The evolution of scientific thought from Newton to Einstein

by A. D'Abro

For instance, we mentioned that a charged body at rest was surrounded by an electric field of force, whereas the same body in motion (or an electric current) was surrounded both by an electric and a magnetic field. Ampère had given a formula describing the distribution and intensity of the electromagnetic field surrounding an electric current of any given intensity. But this formula was purely empirical, and it was felt that we should have been able to anticipate the existence of this electromagnetic field and derive an exact expression of its disposition and magnitude by purely rational methods. These hopes were disappointed; for there appeared to be no rational connection between the field developed by an electrified body when at rest and its field when set in motion.

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 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]

In a general way the transformations show us that a field which appears to be exclusively electric or exclusively magnetic in one Galilean frame will appear to be electromagnetic in another frame, thereby compelling us to recognise the relativity of electric and magnetic forces. We shall see in due course that this relativity of force is general.

Let us consider another type of phenomenon which is also explained by the transformations. We refer to the Fresnel convection coefficient illustrated by Fizeau’s experiment. Experiment proves that the ray of light progressing through the running water is not carried along bodily by the water; it lags behind a little. Lorentz who, though he had discovered the transformations, did not recognise their general validity, sought to explain this phenomenon by postulating a suitable electronic constitution for the water. But Einstein by merely applying the transformations, without having to appeal to our highly problematic knowledge of the precise electronic constitution of matter, found that they anticipated Fizeau’s result with marvellous precision; for according to the transformations, velocities do not add up like numbers, as they did in classical science. It follows that the velocity of the light with respect to the tube must necessarily be less than the velocity of the light through the water plus the velocity of the water in the tube.[48]

Consider again the FitzGerald contraction. Here Lorentz thought it permissible to apply the transformations; but owing to the slight difference in their significance in his theory, he concluded that a body in motion was really contracted owing to its real motion through the ether. Although the observer carried along with the body could not detect the contraction, yet it was physically real and would be observed by the observer at rest in the ether. A similar interpretation would have to be placed on the slowing down of phenomena. In Lorentz’s theory the difficulty consisted in accounting for an identical contraction manifesting itself in exactly the same way for all bodies, soft or hard. Lorentz again appeals to the electronic and atomic constitution of matter and has to take into consideration elastic forces.

With Einstein the explanation is simple. The contraction is due solely to a modification in our space and time measurements due to relative motion, and is completely irrelevant to the hardness or softness of the body, whose atomic or electronic structure need not be taken into consideration at all. In much the same way an object appears magnified under the microscope, and this magnification is independent of the body’s nature.

In short, the modifications are due to variations (as a result of relative motion) in our space and time measurements and perceptions, and in every case they are irrelevant to the microscopic constitution of matter. We see, then, that so far as all these curious modifications are concerned, Einstein s theory does not require any particular knowledge of the microscopic constitution and hidden mechanisms that are assumed to underlie matter. Herein resides one of the principal advantages of Einstein’s theory over that of Lorentz; for we know very little about the mysterious nature of electricity and matter, and were all progress to be arrested until such knowledge was forthcoming, we might have to wait many a day without result.