For a long time physicists have admitted that the ether as a whole must be considered as being immovable and capable of serving, so to speak, as a support for the axes of Galileo, in relation to which axes the principle of inertia is applicable,—or better still, as M. Painlevé has shown, they alone allow us to render obedience to the principle of causality.
But if it were so, we might apparently hope, by experiments in electromagnetism, to obtain absolute motion, and to place in evidence the translation of the earth relatively to the ether. But all the researches attempted by the most ingenious physicists towards this end have always failed, and this tends towards the idea held by many geometricians that these negative results are not due to imperfections in the experiments, but have a deep and general cause. Now Lorentz has endeavoured to find the conditions in which the electromagnetic theory proposed by him might agree with the postulate of the complete impossibility of determining absolute motion. It is necessary, in order to realise this concord, to imagine that a mobile system contracts very slightly in the direction of its translation to a degree proportioned to the square of the ratio of the velocity of transport to that of light. The electrons themselves do not escape this contraction, although the observer, since he participates in the same motion, naturally cannot notice it. Lorentz supposes, besides, that all forces, whatever their origin, are affected by a translation in the same way as electromagnetic forces. M. Langevin and M. H. Poincaré have studied this same question and have noted with precision various delicate consequences of it. The singularity of the hypotheses which we are thus led to construct in no way constitutes an argument against the theory of Lorentz; but it has, we must acknowledge, discouraged some of the more timid partisans of this theory.[48]
§ 3. THE MASS OF ELECTRONS
Other conceptions, bolder still, are suggested by the results of certain interesting experiments. The electron affords us the possibility of considering inertia and mass to be no longer a fundamental notion, but a consequence of the electromagnetic phenomena.
Professor J.J. Thomson was the first to have the clear idea that a part, at least, of the inertia of an electrified body is due to its electric charge. This idea was taken up and precisely stated by Professor Max Abraham, who, for the first time, was led to regard seriously the seemingly paradoxical notion of mass as a function of velocity. Consider a small particle bearing a given electric charge, and let us suppose that this particle moves through the ether. It is, as we know, equivalent to a current proportional to its velocity, and it therefore creates a magnetic field the intensity of which is likewise proportional to its velocity: to set it in motion, therefore, there must be communicated to it over and above the expenditure corresponding to the acquisition of its ordinary kinetic energy, a quantity of energy proportional to the square of its velocity. Everything, therefore, takes place as if, by the fact of electrification, its capacity for kinetic energy and its material mass had been increased by a certain constant quantity. To the ordinary mass may be added, if you will, an electromagnetic mass.
This is the state of things so long as the speed of the translation of the particle is not very great, but they are no longer quite the same when this particle is animated with a movement whose rapidity becomes comparable to that with which light is propagated.
The magnetic field created is then no longer a field in repose, but its energy depends, in a complicated manner, on the velocity, and the apparent increase in the mass of the particle itself becomes a function of the velocity. More than this, this increase may not be the same for the same velocity, but varies according to whether the acceleration is parallel with or perpendicular to the direction of this velocity. In other words, there seems to be a longitudinal; and a transversal mass which need not be the same.
All these results would persist even if the material mass were very small relatively to the electromagnetic mass; and the electron possesses some inertia even if its ordinary mass becomes slighter and slighter. The apparent mass, it can be easily shown, increases indefinitely when the velocity with which the electrified particle is animated tends towards the velocity of light, and thus the work necessary to communicate such a velocity to an electron would be infinite. It is in consequence impossible that the speed of an electron, in relation to the ether, can ever exceed, or even permanently attain to, 300,000 kilometres per second.
All the facts thus predicted by the theory are confirmed by experiment. There is no known process which permits the direct measurement of the mass of an electron, but it is possible, as we have seen, to measure simultaneously its velocity and the relation of the electric charge to its mass. In the case of the cathode rays emitted by radium, these measurements are particularly interesting, for the reason that the rays which compose a pencil of cathode rays are animated by very different speeds, as is shown by the size of the stain produced on a photographic plate by a pencil of them at first very constricted and subsequently dispersed by the action of an electric or magnetic field. Professor Kaufmann has effected some very careful experiments by a method he terms the method of crossed spectra, which consists in superposing the deviations produced by a magnetic and an electric field respectively acting in directions at right angles one to another. He has thus been enabled by working in vacuo to register the very different velocities which, starting in the case of certain rays from about seven-tenths of the velocity of light, attain in other cases to ninety-five hundredths of it.
It is thus noted that the ratio of charge to mass—which for ordinary speeds is constant and equal to that already found by so many experiments—diminishes slowly at first, and then very rapidly when the velocity of the ray increases and approaches that of light. If we represent this variation by a curve, the shape of this curve inclines us to think that the ratio tends toward zero when the velocity tends towards that of light.