 Quote by TrickyDicky
Do you agree that starting with the loop integral of A to get the flux is not allowed unless you consider the vector potential physically significant to begin with, ...
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yes, one must attribute a fundamental, physical role to the vector potential; otherwise this reasoning would not be
forbidden, but physically unreasonable (*)
Quote by TrickyDicky
... but that is something that classically was not considered possible, ...
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no, it is
possible classically, but it's not
necessary in classical electrodynamics; there everything, including interaction with charged particles, can be described in terms of E and B; A is only an auxiliary variable;
(*) one could even say that using A introduces gauge invariance and unphysical redundancy which has to be removed via gauge fixing, so in some sense using A instead of E and B could even be seen as pointless
Quote by TrickyDicky
... and that is only considered the right explanation from a prediction in QM and the empirical proof of the AB effect.
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yes, it's QM which indicates that one should use A instead of B; [itex]\oint_C A[/itex] is a physical, gauge invariant observable in classical electrodynamics; but it's QM which tells us that we should better use [itex]\oint_C A[/itex] instead od [itex]\int_S B[/itex]; in classical electrodynamics based on (*) we would prefer [itex]\int_S B[/itex]
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