Contrast our ignorance on this score with our ability to understand the nature of other problems attendant on relative motion. For example, a monochromatic source of light at rest appears yellow, whereas, when moving towards us with a sufficiently high speed, it appears greenish. But there is nothing mysterious about this change in colour; we could have foreseen it, knowing what we do of the wave nature of light. The situation was much more obscure in the case of electromagnetics. Einstein’s theory solves the entire problem. Consider the simple case of a charge in uniform motion. We have said that owing to its motion it develops a magnetic field (just like a current), in addition to its electric field. But in Einstein’s theory velocity through the ether is meaningless; hence there is no such thing as a charge in uniform motion in any absolute sense. If we were to rush after the electrified body and accompany it in its motion, it would cease, according to Einstein, to be a moving charge and would become a charge at rest in our frame; but then its erstwhile magnetic field would necessarily have vanished, the electric field alone remaining. We must assume, therefore, that the appearance of the magnetic field arises only because we have changed our Galilean frame of reference by passing from one fixed with respect to the charge to one in relative motion. Now, the Lorentz-Einstein transformations tell us how our space and time measurements change under these circumstances; and by applying the transformations to the equations of electrodynamics we are able to ascertain how an electric field which is purely electric when viewed from one frame should appear to us when viewed from another Galilean frame. Proceeding in this way, we do in fact find that the electric field of the electrified body at rest will appear as an electromagnetic field when the body is set in relative motion. Likewise, the precise mathematical formula for the new field is obtained, proving [Pg 149] incidentally that our classical empirical formula was only approximate. Thus a rational justification for the appearance of a magnetic field round an electrified charge in motion is finally obtained, and this field is seen to be a direct consequence of the variations in those fundamental space and time forms of perception—variations which are expressed by the Lorentz-Einstein transformations. In exactly the same way a magnetic pole in motion develops an electric field around it in addition to its magnetic field when at rest, and it is this phenomenon that gives rise to the electromagnetic induction on which we base our generators and dynamos. Here again the Lorentz-Einstein transformations throw complete light on the subject.[47]