ON THE DISCUSSION OF THE CONCEPT OF “MASS”

In connection with the discussion of mass*) carried out by your journal, I wish to point out some aspects of the question that were insufficiently touched upon in the discussion.

1. The participants in the discussion are unanimous in treating mass as a measure of inertia, and not as a measure of the “quantity of matter.” However, they did not note that the term “quantity of matter” itself is so indeterminate that its use (like the term “quantity of motion”) should be regarded as generally undesirable.

Indeed, the concepts of matter (objective reality) and of its motion (change) are the most general concepts underlying all other physical concepts, which specify particular properties of matter. Mentally singling out from the surrounding world certain physical objects, we can, by learning their properties (for example, inertia, the ability to conduct electric current, to refract light, etc.), find quantitative characteristics of these properties (mass, electrical conductivity, refractive index). These quantitative characteristics allow us to compare certain objects according to features common to them.

Thus, one can compare atomic nuclei by their charge, mass, and spin; one can compare waves by frequency, amplitude, and phase; one can compare sound timbres by their spectra.

But the terms “quantity of atom,” “quantity of wave,” or “quantity of timbre” are devoid of content. Equally devoid of content is the term “quantity of matter,” often erroneously used in those cases where simply the number of particles of a substance is meant.

Thus, Newton wrote[^1]: “Resistance... is proportional to the quantity of matter, that is, to the number of particles experiencing resistance.” It is interesting to note that Lomonosov already sensed the indefiniteness of the term “quantity of matter.” In his dissertation[^2] “On the Relation of the Quantity of Matter and Its Weight” he says: “There is no doubt that in one pound of gold there is half as much matter as in two pounds of it (that is, half as many particles—N. M.). But it is doubtful that in one pound of water and two pounds of gold there should be the same relation of matter.”

Uncritically using in modern physics the obsolete term “quantity of matter,” people lose sight of the fact that matter is not exhausted by substance, which is likewise a form of matter.

Since inertia (i.e., the preservation of the state of a material object in the absence of external influences) is one of the characteristic—

...of these properties of matter, since it is quite natural that the field, like substance, possesses mass. But it is completely impossible to understand the assertion that water “contains as much matter” as is “contained” in \(1\ \text{cm}^3\) of an electric field with an intensity of about \(6\ \text{V}/\text{cm}\), created in a vacuum.

The concept of matter corresponds to objective reality; no other “physical concept of matter” can be constructed. Therefore the assertion about a “greater quantity of matter” in one of two objects being compared is equivalent to the assertion that in one of the objects there is “more objective reality” than in the other. But this either means that some objects (with greater mass) are more real than others, which is clearly absurd, or else means nothing at all.

Consequently, the term “quantity of matter” must be recognized as devoid of content.

The same should also be said with regard to the term “quantity of motion,” since the diverse properties of the broad concept of “motion” cannot be described by any single quantitative characteristic. One can only welcome the increasingly widespread use in the scientific literature of the more appropriate term “momentum.”

1. It is also inadmissible to confuse the general materialistic principle of the indestructibility of matter and its motion with its particular manifestations in physics—the quantitative conservation laws of certain properties of matter and motion that hold in closed systems.

The all-embracing principle of the indestructibility of matter and its motion does not assert the conservation of any definite particular properties of matter, but speaks of indestructibility, i.e. of the eternity of matter and its motion. This principle is applicable both to closed and to non-closed systems and may be used in considering the universe as a whole.

The physical concretization of this principle within narrower limits (only in closed systems) is manifested in the laws of conservation of certain properties of matter and their quantitative characteristics—mass, energy, momentum, angular momentum, and charge. But a whole series of other properties of matter and their characteristics are not conserved in physical processes, which, however, in no way contradicts the principle of the indestructibility of matter, just as the absence of any physical conservation laws in non-closed systems does not.

The connection and distinction between the principle of the indestructibility of matter and the physical conservation laws are also manifested in the following: no matter how we change (for example, increase) the dimensions of a closed system, considering an ever greater number of interacting material objects, we are certain that the conservation laws will be fulfilled in each of these systems (the guarantee of this is all the accumulated experience of studying the external world). But we have no right to extend the physical conservation laws to the universe, since to ascribe to the universe a finite mass, energy, etc., would be erroneous both in the physical and in the philosophical sense. The principle of the indestructibility of matter and its motion, however, is applicable to the objective external world without any limitation whatsoever.

1. The propositions developed here are not narrowly terminological, since unfortunate terminology leads to errors of both a physical and a philosophical character. One may also point to the wholly unsatisfactory obsolete terminology in the field of thermal phenomena, in particular to the terms “quantity of heat” and “heat capacity.” It creates great difficulties in the careful analysis of these phenomena.

In the work Economic Problems of Socialism in the USSR, I. V. Stalin spoke of the necessity of revising the outdated concepts and terms of political economy.^3

The same situation has arisen in physics as well (at least in some of its branches, the oldest in terms of the time of their development); therefore, bringing physical terminology into order and coordinating it with the philosophical foundations of physics, as well as with the achieved level of physical knowledge, is becoming one of the urgent tasks of contemporary science.

N. N. Malov

Cited Literature

1. A. N. Krylov, Collected Works, vol. 7, p. 421, Moscow, 1936.
2. M. V. Lomonosov, Complete Collected Works, vol. 3, p. 349, Moscow, 1952.
3. I. V. Stalin, Economic Problems of Socialism in the USSR, pp. 18–19, Moscow, 1952.

1. UFN, vol. 48, issue 2, 1952. ↩