Dialogue at War Times: Exner Versus Planck

On August 3, 1914, Planck – then Rector of the University of Berlin – delivered the annual speech commemorating the founder of the University “On Dynamical and Statistical Regularities.” After an introduction alluding to the patriotic virtues indispensable in the war that had just begun, Planck rejected a distinction in principle between absolute and exceptionless lawfulness [Gesetzlichkeit or Gesetzmäßigkeit are used interchangeably] in the natural sciences and arbitrariness and chance in the intellectual realm. So far Planck’s thesis was in accord with what Exner had advocated in the Inaugural Address; but the lines of argument were starkly different, if not in direct opposition to one another. Exner had put the law of large numbers and the second law of thermodynamics on top. Planck countered as such:

On the one hand, for all human thinking, even on the highest heights of human intellect [Geist], the assumption of an absolute lawfulness superior to arbitrariness and chance represents an indispensable prerequisite; and, on the other hand, the most exact of all sciences, physics, is often compelled to operate with processes the lawful connection of which for the time being remains in the dark, and which, accordingly, can safely be called random in a properly understood sense of this word. (Planck, 1914, p. 55f.)

Planck emphasized that for practical investigations statistical methods are unavoidable and that statistical quantities already intrude into physics by the simple fact that each measurement contains errors. But this only teaches “the fundamental importance of performing an exact and fundamental separation between … the dynamical, strictly causal, and the merely statistical type of lawfulness for understanding the essence of all scientific knowledge.” (Ibid., p. 57) This distinction finds its expression in the sharp contrast between reversible processes, which are subsumed under one dynamical law: the Principle of Least Action, and irreversible processes governed by the second law of thermodynamics. While in the field of practical physics the causality violations implied by statistical laws do not justify any objection to them, the theorist must insist on the distinction between necessity and probability.

This dualism which has inevitably been carried into all physical regularities by introducing statistical considerations, to some may appear unsatisfactory, and one has already attempted to remove it – as it does not work out otherwise – by denying absolute certainty and impossibility at all and admitting only higher or lower degrees of probability. Accordingly, there would no longer be any dynamical laws in nature, but only statistical ones; the concept of absolute necessity would be abrogated in

physics at all. But such a view should very soon turn out to be a fatal and shortsighted mistake. (Ibid., p. 63)

Planck here precisely targeted the program Exner had launched in 1908. That his opponent’s name was not mentioned was characteristic for Planck’s style of scientific argument – except for his repeated personal attacks on Mach.

Exner well understood that the above passage was directed at him and responded to Planck point by point in his 94^th lecture, the last before the summary.

While he himself studied how probabilistic macroscopic laws emerge, so Exner related, Planck assumed a priori the existence of an absolute causality as a necessary precondition to understand both Nature and the intellectual realm. “But Nature does not ask whether man understands her or not, nor are we to construe a Nature adequate to our understanding, but only to reconcile ourselves as much as possible with the given one.” (Exner, 1922, p. 709) Mach could not have said it better. Exner also criticized Planck’s unjustified trust in our habits of thought, which made it likely “to fall into a sort of physical mythology” (Ibid., p. 709) by distinguishing a real world in which all natural processes are irreversible and an ideal world of frictionless motions, undamped oscillations, and the like. In empirical fact, one only encounters

“irreversible processes that can come, however, arbitrarily close to reversibility.”

(Ibid., p. 710) Between both idealizations there are many intermediate cases. “Whether a process is reversible or irreversible in fact only depends upon whether the recurrence of a certain state is practically observable.” (Ibid., p. 711)

The other crucial disagreement between Exner and Planck concerned probability theory. “It is claimed that in its applications probability calculus cannot dispense with the assumption of absolutely dynamical laws for the elementary processes” – here Exner almost literally quoted Planck (1914, p. 64) – “[however in actual fact] the assumption suffices that the elementary processes be equally characterized by average laws.” (Exner, 1922, p. 712) While Planck called for a dynamical explanation of statistical laws, Exner, on the contrary, asserted: “Nothing prevents us from regarding the so-called dynamical laws as the ideal limiting cases to which the real statistical laws converge for the highest degrees of probability.” (Ibid., p. 713) The only empirically justifiable requirement for the microscopic scenario is that in the limit it reproduces the macroscopically observed laws.

Planck’s rectorial address – in the same vein as the Leyden speech – emphasized instead that one could very well find an exact formulation of the second law that makes a precise assertion about single processes by amending it with the hypothesis of elementary disorder, that is, by claiming that each individual process does not deviate too strongly from the average of very many processes.

Experimentally there exist no other means than repeating the respective experiment many times in succession, or equivalently to have it reproduced by distinct observers working independently from one another. Such a repetition of a particular experiment, or performing a whole series of experiments, is in fact precisely that procedure which is generally applied in practical physics. No physicist will ever limit himself in his measurements to a single experiment, if just because of the unavoidable measurement errors. (Ibid., p. 65)

Planck’s reinterpretation of statistical laws by adding a condition about the relation between single experiments and their average result proves too much. It would even solve the notorious paradoxes of quantum mechanics because nobody doubts that this

theory accurately describes a long series of similar experiments. Moreover, pointing to experimental practices seems to be rather disingenuous for someone who advocates a categorical notion of causality. To be sure, Planck’s worries about quantum mechanics would be of a more basic kind because it became in principle impossible to posit a dynamical microlevel. Notice that after the 1914 speech he would no longer repeat the argument about elementary disorder in this form and stick to the aforementioned general argument about the necessary deterministic foundations of any probabilistic theory.

Planck also made clear that he intended to defend his reading of Boltzmann against Exner’s. Concerning the atomist hypothesis, Planck commended that

“Boltzmann apparently avoided to endanger the import of his views and calculations by charging forward too boldly; it was important to him to describe the atomistic hypothesis as a mere picture of reality. Today we are able to go beyond this.” (Planck, 1914, p. 60) This tamed Boltzmann neither reflected the universality of his atomism nor agreed with his partial adoption of Machian epistemology; for Boltzmann there was nothing beneath the atomistic pictures. At bottom, thus, Planck simply rehearsed the argument which he had already leveled against Mach: positivism can well provide an unassailable better-safe-than-sorry strategy but becomes infertile in the long run.

The final pages of Planck’s address returned to the humanities and intellectual life, using a piece of terminology which Exner would take up in the Lectures.

[In this realm,] strict causality becomes much less important than probability, the microcosm totally falls behind the macrocosm. But nevertheless, also here in all domains up to the highest problems of human will and morality, the assumption of absolute determinism is the indispensable foundation of all scientific enquiry. But this requires some caution …, that the process to be measured is not disturbed in its course by an investigation. (Ibid., p. 66)

And Planck introduced an argument that would remain, in increasingly detailed versions, his proof for the reconcilability of free will and absolute determinism. It is only possible to give a complete account of other personalities; if the thinking subject coincides with the object of investigation it constantly changes as knowledge of it proceeds.

In this way science sets itself its own insurmountable limit. But man in his incessant aspiration cannot content himself with this limit, he desires to and must transcend it because he needs an answer to the most important, constantly recurring questions of life: How shall I act? – And a complete answer to this question he cannot find in determinism, nor in causality, but only in his moral sentiments, his character, and his world view [Weltanschauung]. (Ibid., p. 66)

The difference to Exner is substantial because Planck posited a prereflective and spontaneous Ego that could be approached only by morality – the only field where Kantian reason can give laws to itself. For Mach the dualist Ego was unsalvable, while for Exner it was at least no fixed ground upon which to erect a Kantian-style ethics. To be sure, Exner rejected a mathematical description of our subjective sentiments. But he naturalized ethical feelings and religion; they emerged in the history of culture as did objective science itself.