In their article, Chandralekha Singh, Mario Belloni, and Wolfgang Christian focus exclusively on “functional understanding of quantum mechanics,” which they claim “is quite distinct from the foundational issues alluded to by Feynman.”
But are the foundational and the functional really so distinct? The work of other physics education researchers suggests not. For example, in a classic article, Alan Van Heuvelen discusses students’ prevalent and frustrating use of “primitive formula-centered problem-solving strategies” 1 and suggests that physical, intuitive understanding developed through qualitative diagrams and models “must come before students start using math in problem solving. The equations become crutches that short-circuit attempts at understanding.” Van Heuvelen also urges that “instead of thinking of [problems] as an effort to determine some unknown quantity, [teachers] might … encourage students to think of the problem statement as describing a physical process—a movie of a region of space during a short time interval or of an event at one instant of time.” I suspect Singh, Belloni, and Christian would agree with this advice. They comment that such “qualitative understanding of quantum mechanics is much more challenging than facility with the technical aspects.”
But isn't the main barrier to such intuitive, qualitative understanding the nature of quantum mechanics itself—at least, the version of the theory advocated by Niels Bohr, Werner Heisenberg, and virtually every textbook writer since? Why should we expect students to invest the time and energy necessary to, say, visualize the time-dependence of |ψ|2 when we also preach the ambiguous and contradictory Copenhagen dogma that ψ does not represent anything physically real, yet still provides a complete description of physical reality? Why are we surprised that students are confused about, and don't take seriously, something that we assure them is, at best, some kind of algorithmic fantasy? Is there really any difference between “shut up and calculate” and “plug and chug”?
Why not teach them Bohmian mechanics—an alternative (deterministic) version of quantum theory in which particles are particles (and really exist, all the time) and the same dynamical laws apply whether anyone is looking or not? 2 About this alternative theory John S. Bell asked, “Why is [it] ignored in text books? Should it not be taught … as an antidote to the prevailing complacency? To show that vagueness, subjectivity, and indeterminism are not forced upon us by experimental facts, but by deliberate theoretical choice?” 3
If we really want to help students understand quantum mechanics, the first step is to reject the confusion-spawning foundational vagueness, ambiguity, and philosophical absurdity of Copenhagen quantum theory, and adopt a clearer, more scientific, less fuzzy version. (See Sheldon Goldstein's two-part article “Quantum Theory Without Observers,” Physics Today, March 1998, page 42, and Physics Today, April 1998, page 38) The first step, in short, is to present them with a theory that can be understood.
