Smoluchowski, Marian

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(b. Vorderbrühl, near Vienna, Austria, 28 May 1872; d. Cracow, Poland, 5 September 1917)


Born to a Polish family, Smoluchowski spent his youth in Vienna. His father, Wilhelm, was a senior official in the chancellery of Emperor Franz Josef; his mother was the former Teofila szczepanowska. Smoluchowski attended the Collegium Teresianum from 1880 to 1885 and was an outstanding student. From 1890 to 1895 he studied at the University of Vienna under the direction of Josef Stefan and F. Exner: his doctoral dissertation was entitled “Akustische Untersuehungen üiber die Elastizität weicher Körper.”

From November 1895 to August 1897 Smoluchowski worked under Lippmann in Paris, with Lord Kelvin in Glasgow, and with Warburg in Berlin, Two papers published during his stay in Paris dealt with thermal radiation (the kirchhoff-Clausius law). At Glasgow he investigated the influence of Röntgen and Becquerel rays on the conductance of gases. In 1901 Smoluchowski received the L.L.D. from Glasgow, where he had been a research fellow. In Berlin he worked on the discontinuity of temperature in gases, a problem suggested to him by Warburg, In 1875 Warburg and A. Kundt, on the basis of the kinetic theory of gases, had predicted that if the temperature of a gas differed from that of the container wall, the former temperature would not pass continuously to the latter: there would be a discontinuity of temperature between the gas and the wall. Their experiments, successful in the case of the analogous phenomenon of the slipping of gases, had not been decisive for temperature discontinuity. Smoluchowski, observing the cooling time of a thermometer in a gas-filled container, demonstrated that an effect exists and reached significant values with rarefied gas in “Uber Wärmeleitung in verdünnten Gasen” (1898).

This work was of special importance. For by publishing it Smoluchowski joined the dispute on the validity of atomic conceptions. These, represented in physics mainly by the kinetic theory of gases developed by Boltzmann. were far from accepted at the end of the nineteenth century; and their recognition was partly due to Smoluchowski At that time only a few phenomena were predicted by the kinetic theory or required it for intelligibility. Among them was discontinuity of temperature, for its existence was wholly unexplained from a classical point of view. Moreover, in 1897 after his return to Vienna, Smoluchowski pointed out the quantitative agreement of his experimental results with the kinetic theory. In 1898 the University of Vienna admitted him veniam legendi.

From 1899 Smoluchowski worked at the University of Lvov. Appointed professor in 1900, he held the chair of mathematical physics there until 1913. His first works at Lvov concerned atmospheric physics, aerodynamics and hydrodynamics, electrophoresis, and the theory of mountain folding. Recognition for these specialized works was show by his being asked to write the chapter on endosmosis phenomena in Handbuch der Elektrizitätund des Magnetismus, edited by J. A. Barth (Leipzig, 1914).

From about 1900 Smoluchowski worked on Brownian movement. He wished to use experi mental data to verify the theory he had obtained desire complicated by the confused situation of experimental research. In the meantime Einstein, in papers of 1905 and 1906, had presented a solution to the problem. Smoluchowski then decided to publish his results in “Zarys kinetycznej teorii ruchow Browna” (“An Outline of the Kinetic Theory of Brownian Movement,” 1906), which presented his different method. Einstein started from general relations of statistical physics, an approach that was universal but did not lend itself to visualization. For example, Einstein said nothing of the collisions between a Brownian particle and the surrounding molecules. Smoluchowski started by examining the effects of successive collisions and obtained a final formula that differed little from Einstein’s. Smoluchowski’s further works in this field extend through an examination of the Brownian movement of a particle undergoing the influence of a quasi-elastic force to the Brownian movements of macroscopic bodies. At the Conference of Natural Scientists at Münster in 1912, Smoluchowski proposed the observation of the Brownian rotative movement of a small mirror suspended on a thin quartz fiber and the observation free end of a similar fiber. The first experiment was performed by W. Gerlach and E. Lehrer in 1927, and later by Eugen Kappler; the second, by A Houdijk and P. Zeeman, and by E. Einthoven. In 1925, Both experiments confirmed Smoluchowski’s calculations.

Another of Smoluchowski’s interests concerned fluctuations and was related to the second law of thermodynamics. The kinetic approach to the seeond law proposed by Boltzmann implied the occurrence of spontaneous deviations from a state of maximum entropy. Because the occurrence of such deviations had not been experimentally confirmed, however, the kinetic theory lay open to attack.Boltzmann, in defense, calculated the time of return for given micro states and showed how rare and difficult to observe these phenomena are. Smoluchowski, on the other hand, laid the foundations of the theory of fluctuations, calculated the times of return for macro states, linked the theory to measurable parameters, and proved the actual existence of fluctuations.

In his first paper dealing with this problem, “Über Unregelmässigkeiten in der Verteilung von Gasmlolekülen” (1904), Smoluchowski gave a theoretical approach to the fluctuations of density in a gas. At the same time he indicated the experimental possibility of detecting these fluctuations either by optical methods or when the number of particles is not too great, as in the case of colloidal suspensions. In 1910 Theodor Svedberg based his experiments on Smoluchowski’s calculations, observing how many particles of a suspension can be seen in the field of vision of a microscope at a given time and experimentally confirming Smoluchowski’s predictions to an astonishingly high degree Smoluchowski himself had previously proved the existence of fluctuations of density in a pure gas by demonstrating that they are responsible for the known but unexplained phenomenon of the opalescence of a gas at a critical state. His paper “Teoria kinetyczna opalescencji gazów w stanie krytycznym” (“kinetic Theory of Gas Opalescence at the Critical Stale” 1907) shows why the critical point plays such an important role and states that the opalescence of pure gas also should be observable under normal conditions: “Each of us has observed it innumerable times when admiring the blue of the sky or the glow of the rising sun.” Smoluchowski combined the theory of fluctuations with the results of Lord Rayleigh’s researches on the blue of the sky; his finding (Einstein also took part in the discussion) was that the blueness of the sky was caused by fluctuations in the density of the air. Smoiuchowski’s laboratory production of sky blue closed the investigation to a certain extent. In “Experimentelle Beslätigung der Rayleighsehen Theorie des Himmelsbkius” (1916) Smoluchowski demonstrated that pure air can opalesce in the laboratory under normal conditions.

Experimental proofs of the existence of fluctuations and the revelation of the causes of Brownian movement have limited the validity of the classical formulation of the second law of thermodynamics. A new. statistical formulation of this principle that had been initiated by Boltzmann was developed by Smoluchowski. He concluded that the deeper one goes into microscopic processes, the more visible the reversibility becomes. Macroscopic processes, although theoretically reversible, are practically irreversible because of the unimaginably long times of return. Statistical interpretation of the second law gave ground, at that time, for hopes of constructing the perpettuum mobile of the second kind. Smoluchowski resolved this question in his lectures at Münster (1912) and Göttingen (1914): If we expect great deviations from the state of maximum entropy, the efficiency of the machine will be infinitesimal, since great deviations are extremely rare; and if we hope for microscopic deviations, the valves and other parts needed to eliminate deviations occurring in an adverse direction will have to be so fine that they themselves will undergo Brownian movement and will not be able to perform their task. Thus it is not possible to construct a perpetuum mobile of the second kind if we mean a machine with any finite efficiency.

Smoluchowski obtained important results in the physics of colloids. His interest in the methodology of teaching physics can be seen in the chapters he wrote for Poradnik dla sumouków (“Primer for Home Studies”), edited by A. Heflich and S. Michalski (Warsaw, 1917). The title of the book is a bit misleading, for it is really a report on physical research and aims.

In 1913 Smoluchowski became professor of experimental physics at the Jagiellonian University in Cracow. In 1917 he was elected rector of the university. Later that year he died of dysentery, at the age of forty-five.


I. Original Works. Smoluchowski’s writings were collected as Pisma Mariana Smoluchowskiego (“The Works of Marian Smoluchowskki”), W. Natanson, ed., 3 vol. (Cracow, 1924–1928). Besides texts in Polish, this collection includes versions published in other languages.

His most important works are “Über Wärmeleitung in verdünnten Gasen,” in Annalen der Physik und Chemie, 64 (1898), 101–130: “Über Unregelmässigkeiten in der Verteilung von Gasmolekülen und deren Einfluss auf Entropie und Zustandsgleichung,” in Boltzmann-Festschrift (Leipzig, 1904), 626–641; “Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen.” in Annalen der Physik, 4th ser., 21 (1906), 756–781: “Molekular-kinetische Theorie der Opaleszenz von Gasen in kritisehen Zustande. sowie einiger verwandter Erscheinungen,” ibid., 25 (1908), 205–226: “Beitrag zur Theorie der Opaleszenz von Gasen in kritischen Zustande,” in Bulletin internautional de l’Acadámie des sciencese et des lettres de Cracovie. ser. A (1911). 493–502: “Experimentell nachweisbare, der üblichen Thermodynamik widersprechende Molekularphänomene,” in Physikalische Zeitschrift.13 (1912). 1069–1079: “Gülcigkeitsgrenzen des zweitcn Hauptsatzes der Wärmetheorie.” in Vorträge über die kinetische Theorie der Materie und der Elektrizität (Leipzig-Berlin, 1914), 89: “Studien über Molekularstatistik von Emulsion und deren Zusammcnhang mit der Brownschen Bewegung,” in Sitzungsberichte der Akademie der Wissenschaften in Wien. Math.-nat. Kl., Abt. IIa. 123 (1914), 2381–2405: “Molekular-theoretisehe Studien über umkehr thermodynamisch irreversibler Vorgänge und über Wiederkehr abnormaler Zustände,” ibid. 124 (1915), 339–368; “Über Brownsche Molekularbewegung unter Einwirkung äusserer Kräfte und deren Zusammenhang mit der verallgemeinerten Diffusionsgleichung,” in Annalen der Physik, 48 (1915), 1103–1112: “Experinmentelle Bestätigung der Rayleighschen Theorie des Himmelsblaus,” in Bulletin international de l’Acatdémie des sciences et des lettres de Cracovie, ser. A (1916). 218–222; “Drei Vorträge über Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen,” in Physikalische Zeitschrift, 17 (1916), 557–571, 585–599: and “Über den Begriff des zufalls und den Ursprung der Wahrscheinlichkeitsgesetze in der Physik.” in Naturwissenschaften. 6 (1918), 253–263.

II. Secondary Literature, Polish sources are W. Kapuściński. “Poylady filozoficzne Mariana Smoluchowskiego” (“Marian Smoluchowski’a Philosophical Views”), in Fizyka i chemia. 6 (1953). 200: W. Krajewski. Swiatopoglad Mariana Smoluchowskiego (“Marian Smoluchowski’s Weltanschauung”; Warsaw, 1956): S. Loria, “Marian Smoluchowski i jego dzielo” (“Marian Smoluchowski and His Work”), in Postepyfizyki, 4 (1953) 5: and A. Teske. Marian Smoluchowski—zycie, I twórczość (“Marian Smoluchowski—Life and Work” Warsaw, 1955).

Other sources are A. Einstein. “Marian von Smoluchowski,” in Naturwissenschaften. 5 (1917), 737–738; A. Sommerfeld. “Zum Andenken an Marian von Smoulchowski,” in PhysikalischeZeitschrift. 18 (1917) 533–539. with bibliography; A. Teske, “An Outline Account of the Work of Marian Smohichowski,” in Études consacrées à Maria Skłodouska-Curie et à Marian Smoluchowski (Wroclaw-Warsaw-Cracow. 1970): and S Ulam, “Marian Smoluchowski and the Theory of Probabilities in Physics,” in American Journal of Physics. 25 (1957), 475–481.

Andrzej A. Teske