Bibliography

P. G. Bergmann. Introduction to the Theory of Relativity. State Publishing House of Foreign Literature, Moscow, 1947. Price 20 rubles. 380 pp.

The role of the theory of relativity in modern science is extraordinarily great. Although for a long time the results obtained in the theory of relativity did not find direct practical application, the very analysis of the fundamental physical concepts that it produced exerted an enormous influence on the development of theoretical physics in the subsequent period. There is no doubt that, in clarifying the very subtle fundamental questions raised by the rapid development of quantum physics, invaluable assistance was provided by the experience acquired in connection with the development of the theory of relativity.

In recent years, however, the results and methods of the theory of relativity have been acquiring ever greater practical significance in the field of atomic and nuclear physics. The most urgent problems of the modern theory of elementary particles can be solved only by treating them relativistically. This naturally gives rise to a need for a textbook on the theory of relativity that could satisfy the demands of fairly broad circles of physicists. The book under review was written precisely for this purpose, and not without success. It is written in such a way that studying it can teach the reader to use independently the results and methods of the theory of relativity.

The author of the book, P. G. Bergmann, is a colleague of Albert Einstein, the creator of the theory of relativity. Einstein wrote the preface to the book, in which he notes that together with the author he devoted considerable effort to making the book more satisfactory both logically and pedagogically. Thus, Einstein is in fact a co-author of the book, which gives it special interest.

The book consists of three parts. In the first part, the special theory of relativity is set forth quite fully, together with its experimental justification and applications in atomic physics. The exposition begins with an explanation of the contradictions in nonrelativistic physics and with an elucidation of the physical ideas of the theory of relativity. Despite the high scientific level, these chapters are written exceptionally clearly and are accessible even to the least prepared reader. There follows a very full and concrete presentation of tensor analysis. Having carefully studied this chapter, the reader will learn to use independently the methods of tensor analysis; and when studying the subsequent chapters, devoted to relativistic mechanics and electrodynamics, the reader has the impression that he is taking part in the development of these questions. This is, of course, a very valuable quality of the textbook—it instills in the reader confidence in his own abilities. This is also aided by the large number of problems included in the first part of the book.

It should also be noted that Chapter VIII, devoted to the mechanics of continuous media, is of great interest. In most books on the theory of relativity this question is not touched upon. Meanwhile, the consideration of

mechanics of continuous media shows very clearly how mechanical concepts of energy and momentum are introduced into field theory, in particular into the theory of the electromagnetic field.

The second part of the book is devoted to the general theory of relativity. It begins with a very clear and lucid exposition of the principle of equivalence and the principle of general covariance. Next, the Riemann–Christoffel tensors and the equations of the gravitational field are set forth. In this part, as in the first, the exposition is distinguished by depth and simplicity, although, naturally, reading this part of the book, in view of the complexity of the subject, will require considerable effort from the reader.

Of particular interest in the second part of the book are the chapters devoted to questions that until now have been treated only in journal literature. These are the question of carrying out exact solutions of the field equations, which is of great importance for studying the character of particle motion in the general theory of relativity, and, in particular, the question of deriving the equations of motion from the field equations. The possibility of deriving the equations of motion from the equations of gravitation is of enormous fundamental significance. From the equations of the electromagnetic field one cannot derive the equations of motion. Here the profound differences between electromagnetic and gravitational fields become clear.

Finally, the third part of the book, the smallest in volume, is devoted to the so-called unified field theories, i.e., theories that try to regard gravitational and electromagnetic fields as constituent parts of the geometrical structure of space. Several variants of such theories have been proposed, but, as is known, they have not led to any concrete physical results. Nevertheless, the exposition of these questions in Bergmann’s textbook gives the reader the opportunity to become acquainted in a comparatively accessible form with research in this field. But it should be noted that this part is written much more tersely than the preceding ones and is read with greater effort, although the previous two parts fully prepare the reader for this work.

The translation, edited by Prof. V. L. Ginzburg, has been carried out very well. The book has also been published very well.

While welcoming the publication of the translation of Bergmann’s textbook and highly appreciating its merits, it should be said that there is one aspect of the matter that cannot satisfy the Soviet reader.

Such a major stage in the development of science as the creation of the theory of relativity could not and did not pass without leaving a trace on the scientific worldview. The theory of relativity proved to be the arena of very sharp philosophical discussions. The Soviet reader feels an urgent need for an elucidation of the philosophical significance of the theory of relativity from the point of view of dialectical materialism. This question ought to be given its proper place in a textbook. Unfortunately, the book contains no reflection of the remarkable work of Soviet scholars (Friedmann, Fock, and others) on the theory of relativity.

Therefore we believe that the publication of Bergmann’s textbook does not remove from the agenda the urgent task of developing a Soviet textbook on the theory of relativity.

A. G. Samoilovich