45
This shows37 that Maxwell's equations have relativistic solutions only when relativistic treatment of charges and currents is introduced, while they can have equally good "classical" solutions when these terms are defined in a classical way. Let us remark too that the difference between AS and A*S is "very small", since the two potentials are indeed equal up to second order in β , but that it is not so small to be neglected (see footnote 32), since, in force of (7), one must have (and one has): div(AS) = - c-2
∂Φ S , ∂t
∂ Φ *S div(A*S) = - c-2 ∂ t , and these formulae show that the small difference becomes essential in the second case, when a small term (the divergence of the magnetic potential) is multiplied by c 2 , and thus it gives a meaningful non-zero time-variation of the electric potential, a potential which cannot vanish (in the first case, instead, the divergence of the magnetic potential is exactly equal to zero). In conclusion, we should ask once again: who is really (that is to say: experimentally) right, C or E ? The aforesaid divergence can be elaborated in view of the proposal of a new gedankenexperiment aimed to discriminate between classical and relativistic interpretations of ME . One could either try to perform direct measures of the force acting on the charge q , or better of the electric potential difference across a thin linear conductor T placed along a radius with an extremity in the centre of C and the other one close to the current wire, as in the following picture:
We could attempt to make in evidence a possible Earth's absolute velocity (and this is why the sensor and the circuit's plane have been projected to be able to rotate, since this velocity is unknown), but, as we already said many times, the apparatus should be put in a real motion with respect to an ordinary Earth's laboratory, before saying that this test has given all possible information. The fact that the force predicted by C does depend both on the intensity and on the direction of the current, should make it possible to separate a non-zero effect from other possible "disturbances" (due for instance to the electromagnetic fields existing in the terrestrial reference frame, and to other sources of systematic errors, or even to the possible