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Dear Reinhard, I don’t understand what you find “Platonic” about “claiming reality for the particles and their trajectories”. How is this, in principle, any different from the claims that people made in the 19th century about matter being made of atoms?
You ask: “how would you convince me that we live in such a world?” I guess I would start by pointing out that the story told by the theory about how big, directly-observable, macroscopic collections of particles move, is consistent with what we see in fact happening. That of course doesn’t prove that the theory is right. But surely it counts for something — it’s enough that it should make one take the theory very seriously as a real possibility. You say Bohmians “don’t give a rule of how to make the connection to the real world”. But the connection is crystal clear: what the theory says about how (macroscopic collections of) particles (like pointers, etc.) should move, matches how we in fact observe them to move. If that isn’t what you’re looking for, what in the world are you looking for? What kind of connection between a physical theory, and the real world of direct perception, would satisfy you??
Your paragraph starting “I suppose…” contains several confusions/misconceptions about the theory. 1. There is no “averaging” of the “point distribution” involved. The particles have actual positions. There’s a definite configuration. That (not some average of anything) is the “real world matter distribution” according to the theory. 2. You say “the interaction is always with the wave function”. I think you mean that, according to Bohm’s theory, you (who are, of course, according to that theory, made of particles) cannot interact with the other particles (also posited to exist by the theory); you can only interact with the wave function. That’s just not right. I suppose you could say that in some sense the interactions between particles are mediated by the wave function. But it’s just ridiculous to understand the theory as saying that particles can’t interact with each other. 3. You suggest in particular that “the BM particles themselves are gravitationally and electrodynamically invisible”. That’s simply wrong. Maybe what you mean here is that the particles do not move (and do not influence other particles) according to the laws of Newtonian mechanics (with gravitational/electromagnetic interactions). That’s true. But just because something has a new, quantum dynamics doesn’t make it invisible. If there are gravitational/electromagnetic interactions in the Hamiltonian, then the particles interact gravitationally/electromagnetically, and are simply not “invisible” in the sense you mean.
I’ll stop there (although there are more confusions/misconceptions). But I’ll just highlight this comment, which I think is quite revealing: “This is precisely the virtue of the Heisenberg/von Neumann/whoever cut: It allows you to come to a theory that actually allows predictions.” I think it is clear that you are continuing to think about Bohm’s theory in exactly the (wrong) way I outlined in my previously-linked-to comment on the thread started by Richard Healey.