On the Galilean non-invariance of classical electromagnetism

When asked to explain the Galilean non-invariance of classical electromagnetism on the basis of pre-relativistic considerations alone, students-and sometimes their teachers too-may face an impasse. Indeed, they often argue that a pre-relativistic physicist could most obviously have provided the explanation 'at a glance', on the basis of the presence of a parameter c with the dimensions of a velocity in Maxwell's equations, being well aware of the fact that any velocity is non-invariant in Galilean relativity. This 'obvious' answer, however popular, is not correct due to the actual observer-invariance of the Maxwell parameter c in pre-relativistic physics too. A pre-relativistic physicist would therefore have needed a different explanation. Playing the role of this physicist, we pedagogically show how a proof of the Galilean non-invariance of classical electromagnetism can be obtained, resting on simple pre-relativistic considerations alone.