On Methodological Errors in Prof. S. E. Khaikin’s Book Mechanics *)

(second edition, State Publishing House of Technical-Theoretical Literature, 1947)

F. A. Korolev

Prof. Khaikin’s book Mechanics is intended as a textbook for the physics faculties of universities in the course of general physics. According to the curricula of the physics faculties of universities, the section “Mechanics” is taught in the first year. It goes without saying that students’ preparation in methodological questions during this period is considerably weaker than in the senior years, when students have taken a number of socio-political disciplines. From this point of view, especially high demands must be made of textbooks for the lower years with regard to their consistency in questions of Marxist-Leninist methodology.

The results of the VASKhNIL session showed with complete obviousness the disastrous consequences to which the penetration, into the milieu of Soviet scholars, of bourgeois ideology hostile to Marxism-Leninism leads.

Having yielded to bourgeois ideology, a scholar not only takes the path of servility before foreign science, but, following bourgeois scholars, also takes the path of distorting the special sciences, of adapting them to the idealist tenets of bourgeois ideology. By distorting science, such scholars tear it away from the practical tasks of socialist construction and lead science into the swamp of formalism.

A vivid confirmation of these propositions is the struggle of the Mendelist-Morganists against the advanced Michurin teaching. The penetration of an ideology alien to Marxism into the milieu of Soviet scholars is not confined to the biological sciences, but also occurs in other sciences, in particular in physics.

One example of such penetration is Prof. Khaikin’s book Mechanics. Being intended as a textbook

*) Published for discussion.

for first-year students of university physics faculties, this book is wholly unsuitable for these purposes, since it contains major methodological distortions.

The chief defect of this book is its tendency to inculcate in the reader a worldview that is wholly at variance with the Marxist-Leninist worldview. In order to show this, it is enough to pose the question of how the fundamental question of philosophy—the relation of thought to being—is resolved in Prof. Khaikin’s book. Dialectical materialism proceeds from the proposition that matter, nature, and its laws are primary, while consciousness is a property of nature, a reflection of its objective regularities. Idealism proceeds from the recognition of the primacy of consciousness, and regards matter, nature, and its laws as the product of our consciousness.

Let us now turn to Prof. Khaikin’s book and see how the fundamental question of philosophy is resolved in it.

On p. 22 (2nd edition) Khaikin gives the definition of a law in the following formulation: “Every quantitative physical law contains within itself a statement concerning the relations between certain physical quantities.”

In the first edition Prof. Khaikin formulated this somewhat more laconically: “Every quantitative law is a statement concerning the relation between certain quantities” (1st edition, p. 18). Thus consciousness is brought to the foreground, in contrast to dialectical materialism, which recognizes as primary not consciousness, but an objective regularity existing outside and independently of our consciousness.

The understanding of a law as a statement given above is developed and carried through the whole subsequent exposition. Thus a subjective-idealist point of view is persistently pursued.

To the inexperienced reader it may seem that there is a difference between the formulations of law in the first edition and in the second edition of Prof. Khaikin’s book. However, this is only at first glance. On further reading one becomes convinced that Prof. Khaikin applied much “creative effort” and virtuosity in order somehow to disguise the obvious, subjective-idealist formulation of the concept of law. On p. 23 (2nd edition) Prof. Khaikin writes:

“When formulating any physical laws, one must clearly take account of the extent to which certain propositions constitute statements that require verification by experience, and the extent to which they are merely definitions of new physical quantities. It is necessary to distinguish statements from definitions because statements and definitions stand in an entirely different relation to experience. Statements can and must be verified by experience. Precisely insofar as these statements admit of experimental verification and are confirmed by experience, they constitute physical laws (italics—Khaikin).”

“Verification consists in the fact that the results of several independent measurements of various physical quantities satisfy the relation expressed by the law. Definitions, however, do not require experimental verification of this kind.”

In the first edition Prof. Khaikin was somewhat more explicit. There he says directly that “statements can and must be verified by experiment; definitions cannot” (p. 18, 1st edition). Thus, according to Khaikin it turns out that there are such propositions as are a priori creations of pure reason.

In the quotation given above from p. 23 of the second edition it is categorically asserted that a law is a “statement,” i.e. a subjective category.

The fact that “statements can and must be verified by experiment,” as Khaikin says, does not improve matters in the least, since the little word “experiment” is a common category of the Machists, who believe that in experiment we are dealing only with our own sensations and experiences, and not with material objects and phenomena.

But what is still worse is that one and the same propositions may, depending on circumstances, be regarded both as statements (i.e. in Khaikin’s definition—as laws) and as definitions (which, according to Khaikin, are no longer laws). That is, one and the same proposition can both be a law and not be one, depending on the person who is dealing with these propositions. In support of what has been said here, let us give one more quotation from p. 22 of the second edition. There the following is said:

“Thus, the proposition contained in Newton’s second law, that acceleration is proportional to the acting force, can be regarded as a statement subject to verification by experiment only if we have an independent method of measuring accelerations and forces. If, however, we do not have an independent method of measuring force, but determine forces by those accelerations which they impart to a body, then the proposition that acceleration is proportional to force is no longer a statement subject to experimental verification, but is a definition of force which, like every definition, does not require direct experimental verification.”

In the quotation given, Prof. Khaikin has set forth everything he thought: both that statements (i.e. laws) can become definitions (i.e. not laws), and that definitions are extra-experimental a priori categories.

Allow me to ask Prof. Khaikin a question which is always put in such cases to subjective idealists. If there were no one in the world to utter “statements and definitions,” would the laws of nature, including Newton’s laws, then exist or not? It is enough to pose the question in this way for it to become perfectly obvious that Prof. Khaikin is developing in his Mechanics a subjective-idealistic worldview.

This worldview Prof. Khaikin also carries over into the exposition of the basic laws of mechanics—the laws of Newton. On p. 86 (2nd edition) he says:

“In the above exposition of the fundamental laws of motion, the method of measuring mass was borrowed from Newton’s second law. As a result, Newton’s second law could no longer be regarded wholly as an assertion subject to experimental verification. It is possible, however, to proceed otherwise, namely, to borrow the method of measuring mass from Newton’s third law. Then the character of the assertions contained in Newton’s second and third laws will change accordingly.” And somewhat further on, on p. 87 (2nd edition), Prof. Khaikin says: “Thus, depending on how we choose (italics ours—F. K.) the method of measuring mass, the character of the assertions contained in Newton’s second and third laws proves to be different.”

Thus, according to Khaikin, the content of the laws of nature depends wholly on the will of the subject who operates with these laws. Mach would have praised Prof. Khaikin for his frank exposition of Mach’s worldview.

Such is the state of affairs with the exposition of the fundamental laws of mechanics, the laws of Newton.

Matters are no better with questions of space and time. In the section “Mechanics of the Special Theory of Relativity,” Prof. Khaikin discusses methods of measuring spatial and temporal intervals. Concerning methods of measuring spatial intervals, Khaikin says (p. 512, 2nd edition):

“In order that the results of measuring lengths should satisfy the known requirements of repeatability, uniqueness, etc., the ruler which we use for this purpose must possess certain physical properties (it must be sufficiently rigid). But so long as, for measuring lengths, we use only a ruler—for example, the meter preserved in the Chamber of Weights and Measures—we are deprived of the possibility of verifying by experiment whether this ruler changes its length; by definition its length is constant.”

A remarkable conclusion, Prof. Khaikin!

Thus, the properties of bodies are not objective phenomena, but depend on your wishes, definitions, and requirements (as you put it, the requirements of repeatability, uniqueness, etc.). Sensing the shakiness of his positions, Khaikin tries in a footnote to make an amendment to these arguments of his. But this amendment does not improve matters; it makes them still worse, and it is evidently calculated only for the uninformed reader—such as first-year students still are. In this footnote (p. 512, 2nd edition) Prof. Khaikin explains: “Of course, using different rulers and comparing them with one another, we may discover that some of them change length in comparison with others; but some one ruler (the most rigid) we must adopt as the sta—”

…fields, and its length by definition is constant. At the present time, as a standard of length the length of a certain light wave is often used, but this means only that the length of this light wave is by definition considered constant.” Thus, Prof. Khaikin has explained!

It follows, then, that all the properties of bodies are nevertheless the result of definitions. Prof. Khaikin wanted light waves to have a constant wavelength; he uttered a definition and that was that—the wavelengths become constant by definition. This is an entirely frank subjectivist-idealist point of view, distorting concrete physical facts as well.

It is well known to physicist-spectroscopists and physicist-metrologists who deal with light waves that the lengths of light waves are not constant, just as any other physical objects are not constant. With some light sources they are more constant, with others less so. But this depends not on “definitions,” and in general not on our wishes, but on the objective properties of the light sources. The principal metrological institutions are engaged in carefully studying the degree of reproducibility of the lengths of light waves, and only experience will show with which light sources the wavelengths prove sufficiently reproducible for them to be able to replace the meter in measurements of length. Thus, the matter stands quite the reverse of how Prof. Khaikin wishes to depict it.

After such “justifications” that the properties of space must satisfy the subjective requirements of the observer, Prof. Khaikin turns to the properties of time and its measurement. On this subject he says the following (p. 512, 2nd edition): “In exactly the same way, the light signals with whose aid we establish the time when ‘there’ an event occurred, i.e., determine the simultaneity of two events taking place in different places, must possess definite physical properties, so that the results of the measurement of time satisfy the requirements of uniqueness, repeatability, etc. But we cannot, for example, verify experimentally that the speed of light there and back is always the same—it is by definition one and the same.”

Thus, again a Kantian thing-in-itself, an a priori, non-empirical category, as in the case of Khaikin’s instrument for measuring length.

On the impossibility of an experimental verification of the equal speed of propagation of light there and back Prof. Khaikin speaks further, on p. 517. In a note on this page Prof. Khaikin says:

“Only Einstein pointed out the postulational character of the assumptions about the constancy of the length of rods and the rate of clocks—assumptions which in classical physics were regarded not as possible postulates, but as facts borrowed from experience.”

Thus, all the dots over the “i” have been placed! Prof. Khaikin has presented us with a fine gift—postulates which are creations of pure…

reason, standing outside experience, not borrowed from experience, from objective reality.

For more than 50 years experimental physicists have investigated these propositions experimentally and have come to the conclusion that the speed of light is constant there and back, whereas Prof. Khaikin wants to assure the inexperienced reader that these are extra-experimental postulates, borrowed merely from the human head.

Thus, Prof. Khaikin not only promotes an idealist worldview, but also distorts the concrete content of physical science, as he does in questions concerning standards of length. It is not our task to give a detailed review of Prof. Khaikin’s book. The purpose of this article is to ascertain what worldview is being promoted in it. From what has been adduced above it is clear that this worldview is an idealist one, of a Machist-Kantian type. We should like, however, to dwell also on certain points of the book which likewise reflect its general tendency.

Already in the introduction Prof. Khaikin insistently emphasizes that in his book he intends to deal with “idealized schemes.” This reverence of his for idealized schemes apparently compels him to present the material on incorrect physical models. Thus, on p. 275 a model of an elastic body is depicted which gives students an incorrect, distorted conception of an elastic body. The same can explain the fact that on p. 304 Prof. Khaikin asserts: “A solid body can be stretched or compressed in some one direction.” All knowledgeable people know that this cannot be done. Whenever there is stretching in one direction, compression appears in another. Why then does Prof. Khaikin write this for the inexperienced reader? And a little further on there is such confusion that it is not known why it is presented. On p. 305 Prof. Khaikin writes: “As for gases, in them, in principle, only deformations of compression occur.” But half a page lower Prof. Khaikin writes: “With rapid shear deformations in a liquid and a gas, noticeable forces may arise.”

On one page, in the formulation of the basic propositions of the mechanics of liquids and gases, such absurd contradictions are set forth.

Prof. Khaikin’s attempts to ascribe to bodies properties which they do not possess lead to nothing good.

On p. 89 in § 28 Prof. Khaikin makes a simplification, excluding frictional forces from consideration, i.e. passing to particular cases of motion. But, having passed to particular cases, Prof. Khaikin immediately on this basis makes a falsification and on p. 90 formulates what is already the fundamental proposition of mechanics. He writes: “We can now formulate in a new way the fundamental proposition of Newtonian mechanics. For a system of bodies at any moment of time, the second time derivatives of the coordinates of the bodies are uniquely determined by the coordinates of these bodies” (Khaikin’s italics).

Why did Prof. Khaikin need to give this knowingly incorrect formulation of the fundamental proposition of mechanics? This was done in order to banish motion, this attribute of matter, from the explanation of the origin of accelerations, and therefore of forces. On the same p. 90 Prof. Khaikin writes: “Figuratively speaking, in order to determine the accelerations of a system of bodies at some moment of time, one need have only an instantaneous photograph of the system corresponding to that moment, and there is absolutely no need to know whether the bodies are moving or at rest.”

This is what Prof. Khaikin had to prove, i.e., that in order to determine accelerations (and consequently forces) there is no need at all to reason about the motion of bodies. In the first edition, on this question, Prof. Khaikin was more frank, and on p. 72 he formulated it directly: “Therefore, in explaining the origin of forces in some system of bodies, one should never (italics ours—F. K.) introduce considerations as to the fact that the bodies are moving. The origin of forces can and must always be explained only on the basis of what position, at the given moment, is occupied by all the bodies of the system or by their separate parts.” This is why Prof. Khaikin needed all his contortions with the formulations of Newton’s fundamental proposition of mechanics. Finally, one more point deserves attention. This is the question of the role of Russian scientists in the development of science. The outstanding role of N. E. Zhukovsky and S. A. Chaplygin in the development of questions of the lifting force of an airplane wing and other questions of aviation is well known. Prof. Khaikin considered it only possible to mention the names of Zhukovsky and Chaplygin on p. 373, in § 129, under the heading: “The Magnus Effect—Circulation.”

In § 127, however, where lift is discussed, there is not a word about Zhukovsky, and in general it remains entirely unclear what the great Russian scientist Zhukovsky did. The reader obtains a completely distorted impression on this question. Not a word is said about Zhukovsky’s outstanding works connected with hydraulic shock.

In § 162, “Ultrasound,” not a word is said about the brilliant works of the Russian physicists Lebedev and Neklepaev.

In the paragraph “Reactive Motion,” there is not a word about Tsiolkovsky, etc. Not a sound is uttered about the works of Soviet scientists and, in general, about the achievements of Soviet science in the field of mechanics, as though such a science did not exist.

The question arises: who needs such a textbook, in which an idealistic worldview is carried through, the concrete content of science is distorted, and the role of Russian and Soviet scientists is belittled?