Today we had an interesting Quantum Science Seminar by Peter Riggs, author of

*Quantum Causality: Conceptual Issues in the Causal Theory of Quantum Mechanics.*

Other names for the causal theory are Bohmian mechanics, De Broglie's pilot-wave theory, ontological quantum theory...

The talk provided a nice overview of the theory and different objections to it. Riggs is an advocate of the theory, claiming it "solves" the measurement problem.

He does not seem concerned that relativistic and spin versions of the theory seem a rare species or intractable.

I was intrigued that Riggs invoked physical chemists, such as Robert E. Wyatt, in a manner that suggested that they were advocates of the theory. Wyatt has had considerable success in applying the mathematics of Bohmian mechanics to solve quantum dynamics problems in chemistry. He is the author of Quantum dynamics with trajectories. However, my impression is that Wyatt and his collaborators are purely motivated by the fact that the Bohmian equations [without any philosophy attached] allow considerable computational savings. They are just a different way of encoding the standard quantum physics.

In fact, in a comment on a Science paper "Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer"[which incidentally contained lots of technical errors...] Wyatt concludes

So, Eric Bittner, are you a Bohmian? or just a pragmatic quantum guy?Many adherents to Bohm’s version of quantum mechanics assert that the trajectories are what particles actually do in nature.From the experimental results above no one would claim that photons actually traversed these trajectories, since the momentum was only measured on average and the pixel size of the CCD is still quite large. Other views of Bohm’s trajectories do not go as far as to claim that they are what particles actually do in nature. But instead, the Bohm trajectories can be viewed simply as hydrodynamical trajectories [5, 7] that have equations of motion with an internal force that appears when one changes from a phase space to a position space discription. Recently, it has also been shown that the Bohm trajectories can in fact be generated without any equations of motion ...., one concludes again that theyBohm trajectories are simply hydrodynamical and kinematically portraying the evolution of the probability density. The average photon trajectories can be viewed likewise.

What disappointed me most was the requirement that statistical uncertainty be introduced (so as to recapture the uncertainty principle), but the origin of the statistical uncertainty was not explained. In standard QM, one can explain the introduction of statistical uncertainty by invoking measurement. If the theory is deterministic, it preserves information. So, this means that all the uncertainty in a dynamics must be buried already in the initial conditions... but no "why" is given for why we must always have statistical initial conditions (other than that we already know the uncertainty principle works).

ReplyDeleteIt was not clear to me how the partition function would be written in this formalism. Is it an integral over classical phase space? Is the definition of the momentum in Bohmian mechanics consistent with this? If the state space is composed of pairs (particle, wave field) than doesn't one have to sum over the "phase spaces" of both? (this actually doesn't make sense, because the wave field is a solution of the Schrodinger Eq., so it can't depend on a joint distribution over momenta & position). I got confused here. For me, the real beauty of QM is that it works so well with classical statistics (map distributions -> density matrices, and the rest looks pretty much the same).

Bohmian mechanics seems geared to people that like point particles and really want to have them in a theory. Bohm says "OK, sure", but it is not clear that the particles have the content we want. The whole thing seems a bit silly because point particles were never actually measureable, even in principle! There are known results of classical estimation theory that say you couldn't get a delta-function distribution in the phase space even asymptotically, if you were to make measurements on any classical particle.

Ross,

ReplyDeleteAre you trying to out me? Just kidding. We just had a nice Telluride meeting on this topic with those foolish few of us who are still playing with the approach in spite of NSF's best efforts. I would put myself very much in the pragmatic camp--and I think most physical chemists would do the same.

On the other hand, I was pretty much blown away by some recent works by Aephraim Steinberg's group in Toronto on single-photon trajectories (http://www.physics.utoronto.ca/~aephraim/aephraim.html) that do appear to follow Bohmian paths.

Eric

ReplyDeleteThanks for letting us know what you think.

The Science paper I refer to is from Steinberg's group.