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An outline is given as to how gauge transformations in a frame fiber can be interpreted as defining various types of transport of a moving frame along a path. The cases of general linear, parallel, Lorentz, and other transport groups are examined in Minkowski space-time. A specific set of frame coordinates is introduced. A number of results are obtained including a generalization of Frenet-Serret transport, an extension of Fermi-Walker transport, a relation between frame spaces and certain types of Finsler space, and a derivation of a Kaluza-Klein type metric. Frame transport in general Riemannian space-time is also discussed.

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.