Archive for March 2007

Teaching Quantum Theory

26th March 2007

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.

Foundations Summer School: Apply Now!

12th March 2007

Just a short note to let you know that the application form for the Perimeter Institute Quantum Foundations Summer School is now available online from here. The application deadline is 20th May.

Update: I should have mentioned that for successful applicants who are grad students all expenses will be paid by Perimeter. That should make it easier to persuade your advisor to let you go. You don’t have to be an expert on foundations and we are hoping that students studying a wide variety of areas of Physics will attend.

Update 2: Whether non-students, e.g. postdocs, will be allowed to attend is still an open question. I’m waiting to hear more about this from the organizers. Clearly, the priority for a summer school has to be grad students, so I would speculate that it will depend on the number and quality of applications that we get. I’m just guessing at the moment though and I’ll post another update once I hear the official word.

Update 3: I have just heard that there will be up to 10 places will be made available at the summer school for postdocs and junior faculty.

Foundations at APS, take 2

6th March 2007

It doesn’t seem that a year has gone by since I wrote about the first sessions on quantum foundations organized by the topical group on quantum information, concepts and computation at the APS March meeting. Nevertheless it has, and I am here in Denver after possibly the longest day of continuous sitting through talks in my life. I arrived at 8am to chair the session on Quantum Limited Measurements, which was interesting, but readers of this blog won’t want to hear about such practical matters, so instead I’ll spill the beans on the two foundations sessions that followed.

In the first foundations session, things got off to a good start with Rob Spekkens as the invited speaker explaining to us once again why quantum states are states of knowledge. OK, I’m biased because he’s a collaborator, but he did throw us a new tidbit on how to make an analog of the Elitzur Vaidman bomb experiment in his toy theory by constructing a version for field theory.

Next, there was a talk by some complete crackpot called Matt Leifer. He talked about this.

Frank Schroeck gave an overview of his formulation of quantum mechanics on phase space, which did pique my interest, but 10 minutes was really too short to do it justice. Someday I’ll read his book.

Chris Fuchs gave a talk which was surprisingly not the same as his usual quantum Bayesian propaganda speech. It contained some new results about Symmetric Informationally Complete POVMs, including the fact that the states the POVM elements are proportional to are minimum uncertainty states with respect to mutually unbiased bases. This should be hitting an arXiv near you very soon.

Caslav Brukner talked about his recent work on the emergence of classicality via coarse graining. I’ve mentioned it before on this blog, and it’s definitely a topic I’m becoming much more interested in.

Later on, Jeff Tollaksen talked about generalizing a theorem proved by Rob Spekkens and myself about pre- and post-selected quantum systems to the case of weak measurements. I’m not sure I agree with the particular spin he gives on it, especially his idea of “quantum contextuality”, but you can decide for yourself by reading this.

Jan-Ake Larrson gave a very comprehensible talk about a “loophole” (he prefers the term “experimental problem”) in Bell inequality tests to do with coincidence times of photon detection. You can deal with it by having a detection efficiency just a few percent higher than that needed to overcome the detection loophole. Read all about it here.

Most of the rest of the talks in this session were more quantum information oriented, but I suppose you can argue they were at the foundational end of quantum information. Animesh Datta talked about the role of entanglement in the Knill-Laflamme model of quantum computation with one pure qubit, Anil Shaji talked about using easily computable entanglement measures to put bounds on those that aren’t so easy to compute and finally Ian Durham made some interesting observations about the connections between entropy, information and Bell inequalities.

The second foundations session was more of a mixed bag, but let me just mention a couple of the talks that appealed to me. Marcello Sarandy Alioscia Hamma talked about generalizing the quantum adiabatic theorem to open systems, where you don’t necessarily have a Hamiltonian with well-defined eigenstates to talk about and Kicheon Kang talked about a proposal for a quantum eraser experiment with electrons.

On Tuesday, Bill Wootters won a prize for best research at an undergraduate teaching college. He gave a great talk about his discrete Wigner functions, which included some new stuff about minumum uncertainty states and analogs of coherent states.

That’s pretty much it for the foundations talks at APS this year. It’s all quantum information from here on in. That is unless you count Zeilinger, who is talking on Thursday. He’s supposed to be talking about quantum cryptography, but perhaps he will say something about the more foundationy experiments going on in his lab as well.


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