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.
Bibliographical noteFunding Information:
I would like to thank Yemima Ben-Menahem and Daniel Rohrlich for their guidance and advice, and an anonymous reviewer for his helpful feedback. This research was supported by the Israel Science Foundation (Grant No. 1190/13) and by The Open University of Israel’s Research Fund (Grant No. 41240).
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- Aharonov–Bohm effect
- Gauge symmetries
- Principle of equivalence
- Quantum mechanics