  This paper formulates generalized versions of the general principle of
relativity and of the principle of equivalence that can be applied to general
abstract spaces. It is shown that when the principles are applied to the
Hilbert space of a quantum particle, its law of coupling to electromagnetic
fields is obtained. It is suggested to understand the Aharonov-Bohm effect in
light of these principles, and the implications for some related foundational
controversies are discussed.
