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Caledonian: There is no difference at the level of predictions, because I'm not calling for any new laws of physics beyond QM. It's a matter of what makes sense as interpretation.
Don Geddis: I don't agree that "multiple worlds are observed, in subatomic phenomena. That's what superposition is." That is your preferred interpretation. I prefer to think that the wavefunction is real, but it is a function over potential configurations, only one of which is real. Superposition reflects the influence of other physically equivalent configurations. I would not call my interpretation a "collapse" interpretation. The wavefunction is always there, in the sense that nature "knows" the probability amplitude for points in configuration space other than the that represented by the real state of the universe.
I am also puzzled by your statement that "determinism is observed". It most certainly is not. When an atom is in an excited state, the time and direction of the photon emitted is essentially random. Isn't it more satisfactory to just acknowledge this than to postulate an infinity of other worlds being spawned for every possible direction and time of emission?
So to preserve the illusion of determinism, which is not observed, you concoct the illusion of multiple worlds, which are also not observed. (feel free to imagine the preceding in all caps, to reflect my righteous indignation).
It seems that many physicists are strongly biased to deterministic theories, and that this is a prime selling point for MWI. So we have a configuration space that comprises every possible state of the universe. And we have a wavefunction over that space which evolves deterministically. So game over: there is no novelty in the universe. There is no meaningful distinction between past, present or future; they are just points on the trajectory through the configuration space, any one of which is completely determined by any other along with the universal wave equation. How boring. I think this is more of a bug than a feature.
I've already said a little about what kind of interpretation I prefer. It's along the lines of Lande's theory. Realistic interpretation of the wavefunction; reality as a single point in configuration space, and random time evolution under the influence of the wave equation.
Eliezer: No doubt I am missing a lot. I have the idea of the wavefunction as a real thing, and I am not advocating a collapse interpretation. I am also uncomfortable with any kind of preferred basis. My idea is that the configuration space of the universe is the classical configuration space, but that its evolution is determined by the wavefunction over the quantum mechanical configuration space (in whatever basis you choose). So a point-particle has a real momentum and a real position, which are not simultaneously measureable. For electromagnetism, the electric and magnetic fields have actual values, which are also not simultaneously measurable. The fields evolve continuously but non-deterministically in accordance with the evolution of the wavefunction. There are still blobs of amplitude in configuration space, but only one point in one of those blobs is the real configuration.
Anonymous: I'll look at your reference to refresh my memory of Bohm. The last I heard, there were problems with relativistic versions of that theory.
Bob: We may still believe that the universe comprises a single point in configuration space, >>corresponding to a single value of the wavefunction
How is this not immediately ruled out by Bell's Theorem?
Bell's Theorem rules out local realism. I'm going with "non-local".
Does the reality of the wavefunction imply MWI? The wavefunction is a function over every possible configuration of the universe. We may still believe that the universe comprises a single point in configuration space, corresponding to a single value of the wavefunction, along with the value of the wavefunction for every other (counterfactual) point in the configuration space. The reality is the particular configuration space point along with the shape of the wavefunction. This does not imply that the wavefunction is a delta-function in configuration space. Other counterfactual configurations may have similar probability amplitudes depending on their "degree of possibility" compared to the existing configuration.
OK, so now it's pretty clear you're committed to a many-worlds interpretation. When I'm done with your experiment, I don't see two blobs, just one. Because there is a separate Bob-blob corresponding to each outcome.
This has been a fascinating series of posts. You are suggesting a realistic interpretation of QM. Do you take the real universe to be the (single) point in the universal QM configuration space, along with the single complex value of the universal wavefunction? Or, since the wavefunction is a function of all possible configurations, are those other configurations somehow real as well (which would be some sort of multiverse theory)? Quantum mechanics certainly allows wavefunctions comprising superpositions of different configurations. Are these superposition states not fundamental?