The recent article by Chandralekha Singh, Mario Belloni and Wolfgang Christian on Students’ understanding of Quantum Mechanics in Physics Today provoked an interesting series of letters in response. Both Robert Griffith and Travis Norsen argue that students’ understanding would be improved by replacing the usual Copenhagen/Orthodox dogma by discussion of some more recent developments in the foundations of quantum theory.
Given that I don’t actually have much experience teaching quantum theory (I have only covered a lecturer’s absence for two lectures) it is perhaps a bit presumptuous for me to contribute my thoughts on this topic. Nevertheless, I do agree wholeheartedly with the basic sentiment of both these letters. I think one can easily see that at least some of the misconceptions that Sing, Belloni and Christian have written about could be easily remedied by a bit more foundational discussion at the ground level. For example, I think the common misconception that stationary states are the only allowed states of a quantum system could be dispelled by a deeper discussion of the sense in which quantum theory is analogous to classical probability theory.
However, I think both Griffith and Norsen make a mistake in the approaches they advocate in their letters. Griffith suggests replacing the orthodoxy with his own favored approach, namely decoherent/consistent histories, and Norsen thinks we should teach students Bohmian mechanics. In fact, in his letter Griffith gives the misleading impression that his approach is universally and unproblematicallly accepted by all right-thinking physicists. Whilst the formalism certainly has quite a few adherents in quantum cosmology, it is far from true that it has received universal support from all serious thinkers on the foundations of quantum theory. Similarly, whilst I agree that Bohmian mechanics presents the clearest counterexample to many common misconceptions about quantum theory, it is far from clear that it represents the best road to future progress.
In my view, the problem is not that we are teaching the wrong orthodoxy to students, but rather that we are teaching them any orthodoxy at all, since foundations is a subject that is still mired in controversy to this day. It is hard for me to imagine any physicist who is not directly involved in foundations taking either Griffith’s or Norsen’s arguments seriously, since their letters directly contradict each other about what is the best approach to teach, and a non-specialist really has no way of deciding which one of them they should trust. The view that foundations is a murky area, with no clear reason for choosing one approach over any other is only reinforced by such arguments and it is unlikely to persuade a skeptic to change their whole teaching strategy.
On the other hand, I do believe that there are a lot of developments in foundations that have made our current understanding much clearer, and these could be usefully communicated to students. For example, we have a much clearer understanding of the “no-go” theorems, such as Bell’s theorem, and their possible loopholes, and a much clearer understanding of the space of possible realist interpretations of quantum theory. We have an improved understanding of the classical limit, via decoherence theory amongst other approaches, and quantum information theory has shown that entanglement and the understanding of quantum theory as a generalized probability theory actually have useful consequences. I believe we should teach these things as a central part of quantum mechanics courses, and not just as peripheral topics covered in the last one or two lectures, which students are instructed not to worry about because it won’t be on the final exam! We should also give students an understanding of the space of possible resolutions to foundational problems, to equip them with a BS detector for statements they are likely to hear about quantum theory. Why do I believe this? Well, simply because I think it will leave students less confused about how to understand quantum theory and because I think these areas are all increasingly fruitful avenues of research that we might want to encourage them to pursue.
The difficult question, I think, is not the why but the how. It would entail battling against the prevailing wisdom that foundations are to be de-emphasised and relegated to the end of the course. Also, good teaching materials at an appropriate level that could supplement the existing curriculum are not readily available, and that is a problem we definitely have to address if we want this to happen.
Copyright © 2007 Matthew Leifer. All Rights Reserved.