Albert's quantum leap

In the period between 1902 and 1911 Albert Einstein grew from an unknown, mostly unemployed, graduate of the Swiss Polytechnical Institute (ETH) into a world-famous scientist by supplying a series of revolutionary papers which established the theory of (special) relativity and promoted the semidormant quantum theory of Max Planck. These publications have been collected in volumes two and three of the monumental Princeton University Press Einstein Papers project. Of the two books reviewed here, the first half of volume five illustrates the glorious rise of the young scholar.

After obtaining his first established employment, at the Swiss Patent Office in Bern, in the summer of 1902, Einstein wrote to a friend from his school days in Aargau: "I am frightfully busy. Every day eight hours at the office and at least one hour private lessons, and then, in addition I do some scientific work.'' In January 1903 he married his fiancee Mileva Marity (or Maric), who bore him two children and set up a proper household which became the background for fruitful scientific and social exchange with friends (the so-called "Olympic Academy"). At this time he discussed the results of his early scientific work mainly with two ETH costudents, Michele Besso and Conrad Habicht. Thus in May 1905, his annus mirabilis, he wrote to Habicht: "But why have you still not sent me your dissertation? ... I promise you four papers in return, the first of which I might send you very soon. ... The paper deals with radiation and energy properties of light and is very revolutionary. ... The second paper is a determination of the true size of atoms from the diffusion and the viscosity of dilute solutions of neutral substances. The third proves that, on the assumption of the molecular theory of heat, bodies of the order of magnitude of 1/1000 mm suspended in liquids, must already perform an observable random motion that is produced by thermal motion. ... The fourth paper is only a rough draft at this point, and is on electrodynamics of moving bodies which employs a modification of the theory of space and time." Immediately after this explosion of ingenuity, Einstein began to correspond with luminaries in physics, such as Philipp Lenard, Wilhelm Conrad Rontgen, Max Planck and Willy Wien, and younger colleagues, such as Max Laue, Jakob Laub or Johannes Stark. His surviving letters contain 70 items up to the end of 1907, and more than 100 over the next two years, after which he continued at this rate.

His career prospered academically too. In 1909 he was extraordinary professor at Zurich University, by 1911 full professor at Prague. Celebrated as a rising star at the first (1911) Solvay Conference in Brussels, Einstein soon received invitations to Utrecht, the ETH (which he accepted) and Leiden. His correspondence with the Berliners Fritz Haber, Erwin Freundlich and his cousin Elsa Lowenthal prepared the ground for his later move to the German capital. The stature of his work during his second period in Switzerland, 1912-14, may be deduced from a letter of October 29 1912 he wrote to Arnold Sommerfeld: "Your friendly note makes me feel even more embarrassed. But I assure you that I have nothing now to add to the question of quanta that might be of any interest. ... I am now working exclusively on the gravitation problem and believe that I can overcome all difficulties with the help of a mathematical friend of mine. But one thing is certain: never before in my life have I troubled myself over anything so much."

The years between 1912 and 1914 were a period of hard labour, both on problems of quantum theory and relativity theory; perhaps they should be regarded as a real crisis point in Einstein's work. To begin with quantum theory, to which his contribution was less significant, he attempted to derive phenomena that he had earlier explained with the light-quantum concept without reference to light quanta. Thus he wrote several papers dealing with the law of photochemical equivalence (and quarrelled about priority with his former supporter Johannes Stark): these considerations contributed later, in 1916, to an important result, the derivation of Planck's radiation law with the help of spontaneous and stimulated emission of atomic radiation (providing the basis of the laser). But Einstein was now equalled or even surpassed by his competitors, Planck and especially Sommerfeld, in dealing with new quantum phenomena.

The second area mentioned above, the generalisation of relativity theory to take account of accelerated coordinate systems and gravitational effects, became Einstein's major preoccupation. While still in Prague he had begun to formulate what he called "the statics of the gravitational field". In particular, he generalised the Poisson equation of Newton's dynamics, assuming c, the velocity of light (in vacuo) to be a linear function of the coordinates; but then the principle of equivalence (for all accelerated coordinate systems, assumed to be an essential foundation of "general relativity theory") could be satisfied only for infinitesimally small regions. His papers on statics of February and March 1912 attracted the criticism of Max Abraham (for abandoning c as a constant) and stimulated Gunnar Nordstrom's alternative (scalar) gravitation theory. Einstein responded to Abraham politely but insisted on the correctness of his procedure, which satisfied Mach's principle (July 1912). Back in Zurich, he collaborated with his former fellow student Marcel Grossmann, now professor of geometry at the ETH, on the "Outline of a generalised theory of relativity'' (Entwurf theory), based on Riemannian geometry and the advanced Christoffel and Ricci differential calculus.

The Einstein-Grossman Entwurf theory failed to be generally covariant - it was covariant only under general linear transformations - but Einstein, who was responsible for the physical part of the work piled up arguments in its favour, all of which were later shown to be fallacious. He simultaneously discussed and mildly criticised Nordstrom's original theory, which the latter improved in 1913, such that it satisfied the principle of equivalence of gravitational and inert mass. (In February 1914, Einstein, and his Dutch collaborator Adriaan Fokker, cast this Nordstrom theory into a generally relativistic tensor form.) Another competing scheme, that of Gustav Mie, uniting gravitation and electromagnetism in 1912-1913, Einstein ruled out by a new argument favouring his semi-generally relativistic Entwurf theory.

From the point of view of the final gravitation theory of 1915, these confusing exchanges with Abraham, Mie and Nordstrom were of vital help to Einstein's work. As he wrote to Besso (with whom he carried out a calculation of the motion of the planet Mercury's perihelion, obtaining the incorrect value of 18" as compared to 43"): "Abraham seems to have the greatest understanding of it. To be sure, he fulminates against all relativity in Scienza (an Italian science journal), but he does so with understanding (Verstand).'' Indeed, Einstein's intermediate steps, detours and blind alleys, which he traversed in Prague, Zurich, and Berlin, seemed to have been designed to achieve the final goal, the general covariance of the laws of gravitation.

There is one previously unpublished document, number ten in volume four, which the editors date between August 1912 and May 1913 and to which they give particular attention. It consists of handwritten research notes revealing the gradual training of Einstein in the mathematical differential calculus and indicating first steps to the Einstein-Grossmann Entwurf theory. The editors claim that certain parts of this manuscript provide the most complete record of what would become a substantial advance in Einstein's thinking as he explored the possibilities for the field equations of gravitation, before he abandoned them in favour of the misleading Entwurf theory. In some German publications the manuscript is even termed "the Rosetta stone", requiring the history of general relativity to be rewritten. Such exaggerated statements overrate this innocent document. The editors' arguments in their introduction are perhaps unconsciously biased by a belief that Einstein knew, from the start, his final conclusion, but that his guess was spoiled by Grossman, his mathematician collaborator. Nothing could be less likely, however: Grossmann must have felt very uneasy about the mathematically ugly Entwurf theory, and may have accepted it only because he deferred to the superior physical understanding of his friend.

Perhaps one remark should be made about the presentation of the unpublished manuscripts, notably documents ten and 14. Both are reproduced in facsimile, including crossed-out passages, sentences, fragments and words. This is unnecessarily clumsy, and at times very puzzling for the reader. The editors should here have preferred a simpler style, giving the original text on the left-hand page and the footnotes on the right-hand side. Apart from this, the editorial work in volumes four and five is basically fine and very helpful. Overall, these two volumes, with their supplementary English translation, provide valuable insights into a period of Einstein's life and work which is less familiar than that of his later years.

Helmut Rechenberg is a theoretical physicist and historian of physics, Max Planck Institute for Physics, Munich.