Relativity

“ This idea, that the velocity of light will seem the same to two different observers, even though one may be moving towards and the other away from the source of light, constitutes the really remarkable feature of the principle of relativity, and forces us to the strange conclusions which we are about to deduce. ”

“ What is relativity? By relativity, the theory of relativity, the principle of relativity, the doctrine of relativity, is meant a new conception of the fundamental ideas of mechanics. By the relativity mechanics, or as we may sometimes say, the new mechanics, is meant that body of doctrine which is based on these new conceptions. ”

“ If I have succeeded in my object, you will have realized that the present revolution of scientific thought follows in natural sequence on the great revolutions at earlier epochs in the history of science. Einstein's special theory of relativity, which explains the indeterminateness of the frame of space and time, crowns the work of Copernicus who first led us to give up our insistence on a geocentric outlook on nature; ”

“ But if one does not share this opinion it is still legitimate to accept the theory of relativity as a working hypothesis, to be proved or disproved by future experiment. It is an historical fact, patent to every student of scientific progress, that many of our fundamental laws have been accepted just in this way. ”

“ We now inquire whether there is a relativity with respect to the state of motion of the space of reference; in other words, whether there are spaces of reference in motion relatively to each other which are physically equivalent. From the standpoint of mechanics it appears that equivalent spaces of reference do exist. For experiments upon the earth tell us nothing of the fact that we are moving about the sun with a velocity of approximately 30 kilometres a second. ”

“ The theory of relativity is often criticized for giving, without justification, a central theoretical role to the propagation of light, in that it founds the concept of time upon the law of propagation of light. ”

“ The object of the relativity theory, however, is not to attempt the hopeless task of apportioning responsibility between the observer and the external world, but to emphasise that in our ordinary description and in our scientific description of natural phenomena the two factors are indissolubly united. All the familiar terms of physics—length, duration of time, motion, force, mass, energy, and so on—refer primarily to this relative knowledge of the world ”

“ We shall be true to the principle of relativity in its broadest sense if we give such a form to the laws that they are valid in every such four-dimensional system of co-ordinates, that is, if the equations expressing the laws are co-variant with respect to arbitrary transformations. ”

“ Force is another important concept on which the theory of relativity has shed new light; though to avoid any misunderstanding we may state that by force we refer not to muscular pulls, but to the forces of gravitation, of inertia and of the electromagnetic field. Let us recall how the new ideas were obtained. We saw that the fundamental continuum of the world was space-time, and that observers, according to their relative motions, carved it up into space and time in various ways. ”

“ Another important consequence of the theory, which can be tested experimentally, has to do with the path of rays of light. In the general theory of relativity also the velocity of light is everywhere the same, relatively to a local inertial system. ”

“ 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. ”

“ A FEW INFERENCES FROM THE GENERAL PRINCIPLE OF RELATIVITY
The considerations of Section XX show that the general principle of relativity puts us in a position to derive properties of the gravitational field in a purely theoretical manner. ”

“ It is most important to note that the relativity of all motion, as expressed by the general principle of relativity, stands on an entirely different footing from the ultra-relativistic conception of rotation as upheld by Mach. ”

“ The entire philosophy of the relativity theory is to separate entities which have no significance except as expressing relationships to the frame of the observer, from entities which can be conceived of as enduring regardless of the observer’s presence. We recognise these absolute entities as those which remain unaltered for all observers. Mathematically, they are expressed by invariants and tensors in space-time. ”

“ When the theory of relativity supplanted classical science, it was recognised that the classical equations of mechanics were only approximate, and it became necessary to reformulate the principle of action so as to render it compatible with the mechanics of relativity, hence also with space-time. ”

“ The special relativity theory is therefore the application of the following proposition to any natural process: "Every law of nature which holds good with respect to a coordinate system K must also hold good for any other system K' provided page 9 that K and K' are in uniform movement of translation." ”

“ That is a special property, which all forces of nature must have, when the relativity principle shall hold. If we presuppose this, then one can calculate the forces acting on moving bodies, when one know them for the case of rest. ”

“ The principle of relativity, first developed in connection with the electromagnetic theory of light, has in recent years been more and more considered as of universal application, and the claim has been made that the whole of our physical sciences should be framed in conformity with it. ”

“ From our consideration of the accelerated chest we see that a general theory of relativity must yield important results on the laws of gravitation. In point of fact, the systematic pursuit of the general idea of relativity has supplied the laws satisfied by the gravitational field. ”

“ We see that the only difference between Einstein’s principle and the Newtonian principle of relativity is that henceforth the relativity of velocity holds for all manner of experiments, or, again, that ether and space are identified. ”

“ The theory of relativity has arisen from the study of what goes on in the regions where there are no electrons and protons. While the study of the atom has led us to discontinuities, relativity has produced a completely continuous theory of the intervening medium—far more continuous than any theory formerly imagined. ”

“ The relativity principle asserts the following: When a physical phenomenon is described in reference system by certain equations, then a phenomenon which can be described in another reference system by the same equations, will exist as well. There, both reference systems are connected by relations in which the speed of light occurs, and which express that a system is moving with uniform velocity relative to the other one. ”

“ It is my purpose to discuss with you today an hypothesis which represents a magnificent attempt to establish quite generally the dependency of the kinetic potential upon the velocities, and which is commonly designated as the principle of relativity. The gist of this principle is: it is in no wise possible to detect the motion of a body relative to empty space ”

“ 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. ”

“ The required generalisation must likewise satisfy the general postulate of relativity. (b) If there is any matter in the domain under consideration, only its inertial mass, and thus according to Section XV only its energy is of importance for its effect in exciting a field. ”

“ To us, the causal essence of the Power lies in the relativity itself, and we often actually recognize the Power passing over into its Function, and becoming lost in it. An example in point, lies in the active combination of uncombined atoms and molecules;—the relativity (or, as in such a case it is termed, the attraction) is the immediate cause of the production. ”

“ What I mean is that they were derived from certain general characteristics of physical experience, which showed that Newton must be wrong and that something like Einstein’s law must be substituted.
The arguments in favor of the relativity of motion are, as we saw in earlier chapters, quite conclusive. In daily life, when we say that something moves, we mean that it moves relatively to the earth. In dealing with the motions of the planets, we consider them as moving [Pg 138] relatively to the sun, or to the center of mass of the solar system. ”

“ If every ray of light is propagated relative to the embankment with the velocity c, then for this reason it would appear that another law of propagation of light must necessarily hold with respect to the carriage—a result contradictory to the principle of relativity. ”

“ As a result of this discussion, a most interesting question arises for astronomers and physicists, and that is whether the universe in which we live is infinite, or whether it is finite in the manner of the spherical universe. Our experience is far from being sufficient to enable us to answer this question. But the general theory of relativity permits of our answering it with a moderate degree of certainty, and in this connection the difficulty mentioned in Section XXX finds its solution. ”

“ I should like to make it clear that the limitation of the scope of physics to pointer readings and the like is not a philosophical craze of my own but is essentially the current scientific doctrine. It is the outcome of a tendency discernible far back in the last century but only formulated comprehensively with the advent of the relativity theory. The vocabulary of the physicist comprises a number of words such as length, angle, velocity, force, potential, current, etc., which we call “physical quantities”. ”

“ 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. ”

“ Hence, when a body moves, its relative place, or, better, the relativity of its place to the places of other bodies, is changed; but its absolute place remains the same. Thus the earth, in describing its orbit, takes different positions round the sun, and, while preserving its absolute place unchanged, it undergoes a continuous change of its relativity. ”

“ As we shall see in the following section, the general theory of relativity leads us, rather, to the view that we may regard the metrical conditions in the neighbourhood of bodies as being conditioned by their gravitation. ”

“ THE negative result of all experiments to detect the earth's motion through space by its effect on terrestrial phenomena positively requires explanation, and the modern principle of relativity is generally conceded to be the most successful attempt to explain so far made. ”