Gauging the Aharonov-Bohm effect.

Gauging the Aharonov-Bohm effect 

Now seems to be the season for the experimental realization of paradoxical quantum mechanical effects (SN: 2/1/86, p. 70; 2/8/86, p. 87). This week it's the Aharonov-Bohm effect, in which a magnetic field alters the behavior of electrons without touching them. In the Feb. 24 PHYSICAL LETTERS, Akira Tonomura and six colleagues working in the laboratories of Hitachi Ltd. in Tokyo report what they describe as the definitive experiment.

In 1959 Yakir Aharonov of the University of South Carolina-Columbia and David Bohm of Birkbeck College of the University of London, England, predicted that if two beams of electrons passed on either side of a space in which a magnetic field was present, the phase of the quantum mechanical waves belonging to one of the beams would be retarded with respect to the phase of the other, even though the field did not penetrate the space in which the electrons moved and the electron waves did not touch the field. "such an effect is inconceivable in classical physics...," Tonomura and co-workers point out. One possible interpretation of the effect is that it is an "action at a distance," in which one thing affects another thing without any physical contact.

To demonstrate the effect, experimenters must thoroughly shield the magnetic field. Since 1959 several experiments, including one reported by Tonomura's group in 1982, have purported to show the Aharonov-Bohm effect, but they have been severely criticized on grounds that magnetic field might be leaking into the space traversed by the electrons. Tonomura and co-workers assert that this time they have done all possible to satisfy the critics, and their results is iron-clad -- or rather, niobium- and copper-clad.

They made a ring-shaped magnet out of nickel-iron Permalloy coated with niobium. At temperatures near absolute zero, niobium is a superconductor and therefore expels magnetic fields that try to penetrate it. Laying it all around the magnet forces the magnetic field to remain effectively inside the magnet itself. Outside the niobium shield they put a copper shield. Copper prevents the electron waves from any possible penetration into the magnet. One beam of electrons went through the hole in the ring; the other went outside the ring. After passing by the field, the electron beams were made to interfere with each other, producing a hologram that revealed the relation between their phases.

Tonomura and co-workers concede that experimentally it is impossible ever to get exactly zero magnetic field, and they hope the critics will agree that what occurs at a negligible amount of field is effectively the same as what happens at zero field, and not demand the ideal. Otherwise "only a futile agnosticism results," they point out.

In addition to action at a distance, the Aharonov-Bohm effect has another interpretation, related to a mathematical quantity known as the electromagnetic vector potential. Many decades ago, physicists working on a unified mathematical description of electricity and magnetism found this vector potential, from which descriptions of both electric and magnetic phenomena could be derived. However, this mathematical unifier seemed to have no physical existence in itself. No phenomena could be directly attributed to it.

In 1916 Albert Einstein published his general relativity theory, which attributes gravitational forces to changes in the curvature of space from point to point. Following Einstein's example, Hermann Weyl tried to relate electromagnetic forces to geometry. He used the vector potential, and because of the way it acts mathematically, he tried to relate it to changes of scale or "gauge" that he imagined between different points in space. This somewhat weird idea is akin to meter sticks or other measuring standards having different sizes at different points in space. The attempt failed as physicists found that subatomic particles have an intrinsic scale or gauge that cannot change from place to place.

As quantum mechanics developed, however, Weyl found a quantity that does change in the proper way and to which he could relate the vector potential: the phases of the waves associated with material objects. Confusingly the term "gauge" is still used although it refers no longer to changes in the phases of matter waves and of the internal properties of subatomic particles (the properties that determine their identities, really) that are related to the phases. In this sense the guage principle has become very important in theories of particle physics, which are concerned with how the identities of the particles come to be. The Aharonov-Bohm effect can be interpreted to mean that the magnetic field acts on the phases of the electron waves through the vector potential. It is thus evidence of the physical reality of the vector potential and of the "gauge" nature of electromagnetism.