Interpretating Quantum Mechanics

I just got my copy of the October American Journal of Physics (the best, though not the most prestigious, physics journal in the world). The Letters to the Editor section contains a letter by Art Hobson, written in response to a book review by N. David Mermin. The book that Mermin reviewed was Quantum Enigma by Rosenblum and Kuttner. I've not read the book myself, but I did read Mermin's review. One of his chief complaints (though not his only complaint, nor was his review wholly critical) was that in discussing various interpretations of quantum mechanics Rosenblum and Kuttner ignore the view that quantum states represent not physical states of a particle but rather states of our knowledge. Hobson rejects this view (as well as the view, evidently emphasized by Rosenblum and Kuttner, that perception of a measurement result by a conscious entity brings about a collapse of the wavefunction).

Now I have a great deal of admiration for both of the participants here. I am in the process of reading Mermin's Boojums All the Way Through. Mermin is without question the best prose stylist in physics (and apparently a major contributor in condensed matter physics, though that's not my field so I can hardly judge). Hobson, on the other hand, has been a champion for the social relevance of physics and for the teaching of physics to non-science students. I use his Physics: Concepts and Conncetions textbook for my liberal-arts physics course. While I would have read any letters on interpreting quantum mechanics with interest, the name recognition definitely made these letters stand out to me.

Hobson claims the view that quantum states are states of knowledge rather than states of some objective physical reality is an unnecessary extravagance. He argues that the analysis should really be done from the perspective of quantum field theory, and that most physicists certainly believe that quantum fields are objectively real (offering a quote from Weinberg that I have seen him use before). He then goes on to explain how decoherence explains how a quantum superposition can be transformed, through interaction between the quantum system and its environment, into an incoherent state that can be described with a diagonal density operator. Hobson then declares that these incoherent states are no more mysterious than the proposition that there is a 0.5 probability that a coin flip will come up heads.

I find this last comment by Hobson particularly interesting in light of the position he is attacking. He wants to avoid the claim that quantum states are states of knowledge, but yet he is reduced to saying that quantum probabilities are just like the probabilities involved in flipping a coin. But classical probabilities, like those for a coin toss, are invoked exactly because we lack knowledge. The equal probability of getting heads or tails when a coin is flipped does not represent anything objectively real about the state of the coin on a given flip. What it represents is the state of our knowledge about the coin. If we knew a great deal more about the coins initial state, and about all the forces that act upon the coin, we could determine with near certainty which side of the coin would land up. It is only because we are ignorant of all this information that we must resort to probabilities. So Hobson's invocation of decoherence seems to support Mermin's view, rather than refute it. Indeed, decoherence can only be deemed to have fully solved the measurement problem if quantum states are only states of knowledge (because it reduces the quantum superposition to a classical mixture). If we believe that quantum states represent an objective reality then we are left wondering why decoherence fails to produce a single outcome (rather than a classical mixture of various outcomes). Certainly when we do measurements in the lab we get a single outcome each time (though not the same outcome every time we repeat the measurement).

I also find Hobson's reliance on quantum field theory to be a little problematic. Not so much for technical reasons as for pedagogical reasons. In fact, I have avoided moving to the new edition of his text in part because of this. It is not clear to me that all of the mysteries of quantum mechanics can be swept under the rug of quantum field theory. Quantum field theory has been very successful in describing a rather limited range of phenomena. But it's not clear to me that quantum field theory, as a model of physical interactions, completely contains and therefore exceeds non-relativistic quantum mechanics. In the same way, I have yet to be fully convinced that quantum mechanics completely contains classical mechanics. The idea that our "most fundamental" theory might not contain all the other "less fundamental" theories is anathema to most physicists, but it doesn't bother me since I don't believe in the idea of a final theory anyway. In any case, from the perspective of a non-science student I think blaming the whole mess on quantum fields is a bit like saying the Wazzleblatchet did it (which might be great for a Dr. Seuss tale, but not in my physics class).

Now this isn't to say that I side fully with Mermin on this debate. I have some issues with the idea that quantum states are "nothing more" than states of knowledge. As I said above, we use classical probabilities to represent states of knowledge. But clearly there is something different going on in quantum mechanics. So if quantum states are states of knowledge then our knowledge about quantum particles is constrained in some rather odd ways. In this sense, saying that quantum states are states of knowledge does little to dispel the mysteries of quantum mechanics. I'm not sure that is really Mermin's goal. His goal in the review was to combat the idea that consciousness brings about physical changes in some objectively real quantum state. If quantum states are states of knowledge then it is no surprise that the quantum state changes when a conscious entity becomes aware of a measurement result. But even this point of view does not wholly discount the idea that there IS an objective physical reality. I personally view any science (not just quantum mechanics) as the result of an interplay between our minds and an objective physical reality. Neither piece is wholly absent from classical physics, nor from quantum physics.