Part 3 — CHAPTER XXX THE VERIFICATION OF EINSTEIN’S LAW
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EINSTEIN’S law, as we have expressed it, is one of space-time curvature around matter and in the interior of matter. It is also the law of distribution of the ten potentials or ’s throughout space-time, or, again, the law of distribution of the four-dimensional metrical field or guiding field of space-time. But in order to study the implications of the law we may discuss it from yet another angle.
Being a law of space-time curvature or structure, we are able to derive from it the precise lay of the geodesics of space-time around matter. These geodesics, or paths of least resistance, are, we remember, the paths which planets, light rays and all free bodies will pursue. A knowledge of the lay of the geodesics around the sun will therefore allow us to determine the precise courses in space and the precise motions along these courses of all free bodies moving in a gravitational field. When these geodesics are submitted to mathematical analysis, it is found that the courses and motions of the planets should be very nearly identical with those required by Newton’s law.
There would be slight discrepancies, however, between the requirements of the two laws. In particular, Einstein’s law of gravitation would predict that the courses of the planets should be very nearly elliptical, but not exactly so; there should be a slight precession of the perihelion of the planet, increasing in magnitude with the velocity of the planet on its orbit. Now the most rapidly moving planet of the solar system is Mercury; and Leverrier had observed nearly a century ago that Mercury’s perihelion displayed a precessional motion which Newton’s law was unable to explain. Einstein’s law accounts for this precessional motion, not only qualitatively, but quantitatively as well. Hence, a first verification of Einstein’s law was obtained.
Here it must be noticed that, in the preceding example, Mercury’s curious motion was already known to astronomers. But we have said enough of Einstein’s methodology in his discovery of the law of space-time curvature to realise that he did not adjust his law of space-time so as to account for Mercury’s hitherto unexplained motion. We saw, indeed, that the law of gravitation, as formulated by him, was practically inevitable if the principle of action, the most fundamental pillar of science, was to endure. However, in the following verification, we shall see that Einstein’s law was able to foretell the existence of a phenomenon totally unsuspected by classical science. We refer to the deviation of a light ray in a gravitational field.
Classical science had always assumed that a gravitational field, such as that of the sun, would attract material bodies, but that it would be without effect on light rays, which were considered to be immune from gravitational attractions. Had classical science been thoroughly convinced of the identity of the two types of mass, it would have realised that light waves must be possessed of gravitational mass, since they were known to manifest the characteristics of inertial mass. This inertial property of light rays had been foreseen theoretically by Maxwell and proved experimentally by Lebedew, who detected the pressure exerted by rays of light on a body on which they impinge. It is a pressure of this type which is supposed to be responsible for the apparent repulsion of comets’ tails away from the sun. It would have been, therefore, only a step to assume that light rays must manifest gravitational mass, and hence must be attracted by the sun.
Classical science, however, had never felt justified in taking this step. As a result, it was thought that light rays would proceed in straight lines through a gravitational field just as they would through free space far from matter. When, therefore, the first eclipse observations prompted by Einstein’s predictions revealed an undeniable bend in the course of a ray of light emitted by a star and grazing the sun’s limb, classical scientists did not consider it necessary to abandon Newton’s law on this account. They merely recognised that light was attracted by a gravitational field in common with all other forms of matter, and calculation showed that assuming Newton’s law to be correct, the angle of this deflection would be 0".87 for a ray grazing the sun’s limb. The first eclipse observations were conducted under very unfavourable conditions, and all that could be ascertained was that a certain amount of bending was present. The precise degree could not be determined in any reliable way, so that Newton’s law still had its defenders.
Let us now pass to Einstein’s attack. Of course, in Einstein’s theory, even prior to his discovery of the new law of gravitation, a ray of light would certainly have been bent in a gravitational field in virtue of the postulate of equivalence. It is easy to see how this would arise. Consider a chest, floating vertically in interstellar space, and a ray of light traversing it horizontally. If now the chest be accelerated upwards along the vertical, the floor of the chest will move with acceleration across the ray and, as a result, the light ray will follow a curved path through the chest. But in this case the postulate of equivalence allows us to regard the chest as unaccelerated but permeated by a gravitational field; we may infer, therefore, that the ray of light would bend downwards under the action of this field. Hence, the mere qualitative bending of a ray of light in the sun’s gravitational field would not vindicate Einstein’s law of gravitation and dethrone Newton’s; it would merely prove the correctness of the postulate of equivalence and the identity of the two species of masses. It is the precise quantitative bending of the ray, as determined by Einstein’s law of gravitation, that constitutes the crucial test of the correctness of Einstein’s law. This bending, as computed from the lay of the geodesic which a light ray grazing the limb of the sun would follow, turns out to be 1".75; that is, just twice as great as the Newtonian deflection 0".87. When this precise angle predicted by Einstein was observed during the subsequent solar eclipse of 1919, interest in relativity became widespread; for it was recognised at last that the theory was not a mere mathematical dream.
But even this verification of Einstein’s law of gravitation would have been insufficient to establish the theory. As we shall see in the next chapter, other very curious phenomena were suggested by the new law of gravitation; and if these new phenomena should not be verified in turn, the theory, in spite of its wonderful achievements, would have to be abandoned.