S. E. Khaikin, What Are Inertial Forces (a physical introduction to mechanics), Gostekhizdat, 1940, 120 pp., 44 figs.

S. E. Khaikin’s book is undoubtedly a valuable contribution to the textbook literature on classical mechanics. The question to which it is devoted is, of course, not new and, as the author himself rightly notes, contains no physical problems (at least within the framework of classical mechanics). Nevertheless, “the problem of inertial forces” is not trivial. The concept of inertial forces is often a stumbling block not only for those beginning the study of mechanics, but also for persons who, by the nature of their work, ought to have clear ideas about the foundations of mechanics.

The author begins the book with one of the fundamental concepts of mechanics—the concept of force. A detailed analysis of this concept can by no means be considered superfluous. The concept of force is usually introduced very early and in a far from critical manner. People become accustomed to it without thinking about it very much, and this later leads to misunderstandings. Dwelling in detail on the definition of force derived from the method of its measurement, the author correctly develops the basic idea that force is a manifestation of the interaction of bodies. This enables him subsequently to reveal the ambiguity present in the usual use of the phrase “inertial force.” He shows with complete clarity that in many cases what is called an “inertial force” is in no way a force in the Newtonian sense (i.e., expressing the interaction of bodies), whereas in other cases (accelerated frames of reference) we really do arrive at true inertial forces, representing a certain extension of the concept of force. §§ 9–11, devoted to this aspect of the matter, are set out flawlessly and with utmost clarity, so that the reader can easily grasp the essence of the question.

Now a few words about the shortcomings of the book, which, in our opinion, it nevertheless has. Excessive rigorism—the desire, at every point, immediately to stipulate all possible deviations from the main assertion—although it gives the book a very elevated character in our opinion, nevertheless makes reading it very difficult. These qualifications are scattered everywhere (for example, on forces depending on velocities, pp. 14, 15, 16, 17, 22, 26, 73, despite the fact that a special paragraph is devoted to frictional forces). Sometimes, as if incidentally, assertions are made which are hardly likely to reach the reader (for example, on the Lorentz force and the theory of relativity, p. 43). The book would gain if these same reservations were presented more systematically, without unnecessary repetitions.

Further, it should be noted that the author has been somewhat carried away by macrophysics, without stipulating that he restricts himself to this field of application of Newtonian mechanics. For this reason elastic forces turn out to be the most frequently encountered. In fact, the range of applicability of Newtonian mechanics is broader, and the simplest, most frequently encountered forces are precisely forces “of the type of gravitational forces,” to which the author assigns second place.

The very detailed explanation that deformation is caused not by forces but by motions seems to us excessively long. In fact, this is quite trivial: in general, any change in the configuration of a system is, of course, caused by motions. A deeper consideration of elastic forces as interparticle forces would show that, in essence, they are the same forces, determined by the configuration of a body, as, for example, gravitational forces.

The shortcomings indicated are, however, of secondary importance and do not diminish the great value and originality of S. E. Khaikin’s book.

D. I. Blokhintsev, Moscow