Craving for Crisis

The third ideological adaptation to the milieu concerned the ‘craving for crisis’. “By applying the word ‘crisis’ to his own discipline the scientist has not only made contact with his audience, but has ipso facto shown that his field – and he himself – is ‘with it’, sharing the spirit of the time.” (Forman, 1971, p. 58f.) Once again, we encounter Hermann Weyl in first line. The crisis in the foundations of mathematics proclaimed by him “was precipitated virtually out of thin air in the two or three years following

17 Recall the end of the Zarathustra! Schiemann (1996, p. 358) reads von Mises’s creative impulse at dusk as somewhat ironical.

Germany’s defeat. With extraordinary suddenness the German mathematical community began to feel how insecure the foundations upon which the entire structure of mathematical analysis rested.” (Ibid., p. 60) Unfortunately, the crisis was stirred up by the Dutchman Luitzen E.J. Brouwer. The Vienna Circle, on the other hand, took the crisis more seriously than most working mathematicians. Thus, in the case of the foundational crisis in mathematics Forman faces the paradox to classify the modernist fringe movement Vienna Circle as converts to the milieu. Let me turn to three other crises.

Once again, Forman calls von Mises to the witness stand; this time he testifies

“On the Present Crisis of Mechanics” (Mises, 1922a). As we shall see in Section 8.2., Mises advocated the application of statistical methods because, e.g., in fluid dynamics the reduction to an allegedly deterministic micro-level could not produce any applicable result at all. However, the crisis of mechanics as a reductionist program already dates back to the failures to incorporate electrodynamics that had led to the special theory of relativity in 1905. Finally, the “possibility of the crisis of the old quantum theory was, I think, dependent upon the physicists’ own craving for crises, arising from participation in, and adaptation to, the Weimar intellectual milieu.”

(Forman, 1971, p. 62) But, to my mind, there were clear physical indications of a failure of the Bohr-Sommerfeld theory.¹⁸ There were internal inconsistencies, problems with the interaction between electrons, and in 1922 and 1923 the theory produced empirically wrong results about the Helium atom. When in July 1923 Die Naturwissenschaften published a special issue dedicated to “The first ten years of Niels Bohr’s theory of the constitution of atoms”, Planck’s keynote paper mentioned the helium atom and many electron problems in general as a prominent example for the need of a “deep intervention into the system of ideas of the classical theory.”

(Planck, 1923b, p. 536) Moreover, “[a]t present an, at least to some extent, satisfactory solution of the problems raised by the introduction of quantum mechanics into atomistic is out of the question by far. Not even the question about the domain of validity of the classical theory can today be finally decided.” (Ibid., p. 536) Nevertheless, Planck warned against a global indeterminism.

There are eminent physicists who at bottom want to allow the principles of the classical theory only a statistical significance … Such a conception seems to me, however, to overshoot the mark by far, if only because with the abandonment of classical dynamics they simultaneously pull out the foundations of every rational statistics. (Ibid., p. 536)

According to Forman, those meant by Planck’s criticism were “Exner, Nernst, Schrödinger, and, yes, Bohr, himself.” (Forman, 1971, p. 93) But Exner had to stand the same criticism already a decade before. The fact that Planck basically repeated his earlier criticism (Cf. Planck, 1914, p. 63-64; see Section 4.5.) makes this passage practically worthless for Forman’s adaptation thesis. Towards the end of the paper, Planck, interestingly, was less rigid about the validity of the principle of energy conservation, which would be indeed abandoned in the following year by the Bohr-Kramers-Slater (BKS) theory. Thus we see that, in Planck’s case, the diagnosis of crisis did not entail abrogating deterministic causality.

More generally, I doubt that more than a few of the protagonists had taken the old theory that was based on the correspondence principle and a calculatory machinery, as anything close to the final word. Of course, one can grant Forman that on the rhetorical level physicists adapted to the catchwords of the milieu. And they had not yet the slightest idea about the way out of the crisis. Sommerfeld’s much-debated “Zahlenmysterium” is a case in point. The table of spectral series for the anomalous Zeeman effect was so mysteriously regular that for every physicist it was clear that it indicated an important fundamental law still to be discovered and not just an unexplainable fact. Thus was the thrust of the two final paragraphs of Sommerfeld’s paper.

The musical beauty of our table of numbers is not impaired by the fact that for the time being it represents a number mystery. … In the case of the spectral series it has turned out that the arithmetic relations prevailing here have their reason in quantum theory. It is beyond doubt that our still mysterious table of numbers indicates the workings of hidden quantum numbers and quantum relations. (Sommerfeld, 1920, p. 64)

Sommerfeld was fully right: the theories of Schrödinger and Heisenberg introduced the new magnetic quantum number m and modified the algebraic relations for the orbital momentum l in such a way that the anomalous Zeeman effect became the standard case while the normal Zeeman effect represented a degeneracy of the quantum numbers. Thus John Hendry is fully right to consider the heading of the article as a “linguistic accommodation to the milieu” (1980, p. 159) – perhaps for the sake of popularization. To the German translation of Hendry’s paper, Karl von Meyenn (1994, p. 209) adds that the term “Zahlenmystik” had been used in the same context as early as in 1917 by the Polish physicist A. Rubinowicz who was working with Sommerfeld in Munich. At bottom, Sommerfeld was quite convinced that one had already isolated the empirical evidence to be condensed in a law. To be sure, in later years he would at first skeptical about the radical epistemological changes required by his student Heisenberg.

The pronouncements of “crisis” by scientists investigated by the present study, and within the community represented by Die Naturwisssenschaften, typically combined the diagnosis of a foundational crisis with the conviction, or already the first indications, that it would be overcome by developing new foundations. This rhetorical figure can be found in at least two places appertaining to both sides of the aisle in the causality debate.

The first location is even mentioned in a footnote of Forman (1971, p. 59, fn.

135). In 1933, Karl Menger organized a much-frequented lecture series Krise und Neuaufbau in den exakten Wissenschaften (Crisis and Reconstruction in the Exact Sciences) the Preface of which declared: “The growing interest of ever wider circles for the exact sciences is surely above all a seeking after one of the regions which are far removed from the world of crisis. … In truth the exact sciences are by no means secure from crises and precisely in recent decades, from theoretical physics on out into logic, they have been shaken by severe crises.” (From Forman, 1971, p. 59, fn.)¹⁹ But this lecture series is no convincing evidence for Forman’s case. If there was a feeling of crisis in 1933 and among these lecturers invited by Menger, it was Hitler’s seizure of power. And taking Hahn’s contribution “The Crisis of Intuition” (1933) as a

19 See (Stadler, 2001, p. 420) for the further context of these lecture series.

paradigmatic example, the span of the crisis extended back to the rejection of intuition as a criterion of justifying mathematical axioms that had become the basis of modern mathematics as brought about by Weierstraß and Hilbert. Hahn rejected Kant’s pure intuition and its contemporary heirs because they hampered mathematical progress.

Die Naturwissenschaften published a review of these lectures by von Mises who concluded that they fortunately disappointed the skepticism aroused by the oft-misused word ‘crisis’ in the most pleasant way. “One would wish that each one of the assiduous poets of world views [Weltanschauungsdichter] take notice of the fact that also physics does not do anything else than what it did at each instance of its development, to wit, to adapt the intellectual images of theory to new observational results.” (Mises, 1933c, p. 867)

The same rhetorical figure is constantly present in the writings of Planck who is Forman’s upright fighter under the banner of causality. In an address to the 1910 Naturforscherversammlung entitled “The Position of Modern Physics With Respect to the Mechanical World View”, Planck initially surveyed the impressive achievements in experimental techniques. “Also the theoreticians have been imparted a large part of the boldness that has emerged among the practitioners, … no physical theorem at present is secure against being called into question, every physical truth is open to debate. It appears as if in theoretical physics chaos is drawing near.” (Planck, 1910, p.

25) After a sketch of the long-lasting dispute about the ideal of mechanical reductionism, Planck suggested a resolution through relativity theory. “What has led to this revolution and how the crisis [Krisis] caused by it will perhaps be overcome shall be outlined in the following.” (Ibid., p. 26) Twenty years later, his famous article

“Positivism and the Real World” also commenced with the motive of crisis.

We are living in a very singular moment of history. Wherever we turn our attention, in every branch of our spiritual and material culture, we have got into a moment of severe crises. … Some people view this as the beginning of a great improvement, others interpret it as the herald of the inevitable decline.

As has long been common in religion and in the arts, nowadays in science there is scarcely any axiom [Grundsatz] that is not denied by somebody, no nonsense that does not find believers and disciples somewhere or other. In the midst of this confusion it is natural to ask whether there is any truth left which is unassailable. … The moment this question is asked the mind turns, no doubt, to the most exact of our natural sciences, namely, physics. But even physical science has not been spared this universal crisis. Even on this field a certain insecurity has emerged and at places the opinions in epistemological matters differ considerably. Physics’ hitherto generally accepted axioms, in some places even causality itself, are thrown overboard. After all, that such could happen just in physics is sometimes counted as a symptom for the unreliability of all human knowledge. (Planck, 1930, p.

201)²⁰

Has Planck here belatedly adapted to the milieu? The body of the paper which reveals a Planck who still – though less certain than before – is breaking a lance for causality²¹. As ever he criticized the infertility of positivism and held with Kant that deterministic causality was fully reconcilable with the freedom of the will. While in 1910 relativity theory had ended the crisis, this time there was no physical remedy in

20 Unfortunately, the differences between the German original and the English translation (Planck, 1981, pp. 65-106) are substantial and entire passages are missing. As moreover the translator Murphy had his own views

sight. Planck retained his optimism and called upon the united forces of science and ethics.

I hope that even those of you who have little connection with physics have gained the impression that even a single science, if performed thoroughly and conscientiously, is able to unearth valuable treasures of aesthetical and ethical nature, and moreover, that precisely the deep crises in spiritual culture which we have initially mentioned as our starting point, at the end of the day only serve to prepare the federation into an new and higher union. (Ibid., p. 218)

Also Johannes Stark, who together with Philipp Lenard would become a leader of the Deutsche Physik under the nationalsocialist regime, contributed a booklet on The Present Crisis in German Physics (1922). To him, the crisis consisted in the ‘dogmatic nature’ of all modern physics, be it relativity or quantum theory. Stark found a resolute response in Die Naturwissenschaften penned by von Laue (1923). After rejecting Stark’s dislike of the bulk of modern physics and insisting that there exists no difference in value between pure and applied physics, von Laue concluded.

There is not doubt about the existence of a crisis in physics, and there is no doubt as well that it must be above all accredited to quantum theory. But the crisis is not limited to German science. It manifests itself in the same way in all countries participating in physical research, and it can be overcome only once science succeeds in solving the quantum riddle [Quantenrätsel]. There exists no other remedy. … All in all we wished that the book had remained unwritten, namely, in the interest of science in general, German science in particular, and not the least in the interest of the author. (Laue, 1923, p.

29f.)

As in Planck’s writings, Laue clearly posed the task to end the crisis by finding an appropriate quantum theory. It was Stark who felt an all-embracing sense of crisis, not the quantum physicists. For the quantum generation, Stark and Lenard were hardly a part of the milieu to seek rhetorical and ideological company with.