpret the wave function in the classical spirit.
Clearly I will have to do some more reading and analysis...

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