By inserting the dialogue between Einstein, Schlick and Reichenbach in a wider network of debates about the epistemology of geometry, the paper shows, that not only Einstein and Logical Empiricists came to disagree about the role, principled or provisional, played by rods and clocks in General Relativity, but they actually, in their life-long interchange, never clearly identified the problem they were discussing. Einstein’s reflections on geometry can be understood only in the context of his “measuring rod objection” against Weyl. Logical (...) Empiricists, though carefully analyzing the Einstein-Weyl debate, tried on the contrary to interpret Einstein’s epistemology of geometry as a continuation of the Helmholtz-Poincaré debate by other means. The origin of the misunderstanding, it is argued, should be found in the failed appreciation of the difference between a “Helmhotzian” and a “Riemannian” tradition. The epistemological problems raised by General Relativity are extraneous to the first tradition and can only be understood in the context of the latter, whose philosophical significance, however, still needs to be fully explored. (shrink)

This paper attempts to explain the emergence of the logical empiricist philosophy of space and time as a collision of mathematical traditions. The historical development of the ``Riemannian'' and ``Helmholtzian'' traditions in 19th century mathematics is investigated. Whereas Helmholtz's insistence on rigid bodies in geometry was developed group theoretically by Lie and philosophically by Poincaré, Riemann's Habilitationsvotrag triggered Christoffel's and Lipschitz's work on quadratic differential forms, paving the way to Ricci's absolute differential calculus. The transition from special to general relativity (...) is briefly sketched as a process of escaping from the Helmholtzian tradition and entering the Riemannian one. Early logical empiricist conventionalism, it is argued, emerges as the failed attempt to interpret Einstein's reflections on rods and clocks in general relativity through the conceptual resources of the Helmholtzian tradition. Einstein's epistemology of geometry should, in spite of his rhetorical appeal to Helmholtz and Poincaré, be understood in the wake the Riemannian tradition and of its aftermath in the work of Levi-Civita, Weyl, Eddington, and others. (shrink)

The paper offers a historical overview of Einstein's oscillating attitude towards a "phenomenological" and "dynamical" treatment of rods and clocks in relativity theory. Contrary to what it has been usually claimed in recent literature, it is argued that this distinction should not be understood in the framework of opposition between principle and constructive theories. In particular Einstein does not seem to have plead for a "dynamical" explanation for the phenomenon rods contraction and clock dilation which was initially described only "kinematically". (...) On the contrary textual evidence shows that, according to Einstein, a realistic microscopic model of rods and clocks was needed to account for the very existence of measuring devices of "identical construction" which always measure the same unit of time and the same unit of length. In fact, it will be shown that the empirical meaningfulness of both relativity theories depends on what, following Max Born, one might call the "principle of the physical identity of the units of measure". In the attempt to justify the validity of such principle, Einstein was forced by different interlocutors, in particular Hermann Weyl and Wolfgang Pauli, to deal with the genuine epistemological, rather then physical question whether a theory should be able or not to described the material devices that serve to its own verification. (shrink)

In his 1916 review paper on general relativity, Einstein made the often-quoted oracular remark that all physical measurements amount to a determination of coincidences, like the coincidence of a pointer with a mark on a scale. This argument, which was meant to express the requirement of general covariance, immediately gained great resonance. Philosophers such as Schlick found that it expressed the novelty of general relativity, but the mathematician Kretschmann deemed it as trivial and valid in all spacetime theories. With the (...) relevant exception of the physicists of Leiden (Ehrenfest, Lorentz, de Sitter, and Nordström), who were in epistolary contact with Einstein, the motivations behind the point-coincidence remark were not fully understood. Only at the turn of the 1960s did Bergmann (Einstein’s former assistant in Princeton) start to use the term ‘coincidence’ in a way that was much closer to Einstein’s intentions. In the 1980s, Stachel, projecting Bergmann’s analysis onto his historical work on Einstein’s correspondence, was able to show that what he started to call ‘the point-coincidence argument’ was nothing but Einstein’s answer to the infamous ‘hole argument’. The latter has enjoyed enormous popularity in the following decades, reshaping the philosophical debate on spacetime theories. The point-coincidence argument did not receive comparable attention. By reconstructing the history of the argument and its reception, this paper argues that this disparity of treatment is not justified. This paper will also show that the notion that only coincidences are observable in physics marks every critical step of Einstein’s struggle with the meaning of coordinates in physics. (shrink)

In 1909, Ehrenfest published a note in the Physikalische Zeitschrift showing that a Born rigid cylinder could not be set into rotation without stresses, as elements of the circumference would be contracted but not the radius. Ignatowski and Varićak challenged Ehrenfest’s result in the same journal, arguing that the stresses would emerge if length contraction were a real dynamical effect, as in Lorentz’s theory. However, no stresses are expected to arise, according to Einstein’s theory, where length contraction is only an (...) apparent effect due to an arbitrary choice of clock synchronization. Ehrenfest and Einstein considered this line of reasoning dangerously misleading and took a public stance in the Physikalische Zeitschrift, countering that relativistic length contraction is both apparent and real. It is apparent since it disappears for the comoving observer, but it is also real since it can be experimentally verified. By drawing on his lesser-known private correspondence with Varićak, this paper shows how Einstein used the Ehrenfest paradox as a tool for an ‘Einsteinian pedagogy’. Einstein’s argumentative stance is contrasted with Bell’s use of the Dewan-Beran thread-between-spaceships paradox to advocate for a ‘Lorentzian pedagogy’. The paper concludes that the disagreement between the two ways of ‘teaching special relativity’ stems from divergent interpretations of philosophical categories such as ‘reality’ and ‘appearance’. (shrink)