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Interesting piece sent along by reader Joe Hatfield–can any of the philosophers of physics (or physicists) out there comment on the adequacy of this presentation and the significance, if any, of all this?
The pilot wave theory is essentially as old as quantum theory itself (1927), and its complete adequacy in the non-Relativistic regime (i.e. its ability to generate the standard quantum-mechanical predictions without any conceptual problems or vague talk about "measurements" of "observables") has been basically clear since Bohm's 1952 paper. A deeper understanding of the origin of the statistical character of the predictions has been established by the work of Shelly Goldstein, Detlef Dürr and Nino Zanghì. There are various strategies for extending the theory to cover Relativistic field theory. All of this is known and appreciated by people working in foundations of physics, and particularly by most philosophers of physics.
These experiments provide a mechanical analog, to some extent, to the single-particle theory, and so can give people a sense of how the theory works. But the analog is very, very partial: it will not extend to entangled pairs of particles, and so cannot even vaguely replicate the most astonishing prediction of quantum theory, viz. the violations of Bell's inequality. It also can be misleading about the structure of the quantum wave function. For a single particle, the wave function is a complex function over physical space, so the waves in the medium here can partially correspond to it. But when there is more than one particle the wave function is defined over the configuration space of the system, which is of greater than 3 dimensions, so this model fails.
Insofar as these experiments bring attention to the pilot wave theory (also known as deBroglie/Bohm theory and Bohmian mechanics), that is a good thing. But there is no conceptual breakthrough, and the model is misleading in some respects. John Bell strongly advocated the pilot wave theory for decades.
Independently of the question about the analogy between these behaviors of these oil bubbles and the Bohmian mechanics of single-particle systems (which do interest me a great deal), aren't there nowadays concrete empirical reasons to think that Bohm's theory is false?
If you have two measurables represented by hermetians whose commutators are non-zero (unlike what one finds in the simple two path experiments), and one of them is position, then facts about spectography predict that in basic set-ups where on the QM account a collection of pairwise entangled particles are each in a superposition of taking two trajectories and on the Bohmian account they each take one or the other trajectory according to statistical predictions, then the patterns of dispersion of the particles predicted by the two theories will differ. This has been known for a while, as it was analytically proved to be true many years ago. More recently (1999), specific experiments were described that would produce different outcomes on the two theories. Even though the experiments are variations of familiar double-slit experiments, there are subtle features that one has to get right. It was thought that the experiments would be too costly to actually conduct, and also that they would be too difficult to implement. But a few years ago one of these experiments was conducted and the results do not weigh in favor of Bohm's theory. I believe this is the first paper about it:
http://arxiv.org/pdf/quant-ph/0206196v1.pdf
It is interesting that in their remarks in Wired, these mathematicians make no mention either of this or of the facts that Bell pointed out 60 years ago about the differences between QM and Bohmian mechanics with respect to Lorenze invariance.
I'm sure many of my colleagues who specialize in these topics can speak to the issues with more clarity and confidence, but I hereby register my amateur puzzlement.
Curtis
The papers cited by Franks above , as far as I can tell, show nothing at all. For example, in the paper by Ghose there is a symmetry argument that would apply only to a set of measure zero in any case, and so cannot have any effect at on of the statistical predictions of the theory. Without going into details, the main paper also makes assertions (e.g. about ergodicity) that make no sense at all.
Other such supposed "proofs" that the pilot wave theory makes different predictions than standard quantum formalism have also been shown to be incorrect, typically because they fail to take account of the physical effects of the experimental set-up, i.e. they fail to appreciate that once one has solved the measurement problem by physical consideration, one can't just ignore those physical considerations when extracting empirical predictions from the theory. So to reply to the puzzlement above: the papers there cited are in error.
After a little more reading of the papers cited in the paper cited by Franks above: the work of Ghose is incompetent (see http://arxiv.org/abs/quant-ph/0007068), and the paper by Golshani and Akhavan also wrong at the critical point, where they claim to derive predictions for an unentangled wave function. (Golshani and Akhavan acknowledge that there are no differences in statistical predictions for "non-selective" measurements, and their claim for deviations elsewhere are incorrect.) Some of the papers cited seem not even to exist any more, i.e. have been deleted from the arXiv. There is really nothing in these claims.
Thanks for clearing that up, Tim.
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