Einstein's Theories of Relativity and Gravitation / A selection of material from the essays submitted in the competition for the Eugene Higgins prize of $5,000

by J. Malcolm Bird

This sounds ridiculous, but not only is it what Jeans says, but it is the logical interpretation of Einstein’s second principle, if Einstein means by velocity, velocity with regard to the observer. If he means velocity with regard to the medium, then the case is exactly the same as that of sound in air, and Michelson’s experiment as well as the Maxwell-Lorentz theory of light are contradicted. This theory is now universally accepted, and Michelson’s experiment has been carefully repeated by other observers, and fully confirmed. This is the very heart of the relativity question.

If we state the matter objectively it comes to this. The velocity of light with regard to the ether is a variable quantity, depending merely on where the observer chooses to go. As Eddington well says, “these relations to the ether have no effect on the phenomena and can be disregarded—a step which appears to divest the ether of the last remnants of substantiality.”^[4]

The only way of avoiding this apparent absurdity seems to be to consider that the ether moves with the earth. Michelson’s result would then be fully explained. Of course this can only be true for a few miles above the earth’s surface. Beyond that the ether must either be stationary or move with the sun. The velocity of light with regard to the ether would then be a constant, just as the velocity of sound is constant with regard to the air. This would contradict Einstein’s second principle as it is generally understood. The trouble with this suggestion is that it fails to account for aberration, which, as already explained, appears to require that the earth should be moving through the ether. To meet this emergency would involve some modification of the undulatory theory of light, which apparently would not be impossible, but has not yet been made.

In 1915 Einstein brought out an extension of his first principle. This he calls the “general theory of relativity.” It states that in our choice of coordinate systems we “should not be limited in any way so far as their state of motion is concerned.”^[1] This leads to the three astronomical consequences mentioned later in this paper, two of which have been more or less confirmed, and the third practically contradicted as far as quantitative measures are concerned.^[5]

As is well known the kinetic energy of a moving body may be expressed as

, but if the body is charged electrically, the fraction becomes

, where m′ is a quantity dependent on the square of the electrical charge. That is to say, we have the normal mass of the body, and also what we may call its electrical mass. If when in this condition a portion of the mass is electrical, the question at once occurs to us, why may not the whole mass be electrical, in other words, a form of energy? Although this has not been satisfactorily proved hitherto, yet such is the general belief among physicists. As Einstein puts it “inert mass is nothing else than latent energy.”^[1] The same idea is sometimes expressed as “the mass of ordinary matter is due to the electromagnetic energy of its ultimate particles, and electromagnetic energy wherever found must possess mass, i.e., inertia.”^[6] If that is so, since a ray of light on the undulatory theory is a form of electromagnetic energy, it too must possess mass. Since all mass with which we are familiar is subject to the attraction of gravitation, it seemed likely that a ray of light would be bent out of its course in passing near the sun, and this as we have seen was proved to be true at the recent solar eclipse.

That portion of the mass of a body due to its electrical charge can be readily shown experimentally to vary with the velocity of the body. Einstein has shown the same to be true of the normal mass, as is illustrated in the advance of the perihelion of the orbit of Mercury. He has also pointed out that gravitation, inertia and centrifugal force are all closely related, and obey similar laws. Thus if we rise from the earth with accelerated velocity, we apparently increase our weight. Again if the velocity of rotation of the earth on its axis should be increased, our weight would be diminished. These facts are suggestive when we come to consider the ultimate cause of gravitation.