Reply To: Why Bohmian theory?

Richard Healey

At the end of your first paragraph you ask “Am I at least close to right so far?”
No. In formulating or understanding quantum theory it is not necessary to appeal to a microscopic/macroscopic distinction. As a fundamental theory, quantum theory may be applied to systems of arbitrary size.
Quantum mechanics may be applied to systems of particles, so by applying it we are committed to the existence of particles, or at least to treating things as systems of particles (perhaps as a permissible idealization, even though we might not treat them that way if we were instead applying a relativistic quantum field theory to the same things). When we apply quantum mechanics to such systems, we assign them a wave-function (density operator, state vector, whatever). This does not represent a beable. It does not represent the particles’ physical properties or relations: its evolution does not represent their behavior. Its function is not descriptive but prescriptive: it tells the one who applies it what statements assigning values to magnitudes are significant enough to be assigned probabilities, and what those probabilities are. What statements are significant depend on what environment the system is in. The environment may include something we could use as a measurement apparatus, or it may not: either way, it is interactions with the environment that constrain to what statements we can legitimately apply the Born rule. These may be statements about the system, the environment, or both. We can use quantum models of environmental decoherence to help us determine what statements are significant enough to be assigned probabilities. Significance is not a “yes/no” matter, and there is no precise criterion that specifies when, and to what, the Born rule may be legitimately applied. Bell would not like this. But it’s important to stress that this is not a vagueness in the formulation of quantum mechanics, but calls for the same kind of decision that is required in any application of a physical theory, classical or quantum.
“Is there some clean, unambiguous way of saying exactly what, according to the theory, is real?”
The quantum state is not a beable: in that sense it is not real. But quantum states are objective: when assigning a quantum state to a system one can make an incorrect assignment. In that sense a quantum state is real. Are particles real? Yes, according to quantum mechanics, since every correct application of quantum mechanics involves claims about systems of particles. Sometimes, according to relativistic quantum field theory: some correct applications of relativistic quantum field theory involve claims about particles (but in other correct applications no such claim would be significant). I expect you and Bell would not like relativistic quantum field theory’s refusal to give a clear, unambiguous answer to the question “Are particles real, or are fields real, in relativistic quantum field theory?” But recent work by philosophers of physics has shown how hard it is to impose either a particle ontology or a field ontology on such a theory! The problem goes away if one rejects the presupposition that a fundamental theory must come equipped with an ontology.
“To me, as long as you can’t specify *sharply* what the theory says is real, I can’t really take it seriously as a candidate fundamental theory.”
OK, but here you are expressing what I have come to regard as a metaphysical prejudice analogous to the Cartesian prejudice against Newtonian forces. Both prejudices attempt to constrain the form of any fundamental physical theory. We are lucky that Newton broke free of the first prejudice and that Heisenberg, Schrodinger etc. broke free of the second.
I hope that helps some. I have published papers containing more details, and I’m presently finishing a book in which I try to lay out my view of quantum theory more carefully and patiently.

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