From X-rays to the h-hypothesis: Sommerfeld and the early quantum theory 1909–1913

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Sommerfeld was deeply interested in the nature of X-rays. In 1900 he concluded from diffraction experiments on slits that, if X-rays are electromagnetic radiation, their “impulse width” should be of the order of magnitude of the size of molecules. In 1905 Sommerfeld regarded it “a shame that after ten years after Rontgen’s discovery one still does not know what is going on with X-rays”. When he became Rontgen’s colleague a year later, he perceived this shame even more as a challenge. By that time it was discovered that X-rays come in two varieties. One sort of X-rays was independent of the anti-cathode material and could be explained by Sommerfeld in 1909 as “Bremsstrahlung”, i.e. as an electromagnetic radiation caused by the deceleration of electrons at their impact in the anti-cathode. The other part had the character of a fluorescent radiation. The “Bremsstrahlung” was polarized and displayed an angular distribution of intensity with a characteristic shape dependent on the energy of the electrons at the impact in the anti-cathode; the other part was unpolarized and characteristic for the material of the anti-cathode. Sommerfeld’s “Bremsstrahlen”-theory could not be elaborated without further assumptions about the impact of electrons in the anti-cathode. Sommerfeld closed his theory by a quantum hypothesis: He linked the time required to stop an electron, t, and the energy released in this process, E, to Planck’s quantum of action, h, via tE = h. This so-called h-hypothesis became the subject of Sommerfeld’s presentation at the first Solvay Conference. Although met with criticism, the quantum effort at Munich raised curiosity. Sommerfeld attempted to verify this hypothesis theoretically and experimentally in his institute with Walther Friedrich, his experimental assistant. Friedrich, a doctoral student from Rontgen’s institute, was persuaded however by Max Laue, then Sommerfeld’s Privatdozent, to perform another experiment which led to the discovery of X-ray diffraction in crystals. Their sensational result, obtained in spring 1912, was among the subjects for the second Solvay Conference in 1913. Sommerfeld regarded this experiment the most important achievement of his institute – and silently buried the h-hypothesis which turned out to be one of the dead-ends of the early quantum theory.