Conclusion
From the conceptual stand-point there are several important consequences of the Generalised or Gravitational Theory of Relativity. Physical space-time is perceived to be intimately connected with the actual local distribution of matter. Euclid-Newtonian space-time is not the actual space-time of Physics, simply because the former completely neglects the actual presence of matter. Euclid-Newtonian continuum is merely an abstraction, while physical space-*time is the actual framework which has some definite curvature due to the presence of matter. Gravitational Theory of Relativity thus brings out clearly the fundamental distinction between actual physical space-time (which is non-isotropic and non-Euclid-Newtonian) on one hand and the abstract Euclid-Newtonian continuum (which is homogeneous, isotropic and a purely intellectual construction) on the other.
The measurements of the rotation of the earth reveals a fundamental framework which may be called the “inertial framework.” This constitutes the actual physical universe. This universe approaches Galilean space-time at a great distance from matter.
The properties of this physical universe may be referred to some world-distribution of matter or the “inertial framework” may be constructed by a suitable modification of the law of gravitation itself. In Einstein’s theory the actual curvature of the “inertial framework” is referred to vast quantities of undetected world-matter. It has interesting consequences. The dimensions of Einsteinian universe would depend on the quantity of matter in it; it would vanish to a point in the total absence of matter. Then again curvature depends on the quantity of matter, and hence in the presence of a sufficient quantity of matter space-time may curve round and close up. Einsteinian universe will then reduce to a finite system without boundaries, like the surface of a sphere. In this “closed up” system, light rays will come to a focus after travelling round the universe and we should see an “anti-sun” (corresponding to the back surface of the sun) at a point in the sky opposite to the real sun. This anti-sun would of course be equally large and equally bright if there is no absorption of light in free space.
In de Sitter’s theory, the existence of vast quantities of world-matter is not required. But beyond a definite distance from an observer, time itself stands still, so that to the observer nothing can ever “happen” there. All these theories are still highly speculative in character, but they have certainly extended the scope of theoretical physics to the central problem of the ultimate nature of the universe itself.
One outstanding peculiarity still attaches to the concept of electric force—it is not amenable to any process of being “transformed away” by a suitable change of framework. H. Weyl, it seems, has developed a geometrical theory (in hyper-space) in which no fundamental distinction is made between gravitational and electrical forces.
Einstein’s theory connects up the law of gravitation with the laws of motion, and serves to establish a very intimate relationship between matter and physical space-*time. Space, time and matter (or energy) were considered to be the three ultimate elements in Physics. The restricted theory fused space-time into one indissoluble whole. The generalised theory has further synthesised space-time and matter into one fundamental physical reality. Space, time and matter taken separately are more abstractions. Physical reality consists of a synthesis of all three.
P. C. Mahalanobis.