Vector Potential, Electromagnetic Induction and 'Physical Meaning'

This is a nice paper exploring the "meaning" of the vector potential that every physics student encounter in classical E&M.

"Vector potential, electromagnetic induction and 'physical meaning'", G. Giuliani, Eur. J. Phys. 31 871 (2010).

{the paper is available for free downloads during the first 30 days of online publication. Paper was published online on 8 June 2010}

This is a good paper for undergraduate students to read, because it clearly shows why the vector potential is not only amazingly useful, but also why it is important. One only needs to see that the vector potential is one of the few quantities that are involved in the quantum Hamiltonian.

What is also interesting about this paper is that there is quite a discussion on what is meant, at least in physics, by the phrase "physical meaning".

These considerations lead us to the crucial point; the physical meaning of a theoretical term relies, primarily, on theoretical grounds. We suggest that a theoretical term has a physical meaning if

(C1) its elimination reduces the predictions—experimentally testable—of a theory; or, in a weaker sense, if

(C2) its elimination reduces the descriptive proficiency of a theory.

Maybe this is a more meaningful definition, rather than discussing what is "real". It reduces the criteria of what has a physical meaning to something more testable, rather than just simply being a matter of tastes or personal preference. This then puts new light into the maddening discussion on whether time is an "illusion". As I've argued earlier, try removing any time dimension out of the Lagrangian/Hamiltonian formulation. Now, do you still have a complete description of the dynamics of the system? Does the removal of time reduces the predictions of a large section of physics, if not all?

Damn right it does!

Time has a physical meaning, and that statement is physically meaningful.

Zz.