Like Thermodynamics before Boltzmann. On the Emergence of Einstein’s Distinction between Constructive and Principle Theories Marco Giovanelli Forum Scientiarum — Universität Tübingen, Doblerstrasse 33 72074 Tübingen, Germany [email protected] How must the laws of nature be constructed in order to rule out the possibility of bringing about perpetual motion? Einstein to Solovine, undated In a 1919 article for the Times of London, Einstein declared the relativity theory to be a ‘principle theory,’ like thermodynamics, rather than a ‘constructive theory,’ like the kinetic theory of gases. The present paper attempts to trace back the prehistory of this famous distinction through a systematic overview of Einstein’s repeated use of the relativity theory/thermodynamics analysis after 1905. Einstein initially used the comparison to address a specic objection. In his 1905 relativity paper he had determined the velocity-dependence of the electron’s mass by adapting Newton’s particle dynamics to the relativity principle. However, according to many, this result was not admissible without making some assumption about the structure of the electron. Einstein replied that the relativity theory is similar to thermodynamics. Unlike the usual physical theories, it does not directly try to construct models of specic physical systems; it provides empirically motivated and mathematically formulated criteria for the acceptability of such theories. New theories can be obtained by modifying existing theories valid in limiting case so that they comply with such criteria. Einstein progressively transformed this line of the defense into a positive heuristics. Instead of directly searching for new theories, it is often more eective to search for conditions which constraint the number of possible theories. The paper argues that the latter was the strategy that led Einstein to most of his major successes. The constructive/principle theories opposition should be considered not only as abstract classication of theories, but also as Einstein’s attempt to formulate a sort of ‘logic of discovery.’ The paper argues that most of Einstein’s scientic successes were obtained by following the principle strategy. Most of his failures happened when he was forced to fall back to the constructive strategy. Keywords: Albert Einstein • Constructive theories • Principle theories • Relativity theory • Electron theories • Scientic discovery Introduction Toward the end of 1919, in a two-column contribution for the Times of London, Einstein (1919d) famously declared relativity theory to be a ‘principle theory,’ like thermodynamics, rather than a ‘constructive theory,’ like the kinetic theory of gases. Over the last decade, this distinction has attracted considerable attention in both the historically and the theoretically-oriented scholarship in the philosophy of physics. On occasion of the centenary of the publication of this brief but iconic article, it might be a good opportunity to try to reconstruct its history and assess its philosophical meaning. As it turns out, its popularity in today scholarship has somewhat hindered the appreciation of its core message. Contemporary philosophers of physics have often believed to have found in Einstein’s sparingly phrased remarks support for their philosophical agenda. However, Einstein’s concerns by writing the article bore probably only a mild relation to those of the participants in today philosophical debate. This paper will argue that the diculties of understanding the constructive/ principle theories opposition is a consequence of its ambiguity. Einstein’s article was, so to speak, at the same time the outline of (a) an ars iudicandi that supply criteria for justication of existing theories; (b) an ars inveniendi, a set of techniques for the discovery of new theories starting from the known ones. The reason of this ambiguity must be probably sought in the motivations with which the 1919 London Times was written. As this paper will try to show, the article should be read not as much as an abstract philosophical reection, but as a personal testimony of a practicing physicist. As Einstein once wrote jokingly to his friend Paul Ehrenfest, he was, with few others, a principle-pincher 1 1 (Prinzipienfuchser), ready to squeeze as much as possible from few fundamental principles, rather than a proigate virtuoso, squandering his calculation mastery in triing puzzle solving (Einstein to Ehrenfest, Sep. 18, 1925; CPAE, Vol. 15, Doc. 71; see Seth, 2010, ch. 6). It was a paper by Francisco Flores, 1999 that, more than two decades ago, attracted new attention toward Einstein’s distinction between constructive/principle theories by recasting in it into the opposition between two forms of explanations, bottom-up and top-down explanations (see also Dieks, 2009; Dorato, 2011; Felline, 2011). Soon thereafter, Jerey Bub (2000) suggested that quantum mechanics, just like special relativity, could be regarded as a ‘theory of principles.’ If the latter was a modication of Newton-Galilei kinematics that satised the light and relativity postulates, matrix mechanics was a modication of classical kinematics that complied with the quantum postulate and the correspondence principle. Quantum mechanics could be then seen as a set of information-theoretic constraints on possible dynamical theories (Clifton, Bub, and Halvorson, 2003). This proposal remained marginal in the literature about the foundation of quantum mechanics. However, at about the same time, Einstein’s distinction between principle and constructive theories became the center of a vaster and still living philosophical debate on the foundation of spacetime theories. When Einstein compared the relativity principle to the second principle of thermodynamics, it was argued, he meant to complain about its lack of explanatory power of special relativity. Einstein ultimately aimed to nd a deeper-level theory that ‘explains’ the relativistic kinematics, just like Ludwig Boltzmann had relied on the kinetic theory to ‘explain’ the increase of entropy. Thus, Harvey Brown and Oliver Pooley (2006) famously suggested that special relativity should ultimately take the form of a constructive theory about the material structure of rods and clocks, not dierently from Hendrik A. Lorentz’s ether theory. Michel Janssen and Yuri Balashov (2003) reacted by claiming that special relativity had actually already found its ‘Boltzmann’; Hermann Minkowski had already transformed it into a constitutive theory, a theory about the geometrical structure of spacetime; it is the latter that explains why rods and clocks behave like they do (Stevens, 2014). The claim that in Einstein’s view ‘principle theories’ lack explanatory power has been challenged by Marc Lange (2014). Partly stimulated by this debate, historically oriented scholarship has attempted to clarify Einstein’s princi- ple/constructive theories opposition (Howard, 2005) by showing how it was deeply rooted in the 19th-century physics’ emphasis on the role of general principles (Howard, 2007; see also Stachel, 2000), an epistemological position well-exemplied by the work of Hermann von Helmholtz (Bevilacqua, 1993). Indeed, the German-speaking physics community appears at rst sight as being traversed by the fault line between a principle-based, phe- nomenological approach defended by Gustav Kirchho or Max Planck and a model-based approach of British ascendancy pursued, for example, by Boltzmann (Darrigol, 2018). Nevertheless, Planck agreed with Boltzmann in rejecting the anti-atomism of Ernst Mach and of the energetists, like Wilhelm Ostwald and Georg Helm (Deltete, 1999; Deltete, 2012). However, Planck sided with Pierre Duhem (Bordoni, 2017) against Boltzmann in indicating thermodynamics and not mechanics as model for scientic practice (Wol, 2010). The dierences between the two fractions were ultimately far from being clear-cut. Nevertheless, at the turn of the century, Lorentz (Frisch, 2005, 2011, see also) and Henri Poincaré (Darrigol, 1995b), the other major protagonists of the relativity revolution, could present the opposition between the ‘physics of principles’ and the ‘physics of models’ as commonplace. In a similar vein, in the early 20th-century, Arnold Sommerfeld opposed a ‘physics of problems,’ a style of doing physics based on concrete puzzle solving, to the ‘practice of principles’ defended by Planck (Seth, 2010). As early as 1909, Philip Frank (1909), relying on a distinction introduced by Abel Rey (1908), had already explicitly classied relativity as a ‘conceptual theory’ like thermodynamics, rather than a ‘mechanical theory’ like the kinetic theory of gases. In 1910, Philip Lenard (1911) made a similar remark but using the less common opposition between two types of models, phenomenological models (relations between measurable quantities) and proper models (aether, electrons, etc.). Thus, following the philosophical debate, one might be lead to the conclusion that Einstein’s 1919 distinction between principle and constructive theories represents Einstein’s fundamental insight into the nature of spacetime. On the contrary, by reading the historical literature, one might get the opposite impression that Einstein’s distinction was a rather unoriginal variation on a threadbare 19th-century theme, with which, by 1919, every working physicist was familiar (see, e.g., Sommerfeld, 1915). Both stances grasp indeed part of the truth but also miss what, in my view, is the fundamental point. As a matter of fact, in spite of the recent spike