## Beiträge zur Quantentheorie. Offprint from Verhandlungen der Deutschen Physikalischen Gesellschaft, 16. Band, 1914.

Braunschweig: Vieweg & Sohn, 1914.

First edition, extremely rare author’s presentation offprint (with ‘Überreicht vom Verfasser’ (Presented by the Author) printed on front wrapper), and the copy of Einstein’s close friend and colleague Paul Ehrenfest, of this crucial transitional paper in which Einstein uses the light quantum hypothesis to give new derivations of Planck's radiation law and Nernst's third law of thermodynamics (Einstein points out that the alleged ‘proofs’ which try to derive the theorem of Nernst from the mere fact that the specific heat of all substances goes to zero at absolute zero temperature, are not genuine). Einstein had first put forward the idea of light quanta in 1905, but in later years he came to doubt the validity of the hypothesis, despite its earlier success in explaining the photoelectric effect. Einstein’s success in the present paper in deriving two of the most important achievements of quantum theory using the light quantum hypothesis re-established his confidence in that hypothesis, and he began to think again about the interaction between radiation and matter, resulting two years later in his great papers on the quantum theory of radiation. The only other copy we have located in auction records is that in Einstein’s own reference collection of offprints formerly in the Richard Green Library (sold Christie’s New York, 17 June 2008, lot 100). OCLC lists three copies in US (American Philosophical Society, Florida, Princeton), one in UK and one in Switzerland.

*Provenance*: The Austro-Dutch physicist Paul Ehrenfest (1880-1933) (‘Ehrenfest’ written in his hand on upper wrapper; seven lines in his hand written in pencil on last page of text, commenting on the first three lines of text on the page – see below). Ehrenfest met Einstein for the first time in 1912 in Prague, where Einstein spent a year as full professor, and the two men remained close friends thereafter. When Einstein returned to Zürich in July 1912, he recommended Ehrenfest to succeed him in his position in Prague, but this was prevented by Ehrenfest’s declaration that he was an atheist. However, just at this time Lorentz resigned his position as professor at the University of Leiden, and on his advice Ehrenfest was appointed as his successor. He remained there for the rest of his career. Einstein said of him: “He was not merely the best teacher in our profession whom I have ever known; he was also passionately preoccupied with the development and destiny of men, especially his students. To understand others, to gain their friendship and trust, to aid anyone embroiled in outer or inner struggles, to encourage youthful talent — all this was his real element, almost more than his immersion in scientific problems” … On his invitation Einstein accepted in 1920 an appointment as extraordinary professor at the University of Leiden. This arrangement allowed Einstein to visit Leiden for a few weeks every year. At these occasions Einstein would stay at Ehrenfest’s home. In 1923 Einstein stayed there for six weeks, after German ultra-nationalists in Berlin had made threats against his life. On the occasion of the 50th anniversary of Lorentz' doctorate (December 1925) Ehrenfest invited both Bohr and Einstein over to Leiden, in an attempt to reconcile their scientific differences about the emerging quantum theory. These discussions were continued at the 1927 Solvay Conference, where Ehrenfest much to his dismay had to side with Bohr's position in this great debate” (Wikipedia, accessed 29 May 2017). In 1922, Einstein and Ehrenfest published a joint paper in *Zeitschrift für Physik* which attempted to explain the Stern-Gerlach experiment, the results of which had been published just weeks earlier. Their paper can be considered the first significant contribution to the quantum measurement problem.

In 1909 Einstein wrote Lorentz that he had never believed in independent, localized light quanta, because, among other reasons, this concept was incompatible with the division of rays during refraction. In July 1910 he wrote to Sommerfeld: “To me the basic question is: ‘Is there a way to unify the energy quanta and Huygens's principle!’ Appearances are against it, but the good Lord has found the trick.” He soon retreated from this quantum view and examined another revolutionary possibility: “At present,” he wrote to Laub in November, “I am very hopeful to solve the radiation problem, without *light quanta. *I am exceedingly curious to see how the thing evolves. Even the energy principle in its present form would have to be given up.” Perhaps he had in mind a virtual, wavelike radiation field correlating quantum jumps in distant molecules, as in the later theory of Bohr, Kramers, and Slater. A week later, Einstein renounced this new attempt: “Again, the solution of the radiation problem has come to naught. The devil has indulged in a rotten trick with me.” Six months later, Einstein confided to Michel Besso his doubts on the existence of quanta in general: “I no longer ask myself if these quanta really exist. And I do not try any more to construct them because I now know that my brain is unable to do it. But I still explore the consequences as carefully as I can to learn the range of validity of this idea.” In February 1912 he wrote to Hopf: “Quanta certainly do what they ought to, but they do not exist, like the immovable ether. At the moment, the latter is turning diligently in its grave intending to come to life again — poor fellow.” In 1913, in a more pronounced retreat from quantum discontinuity, Einstein and Otto Stern derived Planck’s law without quantization at all.

“Einstein forcefully reasserted the reality of quanta in a publication of 1914 [the offered paper]. Perhaps Niels Bohr’s new theory of spectra encouraged him to do so, although there is no trace in his writings of any reflections on this theory before 1916. Perhaps he realized that the zero-point energy failed to solve quantum difficulties that involved other entities than resonators. In any case, he now lent so much reality to the quantum states of a micro-entity as to compare them with different chemical species. This view induced the profound comment: “The concepts of physical and chemical change seem to lose their fundamental difference” [the present paper, pp. 822-3]. For instance, a quantum jump in a resonator and the dissociation of a molecule are comparable processes, for they are both caused by the absorption of an energy quantum.

“Einstein immediately applied this analogy to a new, non-statistical derivation of Planck’s formula for the average energy of a harmonic oscillator at temperature *T. *If the various energy levels *nhv *of a resonator are identified with different chemical species, a thermalized set of resonators is comparable to a chemical mixture in equilibrium. According to the laws of chemical equilibrium, the free energy of the mixture must be a minimum, which implies that the concentration of the species *nhv *should be proportional to *e ^{-nhv/kT}*. Consequently, the average energy of the resonators must be

*U*= 1/(

*e*– 1), in conformity with Planck’s result of 1900.

^{hv/kT}“Through this reasoning, Einstein confirmed the quantum-theoretical version of Gibbs’s canonical law, according to which the probability of the discrete energy value *E _{n} *is proportional to

*e*for a (non-degenerate) system in contact with a thermostat at temperature

^{–En/kT}*T.*He still did not know how to proceed from the quantized resonators to the black-body law … A new, quantum-theoretical picture of the interaction between matter and radiation was needed. Einstein found it in the summer of 1916, after the completion of his new theory of gravitation left him more time for quantum meditation” (

*Cambridge Companion to Einstein*, pp. 133-4).

Ehrenfest’s annotations on p. 828 refer to Einstein’s statement at the top of that page, according to which the thermodynamic state of the system will be unchanged when two different kinds of molecules are interchanged. Ehrenfest remarks that one cannot interchange a molecule of the first kind with one of the second if the spatial separation between the two is too large.

Weil, *Albert Einstein Bibliography, *67.

8vo (230 x 155 mm), pp. [1:blank] 820-828. Original printed wrappers. A very fine copy.

Item #4295

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Price:
$18,500.00
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