A. Einstein and Modern Physics *)

I. E. Tamm

The present session of the Division of Physical and Mathematical Sciences of the Academy of Sciences marks two events: first, the 50th anniversary of the publication of Einstein’s article “On the Electrodynamics of Moving Bodies,” in which the foundations of the theory of relativity were laid, and, second, Einstein’s death, which followed on April 18 of this year.

Einstein, whom Lenin called one of the great transformers of natural science, is rightly compared with Newton. This comparison is justified, in my opinion, not only in the sense that Newton and Einstein represent peaks of human achievement in the knowledge of nature, peaks dominating a 300-year period in the development of the exact sciences and directly echoing one another across this immense distance. Einstein and Newton may, in my view, also be compared in the sense that Newton laid the foundations of modern natural science, while Einstein’s creation—the theory of relativity—crowned the edifice of classical physics. It must be said that classical physics is often understood to mean prerelativistic and prequantum physics. Despite the full depth of the transformation brought about in physics by the theory of relativity, it seems to me more correct to understand classical physics as the physics of the macrocosm, including the theory of relativity, in contrast to the quantum physics of the microcosm. There is no doubt that the mode of thought of the theory of relativity is the mode of thought of classical physics, and that the theory of relativity crowned the edifice of classical physics, that only it gave

*) Introductory address at the meeting of the Division of Physical and Mathematical Sciences on November 30, 1955, devoted to the fiftieth anniversary of the theory of relativity.

classical physics its necessary consistency, coherence, and completeness.

Thus Einstein completed the work begun by Newton. At the same time, the creation of the theory of relativity was of enormous significance for the subsequent stage in the development of physics.

As early as the second half of the last century, in the works of Maxwell and Boltzmann, there arose that conception of statistical physics which in our time led to the creation of quantum mechanics. The foundations of this physics of the microcosm are profoundly different from the foundations of the physics of the macrocosm, crowned by the creation of the theory of relativity. Einstein contributed to the creation of quantum mechanics not only by the fact that, in the same remarkable year 1905 in which he laid the foundations of the theory of relativity, he was the first to advance the radically new hypothesis of light quanta (it was precisely for this work that he was awarded the Nobel Prize in 1922). Einstein did for the creation of quantum physics perhaps more than any of its immediate creators, because the very creation of the theory of relativity paved the way for new fundamental transformations of physics.

For dialectical materialists it had always been clear in principle that, on the one hand, our human ideas and concepts are not a priori but are a generalization of human experience, and that, on the other hand, nature is inexhaustible and that therefore our concepts and representations have limited applicability. Hence every time we penetrate into a circle of new, unknown phenomena, it proves necessary to modify and generalize the basic scientific concepts and representations so that, with their aid, it becomes possible to encompass this new circle of phenomena as well. Nevertheless, by the end of the last century a certain self-assurance and complacency had spread among physicists—the prevailing opinion was that the basic physical regularities had already been elucidated, and only refinements remained—important ones, to be sure, but still not going beyond the firmly established foundations. Such an outstanding physicist as W. Thomson (Lord Kelvin) came forward precisely with a statement of this kind in a speech delivered at the advent of our century. In doing so, it is true, he made the reservation that on the clear and calm physical horizon two little clouds had not yet dispersed—one connected with Michelson’s experiment, the other with the so-called ultraviolet catastrophe arising in the consideration of thermal equilibrium between matter and radiation. From the first “little cloud” there subsequently arose the theory of relativity; from the second, quantum theory.

The creation of the theory of relativity fundamentally destroyed this erroneous scientific frame of mind; it created the understanding that every new stage in the development of physics inevitably requires a radical revision, renewal, and expansion of its most fundamental ...

foundations and concepts, such, for example, as the concepts of space and time.

This new scientific mode of thought paved the way also for the creation of quantum physics. It, too, will undoubtedly play a decisive role in the solution of those fundamental problems that have arisen at the present time in the theory of elementary particles and in the theory of phenomena occurring at extremely high energies—problems whose solution, in my conviction, will raise physics to a new level while all of us here are still alive. There can be no doubt that this new scientific mode of thought will exert a most substantial influence on the development of other natural sciences as well.

It is necessary to note another side of the matter as well. The development of the theory of relativity not only had a revolutionary influence on all of physics, but, at the same time, also emphasized continuity in the development of science. In the example of the theory of relativity, the fact became especially clear that every new stage in the development of science does not cross out or reject the preceding one, but includes it within itself as a particular case of more general laws. Thus classical mechanics is a particular case of relativistic mechanics at velocities small in comparison with the velocity of light.

According to the generally accepted, though perhaps not entirely successful, terminology, one speaks of the special and the general theories of relativity. Most of the reports at our session are devoted to the development of the general theory of relativity; only in the first two survey reports will there also be discussion of the special theory of relativity. This is explained by the fact that the special theory has attained such a degree of completeness that at present the question is not so much of its further development as of its applications to various physical phenomena. The validity of the special theory of relativity cannot be in doubt. It has been confirmed not only by experiments specially designed for its verification, but also—and this is still more important—by the agreement with experiment of the whole aggregate of consequences of modern physical theory, of which it is one of the most important foundations. Moreover, the special theory of relativity has entered into modern technology and serves as the basis not only for the construction of accelerators, but also for many of the most important technical calculations connected with the use of atomic energy. Therefore I shall confine myself to only one remark concerning the special theory of relativity.

This theory not only radically transformed our ideas of space and time, but also revealed the glaring logical inadequacy of the earlier ideas. Thus, for example, it has now become obvious that the most important concept of simultaneity, or, speaking more generally, the concept of the temporal order of two events spatially separated from one another, in pre-relativi-

in physics in general had no unambiguous, definite meaning. In operating with this concept in pre-relativistic physics, one implicitly assumed the existence of signals and actions instantaneously propagating over any distances, whereas in fact no such signals and actions exist in nature. This logical inconsistency of the old conceptions now appears to us almost self-evident.

All of Einstein’s scientific work shows with extraordinary clarity that fundamental advances in the knowledge of nature are achieved through a deep logical analysis of certain few basic, pivotal experimental facts and regularities, which one must be able to pick out from the colossal quantity of information and facts that, by their enormous mass, press upon research in any branch of modern science.

Especially characteristic in this respect is the history of the creation of the general theory of relativity. Einstein was led to the creation of this theory by the analysis of the simplest fact, long and well known: the ratio of a body’s inertial mass to its gravitational mass is the same for all bodies. The principle of equivalence of acceleration and the gravitational field, which lies at the foundation of the general theory of relativity, is in essence a direct generalization of this long-known, simplest fact.

I cannot refrain, in this connection, from mentioning a remark made by Einstein some 15 years ago. The discussion concerned the fact that, in connection with the discovery of a large number of elementary particles, in particular mesons, the problem of constructing a theory of elementary particles had become ripe. Einstein had always held that the electron—the atom of electricity—was already an alien in the land of classical electrodynamics. In the conversation I mentioned, he said that, it would seem, the mere fact of the electron’s existence should already have been sufficient for constructing the foundations of a general theory of elementary particles. This is undoubtedly a hyperbole, but it is very characteristic of Einstein, and it is instructive to contrast it with the widespread view that the solution of the fundamental problems of science must necessarily be preceded by the accumulation of an enormous quantity of experimental data. In reality, the example of both the special and, in particular, the general theory of relativity shows that the decisive role in constructing a fundamentally new theory is played by a deep logical analysis of pivotal experimental facts. Of course, the consequences of the theory must then be tested on the broadest possible experimental material.

The general theory of relativity, as is known, includes within itself a rational theory of gravitation. This theory of gravitation stands in the same relation to Newton’s theory of gravitation as modern electrodynamics stands to the theory of electricity,

based on the application of only Coulomb’s law of the interaction of charges. Along with this, the general theory of relativity solved the question that Lobachevsky had tried to resolve by measuring the sum of the angles of a large triangle: it showed that our real physical space is not Euclidean, but possesses curvature. Finally, having solved the problem of geometry on ordinary human scales and on small astronomical scales—I mean the scales of the Solar System or of our Galaxy—the theory of relativity for the first time created a theoretical basis for the study of geometry on large astronomical scales, on cosmological scales. Now, when the newest telescopes penetrate into the depths of the universe for billions of light-years, the problems of cosmology have become accessible to experimental investigation; and there can be no doubt that Einstein’s theory of relativity will be a reliable guiding thread as humanity penetrates this new, unexplored circle of phenomena, just as classical physics, atomic physics, and electron theory played a guiding role in penetration into the depths of the microcosm. Of course, just as the study of the microcosm led us to a new stage of physics—quantum theory, which in a manner unexpected by all modified the initial physical conceptions—so too future cosmology, in the creation of which the general theory of relativity will undoubtedly play a decisive role, may turn out to be very far from what we can now imagine it to be.

I should like to make one more, final, remark. 101 years ago Riemann, in his dissertation submitted for the degree of Privatdozent, expressed a very profound thought. Considering the metric, or measure-determination, of spaces, he noted that there exist two and only two possibilities: either space is discrete, in which case its metric is embedded in it itself, being given by a simple count of discrete elements; or space is continuous, in which case its metric cannot be contained directly in it itself, but must be conditioned from without, i.e. must be determined, in Riemann’s terminology at the time, by external binding forces—bindende Kräfte.

Einstein proved, by creating his theory, that the metric of our real world—four-dimensional space-time—belongs to the second of the types indicated by Riemann, namely, that it is determined by the masses situated in space (including also mass carried, for example, by light and by other forms of energy). Recently, however, the development of quantum physics has posed anew the question of space and time in the microcosm. For the time being, of course, one can only guess how this question will be resolved, but it seems to me highly probable that on microcosmic scales space is discrete, i.e. that in the microcosm the first of the possibilities indicated by Riemann is realized. I note in this connection that

within the framework of classical conceptions, discrete space, i.e., something like an aggregate of nodes of a crystal lattice, cannot fail to be anisotropic, i.e., it is incompatible with the requirement of the equal status of all spatial directions. However, quantum conceptions, as Snyder showed, open up the possibility of reconciling the discreteness of space with its isotropy and homogeneity.

No one can, of course, predict what the further development of physics will be, but one thing, it seems to me, may be asserted without doubt: Einstein’s ideas, his analysis of the concepts of space and time and of the interrelation between space-time relations and matter existing in space and time, may in the future undergo profound changes, but it is precisely they that will undoubtedly serve as the point of departure for an entire historical epoch in the further development of physics.