Einstein, Albert

Einstein, Albert

(b. Ulm, Germany, 14 March 1879; d. Princeton, New Jersey, 18 April 1955)

physics.

Albert Einstein was the only son of Hermann and Pauline (Koch) Einstein. He grew up in Munich, where his father and his uncle ran a small electrochemical plant. Einstein was a slow child and disliked the regimentation of school. His scientific interests were awakened early and at home—by the mysterious compass his father gave him when he was about four; by the algebra he learned from his uncle; and by the books he read, mostly popular scientific works of the day. A geometry text which he devoured at the age of twelve made a particularly strong impression.

When his family moved to Milan after a business failure, leaving the fifteen-year-old boy behind in Munich to continue his studies, Einstein quit the school he disliked and spent most of a year enjoying life in Italy. Persuaded that he would have to acquire a profession to support himself, he finished the Gymnasium in Aarau, Switzerland, and then studied physics and mathematics at the Eidgenössische Technische Hochschule (the Polytechnic) in Zurich, with a view toward teaching.

After graduation Einstein was unable to obtain a regular position for two years and did occasional tutoring and substitute teaching, until he was appointed an examiner in the Swiss Patent Office at Berne. The seven years Einstein spent at this job, with only evenings and Sundays free for his own scientific work, were years in which he laid the foundations of large parts of twentieth-century physics. They were probably also the happiest years of his life. He liked the fact that his job was quite separate from his thoughts about physics, so that he could pursue these freely and independently, and he often recommended such an arrangement to others later on. In 1903 Einstein married Mileva Marić, a Serbian girl who had been a fellow student in Zurich. Their two sons were born in Switzerland.

Einstein received his doctorate in 1905 from the University of Zurich for a dissertation entitled, “Eineneue Bestimmung der Moleküldimensionen” (“A New Determination of Molecular Dimensions”), a work closely related to his studies of Brownian motion, discussed below. It took only a few years until he received academic recognition for his work, and then he had a wide choice of positions. His first appointment, in 1909, was as associate professor (extraordinarius ) of physics at the University of Zurich. This was followed quickly by professorships at the German University in Prague, in 1911, and at the Polytechnic in Zurich, in 1912. Then, in the spring of 1914, Einstein moved to Berlin as a member of the Prussian Academy of Sciences and director of the Kaiser Wilhelm Institute for Physics, free to lecture at the university or not as he chose. He had mixed feelings about accepting this appointment, partly because he disliked Prussian rigidity and partly because he was unhappy about the implied obligation to produce one successful theory after another. As it turned out he found the scientific atmosphere in Berlin very stimulating, and he greatly enjoyed having colleagues like Max Planck, Walther Nernst, and, later, Erwin Schrödinger and Max von Laue.

During World War I, Einstein’s scientific work reached a culmination in the general theory of relativity, but in most other ways his life did not go well. He would not join in the widespread support given to the German cause by German intellectuals and did what he could to preserve a rational, international spirit and to urge the immediate end of the war. His feeling of isolation was deepened by the end of his marriage. Mileva Einstein and their two sons spent the war years in Switzerland and the Einsteins were divorced soon after the end of the war. Einstein then married his cousin Elsa, a widow with two daughters. Einstein’s health suffered, too. One of his few consolations was his continued correspondence and occasional visits with his friends in the Netherlands—Paul Ehrenfest and H. A. Lorentz, especially the latter, whom Einstein described as having “meant more to me personally than anybody else I have met in my lifetime” ^1. and as “greatest and noblest man of our times,” ^2.

Einstein became suddenly famous to the world at large when the deviation of light passing near the sun, as predicted by his general theory of relativity, was observed during the solar eclipse of 1919. His name and the term relativity became household words. The publicity, even notoriety, that ensued changed the pattern of Einstein’s life. He was now able to put the weight of his name behind causes that he believed in, and he did this, always bravely but taking care not to misuse the influence his scientific fame had given him. The two movements he backed most forcefully in the 1920’s were pacifism and Zionism, particularly the creation of the Hebrew University in Jerusalem. He also took an active part for a few years in the work of the Committee on Intellectual Cooperation of the League of Nations.

Soon after the end of the war, Einstein and relativity became targets of the anti-Semitic extreme right wing. He was viciously attacked in speeches and articles, and his life was threatened. Despite this treatment Einstein stayed in Berlin, declining many offers to go elsewhere. He did accept an appointment as special professor at Leiden and went there regularly for periods of a week or two to lecture and to discuss current problems in physics. In 1933 Einstein was considering an arrangement that would have allowed him to divide his year between Berlin and the new Institute for Advanced Study at Princeton. But when Hitler came to power in Germany, he promptly resigned his position at the Prussian Academy and joined the Institute. Princeton became his home for the remaining twenty-two years of his life. He became an American citizen in 1940.

During the 1930’s Einstein renounced his former pacifist stand, since he was now convinced that the menace to civilization embodied in Hitler’s regime could be put down only by force. In 1939, at the request of Leo Szilard, Edward Teller, and Eugene Wigner, he wrote a letter to President Franklin D. Roosevelt pointing out the dangerous military potentialities offered by nuclear fission and warning him of the possibility that Germany might be developing these potentialities. This letter helped to initiate the American efforts that eventually produced the nuclear reactor and the fission bomb, but Einstein neither participated in nor knew anything about these efforts. After the bomb was used and the war had ended, Einstein devoted his energies to the attempt to achieve a world government and to abolish war once and for all. He also spoke out against repression, urging that intellectuals must be prepared to risk everything to preserve freedom of expression.

Einstein received a variety of honors in his lifetime—from the 1921 Nobel Prize in physics to an offer (which he did not accept) of the presidency of Israel after Chaim Weizmann’s death in 1952.

One of Einstein’s last acts was his signing of a plea, initiated by Bertrand Russell, for the renunciation of nuclear weapons and the abolition of war. He was drafting a speech on the current tensions between Israel and Egypt when he suffered an attack due to an aortic aneurysm; he died a few days later. But despite his concern with world problems and his willingness to do whatever he could to alleviate them, his ultimate loyalty was to his science. As he said once with a sigh to an assistant during a discussion of political activities: “Yes, time has to be divided this way between politics and our equations. But our equations are much more important to me, because politics is for the present, but an equation like that is something for eternity.”^3.

Early Scientific Interests. Albert Einstein started his scientific work at the beginning of the twentieth century. It was a time of startling experimental discoveries, but the problems that drew his attention and forced him to produce the boldly original ideas of a new physics had developed gradually and involved the very foundations of the subject. The closing decades of the nineteenth century were the period when the long-established goal of physical theory—the explanation of all natural phenomena in terms of mechanics—came under serious scrutiny and was directly challenged. Mechanical explanation had had great successes, particularly in the theory of heat and in various aspects of optics and electromagnetism; but even the successful mechanical theory of heat had its serious failures and unresolved paradoxes, and physicists had not been able to provide a really satisfactory mechanical foundation for electromagnetic theory. Many were questioning the whole program of mechanism, and alternatives ranging from the energetics of Wilhelm Ostwald to the electromagnetic world view of Wilhelm Wien were widely considered and vigorously debated.

To a young man who looked to science for nothing less than an insight into the “great eternal riddle”^4. of the universe, these basic questions were the most challenging and also the most fascinating. Einstein was impressed by both the successes and the failures of mechanical physics and was attracted to what he later called the “revolutionary” ideas of James Clerk Maxwell’s field theory of electromagnetism. His study of the writings of the nineteenth-century masters received a new direction when he read Ernst Mach’s Science of Mechanics. This concern with general principles required something else to make it fruitful, however, and Einstein himself described what it was. He realized that each of the separate fields of physics “could devour a short working life without having satisfied the hunger for deeper knowledge,” but he had an unmatched ability “to scent out the paths that led to the depths, and to disregard everything else, all the many things that clutter up the mind and divert it from the essential.”^5. This ability to grasp precisely the particular simple physical situation that could throw light on obscure questions of general principle characterized much of Einstein’s thinking.

His earliest papers—“my two worthless beginner’s works,”^6. as he referred to them a few years later— were an attempt to learn something from experimental materials about intermolecular forces with a view toward their possible relationship with longrange gravitational force, a problem going back to Newton’s time. This work led nowhere, and Einstein’s next series of three articles, published during the years 1902 to 1904, dealt with quite another set of ideas and was clearly the work of a mature scientist. In these articles Einstein rederived by his own methods the basic results of statistical mechanics: the canonical distribution of energy for a system in contact with a heat bath, the equipartition theorem, and the physical interpretations of entropy and temperature. He also emphasized that the probabilities that appear in the theory are to be understood as having a very definite physical meaning. The probability of a macroscopically identifiable state of a system is the fraction of any sufficiently long time interval that the system spends in this state. Equilibrium is dynamic, with the system passing through all its possible states in an irregular sequence. Ludwig Boltzmann had introduced this point of view years before, but Einstein made it very much his own.

It was in the last of this early series of papers, however, that Einstein introduced a new theme. There is one fundamental constant in statistical mechanics, the constant now known as Boltzmann’s constant, k. It appears in the typical exponential factor of the distribution law, exp (–E/kT), Where E is the energy of the system and T is its absolute temperature. It appears too in the relation between the entropy S and the probability W of a state

Einstein asked for the physical significance of this constant K. It was already well-known from the theory of the ideal gas that K was simply related to the gas constant R and to Avogadro’s number, N₀, the number of molecules in a gram-molecular weight of any substance,

Einstein showed that K entered into still another basic equation of the statistical theory, the expression for the mean square fluctuation 〈δ²〉 of the4 energy E about its average value〈E〉:

This meant that k defines the scale of fluctuation phenomena or, as Einstein put it, that it determines the thermal stability of a system. This result shows that fluctuations are normally negligibly small so that the average or thermodynamic value of the energy is a very good measure of this quantity, but Einstein was more interested in its other implications. If one could actually measure the energy fluctuations of any system, then k could be determined and with it Avogadro’s number and the mass of an individual atom. None of these quantities was known with any precision, and previous determinations involved very indirect theoretical arguments. Einstein could not refer to any measurements of fluctuations, but he did give a very plausible analysis of the energy fluctuations in black-body radiation showing how k was related to the constant in Wien’s displacement law.

This 1904 paper made little if any impression on Einstein’s contemporaries, but it contained the seeds of much of his later work. No one before Einstein had taken seriously the fluctuation phenomena predicted by statistical mechanics, but he saw that the existence of such fluctuations could be used to demonstrate the correctness of the whole molecular theory of heat. The problem was to find a situation in which fluctuations could be observed, and Einstein found a solution to this problem in 1905, in his paper “Die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen” (“On the Movement of Small Particles Suspended in a Stationary Liquid Demanded by the Molecular-Kinetic Theory of Heat”). This predicted motion of colloidal particles was already widely known as Brownian motion, but at the time Einstein wrote this paper he knew virtually nothing about what had been observed and hesitated to identify the two motions. He was not trying to explain an old and puzzling phenomenon, but rather to deduce a result that could be used to test the atomic hypothesis and to determine the basic scale of atomic dimensions.

One essential assumption Einstein made was that a colloidal particle will come into thermodynamic equilibrium with the molecules of the fluid in which it is suspended, so that the average kinetic energy of the particle associated with its motion in any one direction is just the equipartition value, kT/2. The quantity for that Einstein calculated for this random motion of colloidal particles was not the velocity, which is unmeasurable even in principle, but rather the mean square displacement in some particular direction x during the time interval т. For spherical particles of radius α, satisfying the same law of resistance that a macroscopic sphere would obey in this fluid of viscosity η, he obtained the result

The hope Einstein expressed at the end of his paper, that “some enquirer” undertake an experimental test of his predictions, was fulfilled several years later when Jean Perrin’s experiments confirmed the correctness of all features of the Brownian motion equation and provided a new determination of Avogadro’s number. These results helped to convince the remaining skeptics, such as Wilhelm Ostwald, that molecules were real and not just a convenient hypothesis. The theory of Brownian motion was developed further by both Einstein and Maryan von Smoluchowski. Several years later both men worked on the theory of another fluctuation phenomenon—the opalescence exhibited by a fluid in the immediate neighborhood of its critical point. Einstein’s work, published in 1910, was especially notable for its generalization of fluctuation theory in a form independent of the mechanical foundations of the theory, an old idea of his and one that later proved to be of considerable influence.

All the work discussed thus far, significant as it was, does not represent the predominant concern of Albert Einstein throughout his career—the search for a unified foundation for all of physics. Neither the attempts at a mechanical theory of the electromagnetic field nor the recent efforts to base mechanics on electromagnetism had been successful. The disparity between the discrete particles of matter and the continuously distributed electromagnetic field came out most clearly in Lorentz’ electron theory, where matter and field were sharply separated for the first time. This theory strongly influenced Einstein, who often referred to the basic electromagnetic equations as the Maxwell-Lorentz equations. The problems generated by the incompatibility between mechanics and electromagnetic theory at several crucial points claimed Einstein’s attention. His struggles with these problems led to his most important early work—the special theory of relativity and the theory of quanta.

For the sake of clarity and convenience, Einstein’s development of relativity theory is treated in a separate article following the discussion of his contribution to quantum mechanics that occupies the remainder of the present article. It must be pointed out, however, that separating these two main themes in Einstein’s work does an injustice to the unity of his fundamental purpose.

Quantum Theory and Statistical Mechanics. Einstein once described his first paper of 1905, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt” (“On a Heuristic Viewpoint Concerning the Production and Transformation of Light”), as “very revolutionary.” He was not exaggerating. The heuristic viewpoint of the title was nothing less than the suggestion that light be considered a collection of independent particles of energy, which he called light quanta. Einstein had his reasons for advancing such a bold suggestion, one that seemed to dismiss a century of evidence supporting the wave theory of light. First among these reasons was a negative result: The combination of the electromagnetic theory of light with the (statistical) mechanics of particles was incapable of dealing with the problem of black-body radiation. It predicted that radiation in theromodynamic equilibrium within an enclosure would have a frequency distribution corresponding to an infinite amount of energy at the high-frequency end of the spectrum. This was incompatible with the experimental results, but, worse than that, it meant that the theory did not give an acceptable answer to the problem. Einstein was the first to point to this result, known later on as the “ultraviolet catastrophe,” as a fundamental failure of the combined classical theories, although Lord Rayleigh had hinted at this in a paper in 1900.

Although he was convinced that a new unified fundamental theory was needed for an adequate treatment of the radiation problem, Einstein had no such theory to offer. What he did instead was to analyze the implications of the observed radiation spectrum, well-described, except at low frequencies, by Wien’s distribution law. To carry out his analysis, Einstein used the methods of thermodynamics (“the only physical theory of universal content concerning which I am convinced that, within the framework of the applicability of its basic concepts, it will never be overthrown”) and statistical mechanics. What he found was that the entropy of black-body radiation in a given frequency interval depends on the volume of the enclosure in the same way that the entropy of a gas depends on its volume. And because the latter dependence has its origin in the independence of the gas molecules rather than the details of their dynamics, Einstein leaped to the conclusion that the radiation, too, must consist of independent particles of energy. This identification required the energy E of the particles to be proportional to the frequency ν of the radiation,

where the universal proportionality constant h was the product of k and one of the constants in Wien’s distribution law.

Einstein showed that his strange proposal of light quanta could immediately account for several puzzling properties of fluorescence, photoionization, and especially of the photoelectric effect. His quantitative prediction of the relationship between the maximum energy of the photoelectrons and the frequency of the incident light was not verified experimentally for a decade. The light quantum hypothesis itself attracted only one or two adherents; it represented too great a departure from accepted ideas. It went far beyond the work Max Planck had done in 1900, in which the energy of certain material oscillators was treated as a discrete variable, capable only of values that were integral multiples of a natural unit proportional to the frequency. Planck’s quantum hypothesis had been introduced as a way of deriving the complete distribution law for black-body radiation, but in 1905 it was only just starting to receive critical study.

During the years between 1905 and 1913 it was Einstein who took the lead in probing the significance of the new ideas on quanta. He soon decided that Planck’s work was complementary to his own and not in conflict with it, as he had first thought. Einstein then realized that if Planck had been right in restricting the energies of his oscillators to integral multiples of hv, in discussing the interaction of molecular oscillators with black-body radiation, then this same restriction should also apply to all oscillations on the molecular scale. The success of Planck’s work had to be looked upon as demonstrating the need for a quantum theory of matter, even as his own 1905 paper demonstrated the need for a quantum theory of radiation.

In 1907 Einstein pointed out how one could use the quantized energy of the oscillations of atoms in solids to account for departures from the rule of Dulong and Petit. This empirical rule, that the specific heat is the same for one mole of any element in solid form, was understood as a consequence of the theorem of equipartition of energy. Many light elements, however, had specific heats at room temperature that were much smaller than the Dulong-Petit value. Einstein showed how one could easily calculate the specific heat of a solid all of whose atoms vibrated with the same frequency (an assumption he made only as a convenient simplification) and obtain a universal curve for the variation of specific heat with temperature. The only parameter in the theory was the frequency of the quantized vibrations. This specific heat curve approached the Dulong-Petit value at high temperatures; accounted qualitatively for all the departures from the equipartition result, including the absence of electronic contributions to the specific heat; and predicted a new and general law: The specific heats of all solids should approach zero as the absolute temperature approaches zero. Einstein indicated how the vibration frequencies could be determined from infrared absorption measurements in many cases; several years later he suggested another way of determining these frequencies using their relationship to the elastic constants of the solid.

As it turned out, Einstein’s quantum theory of specific heats appeared at a time when the behavior of specific heats at low temperatures had just become of interest for very different reasons. Walther Nernst was planning a program of such measurements to establish his own new heat theorem, later known as the third law of thermodynamics. Nernst’s results matched the predictions of Einstein’s theory in all essential respects and convinced him that there was something really significant in this “odd” and “grotesque” theory,^7. as he called it. The success of Einstein’s theory of specific heats in explaining old difficulties, predicting new laws, and establishing unexpected connections among thermal, optical, and elastic properties of crystals was the single most important element in awakening the interest of physicists in the quantum theory.

Wave-Particle Duality. For Einstein, however, the central problem continued to be the nature of radiation. In 1909, speaking in Salzburg at his first major scientific meeting, he argued that the future theory of light which would have to be constructed would be “a kind of fusion of the wave and emission theories.”^8. Einstein’s prediction was based on the results of his continued probings into the implications of Planck’s distribution law for black-body radiation. He had calculated the energy fluctuations of the radiation in a small frequency interval with the help of equation (3) and had found that the fluctuations were the sum of two terms, indicating two apparently independent mechanisms for energy fluctuations. One term was readily intelligible as due to interfering waves, the other as due to variations in the number of light quanta present in the subvolume under study. Neither a wave nor a particle theory could account for the presence of both terms. Einstein confirmed this result by a completely independent calculation of the Brownian motion that a mirror would have to undergo if it were suspended in an enclosure containing a gas and black-body radiation in thermodynamic equilibrium. Once again there were wave and particle contributions to the fluctuations in momentum of the suspended mirror.

Einstein saw this wave-particle duality in radiation as concrete evidence for his conviction that physics needed a new, unified foundation. His view of the role of light quanta in this new fundamental theory had evolved since he put forward the heuristic suggestion of a corpuscular approach to radiation in 1905. Einstein now envisaged a field theory, based on appropriate partial differential equations, probably nonlinear, from which quanta would emerge as singular solutions, along the lines of the electric charges in electrostatics. He found some support for this parallel in the fact that Planck’s constant, h, characteristic for light quanta, was dimensionally equivalent to e ²/c, where e is the unit electric charge and c is the velocity of light. To Einstein this suggested that the discreteness of energy and the discreteness of charge might be explained together by the new fundamental theory.

There was unfortunately very little to go on in the search for this new theory. It would have to be consistent with the special theory of relativity, but Einstein saw that theory as only a universal formal principle, analogous to the laws of thermodynamics, which gave no clue to the structure of matter or radiation. The fluctuation properties of radiation, which he had established, “presented small foothold for setting up a theory.”^9. We know from Einstein’s correspondence as well as from the brief remarks in his papers of this period that he devoted much of his effort to this problem in the years 1908 to 1911, using Lorentz’ theory of electrons as one of his points of departure. His efforts along this line seem to have been comparable in their intensity, although not in their fruitfulness, to his efforts during the following years to create the new gravitational theory—the general theory of relativity.

When in 1911 Einstein put aside his intense work on the problem of developing a theory from which he could “construct” quanta—“because I now know that my brain is incapable of accomplishing such a thing”^10.—he did not give up his interest in quanta. He continued to reflect on the questions surrounding the quantum theory. In a paper in 1914, for example, he used familiar thermodynamic arguments to give a new derivation of Planck’s expression for the average energy of an oscillator. This work led him to suggest the identity of physical and chemical changes at the molecular level: “A quantum type of change in the physical state of a molecule seems to be no different in principle from a chemical change.”^11.

Relation to Bohr’s Early Work. When Einstein returned to the radiation problem in 1916, the quantum theory had undergone a major change. Niels Bohr’s papers had opened a new and fertile domain for the application of quantum concepts—the explanation of atomic structure and atomic spectra. In addition Bohr’s work and its generalizations by Arnold Sommerfeld and others constituted a fresh approach to the foundations of the quantum theory of matter. Einstein’s new work showed the influence of these ideas. He had found still another derivation of Planck’s black-body radiation law, an “astonishingly simple and general” one which, he thought, might properly be called “the derivation”^12. of this important law. It was based on statistical assumptions about the processes of absorption and emission of radiation and on Bohr’s basic quantum hypothesis that atomic systems have a discrete set of possible stationary states. The proof turned on the requirement that absorption and emission of radiation, both spontaneous and stimulated, suffice to keep a gas of atoms in thermodynamic equilibrium. (This paper introduced the concept of stimulated emission into the quantum theory and is therefore often described as the basis of laser physics.) Einstein himself considered the most important contribution of this work to be not the new derivation of the distribution law but rather the arguments he presented for the directional character of energy quanta. Each quantum of frequency v emitted by an atom must carry away momentum hν/c in a definite direction; spherical waves would simply not exist.

Although Einstein put particular emphasis on the directionality of light quanta, there was no direct evidence for it until 1923 when Arthur Compton explained his experiments on the increase in X-ray wavelength after scattering from free electrons. Compton simply treated the process as a collision, obeying the conservation laws, between the electron and a quantum of energy hν and momentum hν/c in the direction of the incident X-ray beam. Even before this, however, Einstein was trying to devise a crucial experiment to settle the question of the nature of radiation. He held fast to his view that light quanta were indispensable since they described the particle properties really manifested by radiation. Light quanta did not have many other supporters until after the Compton effect, and they were particularly unpopular with Bohr and his co-workers. Bohr saw no good way of reconciling them with the correspondence principle and was willing to give up the exact validity of the conservation laws in order to avoid quanta. Experiments to check Bohr’s proposals early in 1925 vindicated Einstein’s belief in both the conservation laws and the validity of light quanta.

Bose-Einstein Statistics and Wave Mechanics. In 1924 Einstein received a paper from a young Indian physicist, S. N. Bose, setting forth a theory in which radiation was treated as a gas of light quanta. By changing the statistical procedure for counting the states of the gas, Bose had arrived at an equilibrium distribution which was identical with Planck’s radiation law. Einstein was much taken with this extension of his old idea. He not only translated Bose’s paper into German and saw to its publication, but he also applied Bose’s new statistical idea to develop an analogous theory for an ideal gas of material particles. A gas obeying the Bose-Einstein statistics, as the new counting procedure was later called, showed a variety of interesting properties. Even though the particles exerted no forces on each other the gas showed a peculiar “condensation” phenomenon: Below a certain temperature a disproportionately large fraction of the total number of particles are found in the state of lowest energy.

Einstein’s interest in the parallel between the gas of particles and the gas of light quanta deepened when he read Louis de Broglie’s Paris thesis late in 1924. De Broglie, inspired by Einstein’s earlier work on the wave-particle duality, had become convinced that this duality must hold for matter as well as radiation. In his thesis he developed the idea that every material particle has a wave associated with it, the frequency ν and wavelength λ of the wave being related to the energy E and momentum p of the particle by the equations

De Broglie had no experimental evidence to support his idea and deduced no experimentally testable conclusions from it, so it aroused very little interest. Einstein, however, was immediately attracted to the idea of matter waves because he saw its relationship to his new theory of the ideal gas. He found a confirmation of de Broglie’s wave-particle duality for matter in the results of his calculation of the density fluctuations of this ideal gas. These fluctuations showed the same structure as had the energy fluctuations of black-body radiation; only now it was the particle term that would have been the only one present in the classical gas theory. Einstein saw the wave term in the fluctuations as a manifestation of the de Broglie waves, and he was sure he was not dealing with a “mere analogy”. He proposed several kinds of experiments which might detect the diffraction of de Broglie waves.

Einstein’s support for de Broglie’s work brought it the attention it deserved, particularly from Erwin Schrodinger. In describing the origins of his wave mechanics a few years later, Schrodinger wrote: “My theory was stimulated by de Broglie’s thesis and by short but infinitely far-seeing remarks by Einstein.” ^13. Those remarks were the ones linking de Broglie’s ideas to the properties of the Bose-Einstein gas.

When the new matrix mechanics appeared, in the papers of Werner Heisenberg, Max Born, and Pascual Jordan, Einstein was interested but not convinced. “An inner voice tells me that it is still not the true Jacob”, ^14. he wrote to Born in 1926. He looked more favorably on Schrodinger’s wave mechanics: “I am convinced that you have made a decisive advance with your formulation of the quantum condition, just as I am equally convinced that the Heisenberg-Born route is off the track.”^15.

Discontent With Quantum Mechanics. In 1927 the synthesis that constituted the new quantum mechanics was worked out. One of its key features was Born’s statistical interpretation of Schrödinger’s wave function. This meant that a full quantum mechanical description of the state of a system would generally specify only probabilities rather than definite values of the dynamical variables of the system. The new theory was intrinsically statistical and renounced as meaningless in principle any attempt to go beyond the probabilities to arrive at a deterministic theory. Bohr expressed what became the generally accepted viewpoint when he described quantum mechanics as a “rational generalization of classical physics”, the result of “a singularly fruitful cooperation of a whole generation of physicists.”^16.

Einstein dissented from this majority opinion. He never accepted the finality of the quantum mechanical renunciation of causality or its limitation of physical theory to the unambiguous description of the outcome of fully defined experiments. From the Solvay Congress of 1927, when the quantum mechanical synthesis was first discussed, to the end of his life, Einstein never stopped raising questions about the new physics to which he had contributed so much. He tried at first to propose conceptual experiments that would prove the logical inconsistency of quantum mechanics, but these arguments were all successfully refuted by Bohr. In 1935 Einstein began to stress another objection to quantum mechanics, arguing that its description of physical reality was essentially incomplete, that there were elements of physical reality which did not have counterparts in the theory. Bohr answered this argument, saying that Einstein’s criterion of physical reality was ambiguous and that from Bohr’s own complementarity standpoint the theory satisfied any reasonable standard of completeness.

Einstein never abandoned his opposition to the prevailing mode of thought despite the enormous success of quantum mechanics. He was convinced that a fundamental theory could not be statistical, “that He does’t play dice”, ^17. Even more serious in Einstein’s view was the incompleteness of the theory. He would not give up the idea that there was such a thing as “the real state of a physical system, something that objectively exists independently of observation or measurement, and which can, in principle, be described in physical terms.”s ^18. The search for a theory that could provide such a description of reality was Einstein’s program. He never lost his hope that a field theory of the right kind might eventually reach this goal.

That Einstein, without whom twentieth-century physics would be unthinkable, should have chosen to follow a separate path was a source of great regret to his colleagues. In Max Born’s words: “Many of us regard this as a tragedy—for him, as he gropes his way in loneliness, and for us who miss our leader and standard-bearer.”^19. But to Einstein himself his choice was inevitable; it was the natural outgrowth of all his years of striving to find a unified foundation for physics. This was what he meant when he ended his scientific autobiography by writing that he had tried to show “how the efforts of a lifetime hang togeather and why they have led to expectations of a definite form.”^20.

Martin J. Klein