## Zur Theorie des Gesetzes der Energieverteilung im Normalspectrum.

Leipzig: Johann Ambrosius Barth, 1900. First edition.

First edition of the first appearance of Planck’s revolutionary quantum theory, arguably the most important development in twentieth-century physics. “In this important paper [Planck] stated that energy flowed not in continuous, indefinitely divisible currents, but in pulses or bursts of action [or *quanta*]” (Dibner). This hypothesis “contradicted the mechanics of Newton and the electromagnetics of Faraday and Maxwell. Moreover it challenged the notion of the continuity of nature” (*PMM*). In this paper Planck uses his eponymous constant *h*, the quantum of action, to explain the observed distribution of energy as a function of frequency in the radiation emitted by a black body. Although Planck’s new theory was initially resisted by many in the scientific community, it gained acceptance after Einstein used the constant *h* to explain the photoelectric effect in 1905, and after Niels Bohr applied it in 1913 to explain the spectrum of the hydrogen atom. The importance of quantum theory is impossible to overstate: it not only revolutionized theoretical physics, but also technology and hence everyday life: modern inventions based on quantum theory include the laser, the transistor, the electron microscope, and magnetic resonance imaging – the entire electronics industry is based on it.

“In 1859–60 [Gustav] Kirchhoff had defined a blackbody as an object that reemits all of the radiant energy incident upon it; i.e., it is a perfect emitter and absorber of radiation. There was, therefore, something absolute about blackbody radiation, and by the 1890s various experimental and theoretical attempts had been made to determine its spectral energy distribution—the curve displaying how much radiant energy is emitted at different frequencies for a given temperature of the blackbody. Planck was particularly attracted to the formula found in 1896 by his colleague Wilhelm Wien at the Physikalisch-Technische Reichsanstalt (PTR) in Berlin-Charlottenburg, and he subsequently made a series of attempts to derive “Wien’s law” on the basis of the second law of thermodynamics. By October 1900, however, other colleagues at the PTR, the experimentalists Otto Richard Lummer, Ernst Pringsheim, Heinrich Rubens, and Ferdinand Kurlbaum, had found definite indications that Wien’s law, while valid at high frequencies, broke down completely at low frequencies.

“Planck learned of these results just before a meeting of the German Physical Society on October 19 [1900]. He knew how the entropy of the radiation had to depend mathematically upon its energy in the high-frequency region if Wien’s law held there. He also saw what this dependence had to be in the low-frequency region in order to reproduce the experimental results there. Planck guessed, therefore, that he should try to combine these two expressions in the simplest way possible, and to transform the result into a formula relating the energy of the radiation to its frequency.

“The result, which is known as Planck’s radiation law, was hailed as indisputably correct. To Planck, however, it was simply a guess, a “lucky intuition.” If it was to be taken seriously, it had to be derived somehow from first principles. That was the task to which Planck immediately directed his energies, and by December 14, 1900, he had succeeded—but at great cost. To achieve his goal, Planck found that he had to relinquish one of his own most cherished beliefs, that the second law of thermodynamics was an absolute law of nature. Instead he had to embrace Ludwig Boltzmann’s interpretation, that the second law was a statistical law. In addition, Planck had to assume that the oscillators comprising the blackbody and re-emitting the radiant energy incident upon them could not absorb this energy continuously but only in discrete amounts, in *quanta* of energy; only by statistically distributing these quanta, each containing an amount of energy *hν* proportional to its frequency *ν*, over all of the oscillators present in the blackbody, could Planck derive the formula he had hit upon two months earlier. He adduced additional evidence for the importance of his formula by using it to evaluate the constant *h* (his value was 6.55 × 10^{−27} erg-second, close to the modern value of 6.626 × 10^{−27} erg-second), as well as the so-called Boltzmann constant (the fundamental constant in kinetic theory and statistical mechanics), Avogadro’s number, and the charge of the electron. As time went on physicists recognized ever more clearly that—because Planck’s constant was not zero but had a small but finite value—the microphysical world, the world of atomic dimensions, could not in principle be described by ordinary classical mechanics. A profound revolution in physical theory was in the making.

“Planck’s concept of energy quanta, in other words, conflicted fundamentally with all past physical theory. He was driven to introduce it strictly by the force of his logic; he was, as one historian put it, a reluctant revolutionary. Indeed, it was years before the far-reaching consequences of Planck’s achievement were generally recognized, and in this Einstein played a central role. In 1905, independently of Planck’s work, Einstein argued that under certain circumstances radiant energy itself seemed to consist of quanta (light quanta, later called photons), and in 1907 he showed the generality of the quantum hypothesis by using it to interpret the temperature dependence of the specific heats of solids. In 1909 Einstein introduced the wave–particle duality into physics. In October 1911 Planck and Einstein were among the group of prominent physicists who attended the first Solvay conference in Brussels. The discussions there stimulated Henri Poincaré to provide a mathematical proof that Planck’s radiation law necessarily required the introduction of quanta—a proof that converted James Jeans and others into supporters of the quantum theory. In 1913 Niels Bohr also contributed greatly to its establishment through his quantum theory of the hydrogen atom. Ironically, Planck himself was one of the last to struggle for a return to classical theory, a stance he later regarded not with regret but as a means by which he had thoroughly convinced himself of the necessity of the quantum theory. Opposition to Einstein’s radical light quantum hypothesis of 1905 persisted until after the discovery of the Compton effect in 1922.

“Planck was 42 years old in 1900 when he made the famous discovery that in 1918 won him the Nobel Prize for Physics and that brought him many other honours. It is not surprising that he subsequently made no discoveries of comparable importance. Nevertheless, he continued to contribute at a high level to various branches of optics, thermodynamics and statistical mechanics, physical chemistry, and other fields. He was also the first prominent physicist to champion Einstein’s special theory of relativity (1905)” (Britannica).

“Planck had the physical interpretation of his radiation law in hand before the middle of November 1900, but he presented his results first at the meeting of the German Physical Society in Berlin on 14 December 1900 in a contribution entitled ‘Zur Theorie des Gesetzes der Energieverteilung im Normalspectrum’ (‘On the Theory of the Law of Energy Distribution in Normal Spectrum’). In this contribution he outlined in short ‘the most essential point of the whole theory as clearly as possible’ (p. 238) … In his *Atombau und Spektrallinien *(1919)*, *Arnold Sommerfeld called 14 December 1900 the ‘birthday of quantum theory’ (‘*Geburtstag der Quantentheorie’*, p. 213). He referred in particular to the fact which Planck had considered to be the 'most essential point' of his derivation of the blackbody radiation law: namely, the assumption that the energy is distributed among the cavity resonators only in integral multiples of finite energy elements … Planck himself continued with his attempts to deepen the theoretical foundations and to elucidate the physical interpretation of his theory of blackbody radiation. In a paper, which he submitted to *Annalen der Physik *in January 1901 [‘Über das Gesetz der Energieverteilung im Normalspectrum,’ 4 Folge, 4 Band, pp. 553-563], Planck again presented the theoretical derivation of his radiation formula, introducing certain changes in his earlier treatment” (Mehra & Rechenberg, pp. 50-53).

Dibner *Heralds of Science* 166; Evans 47; Grolier/Horblit 26a; Norman 1713; *PMM* 391a; Sparrow 162.

Hermann, *The Genesis of Quantum Theory* (*1899-1913*), 1971. Mehra & Rechenberg, *The Historical Development of Quantum Theory*, Vol. 1, 1982. The most detailed account of the development of quantum theory remains Kuhn’s classic *Black-Body Theory and the Quantum Discontinuity*, *1894-1912*.

In: Verhandlungen der Deutschen Physikalischen Gesselschaft im Jahre 1900, Zeiter Jahrgang, pp. 237-245. The entire volume offered here in a fine contemporary half calf binding over marbled boards with no repairs and no library markings at all. 4to (223 x 150 mm), pp vi 260. Fresh and clean throughout.

Item #4317

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