Reply To: God knows where all the particles are!


Dear Bob,

I completely agree with the advice you give via the Wigner anecdote. If you want to understand a theory, start with the minimal examples. However, my impression is that Bohmians have given up on getting any physical sense out of few-particle examples.

I spent a good part of last summer on an exchange with Shelly Goldstein on a simple detector problem: Take two detectors of the kind you describe and ask for the correlations between the passage of a projectile’s Bohmian path near one of them with that particular detector firing. I had a bet going on this with Nicolas Gisin, so I was looking for an informed answer. Shelly was only happy to look at the case where the projectile’s wave function has two terms which have disjoint suports for all times up to ionization (a case which plays a prominent role in the BM theory of measurement), but I could not bring any one to even look at the generic case of a projectile with wave function spanning both detectors. In the end (after about 50 printed pages) I was told by both Shelly and Detlef Dürr that mathematical rigor is overrated, but didn’t get close to an answer.

It also seems (from a pamphlet written as a BSc thesis) that Bohmian students are discouraged from looking at few-particle examples. Instead they should look at Bohmian measurement theory where the supposed empirical equivalence with QM resides. But for those many-particle systems control is very poor, and you have to rely on assuming that all is as expected (wave function splits into branches with disjoint support, so the relative wave functions actually satisfy Schrödinger eqs., and no further interaction (like some reading the results) destroys that property, etc). Of course, two solutions of the non-relativistic Schrödinger eq. never have disjoint supports, and you would need some estimate on the transitions of trajectories between the branches. These will not be trivial, because BM dynamics is chaotic and fast around zeros of the wave function (so very likely in the region between branches). But all this is just ignored.

Anyway, your point was the few-particle part, and I wish you good luck for getting any sensible answer.

Best, Reinhard

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