Vector Potential: Reality or Tool?

[curupira]

Has vector potential in classical electrodynamics a physical reality or it's just a mathematical tool?

 

[Petr Mugver]

It's just a (very useful) tool. Only the electric and magnetic fields have physical meaning. That's why you can make a Gauge transformation on the potentials (they change the potentials but not the fields) without altering the results.

 

[Born2bwire]

But in quantum electrodynamics it is physical in the sense that it is now the primitive constituents of the electromagnetic field. This was proven with the Aharonov-Bohm Effect which showed that while there may not be any fields in a region, a non-zero vector potential (and scalar potential too since you need both to describe the fields) can have measurable effects. This is not true in classical electrodynamics but if you have heard of such things this is probably where it came from.

 

[K^2]

In QM, vector potential is physical, but not observable. In that sense, it is not unlike wave functions. In fact, in QED, it is essentially one of the wave functions.

Of course, the problem with non-observable quantities in QM is that you cannot tell if these are true physical quantities, or merely convenient mathematical representations for something else. So this doesn't mean that vector potential is "real". Merely that there is a real physical object that it represents.

 

[Petar Mali]

Vector potential don't but circulation of vector potential

$$\oint_L\vec{A}\cdot d\vec{l}=\int_S\vec{B}\cdot d\vec{S}=\Phi_B$$

is magnetic flux.

 

[Meir Achuz]

E,B and A,phi are two alternate ways of calculating physical observables. Neither are observable in themselves.