Helmholtz and Kant: The metaphysical foundations of über die erhaltung der kraft

String theorists are certain that they are practicing physicists. Yet, some of their recent critics deny this. This paper argues that this conflict is really about who holds authority in making rational judgment in theoretical physics. At bottom, the conflict centers on the question: who is a proper physicist? To illustrate and understand the differing opinions about proper practice and identity, we discuss different appreciations of epistemic virtues and explanation among string theorists and their critics, and how these have been sourced in accounts of Einstein's biography. Just as Einstein is claimed by both sides, historiography offers examples of both successful and unsuccessful non-empirical science. History of science also teaches that times of conflict are often times of innovation, in which novel scholarly identities may come into being. At the same time, since the contributions of Thomas Kuhn historians have developed a critical attitude towards formal attempts and methodological recipes for epistemic demarcation and justification of scientific practice. These are now, however, being considered in the debate on non-empirical physics.

Recent work on the history of General Relativity by Renn et al. shows that Einstein found his field equations partly by a physical strategy including the Newtonian limit, the electromagnetic analogy, and energy conservation. Such themes are similar to those later used by particle physicists. How do Einstein׳s physical strategy and the particle physics derivations compare? What energy–momentum complex(es) did he use and why? Did Einstein tie conservation to symmetries, and if so, to which? How did his work relate to emerging knowledge (1911–1914) of the canonical energy–momentum tensor and its translation-induced conservation? After initially using energy–momentum tensors hand-crafted from the gravitational field equations, Einstein used an identity from his assumed linear coordinate covariance $x^{{\mu }^{\prime }}=M_{\nu }^{\mu }{x}^{\nu }$ to relate it to the canonical tensor. Usually he avoided using matter Euler–Lagrange equations and so was not well positioned to use or reinvent the Herglotz–Mie–Born understanding that the canonical tensor was conserved due to translation symmetries, a result with roots in Lagrange, Hamilton and Jacobi. Whereas Mie and Born were concerned about the canonical tensor׳s asymmetry, Einstein did not need to worry because his Entwurf Lagrangian is modeled not so much on Maxwell׳s theory (which avoids negative-energies but gets an asymmetric canonical tensor as a result) as on a scalar theory (the Newtonian limit). Einstein׳s theory thus has a symmetric canonical energy–momentum tensor. But as a result, it also has 3 negative-energy field degrees of freedom (later called “ghosts” in particle physics). Thus the Entwurf theory fails a 1920s–1930s a priori particle physics stability test with antecedents in Lagrange׳s and Dirichlet׳s stability work; one might anticipate possible gravitational instability.

This critique of the Entwurf theory can be compared with Einstein׳s 1915 critique of his Entwurf theory for not admitting rotating coordinates and not getting Mercury׳s perihelion right. One can live with absolute rotation but cannot live with instability.

Particle physics also can be useful in the historiography of gravity and space–time, both in assessing the growth of objective knowledge and in suggesting novel lines of inquiry to see whether and how Einstein faced the substantially mathematical issues later encountered in particle physics. This topic can be a useful case study in the history of science on recently reconsidered questions of presentism, whiggism and the like. Future work will show how the history of General Relativity, especially Noether׳s work, sheds light on particle physics.

Discussions on the relation between Mach and Planck usually focus on their famous controversy, a conflict between ‘instrumentalist’ and realist philosophies of science that revolved around the specific issue of the existence of atoms. This article approaches their relation from a different perspective, comparing their analyses of energy and energy conservation. It is argued that this reveals a number of striking similarities and differences. Both Mach and Planck agreed that the law was valid, and they sought to purge energy of its anthropomorphic elements. They did so in radically different ways, however, illustrating the differences between Mach's ‘historical’ and Planck's ‘rationalistic’ accounts of knowledge. Planck's attempt to de-anthropomorphize energy was part of his attempt to demarcate theoretical physics from other disciplines. Mach's attempt to de-anthropomorphize energy is placed in the context of fin-de-siècle Vienna. By doing so, this article also proposes a new interpretation of Mach as a philosopher, historian and sociologist of science.

Sigmund Freud’s concept of transference (Übertragung) was not the discovery of a solitary genius but was an inspired, creative synthesis deeply rooted in prevailing discourses. The author presents three nineteenth-century historical contexts that helped shape early transference theory: neurologic usages of bertragung, notions of hysterical suggestibility and autosuggestion, and perceptual theories of visual illusion.

It has become customary to locate the origins of modern measurement theory in the works of Helmholtz (1887) and Hölder (1901). If by ‘modern measurement theory’ is meant the representational theory, then this may not be an accurate assessment. Both Helmholtz and Hölder present theories of measurement which are closely related to the classical conception of measurement. Indeed, Hölder can be interpreted as bringing this conception to fulfilment in a synthesis of Euclid, Newton, and Dedekind. The first explicitly representational theory appears to have been Russell's. He rejected the traditional concept of quantity and its connection to number, making the use of number in quantitative science problematical. He solved the problem via representationalism.