Relativity (philosophy)

“ 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. ”

“ 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 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 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. ”

“ 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. ”

“ 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. ”

“ Ever since the special theory of relativity has been formulated, the outcome concerning the slowing influence of motion on the rate of clocks has continuously elicited opposition, and - it seems to me - with good reasons. ”

“ The principle of relativity holds, not only for processes in physics, but also for the physicist himself, in that a fixed system of physics exists in reality only for a given physicist and for a given time. But, as in the theory of relativity, there exist invariants in the system of physics: ideas and laws which retain their meaning for all investigators and for all times, and to discover these invariants is always the real endeavor of physical research. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ In short, we see that the general principle of relativity possesses essentially a mathematical and formal significance; the absoluteness of rotation remains, as before, an empirical fact which we cannot conjure away. It is only when we accept the hypothesis of the cylindrical universe, permitted but not obligated by the general principle, that the relativity of all motion in the Machian sense may be possible. ”

“ It follows that a simultaneity of events, or a sameness of time throughout space, becomes an indeterminate concept until an observer or a frame of reference has been specified; in much the same way, the weight of a given brick situated anywhere in space will be indeterminate until such time as the distribution of the surrounding masses has been decided upon. So far as the special theory is concerned, this is the sole difference between classical science and relativity. ”

“ 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 ”

“ Since the introduction of the special principle of relativity has been justified, every intellect which strives after generalisation must feel the temptation to venture the step towards the general principle of relativity. ”

“ The principle of relativity works with a non-euclidean space, that assumes different properties from place to place and in successive times; so there might be something in space whose conditions are the cause of those different properties, and this something is exactly the aether. ”

“ 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; ”

“ 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. ”

“ We can always proceed on the assumption that it does remain true. Thus it is always possible to construct physical laws in such a way that they retain their form when referred to moving coordinates. The ultimate ground for formulating physical laws in this way is merely a subjective conviction that the principle of relativity is universally true. ”

“ We should have had to arrive at relativity physics at one bound, or remain ignorant of scientific laws. It is fortunate for us that we were not faced with this alternative, since it is almost inconceivable that one man could have done the work of Euclid, Galileo, Newton, and Einstein. Yet without such an incredible genius physics could hardly have been discovered in a world where the universal flux was obvious to non-scientific observation. ”

“ Now in virtue of its motion in an orbit round the sun, our earth is comparable with a railway carriage travelling with a velocity of about 30 kilometres per second. If the principle of relativity were not valid we should therefore expect that the direction of motion of the earth at any moment would enter into the laws of nature, and also that physical systems in their behaviour would be dependent on the orientation in space with respect to the earth. ”

“ 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. ”

“ Those of you who have carefully followed the preceding discussion are almost sure to expect that we should retain the principle of relativity, which appeals so convincingly to the intellect because it is so natural and simple. The law of the propagation of light in vacuo would then have to be replaced by a more complicated law conformable to the principle of relativity. The development of theoretical physics shows, however, that we cannot pursue this course. ”

“ I cannot reject the hope that theory is by slow stages leading us nearer to the truth of things. But unless science is to degenerate into idle guessing, the test of value of any theory must be whether it expresses with as little redundancy as possible the facts which it is intended to cover. Accidental truth of a conclusion is no compensation for erroneous deduction.
The relativity standpoint is then a discarding of certain hypotheses, which are uncalled for by any known facts, and stand in the way of an understanding of the simplicity of nature. ”

“ 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. ”

“ 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. ”

“ 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." ”

“ Whether the relativity theory then is to serve as a pattern for the ultimate hypothesis of the universe or whether its end is to illustrate what is to be avoided in the construction of such a hypothesis, is perhaps after all not the important question. ”

“ In the philosophy of Mach a world without matter is unthinkable. Matter in Mach's philosophy is not merely required as a test body to display properties of something already there, which have no physical meaning except in relation to matter; it is an essential factor in causing those properties which it is able to display. Inertia, for example, would not appear by the insertion of one test body in the world; in some way the presence of other matter is a necessary condition. ”

“ 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. ”

“ The relativity treatment, on the other hand, discovers another formula, analogous to the one expressing conservation, which holds always for the kinetic energy. “The relativity treatment adheres to the physical quantity and modifies the law ”

“ In the second place, classical mechanics indicates a limitation which directly demands an extension of the principle of relativity to spaces of reference which are not in uniform motion relatively to each other. The ratio of the masses of two bodies is defined in mechanics in two ways which differ from each other fundamentally ”

“ 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. ”