More than a century after James Clerk Maxwell first elucidated the phenomenon of electromagnetism, the implications of his famous formulas are still not fully understood. Although Maxwell’s equations contain only electric and magnetic fields, they can be conveniently expressed in terms of electric and magnetic potentials, quantities whose spatial and temporal variations determine the field strengths. In theory, the potentials themselves have no significance. All the physics is contained in the forces exerted on charged particles, and because those forces are directly proportional to the field strengths, they vanish where the field strengths vanish. Physicists are free to add terms to the potentials that leave the fields invariant, a flexibility known as gauge freedom.
Maxwell’s classical view, in which the potentials are not physical, was radically revised with the advent of quantum mechanics in the early 20th century. Heisenberg’s uncertainty principle is incompatible with the notion of a point particle....
