outside the solenoid. There is, however, a potential outside the solenoid that suffices to explain the deflection. The effect remained controversial until it was verified experimentally [@tonomura]. This has the basic consequence that potentials are more fundamental than fields. The Aharonov-Bohm effect is founded on a single explicitly quantum-mechanical phenomenon, and commentary about its significance has been in terms of quantum mechanics [@furry; @vaidman].

The concept explored here is different from that of the Aharonov-Bohm effect, and much more consequential. It is shown that a change of gauge can introduce a violation of basic symmetries, even when the usual constraints on allowable gauge transformations have been satisfied. Furthermore, these symmetry violations can occur in classical physics as well as in quantum mechanics with external electromagnetic fields. The consequences of these results are profound. There exist contrasting sets of potentials that yield exactly the same fields, but where one set is consonant with physical requirements but another is not. This proves directly that the selection of the proper set of potentials is the decisive matter, since the predicted fields are the same in both cases. A corollary is that gauge transformations are not unitary transformations. This contradicts the field-based assumption that 