A. EINSTEIN
(1905)

IN MEMORY OF ALBERT EINSTEIN

A. F. Ioffe

Einstein has died—the Newton of the twentieth century, as he was for the broadest public. Apart from Roentgen, whose discovery struck the imagination by making it possible to look inside objects opaque to the eye, Einstein alone among all the physicists of our time attained such wide popularity.

However the concept of “relativity” may have been interpreted, everyone spoke of it; people throughout the world became interested in it. But, unlike Roentgen rays, which were perceived as a new path to the knowledge of things and as a gift of science to human health, Einstein’s ideas became the arena of a fierce struggle.

For physicists throughout the world, and above all for Soviet physicists, there is no question as to the validity of the theory of relativity—this question has long been settled: it is the best generalization of the laws of motion attainable at the present stage of physics, one that has been reached in our time. The task of physicists is the application of the theory to real problems, the further deepening of its content, and a better understanding of its philosophical conclusions.

Einstein is the author of the theory of relativity, a brilliant transformer and continuer of Newton’s principles—and only that is the conception held by circles of the intelligentsia far removed from physics.

For physicists, however, and especially for physicists of my generation—Einstein’s contemporaries—the appearance of Einstein in the arena of science is unforgettable. In 1905, three articles appeared in the Annalen der Physik that laid the foundation for the three most topical directions of twentieth-century physics. These were: the theory of Brownian motion, the photon theory of light, and the theory of relativity. Their author was the until then unknown official of the patent office in Bern, Einstein-Mariti (Mariti was his wife’s surname, which according to Swiss custom was added to the husband’s surname).

The article on Brownian motion revealed the physical nature of thermal motion and soon led to experimental

to the determination of Avogadro’s number and to experimental proof of the atomic structure of matter. After the work of Boltzmann and Maxwell, Einstein took the next decisive step in this direction.

A few years later, considering the diffusion of sugar in water, Einstein was able to estimate the geometrical dimensions of individual molecules. He established a universal relation between the diffusion coefficient \(D\) and the mobility \(u\) in an electric field,

\[ \frac{D}{u}=\frac{kT}{e}. \tag{1} \]

Three more years later, in 1911, proceeding from the quantum character of energy exchange in a solid, Einstein explained the temperature dependence of heat capacity. He showed how, from the behavior of the heat capacity, one can determine the frequency of the natural vibrations of the particles of which the solid is composed.

In this work the foundations were laid for the entire subsequent development of the quantum theory of the solid state. A year later Einstein’s theory of resonators was developed by Born and Karman for the crystal lattice, and another year later by Debye for a continuous elastic body. In this latter form the theory of heat capacity was destined to become classical for a number of decades.

The statistical theory of thermal motion received a new direction in Einstein’s work on the theory of a degenerate gas and on the new kind of Bose–Einstein statistics.

Each of Einstein’s works listed here opened a new page in the doctrine of the thermal properties of physical bodies. Each of these works became the starting point of a new line of research.

The second of the papers of 1905 was devoted to a new understanding of the properties of light. It is well known that as early as 1900 Planck, correcting the expression he had previously given for the entropy of radiation, arrived at the statistics of the radiation process in the form of separate quanta with energy \(h\nu\), where \(\nu\) is the frequency and \(h\) is Planck’s universal constant. Planck regarded the result he had obtained as a consequence of his derivation of the expression for the entropy, and only Ehrenfest later showed that quanta are a hypothesis introduced into the very basis of the derivation of the blackbody-radiation formula, and not a conclusion drawn from it. Planck sought, as far as possible, to narrow the novelty of his theory, limiting it to the specific properties of the emission of light by atoms.

Einstein, whose scientific thought, in contrast to Planck’s, demanded radical solutions expressing the new aspect of natural phenomena that he had perceived, saw in quanta not a successful mathematical device, but a means of revealing the essence of light.

From the radiating mechanism Einstein transferred the quantum nature to the radiant energy emitted by the body. According to Einstein, light itself consists of photons, whose energy \(h\nu\) is entirely determined by the frequency. In all processes of the interaction of light with matter Einstein was able to discern the photon structure of light.

For the liberation of electrons by light (the external photoelectric effect) Einstein derives a fundamental relation between the kinetic energy of the electrons and the frequency of the light in the form of Einstein’s law

\[ \frac{1}{2}mv^2=h\nu-P, \tag{2} \]

where \(P\) is the work expended in crossing the boundary of the body.

In 1907 I was able to show the agreement of the photon theory with Ladenburg’s measurements published at that time, which he associated with Lenard’s resonance theory. At that same time I began a precise verification of Einstein’s law for sodium and potassium. But these results were published by Millikan earlier than mine and, apparently, more accurately.

In 1909 I attempted to derive all the laws of equilibrium radiant energy from the theory of photons and their analogy with the molecules of the kinetic theory of gases. It turned out that, in order to obtain the correct formula for the spectral composition of the radiation of an absolutely black body, it was necessary to apply a modified statistics. Yu. A. Krutkov proved this proposition; the statistics, as became clear later, coincides with Bose–Einstein statistics.

From this example I could become convinced how different were the scientific methods of Einstein (of whom I was a supporter in this question) and Planck. The latter, having become acquainted with my article, which he nevertheless later published in his journal—the Annalen der Physik—urged me of the necessity of remaining on the ground of Maxwell’s classical conceptions and of going no further than was absolutely necessary: to confine oneself to the peculiarity of the mechanism of emission, to admit, if this proved inevitable, a peculiarity in the absorption of light by an electron and a number of other particular hypotheses, but not to break with the theory of the electromagnetic field and not to encroach upon light itself. “Classical theory has given us so much that is useful that it must be treated with the greatest caution and safeguarded,” Planck said.

In 1905 there was as yet no experimental confirmation for formula (2), but the most important property of the external photoelectric effect, paradoxical from the classical point of view, had already been established—the independence of the velocity of photoelectrons from the intensity of the light. This fact found a natural explanation in the theory of photons.

Another domain of phenomena—luminescence—confirmed Einstein’s idea of the qualitative growth of photons with frequency. The empirical

the Stokes rule asserted that the frequency of the absorbed light is always greater than the frequency of the light emitted in fluorescence and phosphorescence. In Stokes’s rule Einstein saw a new confirmation of the idea of photons.

A third broad field for testing the theory was photochemistry. The same independence of the occurrence of a photochemical reaction from the intensity of the light and direct connection with its frequency, the same gradation of the effect with increasing frequency, as in the external photoeffect, as in luminescence.

Einstein’s paper was saturated with such vivid physical content, with such deep penetration into the mechanism of the phenomenon, that it convinced many physicists—primarily those who dealt with electronic phenomena. But opticians long resisted a theory that encroached upon the resonance theory of dispersion and upon the achievements of the diffraction theory of optical instruments. Only the explanation of optical series on the basis of Bohr’s theory of the atom reconciled opticians with quantum ideas.

The 1905 paper on radiant energy did not remain isolated in Einstein’s work. It is enough to recall his theory of equilibrium radiation, which became classical, as the result of emission and absorption under disturbance of equilibrium. The laws of radiation established by this theory served as an example for calculating processes of energy exchange in elementary processes.

There is no need to spend many words on the theory of relativity—every physicist knows its history. The transition from Lorentz transformations and from the Lorentz–FitzGerald hypothesis to Einstein’s special theory of relativity, the laws of velocity addition, the problem of simultaneity, the famous relation between mass \(m\) and a body’s store of energy \(U\):

\[ U = mc^2, \tag{3} \]

where \(c\) is the speed of light, which becomes the limiting speed of propagation of energetic processes—all this has entered into the flesh and blood of modern physics.

It is also known how, after the special theory, there followed in 1911 its generalization to accelerated motion, and in 1915 the general theory of relativity, which included the theory of gravitation and the connection of geometry with the presence of mass.

Einstein set himself a further task—the unified field theory, combining the electromagnetic field with gravitation. Attempts to create a unified theory followed one after another, but all of them, one after another, proved untenable and were rejected by criticism.

Unified field theory meant a decisive turning point in Einstein’s scientific activity. Before it Einstein amazed by the richness and diversity of his interests, up to theories explaining—

of things, why the right banks of rivers are higher than the left, to the invention of new designs of printing machines.

The unified field theory turned Einstein from a narrow specialist into one striving toward broad horizons. Einstein devoted almost the last 40 years of his life to this theory. Around him there passed a turbulent epoch of “new quantum mechanics,” nuclear physics, the rebirth of solid-state physics on semiconductors.

It seems to me that one can understand the reasons that left Einstein aside from the main paths of development of physics in recent decades. As far back as 30 years ago Einstein told me that he would do nothing more in life unless he solved the problem of the unified field theory. Five years later, during our joint trip to the Solvay Congress, I tried to tell him who Einstein was as a physicist and what his debt to physics consisted in. In reply I received the assurance that he would do everything within his power to delve into the physics of the present day and try to resolve its difficulties, but that he doubted success in advance. So long as there is no unified field, for me there is no physics—such was the meaning of his words.

To understand such a cast of mind, one must imagine Einstein’s scientific personality. For him all nature, and still more all physics, appeared as a single whole, within which unresolved contradictions cannot exist. He persistently sought the roots of apparent contradictions and boldly constructed a physical picture free of internal imperfections; he put forward heuristic paths toward a unified theory.

I often recall an incident that showed how Einstein constructed his worldview: once he became interested in my investigations of the properties of crystals and asked me to explain them to him. At 3 o’clock in the afternoon I began this task and after 2 hours finished it. Then there began an astonishing process of assimilating new facts and ideas, comparing them with the most diverse aspects of the physical picture that existed for Einstein, and this process continued for 9 hours—until 2 o’clock at night. All this time Einstein was so absorbed in his thoughts that almost everything around him was not perceived: at dinner, for example, he acted in such a way that, at his wife’s command, he took food on his fork and put it into his mouth, hardly aware that he was eating.

It is possible that the vagueness of Einstein’s political and philosophical views and the inconsistency in his everyday life are explained by the same one-sided concentration of thought.

Einstein was a progressive scientist and highly valued the construction of socialism in our country, which realizes the cherished dreams of the best people of all times. In the struggle of the two worlds, communism and capitalism, he was on our side and, to my direct question, gave an unambiguous answer. However, in Einstein’s philosophical statements one may encounter, alongside clear materialistic

Machian and idealistic ideas, and the transition of “relativism” from physical theory to philosophical agnosticism.

In his private life Einstein was a modest man, who shunned honors. I remember how, having learned of the expected arrival of a group of his admirers, he proposed hiding from them and going off to the park for three hours. I remember how once Einstein arranged to come with me to acquaintances, where his violin playing was to be accompanied on the piano. The hosts of the apartment wanted to make use of this in order to show their guests the famous Einstein. But, seeing strangers, he put on his hat and stayed only on the condition that all the doors would be tightly shut and that no one except the accompanist would be in the room. And Einstein’s playing was extraordinarily musical and expressive. It presented a remarkable contrast to Planck’s high technique and deep, calm harmony as a pianist.

The circle of his close friends included collaborators in physics and in inventing, to which he devoted considerable effort. I saw him inventing, together with a dentist, a new type of printing press.

The new star of Einstein, which flared brightly on the physical horizon in 1905, determined the most important paths in the development of physics for the next 20 years and left an indelible mark on many, and precisely the decisive, areas of our science. If the last 30 years, devoted to a unified field theory, did not yield such useful results, they nevertheless introduced many profound ideas and posed a number of questions for the physics of the future.