Quantum aspects of the equivalence principle

Two thought experiments are discussed which suggest, first, a geometric interpretation of the concept of a (say, vector) potential (i.e., as a kinematic quantity associated with a transformation between moving frames of reference suitably related to the problem) and, second, that, in a quantum treatment one should extend the notion of the equivalence principle to include not only the equivalence of inertial forces with suitable real forces, but also the equivalence of potentials of such inertial forces and the potentials of suitable real forces. The two types of cancellation are physically independent of each other, because of the Aharonov-Bohm effect. Finally, we show that the latter effect itself can be understood geometrically as a kinematic effect arising upon the transformation between the two reference frames.On leave of absence from the Department of Physics, Tel-Aviv University, Israel, and the Department of Physics, Yeshiva University, New York.Supported by the NSF under Contract GP-14911.