General relativity

“ No fairer destiny could be allotted to any physical theory, than that it should of itself point out the way to the introduction of a more comprehensive theory, in which it lives on as a limiting case.
In the example of the transmission of light just dealt with, we have seen that the general theory of relativity enables us to derive theoretically the influence of a gravitational field on the course of natural processes, the laws of which are already known when a gravitational field is absent. ”

“ Clearly physics cannot concern itself with all the possible complexities which may exist in nature, but have not hitherto betrayed themselves in any experiment.
The principle of relativity has implications of a most revolutionary kind. Let us consider what is perhaps an exaggerated case—or perhaps the actual case, for we cannot tell. Let the reader suppose that he is travelling through the aether at 161,000 miles a second vertically upwards; if he likes to make the positive assertion that this is his velocity, no one will be able to find any evidence to contradict him. ”

“ The special theory of relativity can, therefore, be regarded only as a stepping-stone to a more general principle, which orders gravitational phenomena satisfactorily into the principles of mechanics. ”

“ But to those who think that the relativity theory is a passing phase of scientific thought, which may be reversed in the light of future experimental discoveries, we would point out that, though like other theories it may be developed and corrected, there is a certain minimum statement possible which represents irreversible progress. Certain hypotheses enter into all physical descriptions and theories hitherto current, dating back in some cases for 2000 years, in other cases for 200 years. ”

“ It can only be got rid of by means of a physics which is conformable to the general principle of relativity, since the equations of such a theory hold for every body of reference, whatever may be its state of motion. ”

“ They explore the new field and bring back their spoils—a few simple generalisations—to apply them to the practical world of three-dimensions. Some guiding light will be given to the attempts to build a scheme of things entire. For the rest, physics will continue undisturbedly to explore the relative world, and to employ the terms applicable to relative knowledge, but with a fuller appreciation of its relativity. ”

“ Although any other observer perceives this force with additions of his own, it is implied that the original force in nature and the observer's additions can in some way be separated without ambiguity. There is no experimental foundation for this separation, and the relativity view is that a field of force can, like length and duration, be nothing but a link between nature and the observer. ”

“ From the equations of the general theory of relativity it can be deduced that this total reduction of inertia to reciprocal action between masses—as required by E. Mach, for example—is possible only if the universe is spatially finite.
On many physicists and astronomers this argument makes no impression. Experience alone can finally decide which of the two possibilities is realised in nature. How can experience furnish an answer? At first it might seem possible to determine the mean density of matter by observation of that part of the universe which is accessible to our perception. ”

“ So far also relativity theory has proved ineffectual in relation to this most profound physical problem of the present time. Should the form of the general equations some day, by the solution of the quantum problem, undergo a change however profound, even if there is a complete change in the parameters by means of which we represent the elementary process, the relativity principle will not be relinquished and the laws previously derived therefrom will at least retain their significance as limiting laws. ”

“ If, therefore, two observers move with uniform but different velocities, then each of the two with exactly the same right may assert that with respect to empty space he is at rest, and there are no physical methods of measurement enabling us to decide in favor of the one or the other. The principle of relativity in its generalized form is a very recent development. ”

“ Some may be inclined to challenge the right of the Einstein theory, at least as interpreted in this book, to be called a relativity theory. Perhaps it has not all the characteristics which have at one time or another been associated with that name; but the reader, who has followed us so far, will see how our search for an absolute world has been guided by a recognition of the relativity of the measurements of physics. It may be urged that our geodesics ought not to be regarded as fundamental; a geodesic has no meaning in itself ”

“ Later on we shall reach in a more general way the identification of mass with energy and the variation of mass with speed; but, since the experimental measurement of inertia involves the study of a body in non-uniform motion, it is not possible to enter on a satisfactory discussion of mass until the more general theory of relativity for non-uniform motion has been developed. ”

“ Physics, if it wishes to retain its advantage, must take its own course, formulating those laws which are approximately true for the limited data of sense, and extending them into the unknown. The relativity of rotation is not approximately true for the data of sense, although it may possibly be true when the unknown as well as the known are included. ”

“ Nothing short of the assumption of the general validity of the relativity principle in mechanics can justify the inclusion by physics of the Copernican cosmical system, since through it the independence of all processes upon the earth of the progressive motion of the earth is secured. If one were obliged to take account of this motion, I should have, e. g., to admit that the piece of chalk in my hand possesses an enormous kinetic energy, corresponding to a velocity of something like kilometers per second. ”