Reply To: God knows where all the particles are!

Dustin Lazarovici

That the Bohmian trajectories are (in principle) unobservable is, of course, a very common objection against Bohmian mechanics. This objection is usually based on two things: 1. a positivist dogma and 2. a misunderstanding of the logical relationship between Bohmian mechanics and Quantum mechanics.

You also seem to misunderstand the spirit and content of Bohmian mechanics when you think that it is based on or motivated by a “naive realism about the position operator”, but I guess that’s not the main point.

In any case, your argument is based on the assumption that BM is essentially standard quantum mechanics plus an (adhoc) addition of particle trajectories. If that was the case, one could make an occam’s razor argument to the effect that the trajectories add no predictive power or empirical content and thus should be despensed with. In fact, even this statement wouldn’t be correct since (the constituents of) macroscopic objects also move on Bohmian trajectories. Indeed, the whole empirical content of the theory is in the particle positions, i.e. the distribution of matter in space. But let’s grant that the trajectories of subatomic particles per se have no empirical content.

However, Bohmian mechanics is NOT Quantum mechanics plus trajectories. In fact, the Bohmian has quite a bit of work to do in order to derive the usual quantum formalism from the two dynamic equations defining Bohmian mechanics.

Indeed, Bohmian mechanics is the microscopic theory and QM is the measurement formalism derived by statistical analysis. BM is not an extension of QM, but a REDUCTION of QM. The quantum formalism is derived from and explained by BM.

BM is logically prior to and conceptually simpler than textbook QM. Everything follows from two precise mathematical equations rather than a set of fuzzy axioms involving “measurement” or “observers” or “operators” or whatever. For both reasons, the occam’s razor argument doesn’t actually hit BM.

If you forget about the microscopic theory, i.e. about particles and their trajectories, you don’t necessarily lose empirical content. After all, the Bohmian agrees that the standard quantum formalism is – for all practical purposes – correct. However, you lose the physical content of the theory, i.e. the way in which the qauntum formalism actually relates or refers to stuff in the physical world. You literally don’t know what you’re talking about when you do your operator business or solve Schrödinger’s equation or compute transition amplitudes.

Now, you may say that for you, the physical content of a theory is only in observable (macroscopic) quantities. You may say, for instance, that the trace in a cloud chamber is physical – because that’s what you can see – but a microscopic particle that a theory posits as the “cause” of this trace is unphysical, because that you cannot see.

I guess this position is defendable, to some degree. It certainly agrees well with the old Copenhagen school of thouht. But then you are the one who’s being dogmatic, adhering to a very particular positivist philosophy, and who displays a lack of imagination. There’s nothing sophisticated about not believing in atoms.

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