And yet it might be said: “We experience a real physical pull when we stand on the earth, whereas we should experience no such pull were we floating in interstellar space.” Let us see why it is that this real physical pull appears to arise in one case and not in the other.
A freely moving body follows, as we have explained, a geodesic of space-time, regardless of whether space-time be curved by the proximity of matter or whether it be flat. So long as the body is not interfered with, it will continue to follow its geodesic, allowing itself to be guided by the space-time structure or field. But suppose now that the motion is interfered with, so that the body is torn away from the geodesic which it would normally have followed. The guiding field will immediately react and oppose this foreign interference. It is as though the geodesic were a groove from which the body could not easily be diverted.
Consider then a body moving uniformly in interstellar space, according to the law of inertia. If we interfere with this body’s motion, accelerate it along its straight line or compel it to describe a curve, we shall, in effect, be tearing it away from its space-time geodesic. The guiding field will react and we shall experience a physical pull which we call a force of inertia or a centrifugal pull. In exactly the same way we may explain the appearance of the physical pull which we ascribe to gravitation when we stand on the earth’s surface.
Thus, a body which is falling freely towards the earth is following a geodesic in the curved space-time that surrounds the earth. But if, for some reason or other, the free fall of the body is interfered with, if, for instance, the rigidity of the earth’s crust prevents the body from falling farther along the geodesic, the geodesic will react and will strive to force the body through the earth’s crust. It was this force which we formerly ascribed to the pull of gravitation. But we see once again that this force has exactly the same origin as the forces of inertia we discussed previously, so that there exists no essential difference between a force of inertia and one of gravitation. They are both real physical forces in that they will produce physical effects; and they will both disappear in exactly the same way when we cease to interfere with the natural motion of the body. In short, they are both of them but manifestations of the four-dimensional metrical field or guiding field of space-time.
CHAPTER XXX
THE VERIFICATION OF EINSTEIN’S LAW
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.