## Theorie der Opaleszenz von homogenen Flüssigkeiten und Flüssigkeitsgemischen in der Nähe des kritischen Zustandes. Offprint from Annalen der Physik, 4. Folge, 33. Bd., 1910.

Leipzig: Barth, 1910.

First edition, rare author’s presentation offprint with “Überricht von dem Verfasser” printed on the front wrapper, of Einstein’s paper on critical opalescence, his last major paper on classical statistical physics, and one of his most often-cited works. Critical opalescence is a phenomenon that occurs during continuous (second-stage) transitions between gaseous and liquid phases of matter: as the matter reaches the critical point of transition, the sizes of the gas and liquid regions begin to fluctuate over increasingly large length scales. As the density fluctuations become of a size comparable to the wavelength of visible light, the light is scattered and causes the normally transparent fluid to appear cloudy. Critical opalescence was first described in the 19^{th} century by Thomas Andrews, a British scientist. In 1908 the Polish physicist Marian Ritter von Smolan-Smoluchowski became the first to ascribe critical opalescence to large density fluctuations, although he did not carry out a quantitative analysis. This was provided by Einstein in the present paper. Although Einstein mentions it only in passing, his paper is interesting for a general audience as it provides the first correct explanation for why the sky is blue. Already in 1869, John Tyndall had explained the blue colour of the sky in terms of the scattering of light by dust particles or droplets, but Rayleigh later concluded that the inhomogeneities needed to explain this phenomenon were the air molecules themselves. “When the English physicist Lord Rayleigh calculated for the first time how light was scattered by atoms, he found that short wavelengths were more strongly scattered than long ones: blue light is scattered more than red light. If one looks away from the Sun, the eye catches scattered sunlight, thus light in which the blue component is strongest. Thus the sky seems blue. For a while that seemed to solve the puzzle, and even today one can find this explanation in many popular books and on websites. But Einstein, and with him Smoluchowski, realized that this scattering from individual particles would not have the desired effect if the atmospheric particles were arranged in an orderly pattern – it is crucial that they are distributed in an irregular way: density fluctuations in the atmosphere are crucial for the necessary scattering effect to appear. Interestingly, one can view this result as yet another proof of the atomistic constitution of matter” (Janssen & Lehner, p. 115).

“Einstein’s paper on critical opalescence explains the optical effects that occur near the critical point of a gas and near the critical point of a binary mixture of liquids. In spite of its title, the results of this paper fail to hold, as Einstein points out, in the immediate vicinity of the critical point but are, on the other hand, valid far away from it. They thus extend Rayleigh’s earlier studies of the blue color of the sky and relate this phenomenon to the density fluctuations of the light-scattering medium that cause critical opalescence. Einstein’s research on critical opalescence and the blue of the sky follow his studies of Brownian motion and add to the evidence provided by these studies for the atomistic constitution of matter.

“In 1908 Smoluchowski published a paper on critical opalescence in the *Annalen* that had appeared the year before in Polish. Not long after the publication of the German version, he received a postcard in which Einstein asked for reprints of his papers. While it is unclear whether or not Einstein’s request indicates his intent to work on critical opalescence already at that time, Einstein's paper of 1910 evidently takes Smoluchowski’s work as its point of departure. In his paper Smoluchowski sketched an explanation of critical opalescence by density fluctuations of the medium, but he did not derive a quantitative formula for the light scattering due to these fluctuations. Such a quantitative formula was first presented by Keesom in a footnote to a joint paper with Kamerlingh Onnes. Following a suggestion by Einstein, Keesom later published a paper on the argument by which he had obtained his formula. This argument, however, went little beyond what Smoluchowski had already arrived at, and it was left to Einstein to rigorously derive a formula for light scattering by density fluctuations on the basis of Maxwell’s theory of electrodynamics. Einstein later characterized his achievement as a ‘quantitative realization of the theory by Smoluchowski.’

“Einstein’s and Smoluchowski’s lines of research had crossed on an earlier occasion, on their work on Brownian motion in 1905 and 1906. In the case of critical opalescence their common interest in the atomistic constitution of matter once again led them on similar paths, which each followed by developing his characteristic style of doing physics. Einstein’s first encounter with critical opalescence dates from his student days; so his interest in the subject may already have been aroused by the time he read Smoluchowski’s paper. H. F. Weber’s physics course, which Einstein took between 1897 and 1898 as a student at the ETH in Zurich, touched briefly upon critical phenomena and the history of their discovery, including the discovery of opalescence. Einstein’s paper on critical opalescence follows several of his earlier papers in presenting yet another method for determining Avogadro’s number. His continued effort to find new ways of determining this number was motivated, among other reasons, by the role it played in the discussions about Planck’s formula for black-body radiation and its problematic status in contemporary physics. But Einstein’s work on critical opalescence also contributes to the realization of a more general goal that had guided his earlier research on statistical physics, the goal of establishing the molecular constitution of matter as firmly as possible.

“Einstein’s key insight in his paper was that the phenomena of critical opalescence and the blue color of the sky, which are not obviously related to each other, are both due to density fluctuations caused by the molecular constitution of matter. Even after the paper’s publication, however, the relationship between the two phenomena remained unclear to Smoluchowski. In 1911 he published a paper in which he claimed that the blue color of the sky has two causes: Rayleigh scattering by the molecules of the air, and Smoluchowski-Einstein scattering by density fluctuations. Einstein immediately responded to this paper, pointing out that ‘a ‘molecular opalescence’ in addition to the fluctuation opalescence does not exist.’ Smoluchowski readily accepted Einstein’s criticism.

“Statistical physics enters Einstein’s derivation of a formula for light scattering by density fluctuations through his use of Boltzmann’s principle, just as it did in Smoluchowski’s earlier work. This approach was particularly useful at a time when no deeper understanding of the underlying atomistic processes causing phenomena such as opalescence was available. In fact, the use of Boltzmann’s principle had also played a crucial role earlier in Einstein’s contributions to quantum theory and for similar reasons. His paper on critical opalescence, therefore, begins with what could be considered a paper within a paper: a lengthy introduction developing a framework for statistical physics that is essentially based on Boltzmann’s principle. This introductory section became a pioneering contribution to statistical thermodynamics, a theory dealing with statistical fluctuations without using an explicit atomistic framework … Einstein’s work on critical opalescence, comprising both his ideas on the foundations of statistical physics and his derivation of a formula for light scattering by density fluctuations, thus became one of the starting points for several major research traditions in twentieth-century physics” (*Papers*, pp. 283-285).

Weil *36. Shields, “Bibliography of the writings of Albert Einstein to October 1949,”33. *The Cambridge Companion to Einstein* (Janssen & Lehner, eds.), 2014. *The Collected Papers of Albert Einstein**, Vol. 3: The Swiss Years: Writings 1909-1911*.

8vo (223 x 146 mm), pp. 1275-1298. Original printed wrappers (lightly creased horizontally).

Item #5072

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