The Theory of the Relativity of Motion

Abstract

Preface. Thirty or forty years ago, in the field of physical science, there was a widespread feeling that the days of adventurous discovery had passed forever, and the conservative physicist was only too happy to devote his life to the measurement to the sixth decimal place of quantities whose significance for physical theory was already an old story. The passage of time, however, has completely upset such bourgeois ideas as to the state of physical science, through the discovery of some most extraordinary experimental facts and the development of very fundamental theories for their explanation. On the experimental side, the intervening years have seen the discovery of radioactivity, the exhaustive study of the conduction of electricity through gases, the accompanying discoveries of cathode, canal and X-rays, the isolation of the electron, t he study of the distribution of energy in the hohlraum, and the final failure of all attempts to detect the earth's motion through the supposititious ether. During this same time, the theoretical physicist has been working hand in hand with the experimenter endeavoring to correlate the facts already discovered and to point the way to further research. The theoretical achievements, which have been found particularly helpful in performing these functions of explanation and prediction, have been the development of the modern theory of electrons, the application of thermodynamic and statistical reasoning to the phenomena of radiation, and the development of Einstein's brilliant theory of the relativity of motion. It has been the endeavor of the following book to present an introduction to t his theory of relativity, which in the decade since the publication of Einstein's first paper in 1905 (Annalen der Physik) has become a necessary part of the theoretical equipment of every physicist. Even if we regard the Einstein theory of relativity merely as a convenient tool for the prediction of electromagnetic and optical phenomena, its importance to the physicist is very great, not only because its introduction greatly simplifies the deduction of many theorems which were already familiar in the older theories based on a stationary ether, but also because it leads imply and directly to correct conclusions in the case of such experiments as those of Michelson and Morley, Trouton and Noble, and Kaufman and Bucherer, which can be made to agree with the idea of a stationary ether only by the introduction of complicated and ad hoc assumptions. Regarded from a more philosophical point of view, an acceptance of the Einstein theory of relativity shows us the advisability of completely remodelling some of our most fundamental ideas. In particular we shall now do well to change our concepts of space and time in such a way as to give up the old idea of their complete independence, a notion which we have received as the inheritance of a long ancestral experience with bodies moving with low velocities, but which no longer proves pragmatic when we deal with velocities approaching that of light. The method of treatment adopted in the following chapters is to a considerable extent original, partly appearing here for the first time and partly already published elsewhere. Chapter III follows a method which was first developed by Lewis and Tolman, and the last chapter a method developed by Wilson and Lewis. The writer must also express his special obligations to the works of Einstein, Planck, Poincaré, Laue, Ishiwara and Laub. It is hoped that the mode of presentation is one that will be found well adapted not only to introduce the study of relativity theory to those previously unfamiliar with the subject but also to provide the necessary methodological equipment for those who wish to pursue the theory into its more complicated applications. After presenting, in the first chapter, a brief outline of the historical development of ideas as to the nature of the space and time of science, we consider, in Chapter II, the two main postulates upon which the theory of relativity rests and discuss the direct experimental evidence for their truth. The third chapter then presents an elementary and non-mathematical deduction of a number of the most important consequences of the postulates of relativity, and it is hoped that this chapter will prove especially valuable to readers without unusual mathematical equipment, since they will there be able to obtain a real grasp of such important new ideas as the change of mass with velocity, the non-additivity of velocities, and the relation of mass and energy, without encountering any mathematics beyond the elements of analysis and geometry. In Chapter IV we commence the more analytical treatment of the theory of relativity by obtaining from the two postulates of relativity Einstein's transformation equations for space and time as well as transformation equations for velocities, accelerations, and for an important function of the velocity. Chapter V presents various kinematical applications of the theory of relativity following quite closely Einstein's original method of development. In particular we may call attention to the ease with which we may handle the optics of moving media by the methods of the theory of relativity as compared with the difficulty of treatment of the basis of the ether theory. In Chapters VI, VII and YIII we develop and apply a theory of the dynamics of a particle which is based on the Einstein transformation equations for space and time, Newton's three laws of motion, and the principle of the conservation of mass. We then examine, in Chapter IX, the relation between the theory of relativity and the principle of least action, and find it possible to introduce the requirements of relativity theory at the very start into this basic principle for physical science. We point out that we might indeed have used this adapted form of the principle of least action, for developing the dynamics of a particle, and then proceed in Chapters X, XI and XII to develop the dynamics of an elastic body, the dynamics of a thermodynamic system, and the dynamics of an electromagnetic system, all on the basis of our adapted form of the principle of least action. Finally, in Chapter XIII, we consider a four-dimensional method of expressing and treating the results of relativity theory. This chapter contains, in Part I, an epitome of some of the more important methods in four-dimensional vector analysis and it is hoped that it can also be used in connection with the earlier parts of the book as a convenient reference for tho e who are not familiar with ordinary three-dimensional vector analysis. In the present book, the writer has confined his considerations to case in which there is a uniform relative velocity between systems of coordinates. In the future it may be possible greatly to extend the applications of the theory of relativity by considering accelerated systems of coordinates, and in this connection Einstein's latest work on the relation between gravity and acceleration is of great interest. It does not seem wise, however, at the present time to include such considerations in a book which intend to present a survey of accepted theory. The author will feel amply repaid for the work involved in the preparation of the book if, through his efforts, some of the younger American physicists can be helped to obtain a real knowledge of the important work of Einstein. He is also glad to have this opportunity to add his testimony to the growing conviction that the conceptual space and time of science are not God-given and unalterable, but are rather in the nature of human constructs devised for use in the description and correlation of scientific phenomena, and that these spatial and temporal concepts should be altered whenever the discovery of new fact makes such a change pragmatic. The writer wishes to express his indebtedness to Mr. William H. Williams for assisting in the preparation of Chapter I.

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