ON THE LAW OF THE INTERRELATION OF MASS AND ENERGY

(Against Idealistic Distortions in the Interpretation of the Law $E=mc^2$)

A. M. Butov and E. G. Shvidkovsky

This article attempts to expose the idealistic distortions in the interpretation of the conclusions of modern physics connected with the law of the interrelation of mass and energy, quite incorrectly called the “law of the equivalence of mass and energy,” and to subject these distortions to criticism. A complete and general consideration of this law requires an analysis of the concept of the physical field and of its relation to particles, which is an important methodological question of modern physics and one that needs serious development.

However, in order to expose the idealistic distortions in the interpretation of the law of the interrelation of mass and energy, a narrower formulation of the problem proves sufficient—one that does not include an analysis of the concept of the physical field.

1. It is well known that the overwhelming majority of foreign physicists connect with the law $E=mc^2$ false assertions, devoid of any scientific basis, that allegedly not only mass, which is a property of matter, but substance and matter in general are capable of being transformed into energy; that the laws of conservation of mass and energy have no place in modern physics and must be replaced by a “generalized” law of conservation of mass $+$ energy; that mass is a form of energy; and, finally, that energy is supposedly the “sole substance” of nature.

There is no need to cite the relevant quotations. It is enough to look through the works of Einstein and Barnett relating to this question, the widely advertised book by G. D. Smyth on atomic energy, monographic publications such as D. Stranathan’s

“Particles in Modern Physics,” popular books such as, for example, A. Berthelot’s From the Atom to Atomic Energy, P. Auger’s What Are Cosmic Rays?

Translations of such books published in our country are almost never accompanied by any critical remarks concerning the above-mentioned statements.

What is important for us here is not the minor differences that exist in the interpretation of the relation \(E = mc^2\), but rather the general idealistic tendency that unites the views of the majority of bourgeois physicists.

This idealistic tendency common to them all is energetism and takes its origin from W. Ostwald. Ostwald wrote that “... the concept of energy proves to be most capable of fully resolving the problem contained in the concept of substance and not yet resolved by the concept of matter.” Ostwald wrote directly that he “is attempting to construct a worldview exclusively from energetic material, making no use whatever of the concept of matter.” Ostwald devoted his entire book Natural Philosophy to an attempt to provide “proof” that the natural sciences supposedly do not need the concept of matter and that energy is the “fundamental substance” of nature.

Considering his principal thesis on the substantiality of energy to be sufficiently “substantiated,” Ostwald concludes: “That all external phenomena can be represented as processes of transformation of energy finds its simplest explanation in the fact that even the very processes of our consciousness have an energetic character, and this character of theirs is imprinted on all the external phenomena of our experience.”

On this last point V. I. Lenin wrote: “This is pure idealism: it is not our thought that reflects the transformation of energy in the external world, but the external world that reflects the ‘property’ of our consciousness.” (V. I. Lenin, Works, vol. 14, p. 258.)

Such is Ostwald’s very uncomplicated path: having “proved” that energy is the “sole substance” of nature and can exist without matter, having separated, in other words, motion from matter, he arrived at philosophical idealism.

Using Ostwald as an example, we see that the basis of the philosophical idealism of energetism was energetic physics. V. I. Lenin wrote: “Energetic physics is the source of new idealistic attempts to think motion without matter—because of the decomposition of particles of matter that had hitherto been regarded as indivisible, and the discovery of forms of material motion hitherto unknown.” (V. I. Lenin, ibid., p. 260.)

Proceeding from this, we must wage an uncompromising struggle against every kind of manifestation of energetism in physics, in whatever form it may appear.

We must admit that some of our scholars uncritically accepted the statements of foreign physicists and in their works committed serious errors in interpreting the interrelation of mass and energy. Thus, for example, D. Frank-Kamenetskii asserts that “Einstein’s law (the law $E = mc^2$—B. Sh.) in no way contradicts the law of conservation of energy, but we must now broaden the content of the latter. We must regard mass as one of the forms of energy, capable of being transformed into other kinds of energy in a definite ratio” ($^4$, p. 25), and further: “The mutual annihilation of a positron and an electron is the only process known to us in which a complete transformation of mass into energy takes place.” (Ibid., p. 62.)

In the textbook Physical Chemistry A. I. Brodskii writes: “This is one of the fundamental laws of nature, establishing the unity of ponderable matter and energy, toward which science has long been striving. Mass and energy represent different forms of motion of a single matter, which can pass into one another in equivalent quantities” ($^5$, p. 18). Thus, here we encounter a direct identification of a property of matter—mass—and the physical formulation of the concept of motion—energy—with matter itself. The quotation cited characterizes the ambiguities that exist among scholars regarding the content of such concepts as mass, substance, physical kinds of matter, and energy.

T. P. Kravets published the wholly erroneous article “The Evolution of the Doctrine of Energy”$^6$. This article can only deepen the confusion in understanding the relation between mass and energy. In fact it has turned out that Kravets has taken the path of substantiating the fundamental thesis of the energetists concerning the substantiality of energy, understood in the sense of the independent existence of particles of the latter. The article contains not even a mention of Engels’ works relating to energy and the law of its conservation and transformation. In his conclusions Kravets writes: “Energy appears to us as a certain substance, in every respect similar to ponderable substance and endowed with all those properties that compel us to regard ponderable substance as a substance; it is indestructible and uncreatable; it is localized in space; it moves and is transmitted; it possesses inertial mass, it is ponderable; it is divided into atoms. An exact law of equivalence between energy and substance is established. One may assert with confidence that both are to the same extent the essence of what we call matter” ($^6$, p. 357).

Kravets’ conclusions are not the consequence of factual data of science, but essentially the consequence of a confusion of the concepts of matter, energy, substance, and mass.

The views of modern energetists differ in principle in no way from Ostwald’s views, and some of our scholars

suppose that one can somehow turn energetism into materialism if energy is declared to be matter.

In 1941 A. Maksimov’s book[^7] appeared, in which, according to its author, an attempt is made at a “materialist generalization of ideas about matter and motion.”

On page 133 of the named book we read: “Physicists regarded mass as unchanging; therefore, when considering transformations of energy, all attention was concentrated on the change of forms of motion. Hence there arose the formulation of the law of conservation and transformation of energy as a law concerning the change of forms of motion.” It is well known that no physicist posed the question in this way; such a dialectical-materialist formulation of the question belongs to Engels.

Engels rightly wrote: “Any form of motion proves to be capable, and must prove to be capable, of being transformed into any other form of motion. In this form the law attains its final expression. Thanks to new discoveries we can find new proofs of it, give it new, richer content. But to the law itself, as it is expressed here, we can add nothing more.” (K. Marx and F. Engels, Works, vol. 14, p. 496.)

Maksimov, however, emphasizes: “There is no energy that would not be equivalent to mass, and there is no mass that would not be equivalent to energy; therefore the former point of view on the change of energy as on the change of forms of motion must be abandoned” ([^7], p. 134).

Developing these thoughts, Maksimov further writes: “In Engels’s time the question of the variability of mass, of its dependence on velocity, of the equivalence of mass and energy, etc., had not yet arisen in physics. Therefore it is natural that Engels relied on the conception of energy that was generally accepted in nineteenth-century physics. According to this conception, regarding mass as unchanging, in the concept of energy they saw the physical formulation of the general concept of motion.

Modern physics, having discovered the variability of mass, revealed what had already been contained in the definition of energy—namely, that the concept of energy embraces not only the concept of motion, but also that of matter (physically defined as mass, charge, etc.). In this sense Engels’s formulation is refined in full accordance with the general proposition on the unity of matter and motion.” (Ibid., p. 154.)

The views set forth above in Maksimov’s own words are entirely erroneous. In the present case, contrary to the doctrine of dialectical materialism about moving matter, contrary to Engels, who saw in energy the physical formulation of the concept of motion, Maksimov in essence proposes that the concept of energy be considered broader than the concept of matter, uniting—

containing within itself not only matter, but also motion. Maksimov likewise makes a serious error in the passage where he identifies matter with its properties: mass, charge, and so on.

Matter is concretized in an infinite variety of kinds, but at the same time, within the content of physical science, at least two forms of matter may be indicated, uniting the enormous diversity of concrete kinds by virtue of the commonality of certain properties. To the first of these may be assigned the so-called elementary particles and complex formations made up of elementary particles (atoms, molecules, i.e., substance), whose common feature is that they can be in a state of relative rest.

To the second belong those kinds of matter which, despite the qualitative differences between them, possess the common feature that the state of relative rest is not inherent in them (for example, the electromagnetic field).

Since both are forms of moving matter, transformations of one form into the other are also possible. In the physical laws relating to processes of this kind, the indestructibility and uncreatability of matter and motion must find expression.

The singling out, among the diverse kinds of matter, of the two forms just mentioned must of course not be regarded as an exhaustive classification. For us it is for the present essential to emphasize those aspects of commonality (both are forms of moving matter) and those aspects of difference (with respect to the state of relative rest) which exist between elementary particles (excluding photons), on the one hand, and electromagnetic radiation, on the other.

An incorrect understanding of the relation between these two forms of moving matter, and sometimes a distorted interpretation of it, is one of the chief sources of energeticist perversions in modern physics. This is manifested especially clearly in the fact that the photon is often associated with the notion of a particle of “pure” energy. It is therefore necessary to dwell briefly on the nature of the photon and on the history of the discovery of its properties.

1. At the beginning of the twentieth century it seemed that the wave theory of light had been definitively established. However, as early as the end of the preceding century A. G. Stoletov had discovered the phenomenon of the photoelectric effect. The quantum conceptions that arose, which at first had to be introduced to explain the laws of black-body radiation and then to explain the photoelectric effect, once again posed before physicists the question of the nature of light, which had revealed, alongside wave properties, corpuscular properties as well.

From P. N. Lebedev’s experiments on the measurement of light pressure it followed that the electromagnetic field possesses mass. With the development of quantum conceptions of light it became clear that mass belongs to the photon; it is equal to its energy divided by the square of the speed of light.

Subsequently it was shown experimentally that in the scattering of X-rays the collision of a photon and a free electron takes place in accordance with the laws of conservation of energy and momentum.

The experiments indicated proved the fact that the photon has inertial mass, which of course is not rest mass. But since the photon, in comparison with other particles, possesses a qualitative peculiarity—it has no state of relative rest—it must be ascertained that inertial mass is at the same time gravitational mass, i.e., that it is mass precisely in the sense associated with this concept in physics.

If the inertial mass of the photon is at the same time gravitational, then gravitational fields must act on the photon. In this connection two effects may be observed: the first is associated with the passage of a ray near a large mass, the second with the emergence of a photon near a gravitating center. It is known that experimental investigations of both these processes have proved that the photon has gravitational properties. The inertial mass of the photon has turned out also to be gravitational mass.

The further development of physics deepened our knowledge of photons. The phenomenon of the formation of an electron + positron pair and the inverse process, very unfortunately called “annihilation,” were discovered.

Thus our knowledge of the properties of the photon broadened and deepened.

Above all, the energetic aspect of photons was noticed; by virtue of this, among physicists there at first arose the idea of photons as particles of “pure” energy. However, by the present time other properties of the photon have also been revealed: mass, and the capacity to undergo profound qualitative changes. Therefore it is completely incorrect to regard the photon as a particle of “pure” energy.

Pair formation shows that, under corresponding quantitative changes, when the energy of the photon reaches a certain value, possibilities are created in it for the realization of a sharp qualitative leap. The photon is transformed into two new particles—an electron and a positron—which acquire independent existence under the influence of a third particle—the nucleus of the atom.

The photon is one of the concrete forms of matter. The transformation of the photon is connected with a change in the form of motion of matter and is accompanied by the transformation of one kind of energy into another.

It is already evident from this that the assertion that, in pair formation, a complete transformation of mass into energy takes place is physically untenable. The qualitative difference of the photon from other particles consists in the fact that it does not possess a state of relative rest; therefore the photon also has no rest mass. As for the mass which the photon actually possesses, according to all the data of physical science this is the same kind of mass as the mass of other particles.

1. The law of the interrelation of mass and energy consists in the fact that every object of the material world having mass \(m\) possesses a store of total energy equal to

\[ E = mc^{2}. \tag{1} \]

Here, by mass is meant not the rest mass of the given object, but the mass which it possesses in its given state of motion. If experimental observations establish that a given material object possesses a store of total energy \(E\), then it necessarily has a mass equal to \(\frac{E}{c^{2}}\).

The equation \(E = mc^{2}\) is the natural-scientific expression of that property of the material world that energy and mass are inseparably connected. But there is no question in it of any transition of mass into energy or back again.

In order to examine this question in greater detail, it is necessary to consider whether the laws of conservation of mass and energy are obeyed in all known cases, or whether, as foreign and some of our physicists assert, this does not take place.

No one doubts that both laws hold for all macroscopic processes. However, the supporters of the idea of the mutual convertibility of mass and energy point out that this allegedly holds only approximately, within the limits of observational accuracy, owing to the negligible smallness of the effects connected with the transformation of mass into energy. It is a different matter, they say, in elementary acts accompanied by considerable changes in the energy belonging to a particle; there, they claim, the nonobservance of the laws of conservation of mass and energy is clearly revealed, and their replacement by a single law of conservation of mass-plus-energy is required.

Let us examine some elementary processes to which contemporary supporters of energetism in physics often refer.

Consider the reaction

\[ \mathrm{Li}^{7}_{3} + \mathrm{H}^{1}_{1} \to \mathrm{He}^{4}_{2} + \mathrm{He}^{4}_{2}. \tag{2} \]

Its characteristic feature is that the kinetic energy of the particles formed reaches a large value

(on the order of 8.6 MeV per particle), whereas the energy of the bombarding hydrogen nucleus may be relatively small (on the order of several MeV). Along with the change in the kinetic energy of the system, a change is observed in the rest masses of the particles.

The sum of the rest masses of the atomic nuclei entering into the reaction is equal to 8.0263 atomic mass units, while the sum of the rest masses of the nuclei—the products of the reaction—is equal to 8.0078 a.m.u. As a result of the reaction, what is called a mass defect is obtained, equal to 0.0185 a.m.u.

This and similar facts are in many cases mistakenly interpreted as a transformation of mass into energy; in doing so, however, one essential detail is “forgotten”: the masses cited above refer to particles at rest, which in practice is what the particles entering into the reaction are. Meanwhile, as a result of the reaction helium nuclei are obtained, flying with enormous velocity, and these nuclei will in fact possess a greater mass than the rest mass taken into account above, in accordance with the expression

\[ m=\frac{m_0}{\sqrt{1-\beta^2}} . \tag{3} \]

Taking into account the change of mass with velocity according to the equation given above will lead, as is known, to the conservation of the mass of the particles before and after the reaction.

Here it is appropriate to emphasize one more circumstance. The isotope \(\mathrm{Li}^{7}_{3}\) consists of three protons and four neutrons; the sum of the masses of these particles is equal to 7.0606 a.m.u., while the mass of the lithium nucleus is equal to 7.0182 a.m.u. Consequently, in the formation of the lithium nucleus a mass defect is obtained, equal to 0.0420 a.m.u., and the binding energy of the \(\mathrm{Li}^{7}_{3}\) nucleus is determined as 39.09 MeV. This cannot cause bewilderment, because the sum of three neutrons and four protons is not yet a lithium nucleus. Therefore the mass of the simple sum of these particles, generally speaking, need not be equal to the mass of the lithium nucleus. In the process of formation of the \(\mathrm{Li}^{7}_{3}\) nucleus there occurs a qualitative leap, in which a new kind of matter is formed in comparison with the simple sum of these particles.

The formation of the \(\mathrm{Li}^{7}_{3}\) nucleus will be accompanied by intense electromagnetic radiation, and the nucleus itself will acquire the corresponding velocity in such a way that the sum of the masses of the moving nucleus and of the radiation will be exactly equal to the sum of the masses of three protons and four neutrons.

If one more neutron joins this nucleus, then again a new kind of matter will be obtained—the radioactive isotope of lithium \(\mathrm{Li}^{8}_{3}\), and its mass will be different. In every process considered we are dealing with qualitatively new kinds of matter. The mechanical transfer of the properties of free particles to their aggregate is the crudest metaphysics.

ON THE LAW OF INTERRELATION OF MASS AND ENERGY

Let us turn to the energy balance of the reaction under consideration. We shall denote the internal energies of the particles, inherent in them in the state of rest, by \(U\) with the corresponding subscript below, and the kinetic energies of their mechanical motion by \(E\), likewise with a subscript. Then the energy before the reaction will be equal to \(U_{\mathrm{Li}} + U_{\mathrm{H}} + E_{\mathrm{H}}\). Assuming, for simplicity, that the kinetic energies of the alpha particles formed are equal, the total energy of the system after the reaction may be represented in the form: \(2U_{\mathrm{He}} + 2E_{\mathrm{He}}\). The law of conservation of energy gives the equation:

\[ U_{\mathrm{Li}} + U_{\mathrm{H}} + E_{\mathrm{H}} = 2U_{\mathrm{He}} + 2E_{\mathrm{He}}. \tag{4} \]

Let us now transform the last equation, using the law of interrelation of mass and energy. Obviously, we obtain:

\[ c^2\left[m_{\mathrm{Li}}^{0} + m_{\mathrm{H}}^{0} + m_{\mathrm{H}}\right] = c^2\left[2m_{\mathrm{He}}^{0} + 2m_{\mathrm{He}}\right], \tag{5} \]

where \(m^0\) denotes the rest masses of the particles and \(m\) the additive masses due to the fact that the particles possess kinetic energy of translational motion. Obviously, the equation obtained is the law of conservation of mass.

Consequently, since the law of conservation of energy is fulfilled for the process under consideration, the law of conservation of mass is also fulfilled for it. This circumstance can be established owing to the discovery of the law of interrelation of mass and energy.

Let us collect on the left-hand side of equation (4) or (5) the terms referring to the state of rest of the particle, and express them through the masses, and on the right-hand side the terms referring to the state of motion of the particles, and express them through the energy of translational motion. We obtain:

\[ \left(m_{\mathrm{Li}}^{0} + m_{\mathrm{H}}^{0}\right) - 2m_{\mathrm{He}}^{0} = \frac{2E_{\mathrm{He}}}{c^2} - \frac{2E_{\mathrm{H}}}{c^2}. \tag{6} \]

It is precisely in this form that it is customary to write the energy balance of nuclear reactions, and to call the left-hand side of the last equation the mass defect.

This equation, i.e. the transformed law of conservation of energy or of conservation of mass, is interpreted by physicists as the transformation of mass, equal to its defect, into the energy of translational motion of the particles. From what has been set forth it is clear that such an interpretation is physically incorrect and that in reality equation (6) is a consequence of the fact that in nuclear reactions both the law of conservation of energy and the law of conservation of mass are obeyed.

Equation (6) is widely used as a convenient and precise method for determining the energy terms of an excited nucleus

and for calculating the energy effects of nuclear reactions. Thus, the validity of equations (4) and (5) turns out to have been rigorously proven by experiment. Consequently, there are no grounds or possibility to speak of the transformation of mass into energy or of the need to replace the laws of conservation of mass and energy by some “new,” “unified” law of conservation of mass + energy.

Quite similar arguments may be made regarding the process of formation of an electron + positron pair and the reverse process, with the very same conclusions.

On the attempt to pass off an incorrect interpretation of equation (6) as a real phenomenon is built a “new” energetical physics, in which, following Ostwald, energy is declared to be the “sole substance” of experience; Engels’ view of energy as the physical formulation of the concept of the motion of matter is declared obsolete; and both fundamental laws of nature—the conservation of energy and the conservation of mass—are rejected at the same time.

Motion is an attribute of matter. Mechanical displacement does not exhaust motion taken as a whole, but is present in all its more complex forms. Therefore the concepts of motion and rest are relative. When we speak of rest mass or rest energy, what is meant is that numerical value of these quantities which will be obtained in a coordinate system connected with such a material body relative to which the given particle is at rest. The equations of the conservation laws themselves hold independently of the coordinate system in which they are written, but the numerical values substituted into them must be measured precisely in that given coordinate system.

Analysis of the question considered above—the laws of conservation of energy and mass in relativistically invariant form—requires the joint consideration of energy and momentum density. However, since the conservation laws hold in this case as well, and since, on the other hand, in our simplified treatment of the question the existence of the law of conservation of momentum also, of course, holds, the conclusions obtained so far cannot change as a result of a general analysis of the problem.

1. According to Thomson, the energy of a material system is the magnitude, measured in mechanical units of work, of all external actions performed on the system when the latter passes in any manner from the given state into an arbitrarily fixed zero state. This definition expresses the quantitative aspect of the concept of energy (up to an arbitrary constant, of course), under the assumption, naturally, that either the external actions are exclu-

considerably mechanical, or, if they are of some other nature, then their mechanical equivalent exists.

However, this definition of the concept of energy does not reflect the qualitative aspect, since it remains unclear what exactly, in a qualitative respect, is expressed by the concept of work.

The qualitative aspect of the concept of work was revealed by Engels, who indicated that work is the measure of the transition of one form of motion of matter into another form.^3

Since work, as the mechanical equivalent of all external actions, is equal to the change in the total energy of a system, the measure of the transition of one form of motion of matter into another is the change in the total energy of the given body. Consequently, a change in energy appears as a measure of the transformation of one form of motion of matter into another.

The process of development (motion) of matter may be accompanied by an abrupt change in its qualitative state. For example, a qualitative leap in the properties of a photon can occur only under certain conditions \((E > 1.02\ \mathrm{MeV})\). If the transforming photon has an energy greater than \(1.02\ \mathrm{MeV}\), then the excess energy passes into the kinetic energy of the motion of the electron and the positron. Thus, the value of the photon energy corresponding to the nodal point is a measure of the transformation of one form of motion of matter into another.

The analysis of the concept of mass, from the quantitative and qualitative aspects jointly, presents great difficulties. First of all, it must once again be emphasized that mass is not a concept identical either with energy, or with motion, or with matter, or with substance. As was indicated above, failure to understand this circumstance is the cause of a whole series of gnoseological errors.

Mass appears to us as one of the most important physical properties of moving matter. Such an understanding of mass follows from its generality, as a property of all known kinds of matter. Not only substance but also the electromagnetic field possesses mass; it is an inalienable property of any concrete kinds of matter.

The quantitative aspect of the concept of mass can be defined through inertia. This definition makes it possible to establish a method for the quantitative measurement of mass with the aid of a definite system of units. Further, one must proceed along the path that proved fruitful in the analysis of the concept of energy, i.e., it is necessary to disclose the content of the concept of inertia from the qualitative aspect.

The quantitative aspect of mass can also be defined through gravitation, and then an attempt can be made to disclose the qualitative content of the concept of gravitation. Since in both cases we have

...dealing with the real properties of the material world, one may assume that both paths of consideration must lead to the same result with respect to revealing the concept of mass.

There is nothing surprising in the fact that mass, being a reflection of very general features of concrete kinds of matter, in a definite form of matter, situated under definite conditions, can also serve as a characteristic of some of its specific properties. Therefore, for matter in the form of substance at small relative velocities of mechanical motion, mass is also a quantitative measure of substance. To pass over in silence the question raised here concerning the relation of mass to the quantitative measure of substance is completely impossible, unless one consciously breaks in this question with all human practice. Indeed, is it not precisely with the quantitative measure of substance that we are dealing when we speak of the millions of tons of cast iron, steel, and grain produced by our industry and agriculture?

From what has been said, incidentally, one cannot draw the conclusion that if, in the collision of spheres, the energy, and consequently the mass, of one of the spheres increases while that of the other decreases, this means that substance (molecules) is transferred from one sphere to the other. It is well known that no such exchange of substance takes place in the collision of spheres. Hence one also cannot draw the conclusion that the “additional” form of matter in the moving sphere is energy. The inadmissibility of such an interpretation was shown above.

As it seems to us, the correct, though too general, answer to the question posed consists in the following. As was emphasized above, the singling out from the whole variety of kinds of matter of the forms of matter—substance and the electromagnetic field—cannot be regarded as an exhaustive classification. It proves sufficient when considering a definite range of questions, but one must never forget that the process of cognition of the world is infinite, and that as humanity’s cognitive activity develops, ever newer forms of matter, forms of its motion, and new transitions from some forms into others are being discovered and will continue to be discovered. When we establish that the mass of a sphere set in motion has increased, this means that matter, concretized in the form of the sphere, is not exhausted by our concept of substance; that it contains unrevealed forms of material motion which, however, can be revealed. We judge their existence by the motion that has manifested itself.

Let us now return to the analysis of the concept of mass as one of the most important physical properties of matter. Of the two approaches outlined to the question—the “inertial” and the “gravitational”—we shall choose the first. The task consists in revealing the qualitative content of the concept of inertia.

The concept of inertia is connected with the mechanical form of motion, and in mechanics the understanding of this property is still determined by the physical content of the following formulation by Newton^8: “The innate force of matter is its inherent power of resistance, by which every body, taken separately, insofar as it is left to itself, maintains its state of rest or of uniform rectilinear motion. This force is always proportional to the mass, and if it differs from the inertia of mass, it does so only in our conception of it.” Without entering into a theoretical-cognitive analysis of the formulations and views of the author of the Principia, let us note that the idea according to which the capacity of a separately taken body to maintain its state of rest or uniform rectilinear motion, even if it differs from inertia, does so only in our conception of it—this idea determines the content of the concept of inertia in modern mechanics and physics as well. Newton’s reservation that “... This force ... if it differs from inertia ...” is connected with the question of the identity or difference between “quantity of matter” and “inertia,” since the term “mass,” which appears in the first definition of the Principia, was inserted in the translation by A. N. Krylov and is not contained in the original.

Thus, the qualitative content of the concept of inertia, which has proved fruitful for science over almost three hundred years, characterizes the incapacity of material bodies to change their state of mechanical motion without an external action, relative to the given body.

It seems to us that such an understanding of the qualitative content of the concept of inertia is correct, but at the same time it is insufficiently general, since it applies only to mechanical forms of motion. At present it is difficult to give any definite answer to the question of the possibility of extending this understanding of the qualitative content of the concept of inertia to other, non-mechanical forms of motion. However, one example is not without interest in this respect.

Let us imagine that near a gravitating center there arises a photon whose energy is somewhat greater than 1.02 MeV. Such a photon, passing near the nucleus of some element, can transform into an electron–positron pair. However, as it moves away from the gravitating center, the photon will become more and more “red,” and as a result its energy will become less than 1.02 MeV, so that it will already lose the capacity for transformation. Here inertia appears in a broader sense than only for mechanical forms of motion. The property of inertia prevents the transformation of the photon, i.e., prevents a change in the form of motion of matter.

Thus, inertia, within certain limits, expresses a property opposite to motion. In any case, this is valid with respect to the lower forms of motion of matter.

The question of the further clarification of such concepts as mass, substance, physical field, electromagnetic radiation, photon, and a number of other fundamental physical concepts is extremely important. Unclarity in these concepts leaves loopholes for “physical idealism.” The partial solution proposed by the authors is, of course, not exhaustive and should rather be regarded as a concretized formulation of the problem.

CITED LITERATURE

1. V. I. Lenin, Works, vol. 14, 4th ed.
2. K. Marx and F. Engels, Works, vol. 14.
3. F. Engels, Dialectics of Nature, 1946.
4. L. Frank-Kamenetsky, Energy in Nature and Technology, Goskultprosvetizdat, 1948.
5. A. I. Brodsky, Physical Chemistry, vol. 1, Goskhimizdat, 1947.
6. G. P. Kravets, “The Evolution of the Doctrine of Energy,” UFN, vol. XXXVI, no. 3, 1948.
7. A. Maksimov, Introduction to the Modern Doctrine of Matter and Motion, 1941.
8. I. Newton, Mathematical Principles of Natural Philosophy. Translated by A. N. Krylov. Proceedings of the Nikolaev Naval Academy, nos. 4 and 5, Petrograd, 1915.