Potential Arbitrariness in Electrodynamics - How Can It Be?

[paddo]

My electrodynamics lecturer was talking about how potentials are arbitrary and that's why we have different gauges. I'm not too sure about how potentials can be arbitrary. Up to a constant? How?
Cheers,

 

[atyy]

The gravitational potential is arbitrary up to an additive constant. It is arbitrary because physical predictions are made using grad(potential), not the potential itself.

It is the same in (classical) electrostatics. The final step in making a physical prediction always involves the E field, not the electric potential.

The arbitrariness of the vector potential A with respect to the B field is not just a scalar constant.
http://en.wikipedia.org/wiki/Vector_potential

 

[granpa]

true but the amount of energy stored in the field is not arbitrary. that would be the integral of the square of the field strength. classically speaking at least.