Robert Daniel Carmichael

“ 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. ”

“ Now, since our only reason for attempting to measure time is in a matter of convenience, the way in which we measure it will be determined by the dictates of that convenience. The system of time measurement which we shall adopt is just that system by means of which the laws of nature may be stated in the simplest form for our comprehension. ”

“ Furthermore, if any relation other than is the true one, some modification at least of the theory of relativity would have to be made or else one would have to give up postulate which asserts the law of conservation of momentum. ”

“ These and many other considerations suggest the desirability of a fresh analysis of the foundations of physical science. Now it is a ground of gratulation for all those interested in this matter that there has arisen within modern physics itself a new movement capable of contributing most effectively to the construction of a more satisfactory foundation for its superstructure of theory. I refer to the recent widespread interest in the principle of relativity and the rapid developments to which it has led. ”

“ We suppose that observers at A and B again measure the velocity of light as it emanates from S, this time in the direction of the line of motion. Each will carry out his observations on the supposition that his system is at rest, for from M it follows that he cannot detect the motion of his system. The observer at A measures the time of passage of a ray of light from A to C and return to A, the length of AC being d when the measurement is made with a unit belonging to . ”

“ Let us return to the case of the two observers A and B of section III. Suppose that each of them has chosen a system of measuring time that suits his convenience in the interpretation of the laws of nature on his system. There is no a priori reason why the two observers should measure time-intervals in the same way. In fact, since there is an arbitrary element in the case of each method of measurement and since the two systems are in a state of relative motion, it is not at all unnatural that the units of A and B should differ. ”

“ I. The Postulates of Relativity. § I. Postulates of Homogeneity. — There are two fundamental postulates concerning the nature of space and time which underlie all physical theory. They assert in part that every point of space is like every other point and that every instant of time is like every other instant. For our present purpose these postulates can best be given the following more exact and complete statement. ”

“ If it is found that k is different from unity we shall be forced to the conclusion that either our conception of mass in the classical mechanics or our conception of charge in the classical electrical theory is in need of essential modification. ”

“ In the very nature of things speculation must often outrun experiment. The philosopher vaguely and boldly conceives a truth which it requires years of patient labor to establish on a firm and satisfactory foundation.
It is one of the glories of modern science that things hitherto of a speculative nature are being brought under the domain of experimental fact. ”

“ Let x and y be the cartesian coordinates of a point as determined by A, the axes of reference being the major and minor axes of the ellipse in which the balls move. Let and be the coordinates of the same point as determined by B. Then the circular path of motion, as determined by B, has the equations
the angle θ being measured from the major axis of the ellipse. ”

“ Whether in the present state of science experimental facts demand such a radical procedure is a question which will be answered differently by different minds. To one who accepts the postulates of relativity there is indeed no other recourse; one who refuses to accept them must find some other satisfactory way to account for experimental facts. The Lorentz theory of electrons gives striking evidence in favor of supposing that matter is subject to some such deformations as those mentioned above ”

“ In the indirect method some auxiliary law, as for instance the law of conservation of electricity, must usually be employed in deducing the relativity postulates or essential conclusions from the new assumption which one attempts to justify by experiment. There is always the possibility that the auxiliary law is itself wrong; and consequently one's confidence in the accuracy of the relativity postulates as thus deduced can be no stronger than that in the truth of the auxiliary law. ”