ALBERT EINSTEIN (1879–1955)

E. V. Shpolsky

“He gave us a picture of the world surpassing, in its wholeness and harmony, the boldest dreams of the past.”

—N. Bohr.

On April 18 of this year Albert Einstein died. A great scientist has passed away, one whose astonishing activity in the most diverse fields of physics brought about not only a major step forward in the knowledge of nature, but also a genuine revolution in our fundamental conceptions; a brilliant thinker has ended his earthly journey, one whom V. I. Lenin called “one of the great transformers of natural science.”

Einstein’s life was very simple. He was born on March 14, 1879, in the city of Ulm in Württemberg (on the Danube); he spent his childhood and school years up to the age of 14 in Munich, but completed secondary school in the city of Aarau in Switzerland. After finishing the gymnasium, Einstein entered the Zurich Polytechnic Institute, from which he graduated in 1900, receiving the rights of a teacher of mathematics and physics. During the following two years Einstein was a secondary-school teacher in the city of Schaffhausen (German Switzerland), but in 1902 he entered the Federal Patent Office in Bern as an engineer, where he worked until 1909. It is noteworthy that it was precisely in this modest position that he spent the very years in which his works on molecular physics, the quantum theory, and the theory of relativity were produced—works that brought him worldwide fame as one of the most outstanding physicists of his time. In 1909 Einstein was elected extraordinary professor at the University of Zurich, where, however, he remained only for one academic year; after that, in rapid succession, he held chairs in Prague (1911–1912), then at the Zurich Polytechnic (1912–1914). In 1913, on Planck’s initiative

and other Berlin physicists, Einstein was elected to the vacancy, created by the death of Van’t Hoff, of member of the Prussian Academy of Sciences, and in 1914 he became director of the Kaiser Wilhelm Institute of Physics and professor at the University of Berlin. In 1933, when his position as a “non-Aryan” in Nazi Germany became intolerable, he accepted a professorship at the Institute for Advanced Studies in Princeton, USA. This professorship, not connected with the necessity of teaching, he retained until his retirement on grounds of age in 1945. The remaining years until his death he likewise spent in Princeton. In 1921 Einstein received the Nobel Prize for his work on molecular physics and the theory of quanta, and in subsequent years many other distinctions.

In his personal life Einstein was a gentle, simple, and benevolent man. He never shut himself up in the office work of a scholar and responded ardently to all phenomena of public life that concerned progressive humanity; he was a passionate opponent of war and objected especially sharply to the use of atomic weapons.

The most productive period of Einstein’s scientific creativity covers the short interval of time between 1900 and 1906. The beginning of the twentieth century, when Einstein completed his education, is characterized by a fascination with phenomenological thermodynamics. The energetics of Ostwald and Helm, the denial of the reality of atoms by Ostwald and Mach, had a certain success among physicists and chemists. On the contrary, Boltzmann’s statistical mechanics met with a skeptical attitude. Doubt was expressed as to how, in a system of elastic, smooth molecules obeying the strictly time-reversible laws of Newtonian mechanics, thermodynamic irreversibility could arise. The probabilistic interpretation of the second law of thermodynamics, developed by Boltzmann, was considered ingenious but unconvincing. The need was felt to find such phenomena in which, in fact, on a scale accessible to observation, it would be possible to establish a violation of the laws of phenomenological thermodynamics, i.e. an “anti-entropic” course of events. Such an experimentum crucis in favor of atomistics became possible thanks to two small works published by Einstein. In the first of these works, printed in 1905, following previously published works devoted to the foundations of statistical mechanics, Einstein showed that, according to the molecular-kinetic theory, particles suspended in a resting liquid must perform disordered motions in such a way that it is not the displacement itself but the square of its mean value that will be proportional to the time. At that time Einstein, as he himself admits, did not yet have sufficiently definite information

ALBERT EINSTEIN (1879–1955)

on Brownian motion. At the beginning of the paper he notes that if the disordered motion required by the theory and the regularities established for this motion are indeed observed, then “classical thermodynamics can no longer be regarded as fully valid even for microscopic regions,” and at the end of the paper—having calculated, according to his theory, the numerical value of the expected mean displacement—he appeals to experimenters to try to verify these results. The next paper, which substantially develops the results of the preceding one, is already entitled “On the Theory of Brownian Motion,” since after the publication of the first paper Prof. Siedentopf privately informed Einstein that the motion whose laws he had investigated in the preceding paper was evidently the long-known, but quantitatively uninvestigated, Brownian motion.

The appeal to pay attention to the experimental verification of the laws of this motion quickly met with a response. The law established by Einstein of proportionality between the mean square of the displacement and the time was first confirmed by V. A. Henri, who carried out microcinematographic filming of the Brownian motion of rubber balls. Then followed the widely known brilliant works of J. Perrin and his students, which gave full confirmation of Einstein’s theory and led to a new determination of Avogadro’s constant. These and many other works marked such a complete triumph of atomism that even Ostwald himself openly declared his defeat and his recognition of the reality of atoms.

We have allowed ourselves to dwell somewhat longer on these first works of Einstein, since even in broad circles of physicists Einstein is much better known as the creator of the theory of relativity than as one of the founders of modern atomistics.

However great the significance of these works of Einstein may be, more characteristic of his creative work is the theory of light quanta published by him in the same year, 1905. Whereas the founder of quantum theory, M. Planck, somewhat timidly tried to reconcile the inevitable conclusions from his own works with classical notions of the nature of light and limited the domain of applicability of quantum concepts to the interaction between oscillators and radiation, Einstein at once understood the universality of quantum laws and was not afraid to carry them through to their logical conclusion. With astonishing boldness he cut the knot of contradictions that had accumulated in the doctrine of light, replacing Planck’s fictitious oscillators with real light quanta, photons, \(h\nu\). Thereby the discreteness from the mechanism of interaction between matter and field was transferred into the very nature of light. The famous “Einstein photoelectric equation,” formulated on the basis of these ideas, gave a simple explanation of experimentally established, parado-

from the point of view of wave theory, the laws of the photoelectric effect. At the same time, the “Stokes shift” in the fluorescence spectrum was explained and, as an inevitable consequence of the quantum character of absorption, the so-called photochemical law of equivalence was formulated.

The experimental verification of Einstein’s photoelectric equation not only fully confirmed it, but also enabled P. I. Lukirskii and S. S. Prilezhaev to determine Planck’s constant \(h\) with the utmost precision. And the photochemical law of equivalence played an enormous role in the most recent development of photochemistry. In essence, it was precisely this law that made it possible to approach an understanding of the mechanism of photochemical reactions, the determination of the nature of the elementary processes of the chemical action of light and of the subsequent dark reactions.

Of extraordinary interest are the theoretical considerations developed by Einstein in two papers devoted to the quantum theory of light. In the first paper Einstein considers a mirror capable of reflecting radiation only in the frequency interval \(\nu, \nu+d\nu\), while freely transmitting the entire remaining spectrum. Such a mirror, when placed in a space filled with radiation, must, owing to fluctuations in the radiation density, perform a kind of Brownian motion with a mean energy \(\frac{1}{2}kT\).

Using his theory of Brownian motion, Einstein calculates the mean square displacement \(\overline{\Delta^2}\) in the direction normal to the plane of the mirror. In the second paper he applies the general laws of statistics to radiation itself and calculates the mean-square fluctuation of the energy density \(\overline{\varepsilon^2}\) in the radiation field. If one now uses Planck’s formula for the density of equilibrium radiation, which enters into the expressions both for \(\overline{\Delta^2}\) and for \(\overline{\varepsilon^2}\), then in both cases formulas are obtained consisting of two terms. Only one of them corresponds to the wave picture of the nature of radiation, in which fluctuations of energy density are caused by the disordered interferences of wave trains. The other term is naturally interpreted by analogy with fluctuations in the number of gas molecules in a unit volume. With such an interpretation, radiation must be regarded as an aggregate of spatially bounded “radiation atoms,” photons \(h\nu\).

Thus there emerges quite distinctly the striking fact that in the properties of light these two, in essence mutually exclusive, pictures are combined in some mysterious way. In the same paper, however, Einstein indicated, as a “heuristic point of view,” that the unification of the wave and corpuscular pictures can be achieved by statistical means—a point of view fully adopted by modern quantum mechanics.

ALBERT EINSTEIN (1879–1955)

Somewhat later Einstein showed that quantum concepts make it possible to remove contradictions in an entirely different field as well—in the theory of the heat capacity of solids. It was enough to replace the classical expression for the mean energy of one degree of freedom by a quantum one in order to obtain a formula for heat capacity that made it possible to understand the cause of the dependence of heat capacity on temperature and to explain the deviations from the Dulong–Petit law. Although this formula did not give a completely accurate quantitative course of the dependence of heat capacity on temperature, its fundamental significance was very great: in essence, Einstein’s work laid the beginning of the modern theory of the solid state.

Einstein returned to the quantum theory of radiation again considerably later. In 1917 he published his derivation of Planck’s formula, obtained by considering the equilibrium of elementary processes of emission and absorption on the basis of the most general quantum postulates. An extraordinarily attractive aspect of this derivation is its combination of impeccable logical rigor with simplicity and clarity. But the significance of this short work is far from exhausted by these didactic merits. It was precisely in this work that the statistical treatment of quantum transitions in emitting and absorbing systems first received explicit expression. Especially important was the distinction between spontaneous and induced transitions; in particular, the consideration of induced transitions with emission (negative absorption), which at first seemed an artificial device, very quickly acquired a profound physical meaning, since soon after the appearance of Einstein’s work Ladenburg succeeded in showing the existence, alongside negative absorption, also of negative dispersion. Finally, the introduction of the famous “Einstein coefficients” $A_{ik}$, $B_{ik}$, $B_{ki}$ enabled Kramers and Heisenberg to apply the correspondence principle quantitatively to emission and absorption and to construct a quantum theory of dispersion, the deepening and refinement of which led Heisenberg to the formulation of the matrix form of quantum mechanics.

The completion of these works was the paper devoted to the statistics of spinless particles, known as Bose–Einstein statistics.

For all the enormous significance of Einstein’s work in molecular physics and quantum theory, the chief achievement of his life, which immortalized his name for all future time, was and remains the theory of relativity. In 1905, almost simultaneously with the appearance of the papers on the theory of Brownian motion and on the theory of light quanta, under the modest title “On the Electrodynamics of Moving Bodies,” Einstein’s article appeared, containing a completely finished exposition of the special theory of relativity. Exactly fifty years have passed since the appearance of this work, and nevertheless not a single word in it can now be changed. When,

When you reread this remarkable work now, you do not know what to marvel at more: the confident clarity of the exposition, thanks to which this paper can still today serve as a textbook guide for the study of the theory of relativity; the profundity in the posing and resolution of the most difficult problems; or the extraordinary boldness with which a young, 26-year-old, little-known employee of the Swiss patent office breaks with many generally accepted propositions that had seemed “unshakable” and, in any case, fully justified by so-called “common sense.” It would be out of place to recall in this journal the agonizing contradictions to which the numerous experiments in electrodynamics and optics of moving systems led at the end of the nineteenth century: the entire situation that had developed here by the beginning of the twentieth century is too well known to every physicist. It should be remembered, however, that at a time when Einstein’s predecessors sought a way out of the contradictions that had arisen by constructing special hypotheses (such as, for example, the famous Fitzgerald–Lorentz “contraction hypothesis”), Einstein showed with extraordinary clarity and depth that the root of all the difficulties lay not in one or another special property of matter and fields, but in the most general properties of physical space and time—in the insufficient explicitness of those seemingly obvious judgments about space and time which are borrowed from everyday life and which in fact are neither obvious nor necessary at all.

The unusual form of this work by Einstein, and the numerous judgments and conclusions expressed in it that fundamentally contradicted the “symbol of faith” of the physicists of that time, appeared audacious and shocking. All physicists then devoutly believed in the “world ether,” and some even regarded it almost as the only reality; all physicists believed, to no lesser degree, in the inviolability and unlimited applicability of Newtonian mechanics, in the complete obviousness of what we call “time,” “simultaneity,” “coordinate system,” and other basic concepts. But now there appears a young physicist who allows himself, on the very first pages of his work, to express such “heretical” judgments as, for example: “the introduction of a ‘luminiferous ether’ will prove superfluous, since in the theory being proposed no ‘absolutely stationary space’ is introduced,” and so forth; or: “Let there be a coordinate system in which Newton’s mechanical equations are valid,” with the note to this: “What is meant is ‘valid in the first approximation’”; or, finally, the very first section of this work, “Definition of Simultaneity,” which in our day seems so comprehensible, but fifty years ago produced the impression of an exploding bomb. And nevertheless, to this audacious

a young man managed to find a way out of the contradictions for which such brilliant predecessors of his as H. A. Lorentz and A. Poincaré had searched in vain. Both were close to that synthesis which Einstein succeeded in achieving, but neither the one nor the other took the decisive step necessary for it, although, of course, without their profound analysis Einstein could not have completed his synthesis. With the courage of a great scientist and a great man, H. A. Lorentz, in a 1912 note to his famous paper published in 1904*), i.e., immediately before the appearance of Einstein’s work, wrote: “It may be noted that in this article I did not succeed in obtaining, in full measure, the transformation formulas of Einstein’s theory of relativity... Connected with this circumstance is the helplessness in some subsequent arguments in this work. Einstein’s merit consists in the fact that he was the first to express the principle of relativity in the form of a universal, strict, and exactly valid law.”

In a brilliant article devoted to Poincaré on the occasion of the centenary of his birth, L. de Broglie**) gave an interesting explanation of the reason why Poincaré, who already possessed many of the particular propositions of the theory of relativity (up to the theorem of addition of velocities), was nevertheless unable to take the necessary decisive step. In de Broglie’s opinion, the reason lay in Poincaré’s incorrect theoretical-cognitive position. According to Poincaré’s point of view, usually called conventionalism (de Broglie for some reason calls it nominalism, recalling the old scholastics), “there exists, in general, an infinite number of different points of view, different pictures, all logically equivalent, and the choice between them the scientist makes only on the basis of considerations of convenience. This ‘nominalism’ of Poincaré sometimes prevented him from recognizing the fact that among logically possible theories there are some which are closer to physical reality.” “It is precisely for this reason,” adds L. de Broglie, “that Einstein, who was only 25 years old and whose mathematical knowledge was insignificant in comparison with the knowledge of the profound and brilliant French scientist, arrived before him at a generalization which, using and justifying the partial achievements of his predecessors, resolves all difficulties at a single blow—yes, but by the blow of a master, a powerful mind, guided by a deep intuition of physical reality!” (emphasis mine.—E. Sh.).

*) Electromagnetic Phenomena in a System moving with any Velocity smaller than that of Light. — Proc. Acad. Sci. Amsterdam 6, 809, 1904. I quote from the translation in the collection The Principle of Relativity. ONTI, Gostekhizdat, pp. 22–23.

**) L. De Broglie, Henri Poincaré et les Théories de la Physique. Bull. de la Société Astronomique de France, June 1954, p. 217.

Derived by Einstein on the basis of a profound analysis of the concepts of space and time and of two fundamental postulates (the postulate of relativity and the postulate of the constancy of the speed of light), the Lorentz transformations revealed the inseparable connection between space and time and led to a number of unexpected conclusions, such as, for example, the conclusion that the rate of clocks depends on the state of motion.

This conclusion has already in comparatively recent times received full confirmation in Ives’s brilliant experiments with the so-called transverse Doppler effect in canal rays, based on the slowing of the rate of “atomic clocks” (the radiating atom), and in the determination of the lifetime of $\mu$-mesons.

Even earlier, the Lorentz–Einstein formula for the dependence of mass on velocity, differing from Abraham’s formula, which had been derived on the basis of the conception of an incompressible electron, received full experimental confirmation.

Finally, the most important consequence of the special theory of relativity is, of course, the relation between mass and energy $E = mc^2$, which has received impeccable experimental confirmation in experiments with nuclear reactions. Together with the formula for the dependence of mass on velocity, this famous law lies at the foundation of modern nuclear energetics, i.e. it has the most important technical significance. In our day this technical significance of the theory of relativity is ever increasing as the transition is made to ever greater velocities attained in accelerators of elementary particles.

In 1911–1916 Einstein concentrated enormous efforts on the creation of a theory of gravitation. The result of these efforts was the development of the general theory of relativity and the theory of gravitation. While fully preserving the classical character of Newton’s theory of gravitation, Einstein’s theory freed physics from the mystical action at a distance. At the same time it posed and solved physical, mathematical, and philosophical problems even more profound than those of the special theory of relativity. It established an unexpected connection between gravitation and the geometry of the world; in particular, it showed that Euclidean geometry has only approximate significance and that the true geometry of the world is non-Euclidean (Riemannian) geometry, discovered in another form by the great Russian mathematician N. I. Lobachevsky.

As is known, the general theory of relativity led to a number of consequences accessible to verification by subtle astronomical methods. The number of such consequences of the general theory of relativity accessible to verification is very limited. There are only three of them: the motion of the perihelion of Mercury, the red shift of spectral lines in a gravitational field, and the deflection of a light ray in a gravitational field. All these effects are very small. The rotation of Mercury’s orbit amounts to only $574''$ per century, of which $532''$ are explained by the perturbing influence of other planets, and only $42''$ do not fit within the framework

ALBERT EINSTEIN (1879—1955)

of Newtonian mechanics (Einstein’s theory gives \(43''\)). According to Einstein, the deflection of a light ray passing near the edge of the sun should amount to \(1.74''\). In this, one half of the deflection should be due to the presence of an inertial “mass of light,” and the other half to the non-Euclidean properties of space. The magnitude of the deflection of a light ray in the sun’s gravitational field, predicted by Einstein’s theory, although small, is nevertheless quite accessible to observation and measurement by the precise methods available to astronomers. The very prediction of such an astonishing effect as the weight of light, and especially the possibility, by detecting and measuring the magnitude of this effect, of experimentally resolving the profoundest problem of the true geometry of the world—all this together was of outstanding interest. Therefore, when, during the solar eclipse of May 29, 1919, two expeditions of English astronomers actually discovered the existence of the expected deflection of a light ray and showed that it had the magnitude predicted by Einstein’s theory, this caused an unprecedented explosion of interest in the theory of relativity in the history of science. This interest went far beyond the scientific circles of physicists and astronomers; from the general theory of relativity, little accessible to popular exposition, interest returned to the special theory, with its remarkable structure, logical consistency, and unusual conclusions. An enormous popular-science literature appeared; articles were printed in decidedly all newspapers and journals, regardless of the specialty of the latter. At the same time, around the theory of relativity, passionate disputes flared up on an unprecedented scale, often going far beyond the bounds of scientific and philosophical problems. The distinctive consequences of the theory of relativity, and in particular the renunciation it required of certain firmly rooted prejudices justified by appeal to “common sense,”—all this aroused enthusiasm in some and irritation in others. It is interesting to cite in this connection the authoritative testimony of A. Sommerfeld, who, at the request of the editors, published an article on the theory of relativity in a medical (!) journal.* “Never before in the history of science,” we read in this article, “has a scientific discovery been discussed by broad circles in the way that is taking place with the principle of relativity... Until 1919 the theory of relativity is carefully studied in special courses: in Munich, for example, courses devoted to this theory are read almost every year. Since 1919 the theory of relativity has been presented to the general public both by those recognized as specialists in it and by those not recognized as such. In this process the theory itself is either extolled, or mixed with political filth together with the outstanding

* A. Sommerfeld, Münchener Medizinische Wochenschrift, 1920, No. 44, p. 1268.

the author of the theory (as happened at the well-known Berlin meetings*). At the Naugheim congress of natural scientists and physicians, after the chairman in his introductory speech sharply censured the demagogic approach to the principle of relativity, it was only with great difficulty that the discussion could be kept at the proper scientific level. Sommerfeld himself characterized Einstein’s chief achievement already at that time, i.e., 35 years ago, in the following vivid words: “With a depth of thought and consistency of philosophical thinking never before encountered among natural scientists, with a mathematical power reminiscent of Gauss and Riemann, Einstein has in the course of ten years erected an edifice before which we, who from year to year have followed his work with intense attention, stand in amazement and dizziness.”

After completing his work on the theory of gravitation, Einstein concentrated his efforts chiefly on creating a unified field theory embracing both the gravitational and the electromagnetic fields. However, these efforts did not lead, during his lifetime, to the desired result. This is not surprising: the task was even more grandiose than that of creating the theory of gravitation, and what he had already accomplished was so great that it must have exhausted the creative powers even of so brilliant a scientist as Einstein. In summary, one can only say briefly that there is scarcely a direction in modern physics whose origins would not go back to Albert Einstein.

) What is meant are the reactionary speeches, under the banner of criticism of the theory of relativity, which “brought scientific meetings down to the level of antisemitic mass rallies” (from the recollections of the same Sommerfeld on the occasion of Einstein’s seventieth birthday, included in the book Albert Einstein Philosopher—Scientist*, Evanston, 1949, p. 103). — E. Sh.