I’ve just finished reading Sean Carroll’s forthcoming new book, will write something about it in the next few weeks. Reading the book and thinking about it did clarify various issues for me, and I thought it might be a good idea to write about one of them here. Perhaps readers more versed in the controversy and literature surrounding this issue can point me to places where it is cogently discussed.
Carroll (like many others before him, for a recent example see here), sets up two sides of a controversy:
- The traditional “Copenhagen” or “textbook” point of view on quantum mechanics: quantum systems are determined by a vector in the quantum state space, evolving unitarily according to the Schrödinger equation, until such time as we choose to do a measurement or observation. Measuring a classical observable of this physical system is a physical process which gives results that are eigenvalues of the quantum operator corresponding to the observable, with the probability of occurrence of an eigenvalue given in terms of the state vector by the Born rule.
- The “Everettian” point of view on quantum mechanics: the description given here is “The formalism of quantum mechanics, in this view, consists of quantum states as described above and nothing more, which evolve according to the usual Schrödinger equation and nothing more.” In other words, the physical process of making a measurement is just a specific example of the usual unitary evolution of the state vector, there is no need for a separate fundamental physical rule for measurements.
I don’t want to discuss here the question of whether the Everettian point of view implies a “Many Worlds” ontology, that’s something separate which I’ll write about when I get around to writing about the new book.
What strikes me when thinking about these two supposedly very different points of view on quantum mechanics is that I’m having trouble seeing why they are actually any different at all. If you ask a follower of Copenhagen (let’s call her “Alice”) “is the behavior of that spectrometer in your lab governed in principle by the laws of quantum mechanics” I assume that she would say “yes”. She might though go on to point out that this is practically irrelevant to its use in measuring a spectrum, where the results it produces are probability distributions in energy, which can be matched to theory using Born’s rule.
The Everettian (let’s call him “Bob”) will insist on the point that the behavior of the spectrometer, coupled to the environment and system it is measuring, is described in principle by a quantum state and evolves according to the Schrödinger equation. Bob will acknowledge though that this point of principle is useless in practice, since we don’t know what the initial state is, couldn’t write it down if we did, and couldn’t solve the relevant Schrödinger equation even if we could write down the initial state. Bob will explain that for this system, he expects “emergent” classical behavior, producing probability distributions in energy, which can be matched to theory using Born’s rule.
So, what’s the difference between the points of view of Alice and Bob here? It only seems to involve the question of how classical behavior emerges from quantum, with Alice saying she doesn’t know how this works, Bob saying he doesn’t know either, but conjectures it can be done in principle without introducing new physics beyond the usual quantum state/Schrödinger equation story. Alice likely will acknowledge that she has never seen or heard of any evidence of such new physics, so has no reason to believe it is there. They both can agree that understanding how classical emerges from quantum is a difficult problem, well worth studying, one that we are in a much better position now to work on than we were way back when Bohr, Everett and others were struggling with this.
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