Nobel Lecture: Fractional quantization

Abstract

One of my favorite times in the academic year occurs in early spring when I give my class of extremely bright graduate students, who have mastered quantum mechanics but are otherwise unsuspecting and innocent, a take-home exam in which they are asked to deduce superfluidity from first principles. There is no doubt a special place in hell being reserved for me at this very moment for this mean trick, for the task is impossible. Superfluidity, like the fractional quantum Hall effect, is an emergent phenomenon—a low-energy collective effect of huge numbers of particles that cannot be deduced from the microscopic equations of motion in a rigorous way and that disappears completely when the system is taken apart (Anderson, 1972). There are prototypes for superfluids, of course, and students who memorize them have taken the first step down the long road to understanding the phenomenon, but these are all approximate and in the end not deductive at all, but fits to experiment. The students feel betrayed and hurt by this experience because they have been trained to think in reductionist terms and thus to believe that everything not amenable to such thinking is unimportant. But nature is much more heartless than I am, and those students who stay in physics long enough to seriously confront the experimental record eventually come to understand that the reductionist idea is wrong a great deal of the time, and perhaps always. One common response in the early stages of learning is that superconductivity and the quantum Hall effect are not fundamental and therefore not worth taking seriously. When this happens I just open up the AIP Handbook and show the disbeliever that the accepted values of e and h are defined by these effects, and that ends that. The world is full of things for which one’s understanding, i.e., one’s ability to predict what will happen in an experiment, is degraded by taking the system apart, including most delightfully the standard model of elementary particles itself. I myself have come to suspect most of the important outstanding problems in physics are emergent in nature, including particularly quantum gravity. One of the things an emergent phenomenon can do is create new particles. When a large number of atoms condense into a crystal, the phonon, the elementary quantum of sound, becomes a perfectly legitimate particle at low energy scales. It propagates freely, does not decay, carries momentum and energy related to wave-