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Arnold Sommerfeld and the Older Quantum Theory, 1915-1925

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Arnold Sommerfeld and the Older Quantum Theory, 1915-1925 Modeling and Reality in Early Ludwig Boltzmann, “On the Methods of Twentieth-Century Physics 1. Background: The Theoretical Physics,” (1892) “Intellectual Landscape” for Modeling as Method Compare the almost ethereally structured and crystal clear though colourless theory of elasticity in 2. Change Over Kirchhoff's lectures with the crudely realistic account Suman Seth in Vol. 3 of Thomson's Mathematical and Physical Department of Science and Technology Studies Time: Arnold Sommerfeld Papers which concerns not ideally elastic bodies but Cornell University steel, rubber, glue; or with the often childlike naiveté of Maxwell's language, who in the midst of formulae 3. Teasers: Payoffs American Physical Society Annual Meeting, 2011 mentions a really effective method for removing fat for looking at stains. Sommerfeld. Ernst Mach, “The Economical Nature of Physical Inquiry,” (1882) Max Planck on Models Arnold Sommerfeld When a geometer wishes to understand the form of a curve, he (1868-1951) first resolves it into small rectilinear elements. In doing this, however, he is fully aware that these elements are only [1887] “I have the intention to [1943] “What interested me provisional and arbitrary devices for comprehending in parts what extend a little further in most in physics were the great he cannot comprehend as a whole. When the law of the curve is several successive treatments general laws that possess found he no longer thinks of the elements. Similarly, it would not the series of conclusions that meaning for all natural become physical science to see in its self- created, changeable, can be drawn from the processes, independent of the economical tools, molecules and atoms, realities behind Carnot-Clausius principle in characteristics of the bodies phenomena…The atom must remain a tool for representing and of itself, i.e. without that took part in the reference to certain processes.... Hence the two phenomena, like the functions of mathematics. Gradually, conceptions of the essence of laws of thermodynamics however, as the intellect, by contact with its subject-matter, molecular motions, merely captivated me to a particular grows in discipline, physical science will give up its mosaic play taking as a basis the principle degree.” with stones and will seek out the boundaries and forms of the bed of the conservation of in which the living stream of phenomena flows. The goal which it energy.” has set itself is the simplest and most economical abstract expression of facts. Arnold Sommerfeld, “Theoretisches über die Beugung der Röntgenstrahlen,” Zeitschrift für Mathematik und Pauli: Scylla and Charybdis Physik 46 (1901). Wolfgang Pauli (1900-1958), Nobel (Letter to Kramers, July 1925) Lecture, 1945. Two paths to the Exclusion Principle “I feel at the moment a … the most fruitful path for theoretical physics appears little less lonely as around to be this: to lay down as specific and determinate half a year ago, when I [specielle und bestimmte] hypotheses as possible, to At that time there were two approaches to the difficult problems connected with the quantum of action. One was an effort to bring found myself (spiritually as develop their consequences exactly, and to compare abstract order to the new ideas by looking for a key to translate classical well as spatially) pretty these with experiment: if this shows no contradiction mechanics and electrodynamics into quantum language which would form much alone between the with experience, good, then our hypotheses were valid a logical generalization of these. This was the direction which was taken by Bohr's Correspondence Principle. Sommerfeld, however, preferred, in Scylla of the number and may be retained until later; if, however, an view of the difficulties which blocked the use of the concepts of mysticism of the Munich opposition emerges, then all the better; then our kinematical models, a direct interpretation, as independent of models as school and the Charybdis of hypothesis is displayed as invalid and we have gained a possible, of the laws of spectra in terms of integral numbers, following, as Kepler once did in his investigation of the planetary system, an inner the reactionary Copenhagen definitive, if also negative, finding. feeling for harmony. Both methods, which did not appear to me putsch propagated by you irreconcilable, influenced me. with the excesses of a zealot!” The Solvay Congress, 1911 Sommerfeld’s Ellipsenverein (1918) A Number Mystery Runge’s Rule: Let a be the Lorentz separation Δν=q/r * a For my feeling, the artful interlocking of the Sommerfeld’s use of the combination principle electronic paths in our q/r = q /r –q /r = (q r –qr )/r r ‘Ellipsenverein’ is nothing 1 1 2 2 1 2 2 1 1 2 unnatural; I see much Re-Write: more a sign therein for r = r r the high harmony of 1 2 motion that must rule Take home: The “Runge Denominator” is made up of terms within the atom. from the initial and final levels of an electron’s “jump.” 12 For the main series (H. S.) and the second subsidiary series (II. N. S.), Sommerfeld, Innsbruck Lecture, transitions are between s and p Modellmässigkeiten vs orbitals. Gesetzmässigkeiten (Sommerfeld, 1919) September 1924 For doublets in these, r = 3, for triplets, r = 2. …I would like to say a few words about the soundness of our …at the moment we are at a loss with the Modellvorstellungen [conceptions of models]. The difficulties For the first Subsidiary series (I. N. S.) modellmässigen (model-based) meaning of that obtrude ever more clearly into atomic physics appear to me to lie less in an immoderate application of the quantum transitions are between d and p the line-multiplicities of the non-hydrogenic orbitals. theory and much more in a perhaps immoderate belief in the For doublets, r = 15 elements, in spite of repeated efforts from reality of our Modellvorstellungen. Certainly the Hydrogen For triplets, r =6. model functions correctly in all cases (except perhaps in various sides. All the more valuable are all strong magnetic fields) and certainly Bohr’s explanation of the lawful aspects [Gesetzmässigkeiten] that the chemical systematics of the periodic system is sound in present themselves empirically for the line- general terms. But the phenomena are much simpler than one would expect according to the model... The atomic multiplicities, above all when they are of model would then be more of a calculational scheme such a radical and simple kind as those here [Rechenschema] than a state of reality [Zustandsrealität]. at hand. 7/15/2008 15 From Modellmässigkeiten to Pauli to Sommerfeld Oskar Klein (1894-1977) Gesetzmässigkeiten: 1919-1922. 6 December, 1924 on Sommerfeld’s Style I found it particularly beautiful in the presentation of the During Sommerfeld’s lecture I was sitting at }Wolfgang Pauli: In Munich from 1918 to complex structure that you have left all modellmässig the side of Bohr. Sommerfeld had a few July, 1921. considerations to one side. The model-idea now finds itself in a difficult, fundamental [prinzipiellen] crisis, which I believe will numbers for these anomalous levels. The end with a further radical sharpening of the opposition first was so and the second was so—they between classical and quantum theory. One now has the }Werner Heisenberg: In Munich from the Fall impression with all models, that we speak there a language were something like 1, 3, and so. And then of 1920 to mid-1922. that is not sufficiently adequate for the simplicity and beauty of Sommerfeld said the next must be 5, or the quantum world. For that reason I found it so beautiful that something like that. Then Bohr smiled and your presentation of the complex structure is completely free of all model-prejudices. said to me, “I don’t believe that. 7/15/2008 17 Payoff 1: Pauli Payoff II: Heisenberg: The roots Origins of the Exclusion Principle of the Observability Criterion Payoff 3: Re-thinking the “Crisis” in Quantum Mechanics 1. Timing of the Older Quantum Theory 2. Pauli’s own claims. Route 1: Relativity: “To my astonishment, Einstein…thought NOT, When was the crisis, what was its cause etc. 3. Style: Pauli’s paper is phenomenological. that every theory in fact contains unobservable quantities. 4. The path: And when I objected that in this I had merely been applying a. Pauli’s debts to Stoner, via Sommerfeld. the type of philosophy that he, too, had made the basis of BUT rather: What do you have to think in order for his special theory of relativity, he answered, simply: b. Sommerfeld on Stoner: Stoner’s scheme “possesses more of an there to be a crisis in quantum theory in 1923/24? arithmetical than a geometric-mechanical character, makes no ‘Perhaps I did use such philosophy earlier, and also wrote it, assumptions about the symmetry of orbital arrangements and uses but it is nonsense all the same.’ not only a part, but the entirety of Röntgen-spectroscopic facts.” Encounters and Observations with Albert Einstein (1974) OR EVEN BETTER: How do you have to work in order 5. The meaning: Zweideutigkeit: “The doublet structure of the alkali spectrum, as well as the violation of Larmor’s theorem comes for there to be a crisis in quantum theory in about through a peculiar, classically non-describable kind of Route 2: Sommerfeld’s phenomenology in quantum theory. 1923/24? Zweideutigkeit of the quantum-theoretical characteristics of the light-electron.” 20 Woldemar Voigt’s (1850-1919) Heisenberg’s first paper: Pauli on Zweideutigkeit, ‘Coupling Theory,’ as re-worked by “The Quantum Theory of Line Structure and the Sommerfeld Anomalous Zeeman effect.” (1922) 1923 Voigt’s theory provides “the } “…each momentum will act not adequate expression of the facts through a single number, but through a pair of numbers.
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