* * *
Outside matter, as has been explained, the law of gravitation restricts the curvature of time-space. Inside continuous matter the curvature can be of any arbitrary kind or amount; the law of gravitation then connects this curvature with measurable properties of the matter, such as density, velocity, stress, etc. Thus these properties define the curvature, or, if preferred, the curvature defines the properties of matter, i.e. matter itself.
From these definitions the laws of conservation of energy, and of conservation of momentum, can be deduced by a purely mathematical process. Thus these laws, which at one time used to be considered as the most fundamental ones of mechanics, now appear as simple corollaries from the law of gravitation. It must be pointed out that such things as length, velocity, energy, momentum, are not absolute, but relative, i.e. they are not attributes of the physical reality, but relations between this reality and the observer. Consequently the laws of conservation are not laws of the real world, like the law of gravitation, but of the observed phenomena. There is, however one law which, already before the days of relativity, had come to be considered as the most fundamental of all, viz: the principle of least action. Now action is absolute. Accordingly this principle retains its central position in Einstein’s theory. It is even more fundamental than the law of gravitation, since both this law, and the law of motion, can be derived from it. The principle of least action, so far as we can see at present, appears to be the law of the real world.
XI
THE PRINCIPLE OF GENERAL RELATIVITY
How Einstein, to a Degree Never Before Equalled, Isolates the External Reality from the Observer’s Contribution
BY E. T. BELL
UNIVERSITY OF WASHINGTON
SEATTLE
Einstein’s general relativity is of such vast compass, being coextensive with the realm of physical events, that in any brief account a strict selection from its numerous aspects is prescribed. The old, restricted principle being contained in the general, we shall treat the latter, its close relations with gravitation, and the significance of both for our knowledge of space and time. The essence of Einstein’s generalization is its final disentanglement of that part of any physical event which is contributed by the observer from that which is inherent in the nature of things and independent of all observers.
The argument turns upon the fact that an observer must describe any event with reference to some framework from which he makes measurements of time and distance. Thus, suppose that at nine o’clock a ball is tossed across the room. At one second past nine the ball occupies a definite position which we can specify by giving the three distances from the centre of the ball to the north and west walls and the floor. In this way, refining our measurements, we can give a precise description of the entire motion of the ball. Our final description will consist of innumerable separate statements, each of which contains four numbers corresponding to four measurements, and of these one will be for time and three for distances at the time indicated.