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Dear Dustin and Travis,
so, according to Travis, I “have a number of simple factual misconceptions about how Bohm’s theory works and what it says.” I feel that I do understand fairly well how the theory works, but that is somehow at variance with what Bohmians like to say about it. Of course, the root for the whole disagreement is further down in the views of what a scientific theory should be. This forum is no place to work that all out. But let me indicate a few points related to the issues raised.
One key element of a physical theory to me is the point where the connection between the mathematical framework and the real world is made. Somehow Bohmians seem to try to avoid that by directly claiming reality for the particles and their trajectories and that’s that. (“It’s all in two simple equations”…) This kind of reality is entirely in a lofty Platonic world, and we are merely invited to imagine that we live in such a world. No messy questions of interpretation there, and, of course, everything has to work out with respect to experience, because the standing assumption is that the universe, including any potential observer, is already in that harmonious set of equations. All is clear and exact. Peace be with you.
This is very poetic and simple (to the extent that PDEs in zillions of variables are) but how would you convince me that we live in such a world? I know you would probably not try (because of the serious non-uniqueness), and instead try to convince me that that Platonic thing at least is a possible world. That would not be saying much, however, and would put the reality claims of the Bohmian Universe on a par with Middle Earth. Of course, you have distributed Reality tags in your fantasy, e.g., for the “matter distribution”. But those are just words, as long you don’t give a rule of how to make the connection to the real world.
I suppose the idea here is that “matter distribution in the real world” is such an immediately obvious thing that it suffices to say that a suitable averaging of the mathematical point distribution should be the real world matter distribution. But there is nothing obvious about that in BM. How do we actually determine the matter distribution? I know no other way than to somehow interact with it. But since the interaction is always with the wave function, and the BM particles themselves are gravitationally and electrodynamically invisible, the trajectories are not related a priori to anything one might observe via an actual interaction. There seems to be agreement on this for small systems. So why should the Bohmian particle distribution be of any relevance to ascertaining “matter distribution” in the large?
Of course, we expect that for a macroscopic system you can get away with a lot of coarse graining and fuzziness, so probably you can get away with a lot of conceptual fuzziness as well and that identification is probably sort of ok. Not that you have a proof of that which does not assume a solution of the FAP measurement problem, and a counterfactual assumption about disjoint wave function supports. Maybe if you leave your mathematical hat in the closet, you can just make the assumption that things work out as you expect they should. This is all quite fuzzy, and is plagued by a theory of measurement that requires you to solve a many-particle problem, which means that you can never get concrete (I heard the term “unprofessionally vague” in this context).
This is precisely the virtue of the Heisenberg/von Neumann/whoever cut: It allows you to come to a theory that actually allows predictions. You could now say: but this is anyhow included by nostrification (i.e., via the implication BM==>QM). Then the message amounts to this: If you want to solve a problem, like describing an experiment, scrap BM, go QM. On Sundays, when you want to live in that Platonic world, you can still be a Bohmian.
All the best, Reinhard
PS: Travis, you warned me of the dramatic consequences of removing the Bohmian trajectories from the furniture in my house. But I just did that (by forgetting some variables from the guiding ODE), and it looks pretty much the same. So I decided to leave it in its new Bohmian-free state. I hasten to add, I left your furniture nice and real, but frankly, I am not sure how you would ever notice the difference.