On L. Janossy’s Article “Further Considerations on the Physical Interpretation of Lorentz Transformations”

I. E. Tamm

Professor L. Janossy, well known to Soviet physicists for his experimental studies of cosmic radiation, has devoted his article to further considerations on the interpretation of the Lorentz transformations. These considerations are set forth rather indistinctly and at length; we shall try to outline their main content.

First of all, it must be noted that although the author does acknowledge, “as an experimental fact,” the relativistic law of the dependence of mass on velocity (§ 33), the covariance not only of electromagnetic but also of nuclear forces (§ 27 and, in particular, § 37), and so on, the whole article is nevertheless permeated by the author’s characteristic skeptical attitude toward the theory of relativity. This attitude leads him to a number of erroneous assertions. We shall confine ourselves to only two examples.

The author attempts to attribute a number of characteristics of a body, which are obviously dependent on the state of its uniform motion (relative to some inertial frame of reference), to the influence of accelerations previously experienced by the body, although these characteristics in no way depend on precisely what accelerations, and at what instants of time, the body moving with a given velocity experienced in the past. Thus, for example, the dependence of the lifetime of mesons on their velocity, predicted by the theory of relativity and confirmed experimentally, is interpreted by the author as follows: “In fact, mesons are born with very high velocities, so that the experiments apparently show that, by slowing down mesons, we shorten their lifetime. Thus the experiment gives information about the influence of acceleration on the mechanism of decay of μ-mesons” (§ 3).

Apart from other obvious objections, it is sufficient to note that the lifetime of mesons of a given velocity \(v\) is the same both for cosmic mesons born with very high velocities and slowed down in the atmosphere to the velocity \(v\), and for mesons created in accelerators and having acquired this velocity \(v\) at the moment of their birth.

The author further asserts that in the Michelson–Morley experiment “we investigate the influence of accelerated motion on the instrument,” since “a rotation is accelerated motion,” and in the Michelson experiment the interferometer is rotated (§ 3). In reality, of course, the rotation of the interferometer is a convenient, but in principle by no means necessary, procedure. It is unlikely that anyone will doubt that the result of the experiment will not change if the rotating interferometer is replaced by a stationary one with two perpendicular arms, the equality of which is checked by an auxiliary device.

Secondly, the author devotes a great deal of space to investigating the properties of moving bodies without using a transformation of reference frames, but by considering

I. E. TAMM

...in a certain “stationary” reference frame, the equilibrium configuration of the elements of a moving body. This problem is entirely legitimate. In considering it, the author partly sets forth well-known arguments, and partly gives incorrect formulations. Thus, for example, irrespective of how correct the formula (63) obtained by the author is, which determines the dependence of a certain imaginary frequency of rotation of the electron on its velocity, this imaginary rotation, contrary to the author’s assertion, of course has no relation to the transverse Doppler effect (§ 34 and again in § 37).

Most essential, however, is the assessment of the fundamental significance of the “dynamical” treatment of the question—for example, that of the contraction in length of moving bodies, to which the author devotes so much space. From the context it is evident that the author’s basic idea amounts to the following: why are the postulates of the theory of relativity needed, if the same conclusions regarding any phenomenon can be reached without resorting to these postulates, by means of a detailed analysis of this phenomenon from the standpoint of some chosen “stationary” reference frame?

A completely analogous question would be the following: why use the law of conservation of energy, if the operation of any machine, whose construction and the laws of the phenomena occurring in it are known to us, can be calculated on the basis of the equations of mechanics, thermodynamics, electrodynamics, etc., without appeal to the law of conservation of energy, but in agreement with it?

The answer to both these questions, which are of equal standing, consists, of course, not only in pointing to the importance of discovering general regularities and to the enormous simplification in solving concrete problems that is achieved by appealing to these general regularities. What is essential is that the postulates of the theory of relativity, like the law of conservation of energy, make it possible to specify a number of exact characteristics of physical phenomena even in those cases where the exact laws of the forces of interaction of the elements of a given body are unknown to us (as is the case with the constituent parts of atomic nuclei that enter into all bodies), or in those cases where an exact calculation of the results of the action of known forces (for example, the electromagnetic interaction of electrons with one another and with atomic nuclei in solid and liquid bodies) is practically impossible because of its complexity. Of course, very many physical questions cannot be solved solely on the basis of general regularities, but require detailed analysis. However, those questions on which the author has focused his attention do not belong to this category. The author’s “dynamical” treatment of them is necessarily approximate and, as he himself repeatedly notes, is based on a number of special assumptions about the laws of force; therefore, in itself it by no means possesses probative force.

Closely connected with what has just been said is another aspect of this problem, about which the author is completely silent. The fruitfulness, and at the same time the most convincing proof of the correctness, of the theory of relativity lies in the correctness of its predictions: the enormous number of physical phenomena discovered and studied in detail over the last 50 years agrees, in every case without exception, with the predictions that follow essentially already from Einstein’s first paper of 1905.

It would take a great deal more space to examine all of the author’s assertions that are at least debatable. I shall therefore confine myself to just one more general remark.

The author repeatedly emphasizes (see, for example, §§ 7, 8, 38) that not all possible consequences following from the general propositions of the theory of relativity have been tested experimentally, that in the future experiment may perhaps lead to a contradiction with these propositions, and that therefore “this part of the theory of relativity (meaning its general propositions.—I. T.) always needs defense.”

As a result, the impression is created that the theory of relativity is some kind of second-rate theory. But one must not forget that all the statements cited are equally applicable, not only to the theory of relativity, but to any other part of physical theory. Our knowledge is not a priori, but arises as the result of the analysis and generalization of human experience; on the other hand, nature is inexhaustible. Therefore every human penetration into new domains of phenomena, both in the distant past of science and in its most recent past, has led and will necessarily continue to lead to a modification and generalization of our concepts and representations. Moreover, although at present there are no facts contradicting the theory of relativity, the majority of physicists hold the view that the next stage in the development of physical theory will be connected with clarifying the inapplicability of contemporary space-time representations (i.e., the representations of the theory of relativity) to the submicroscopic world of elementary particles and their interactions and transformations.

However, just as the development of twentieth-century physics by no means refuted Newtonian mechanics (which humanity now uses more widely than ever in the past), but merely established the limits of its applicability, so too future physical discoveries will undoubtedly establish the limits of applicability of the theory of relativity, but will in no way be able to refute the fact that this theory (which contains Newtonian mechanics as a special case for \(v \ll c\)) correctly describes the enormous totality of physical phenomena known to us at present. Moreover, one can hardly seriously doubt that the predictions of the theory of relativity will be confirmed in the study of very many new phenomena, still unknown to us.

Summing up all that has been set forth, I must note, unfortunately, that Prof. L. Janossy’s article in no way helps to clarify the physical interpretation of the Lorentz transformations.