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“It would seem that the theory would then have to involve local beables, out of whose configurations facts about results of experiments would arise.”
Appearances can be deceptive!
Assume a fundamental physical theory should not involve talk of measurement or observation. (I don’t mention axioms, because I don’t think theories, fundamental or not, need be derived from axioms.)
Must a fundamental theory posit its own local beables? Must a fundamental theory posit any beables of its own? Of course one could take the attitude that nothing could count as a fundamental theory unless these questions received positive answers. But someone could then adopt a different, more relaxed, attitude toward fundamentality. Observer-free quantum theory is fundamental in two senses: We have been able successfully to use it successfully to predict and explain a host of phenomena that cannot otherwise be predicted or explained (e.g. by classical physical theories) without encountering any empirical problems traceable to its deficiencies; and, in some form, the theory may be applied to all known phenomena with the single exception of those thought (by many) to require a quantum theory of gravity.
But observer-free quantum theory does not posit its own ontology: it “borrows” an independently available ontology from the rest of physics. The wave function is not a beable at all (many experiments are hard to reconcile with the assumption that it is): “observables” are not beables—corresponding physical magnitudes are beables, but quantum theory should not be understood to introduce them as elements of its own ontology. Bell talks about beables recognized in ordinary quantum mechanics, including settings of switches and knobs, and currents. These are not novel quantum posits and don’t have to be built out of elements of quantum ontology; when we apply quantum mechanics we often help ourselves to them (though nothing prevents us from applying quantum mechanics to these things if we want to understand their behavior better). Any legitimate application of the Born rule in quantum theory concerns values of magnitudes not introduced as novel quantum posits but taken over from the rest of physics, new as well as old. Among these applications are many that successfully account for experimental phenomena.
The success of quantum theory should teach us that a fundamental theory need not be “self-standing”. It need not present us with a description or representation of reality solely in its own terms. We might experience metaphysical yearnings for a theory that did, but physics–even supremely successful physics–need not conform to our favorite metaphysics. We can understand quantum theory as currently our best fundamental theory in this less narrow-minded sense without talking about observation and measurement, and without becoming instrumentalists or operationalists. It is Bohmian mechanics, not quantum mechanics, that requires defense using philosophical ideas from outside of physics.