Through this constant radiation of energy, the sun and stars would be gradually losing in mass; for light was of course a form of energy. As such, light should possess mass and momentum and exert a pressure over bodies on which it impinged. This pressure, indeed, was not unknown, since it resulted from Maxwell’s equations and had been verified experimentally by Lebedew and by Nichols and Hull. As a matter of fact it was to this pressure of light that the apparent repulsion of comets’ tails away from the sun was supposed to be due. Nevertheless, though not a new discovery, the fact that Einstein’s theory entailed momentum for light constituted one of the many indirect confirmations of the theory.
An objection which has often been raised by non-mathematical students is the following: They argue that since energy moving with the velocity of light must possess an infinite mass, we should be crushed under the tremendous impact of light rays falling on our bodies. In an elementary book of this sort we cannot go into mathematical details, but we may say that the argument is fallacious. It is only ponderable matter constituted by bound energy which would become infinite in mass when moving with the velocity of light. Light rays represent another type of energy, known as free or loose energy, and calculation shows that the momentum produced by this form of energy moving with the velocity of light is not infinite, but exceedingly minute.
Of course the theory of relativity is not one of pure mathematics. Einstein was not solely interested in juggling with equations and laws to make them fit into his scheme. The final verdict of the correctness of a theory of mathematical physics must always rest with the experimenter, and it remained to be seen whether the Einsteinian equations of mechanics corresponded more accurately to facts than did the classical ones. We may state that the most precise experiments have proved the correctness of the Einsteinian laws of mechanics and that Bucherer’s experiment proving the increase in mass of an electron in rapid motion is a case in point.[51]
It should be clear by now that very important differences distinguish the theory of Einstein from that of Lorentz. Lorentz also had deduced from his theory that the mass of an electron should increase and grow infinite when its speed neared that of light; but the speed in question was the speed of the electron through the stagnant ether; whereas in Einstein’s theory it is merely the speed with respect to the observer. According to Lorentz, the increase in mass of the moving electron was due to its deformation or FitzGerald contraction. The contraction modified the lay of the electromagnetic field round the electron; and it was from this modification that the increase in mass observed by Bucherer was assumed to arise. In Einstein’s theory, however, the increase in mass is absolutely general and need not be ascribed to the electromagnetic field of the electron in motion. An ordinary unelectrified lump of matter like a grain of sand would have increased in mass in exactly the same proportion; and no knowledge of the microscopic constitution of matter is necessary in order to predict these effects, which result directly from the space and time transformations themselves.
Furthermore, the fact that this increase in mass of matter in motion is now due to relative motion and not to motion through the stagnant ether, as in Lorentz’s theory, changes the entire outlook considerably. According to Lorentz, the electron really increased in mass, since its motion through the ether remained a reality. According to Einstein, the electron increases in mass only in so far as it is in relative motion with respect to the observer. Were the observer to be attached to the flying electron no increase in mass would exist; it would be the electron left behind which would now appear to have suffered the increase. Thus mass follows distance, duration and electromagnetic field in being a relative having no definite magnitude of itself and being essentially dependent on the conditions of observation.
Owing to the general validity of the Lorentz-Einstein transformations, it becomes permissible to apply them to all manner of phenomena. In this way it was found that temperature, pressure and many other physical magnitudes turned out to be relatives. On the other hand, entropy, electric charge and the velocity of light in vacuo were absolutes transcending the observer’s motion. Later on we shall see that a number of other entities are found to be absolutes, the most important of which is that abstract mathematical quantity called the Einsteinian interval, which plays so important a part in the fabric of the new objective world of science, the world of four-dimensional space-time.
CHAPTER XV
CONSEQUENCES OF THE NEW SPACE AND TIME MEASUREMENTS—SIMULTANEITY
IN the preceding chapters we endeavoured to show how Einstein’s fundamental premises—the relativity of Galilean motion through space or the ether and the postulate of the invariant velocity of light—had been posited as a result of induction from ultra-precise experiment. Once these postulates are accepted, all the strange consequences of the special theory are obtained deductively by elementary mathematical reasoning.
In view of the extreme importance of the problem let us recall that the postulate of the invariant velocity of light assumes that a ray of light, in vacuo, will pass through any Galilean frame whatever with the same invariant speed
