Why within classical field-theory the electromagnetic four-potential (usually $A_{\mu}$) not an observable?
In classical mechanics we don't have problems with energy measurements and in quantum mechanics we talk all the time about the Hamiltonian which "is the observable of energy".
So why is $A_{\mu}$ not also considered as an observable? If we don't have a smart way to measure it how can we be 100% certain that tomorrow some dude won't figure out how to do it?
This confuses me greatly, especially with respect to the Aharonov–Bohm effect which is within quantum mechanics "a way to measure $A$".
The non-observable nature of $A$ seems to be the reason why we "gauge" it in order to do all kinds of stuff. That is why I'm interested in it.
Answer
The four-potential is not an observable because it is not invariant under a change of gauge. And no predictions of any physical theory are dependent on the choice of gauge, so the four-potential is not observable.
What is gauge invariant and observable is the integral of the four potential around a loop, and that is what is observed in the AB effect. However, it should be noted that the AB effect can be explained entirely in terms of local action by fields. As such, there is no reason to invoke the four potential to explain what's going on. The potential may sometimes be useful for doing calculations, but that is a different issue from whether it is an observable.
No comments:
Post a Comment