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On the Question of the Law of the Relationship Between Mass and Energy
S. G. Suvorov
- In the problem of the relation between mass and energy there are aspects which, for a materialist, are entirely obvious and indisputable. It is clear that the interpretation of energy as allegedly standing above matter (foreign energetics), or even as identical with matter (T. P. Kravets), just like the assertion that modern physics has supposedly proved that the concept of energy embraces not only the concept of motion but also matter (A. A. Maksimov), are non-Marxist, unscientific assertions.
Equally incorrect are assertions that the relation \(E = mc^2\) shows that substance is transformed into energy (as is encountered in a number of brochures and even textbooks); this is confusion of the same order, for substance is one of the forms of matter, while energy is the measure of the motion of matter*).
The struggle against contemporary energetics in physics is necessary. Statements that energetics in our time does not exist and has merely been invented, that energetics died after Ostwald recognized the existence of atoms, show only that the authors of such statements do not understand that the essence of energetics consists not in the denial of atoms (they are recognized by present-day foreign Machists, but only as a construction of our thoughts), but in the tendency to think of motion without matter; such tendencies, in various forms, continue to exist in capitalist countries even now.
The indicated errors among individual authors arise for different reasons: in some cases this is the influence of foreign views, in others—ignorance of the foundations of Marxism, in still others—carelessness regarding philosophy and terminological confusion, while in some cases all these reasons operate at once.
*) The author has already had occasion to express himself on this question; see: S. G. Suvorov, “M. Planck’s Book and the Struggle for the Law of Conservation and Transformation of Energy,” in M. Planck’s book The Principle of Conservation of Energy, 1938.
But one thing should be noted: theoretically this question is perfectly clear. V. I. Lenin analyzed it thoroughly as early as 1908; nothing fundamentally new can be added here.
- In the physical literature one also encounters assertions about the alleged occurrence of mutual transformations of mass and energy. But this is a straightforward misunderstanding: the relation $E = mc^2$ expresses the connection between the mass and energy of one and the same object for any moment of time and, consequently, there can be no question here of transformation. Even in its form the relation $E = mc^2$ cannot be interpreted as an equation of transformation, something many physicists strangely have failed to notice.
The author has had occasion to observe disputes between prominent physicists who interpreted the interrelation of mass and energy in physical processes in different ways. It is not useless to discuss the course of these disputes, since they are typical. Let us call one side by the collective name: physicist Ivanov, and the other—physicist Petrov. Ivanov says: “I consider assertions about the transformation of mass into energy and vice versa to be incorrect. In any reaction both mass and energy are quantitatively conserved. Take, for example, the reaction that occurs when a lithium nucleus is bombarded by a hydrogen nucleus; as a result, two helium nuclei are formed. It then turns out that the rest mass of the two helium nuclei, i.e. the mass of the new products, is less than the rest mass of the initial products; the so-called mass defect is obtained, equal to 0.0185 atomic mass units. But if one takes into account that the helium nuclei also acquire kinetic energy, then to their rest mass one must add still another mass corresponding to the kinetic energy, on the basis of the law of the interrelation of energy and mass $\Delta m = \frac{\Delta E_k}{c^2}$. This additional mass of the helium nuclei may also be taken into account on the basis of the relation: $m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}$. The kinetic energy of the reaction products corresponds exactly to the mass defect. Consequently, the sum of the masses before and after the reaction remains unchanged and, therefore, no transformations of mass into energy occur.”
Let us note that Ivanov tries not to penetrate into the essence of the physical process; he proceeds from the existence of known relations. But he cannot maintain this position; he is driven from it by physicist Petrov. Petrov says: “You want to avoid answering the question—why the mass changes, but in fact you always answer it as follows: because the energy changes; and just now you speak of an additional ‘mass corresponding to kinetic energy.’ And this is no accident: no other terminology exists in physics. I, for my part, do not play the policy of the ostrich and say directly: the change of mass is causally conditioned by the change of energy.
and vice versa. One can give a very graphic example of such causal conditioning. Let, in a vessel filled with gas and adiabatically closed, there occur a process of transformation of an electron-positron pair into photons. Let, under the given conditions, the energy of the photons produced be completely transformed into the thermal energy of the gas. Then the result of the reaction will be as follows: initially there were the sum of the rest masses of the individual gas molecules and of the electron-positron pair, while finally there is only the sum of the rest masses of the gas molecules, i.e. a smaller sum of rest masses than the initial one. Thus there was gas and an electron-positron pair, and only gas was obtained, but in a new energy state (at a higher temperature). Has there not occurred here the transformation of part of the rest mass (namely, the mass of the electron-positron pair) ultimately into thermal energy? One may, of course, say that the increase in the thermal energy of the gas is connected with an increase in its mass, according to the relation
\[ \Delta m = \frac{\Delta E}{c^2}. \]
But where did this additional mass \(\Delta m\) of the gas come from? Why does the mass of the heated gas increase? Is it not because its thermal energy increases? For there is no indication of any other source!”
Then physicist Egorov enters the dispute. He says: “You apparently think that the persuasiveness of the example is increased by the fact that it includes a complex chain of transformations, at the beginning of which stand gas and an electron-positron pair, and at the end only gas, but in a new energy state. I assure you that the same problems arise also in a more ‘simple’ example—the collision of elastic balls. Suppose that, as a result of the collision, the kinetic energy of one of the balls has increased by \(\Delta E_k\). In accordance with the law of the interrelation of mass and energy, we can say that its mass has also increased by the amount \(\Delta m\). I should like to hear how you explain where this increase in the mass of the body came from?”
Ivanov: “I see that they necessarily want to lead me to the answer that the mass of the body in a collision increases because the body acquired energy in the impact. But I do not want to go over to Petrov’s position, and I shall try to explain the increase of mass otherwise. The point is that the law of conservation of mass and the law of conservation of energy are both fulfilled in any process. Although they are inseparably connected with one another, they are nevertheless two separate laws, since the grounds for their validity are independent of one another. By virtue of this, in a collision two independent processes must take place: the transfer of energy from body to body and the transfer of mass. The process of energy transfer is obvious. But how is the process of mass transfer accomplished? I do not agree to ascribe to energy a ‘mass’ which is transferred. There must be some process of transfer of matter during the impact. Since in an impact substance does not pass from body to body, one must conclude
suggesting that some form of matter, still unknown to us, is transferred.”
Petrov: “I do not agree with this. Physics knows of no process of transfer of matter in a collision; a collision is a process connected only with the transfer of energy. A reference to the transfer of mass by means of the transfer of an unknown kind of matter, invented ad hoc, is too shaky a foundation on which to build physical conclusions. To the question why the mass of a body subjected to an impact has increased, we can give only one answer: because its kinetic energy has increased.”
Such are the disputes which the author has repeatedly had occasion to observe among prominent physicists.
As we see, “physicist Petrov” sees in a collision (or in some other physical process, say, in the heating of a gas) only an energetic process, and he places the change of mass in causal connection precisely with the change of energy. Sometimes he admits that he is inclined to think that mass and energy are mutually transformed into one another. However, some “Petrovs” protest against numbering them among the defenders of the concept of transformation. But this is the result of inconsistency: he who regards physical processes only as energetic processes, who because of this places the change of masses in causal connection with the change of energy, thereby inevitably defends the position of the mutual transformation of mass and energy.
As for “physicist Ivanov,” he, as we see, objects to the concept of the mutual transformation of mass and energy. He does not agree to regard the change of energy as the cause of the change of mass, for he feels that this would mean defending the position against which he objects. This forces him to seek a cause of the change of mass independent of energetic processes, and he seeks this cause by means of a hypothesis according to which, in all cases when energy is transferred, matter is simultaneously transferred as well, in a form still hidden for the time being.
- The instructiveness of these disputes consists in the fact that they clearly reveal how little convincing the arguments are so long as both disputing sides remain at the old level of understanding of what the nature of mechanical motion and of physical motion in general is.
Among physicists and philosophers there still persists an understanding of mechanical motion only as a simple change of place.
But precisely such a conception of mechanical motion, as conceived outside any connection with complex physical processes, makes it impossible to indicate any other explanation of a change of mass, say in a collision, except a change in the kinetic energy of the body! Thus, a simplified understanding of mechanical motion (as well as of other physical forms of motion) leads
to the fact that it is precisely energy that is regarded as the direct cause of the change in the mass of a body when its velocity changes, as a substance possessing mass.
However, the data of modern physics, if they are understood correctly, compel us to change our conception of mechanical motion. This demand is now being put forward from all sides. Remaining with the old conceptions, we cannot correctly understand either the theory of rapid motions, or quantum mechanics, or the problem under discussion concerning the relation between mass and energy.
Modern physics has shown that the properties of a moving body in the general case depend on the ratio of the velocity of the body \(v\) to the velocity of light \(c\). In particular, the mass of a moving body is equal to:
\[ m=\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}. \]
This change in the properties of a body as a function of the ratio \(\frac{v}{c}\) shows precisely that mechanical motion can no longer be regarded as a simple transfer of a body, as a simple change of its place with respect to another, arbitrarily chosen body.
Motion is a process taking place in a physical system, a part of which is constituted by the moving body. Motion is a change in the connections of the body with all the other parts of the system, connections realized through the field*).
It is precisely the change in the connections of the body with the other parts of the system that leads to the dependence of the properties of the body, in particular its mass, on velocity. The dependence of mass on the velocity of a body shows that the mass of a body must be determined by the entire aggregate of its connections with other bodies (its field), as well as by the internal connections of the body. The nature of mass is not exhausted by those definitions which rest on the old understanding of mechanics.
As for energy, it is a measure of the motion of a body; there are no physical grounds for abandoning the very broad and just position of Engels and for considering energy a concept that embraces matter (!!), and mass, and charge, and action, and frequency, and in general all the parameters with which it can be connected**).
The views indicated on motion must also underlie the criticism of the Einsteinian conception of the theory of rapid motions
*) In light of this understanding, as R. Ya. Shteinman has indicated, inertial motion is such motion in which the connections at every moment are destroyed and re-created in such a way that these processes compensate one another.
) A. Maksimov, Introduction to the Modern Doctrine of Matter and Motion, 1941, p. 154 ff.
(the theory of relativity), if this criticism is not to be turned into an empty phrase. They also shed light on the question of the relation between mass and energy.
How, in this light, should one regard the result of the collision of bodies? What does the assertion mean that, as a result of impact, a given body has received not only an increase in kinetic energy, but also an increase in mass?
This means that the process of collision cannot be considered only as a process of energy exchange. It is a process in consequence of which there occurs a change in the connections of the colliding bodies with the field, and, as a result of this, a change in their mass.
The increase in the kinetic energy of a body and the increase in its mass are not two processes standing in a causal connection with one another: they are two aspects of one and the same process, in which, essentially, there also occurs a change in the connection of the body with the field. In this case the change in the connection of the body with the field always takes place in proportion to the change in the energy of the body. This latter is the law of the interrelation of mass and energy. Thus, in fact, no conversion of mass into energy or vice versa takes place. Likewise, in an impact there is no transfer from body to body of substance, or of matter in some other, as yet unknown form; rather, there occurs a change in the connection of the body with the field.
That is why those physicists are fundamentally wrong who think as though the proposition that in any process and, in particular, in the collision of bodies, mass is not converted into energy can be proved without resorting to the concept of the field. This cannot be done for the reason that one cannot here avoid the question of the nature of mass; and the question of the nature of mass inevitably leads to the question of the role of the field, of the connection of the parts of a material system through the field.
In the same light one may also consider the example of the increase in the mass of a body when it is heated. The validity of the relation \(\Delta E=\Delta m\cdot c^2\) in thermal processes indicates that they likewise do not proceed outside interaction with the field, and that our usual conception of heat is rather one-sided. Engels was profoundly right in pointing out that thermal processes are not reducible to the mere displacement of molecules.
Since the relation \(\Delta E=\Delta m\cdot c^2\) is valid for all forms of energy, it would be legitimate to conclude that, for any physical processes occurring in matter, one cannot ignore their connection with the field; that ignoring this connection does not lead to direct errors only within certain limits, for quasi-static cases. Thus, the nature of physical forms of motion turns out to be more complex than it is usually still imagined to be.
This, it seems to me, is where this problem of the connection between mass and energy leads. Discussion of this problem on the indicated plane
would be, it seems to me, a creative development of the question under discussion.
The relation between mass and energy can be correctly understood only on the basis of an analysis of how the conception in physics of the structure of matter, of motion, and of the role played by the field in physical processes has changed.
- Some physicists believe that mass, by its nature, is divided into two types—passive and active. The proof for such a conclusion is provided, for example, by the following arguments, varied in different cases. The so-called elementary particles of matter, for example the electron and the positron, possess rest mass, whereas the photon possesses only “mass of motion.” The rest mass of the electron and positron under ordinary conditions is not transformed into anything; it is passive; only under certain conditions can it be transformed into the mass of two moving photons, and at once as a whole, not in parts. The mass of photons, however, is active; it is continuously dispersed in arbitrarily small portions and, in the end, is expended on the excitation of the surrounding atoms, in particular on raising the temperature of the medium; as a result, the mass of the photons is distributed among the atoms, increasing the mass of each of them. Thus, these physicists assert, there are evidently two types of behavior of mass, two masses—passive and active.
However, such a classification of mass and the naming of its types do not disclose the essence of the physical process and may lead to confusion. In reality the difference between the two indicated processes consists in the fact that in the first case we have the transformation of one kind of matter—the “elementary” particles of substance—into another kind—the field. There is nothing surprising in the fact that this transformation takes place only under certain conditions; this is a trivial assertion: transformations of any kinds of matter—the transformations and formation of electron-positron pairs, the decay of nuclei, the radiation of atoms, chemical transformations, etc.—take place under certain quite definite conditions. If this were not so, there would be no stable systems in nature. In view of what has been said, the process of the so-called annihilation of an electron-positron pair is more correctly interpreted as follows: in this process, it is not passive mass that is transformed into active mass, but one kind of matter—substance—is transformed into another kind—the field.
The ability of definite kinds of matter to be transformed, under definite conditions, into other kinds cannot in any way be characterized as the passivity of matter. What has passivity to do with it, if transformations necessarily take place as soon as the corresponding conditions arise?
In the second case considered, there is no transformation of kinds of matter. Since in a closed system, as a result of the annihilation of a pair, two photons are formed, the mass changes
the characteristic of the field in this system changes, the connection of the atoms with the field changes, and thereby their mass changes. In the given process, under the given conditions, such a process of change of mass is just as necessary as, under certain conditions, the transformation of particles of matter into particles of the field is necessary. Thus, there are no grounds to speak of any special property of “activity” of mass of this type, as opposed to the property of “passivity” of rest mass.*)
There is no doubt that rest mass and the mass which a particle possesses as a consequence of motion are different. But their distinction should be formulated by means of a physical characteristic. In what can this characteristic consist? Obviously in an analysis of the nature, origin, and role which the given mass plays in connections, in the motion of the object. Rest mass, apparently, characterizes not only the connections of particles with other components of the system in the case when the former are at rest relative to the latter, but also, to some extent, the internal connections of the particles. The nature of mass is very complex. One may expect that light will be shed on this problem when physics establishes the conditions and investigates the processes of all possible transformations of elementary particles into one another and into various kinds of fields, and creates a theory of transformations, for which it still does not yet see clear paths. In any case, the distinction between the masses \(m_0\) and \(\Delta m\) must be based, as it seems to me, precisely on physical considerations connected with elucidating the nature of mass.
Anthropomorphic characteristics, however, (passive—active mass) of natural phenomena introduce confusion of a gnoseological character, since they direct attention not to the investigation of the nature of the given phenomenon and the conditions of its realization, but substitute for this investigation the attribution to things of metaphysical, primordial properties. And this substitution occurs independently of the wishes of the authors of anthropomorphic characteristics. Therefore they should be abandoned.
*) It should also be noted that the rest mass of “elementary” particles can be transformed into the mass of photons, and not completely, but partially. This occurs in some cases of the joining of nucleons into atomic nuclei (the so-called “mass defect”). The same occurs in the transformations of mesons. The “passivity” of rest mass proves to be a completely non-absolute property. As for the annihilation of nucleons, i.e., the complete transformation of the masses of nucleons into the masses of photons, there are no grounds for considering that this process does not occur at higher interaction energies.