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.
CHAPTER XXXI
THE SEPARATION OF SPACE-TIME INTO SPACE AND TIME IN A GRAVITATIONAL FIELD
WE must remember that the one fundamental continuum of the world is space-time; space and time considered separately, varying as they do with the observer’s motion, have no absolute significance. The law of curvature, or of gravitation, which we have discussed is one of space-time curvature. It is the law giving the distribution of the four-dimensional metrical field of space-time in the interior of matter and around matter to infinity. It is true that we may be able to effect some sort of separation of space-time into the space and time of some particular observer; and this may enable us to represent the law of curvature of space-time as two separate laws of curvature, one affecting space and the other affecting time. But for the reasons we have just mentioned, no absolute significance could be attached to the curvatures we should obtain. Thus, in interstellar space, an observer situated in a Galilean frame would contend that neither space nor time manifested any trace of curvature, whereas an observer on the rim of a rotating disk would recognise that both space and time were curved. On the other hand, regardless of his frame of reference, either observer would always recognise that space-time possessed no trace of curvature.
It is because space-time transcends the observer that its curvature or flatness, as the case may be, can be considered absolute; whereas a curvature of space or of time alone can never represent anything but a mere relationship between the intrinsic condition of space-time and the observer’s motion or frame of reference.
Of course, if we wish to split up space-time into the particular space and time directions of some particular observer we may always attempt to do so. But in the majority of cases this procedure will be impossible.
If these considerations are properly understood, there is no harm done in trying to separate the curved space-time which endures around the sun into the space and time of an observer at rest with respect to the sun and viewing the solar system as a whole. This separation, however, is possible only in the event that the masses of the moving planets can be ignored, so that the only field we have to consider is that of the sun, remaining unchanged as time passes. It is owing to this permanent condition of the gravitational field that the separation into space and time is possible. Fields of this type are called stationary. For non-stationary fields, such as those where the distribution of the field changes with time, the separation into space and time becomes impracticable.