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Physics Today

Walking droplets, pilot waves, and word choices

Jeffery Winkler

Published Mar 31, 2016• 1 citation
Publisher

Abstract

After reading John Bush’s article “The new wave of pilot-wave theory” (Physics Today, August 2015, page 47), I want to remind readers of the limitations of the analogy. The oil-drop experiments provide a tangible partial analogue of the pilot-wave picture, but one that is restricted to single-particle phenomena. Such experiments cannot reproduce the types of phenomena that depend on entanglement; only in the case of a single particle does the wavefunction have the same mathematical form—a scalar function over space—as the waves in the oil.Once two particles are involved, the fact that the wavefunction is defined over the configuration space of the system rather than over physical space becomes crucial, and the partial analogy to the oil drops fails. In other words, the analogy does not extend to what most people consider the most interesting aspects of quantum mechanics.© 2016 American Institute of Physics.

DOI
10.1063/pt.3.3120

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Walking droplets, pilot waves, and word choices

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► Bush replies: I appreciate Jeffery Winkler’s opinion, but it has yet to be proven that dynamic nonlocality of the form exhibited by the walking droplets cannot give rise to a feature analogous to quantum nonlocality, that memory cannot account for entanglement. A proof, rather than an assertion, on this matter would be most welcome.I feel obliged to point out to Leslie Kerby that in my opening paragraph, I was appealing not to my male readership but rather to the careful reader. The cantankerous queen mother was a metaphor for the field of fluid mechanics, not women in science. She was, moreover, cast as the heroine.© 2016 American Institute of Physics.

Physics Today•Mar 31, 2016•0 citations
After reading John Bush’s article “The new wave of pilot-wave theory” (Physics Today, August 2015, page 47), I want to remind readers of the limitations of the analogy. The oil-drop experiments provide a tangible partial analogue of the pilot-wave picture, but one that is restricted to single-particle phenomena. Such experiments cannot reproduce the types of phenomena that depend on entanglement; only in the case of a single particle does the wavefunction have the same mathematical form—a scalar function over space—as the waves in the oil.Once two particles are involved, the fact that the wavefunction is defined over the configuration space of the system rather than over physical space becomes crucial, and the partial analogy to the oil drops fails. In other words, the analogy does not extend to what most people consider the most interesting aspects of quantum mechanics.© 2016 American Institute of Physics.
We describe a series of experimental analogies between fluid mechanics and quantum mechanics recently discovered by a team of physicists. These analogies arise in droplet systems guided by a surface (or pilot) wave. We argue that these experimental facts put ancient theoretical work by Madelung on the analogy between fluid and quantum mechanics into new light. After re-deriving Madelung’s result starting from two basic fluid mechanical equations (the Navier–Stokes equation and the continuity equation), we discuss the relation with the de Broglie–Bohm theory. This allows to make a direct link with the droplet experiments. It is argued that the fluid mechanical interpretation of quantum mechanics, if it can be extended to the general N-particle case, would have a considerable advantage over the Bohm interpretation: it could rid Bohm’s theory of its non-local character.
Abstract For about a century, physicists have been debating over the behavior of particles on a microscopic scale. Although the principle of the wave-particle duality is accepted in the scientific community, many experiments with puzzling results are still challenging quantum mechanics until now, such as the double slit experiment, entanglement, interferences of a single electron, or delayed choice quantum eraser. In this article, we shall bring forth explanations for some of these experiments. Unlike standard quantum mechanics (SQM) built by Schr¨odinger1 and P.Dirac2 which considers that the wave function is an abstract mathematical tool, our model takes up the concept of the pilot wave once initiated by physicists De Broglie and D.Bohm,3 who suggested that the wave associated to a quantum object has a real existence and that it is not simply a wave of probability. We shall discuss how this old-new conception of reality renders quantum mechanics ultimately less mysterious than it seems.
In [2], a detailed argument is presented on a version of pilot-waves, given by at Theory of Exclusively Local Beables. What the author of [2] considers to be his crucial proposal is described in the title of section 3 as 'complicated, ugly, and highly contrived'. The reason for such a proposal is claimed to be the widespread perception among quantum physicists, according to which 'those sympathetic to the pilot-wave ontology no doubt expected that, for a system of N particles moving in three spatial dimensions, the theoretical description would be of N wave-particle pairs - each pair consisting of a point particle guided in some way by an associated wave propagating in 3-space. But Schroedinger's wave function for such an N-particle system was emphatically not a set of N (interacting) waves, each propagating in 3-space. It was, rather, a single wave propagating in the 3N-dimensional configuration space for the system', [2, p. 5]. In the present paper it is argued that the mentioned widespread expectation need not be seen as being betrayed by what actually happens. In particular, the construction in section 3 of [2] may be avoidable.
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.
► Bush replies: I appreciate Jeffery Winkler’s opinion, but it has yet to be proven that dynamic nonlocality of the form exhibited by the walking droplets cannot give rise to a feature analogous to quantum nonlocality, that memory cannot account for entanglement. A proof, rather than an assertion, on this matter would be most welcome.I feel obliged to point out to Leslie Kerby that in my opening paragraph, I was appealing not to my male readership but rather to the careful reader. The cantankerous queen mother was a metaphor for the field of fluid mechanics, not women in science. She was, moreover, cast as the heroine.© 2016 American Institute of Physics.