Reply To: Why Bohmian theory?

AvatarRobert Griffiths

Dear Dustin,

I appreciate your taking a look at [1] in my previous post, and I hope you will look at some of the work referenced there. Regarding the connection of CH and BM the following additional comments may be helpful.

In BM the psi of (Q,psi) in your notation is what I call the uniwave: unitarily developing wave function of the universe. One can employ the uniwave in CH in order to generate probabilities at any given time, which is roughly what is done in SQM, of positions or of anything else. So aside from a few niceties about infinite-dimensional Hilbert space, in CH we have psi(t) -> Pr(Q,t). To that extent BM and CH agree. But notice that Pr(Q,t) refers to just ONE time; the correlations between different times are absent.

In CH if you want to talk about what is happening at two or more times (following the initial time at which psi got started) it is necessary to introduce a family of histories, as in a classical stochastic process, and assign probabilities according to the extended Born rule, provided consistency conditions are satisfied. In BM one instead uses the Q(t) trajectory. And here the answers are sometimes the same, but also sometimes very different. E.g., as pointed out in [2] in my previous post there are cases in which BM supplies a definite answer to what I there call the second measurement problem, and in this respect is to be preferred to GRW or Everett. However there are other cases in which the BM statement contradicts CH and the beliefs of experimental physicists.

I think you need to take these “wrong answer” cases much more seriously. For if we remove Q(t) from BM what remains does NOT provide temporal correlations valid for 2 or more times (initial setup gives psi, and then two later times), and one is left with something very similar to textbooks. So Q(t) has to be there for BM to be interesting. But if it sometimes gives the right answer and sometimes the wrong answer from the perspective of how experimentalists interpret their experiments, what justifies the claim that BM is an interpretation that agrees with experiments? This, it seems to me, is a key question to be addressed.

Bob Griffiths

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