Leibniz Equivalence. On Leibniz's (Bad) Influence on the Logical Empiricist Interpretation of General Relativity

Einstein’s “point-coincidence argument'” as a response to the “hole argument” is usually considered as an expression of “Leibniz equivalence,” a restatement of indiscernibility in the sense of Leibniz. Through a historical-critical analysis of Logical Empiricists' interpretation of General Relativity, the paper attempts to show that this labeling is misleading. Logical Empiricists tried explicitly to understand the point-coincidence argument as an indiscernibility argument of the Leibnizian kind, such as those formulated in the 19th century debate about geometry, by authors such as Poincaré, Helmholtz or Hausdorff. However, they clearly failed to give a plausible account of General Relativity. Thus the point-coincidence/hole argument cannot be interpreted as Leibnizian indiscernibility argument, but must be considered as an indiscernibility argument of a new kind. Weyl's analysis of Leibniz's and Einstein's indiscernibility arguments is used to support this claim

`Physics Is a Kind of Metaphysics': Émile Meyerson and Einstein's Late Rationalistic Realism

Gerald Holton has famously described Einstein's career as a philosophical “pilgrimage". Starting on “the historic ground" of Machian positivism and phenomenalism, following the completion of general relativity in late 1915, Einstein's philosophy endured (a) a speculative turn: physical theorizing appears as ultimately a "pure mathematical construction" guided by faith in the simplicity of nature and (b) a realistic turn: science is “nothing more than a refinement" of the everyday belief in the existence of mind-independent physical reality. Nevertheless, Einstein's mathematical constructivism that supports his unified field theory program appears to be, at first sight, hardly compatible with the common sense realism with which he countered quantum theory. Thus, the literature on Einstein's philosophy of science has often struggled in finding the thread between ostensibly conflicting philosophical pronouncements. This paper supports the claim that Einstein's dialog with Emile Meyerson from the mid 19205 till the early 19305 might be a neglected source to solve this riddle. According to Einstein, Meyerson shared (a) his belief in the independent existence of an external world and (b) his conviction that the latter can be grasped only by speculative means. Einstein could present his search for a unified field theory as a metaphysical-realistic program as opposed to the positivistic-operationalist spirit of quantum mechanics

Seeking the Local Convergence Depth. I. TF Observations of the Clusters A168, A397, A569, A1139, A1228, and A1983

We present first results of an all-sky observing program designed to improve the quality of the I band Tully-Fisher (TF) template and to obtain the reflex motion of the Local Group with respect to clusters to z = 0.06. We are obtaining between 5 and 15 TF measurements per cluster on a sample of 50 clusters at intermediate redshifts (0.02 < z < 0.06). Presentation of the data for seven Abell clusters of galaxies is given here. This data incorporates methods for estimating the true inclination of a spiral disk, an observational parameter undervalued for small angular-sized galaxies or for galaxies observed in poor seeing conditions.Comment: 21 pages, uses AAS LaTeX, 3 tables and 8 postscript figures (only first page of fig. 6 included in this version); to appear in the Astronomical Journa

The Universality of the Fundamental Plane of E and S0 Galaxies. Spectroscopic data

We present here central velocity dispersion measurements for 325 early-type galaxies in eight clusters and groups of galaxies, including new observations for 212 galaxies. The clusters and groups are the A262, A1367, Coma (A1656), A2634, Cancer and Pegasus clusters, and the NGC 383 and NGC 507 groups. The new measurements were derived from medium dispersion spectra, that cover 600 A centered on the Mg Ib triplet at lambda ~ 5175. Velocity dispersions were measured using the Tonry & Davis cross-correlation method, with a typical accuracy of 6%. A detailed comparison with other data sources is made.Comment: 12 pages, 5 tables, 3 figures, to appear in AJ. Note that tables 2 and 3 are in separate files, as they should be printed in landscape forma

Lorentz Contraction vs. Einstein Contraction. Reichenbach and the Philosophical Reception of Miller’s Ether-Drift Experiments

In 1925 Reichenbach, by reacting to the positive result of Miller’s ether-drift experiments, introduced a distinction between two types of rod contraction in special relativity: a kinematical ‘Einstein contraction,’ which depends on the definition of simultaneity, and a dynamical ‘Lorentz contraction.’ He argued that although both contractions happen to amount to the same Lorentz factor, they are conceptually different. In Reichenbach’s view, only the ‘Lorentz contraction’ is at stake in the Michelson-Morley experiment. The arm of Michelson’s interferometer is shorter than it would have been in classical mechanics in both Einstein and Lorentz’s theories. In both theories, the Lorentz contraction requires an atomistic explanation based on a yet-unknown theory of matter. This paper concludes that Reichenbach’s interpretation of special relativity shares features of the current neo-Lorentzian interpretations

Relativity Theory as a Theory of Principles: A Reading of Cassirer’s Zur Einstein’schen Relativitätstheorie

In his Zur Einstein'schen Relativitätstheorie Cassirer presents relativity theory as the last manifestation of the tradition of the 'physics of principles' that, starting from the nineteenth century, has progressively prevailed over that of the 'physics of models.' In particular, according to Cassirer, the relativity principle plays a similar role as the energy principle in previous physics. The paper argues that this comparison represents the core of Cassirer's neo-Kantian interpretation of relativity. Unlike the individual physical laws, these principles do not pretend to provide models of any specific physical system, but they do impose constraints on the law-like statements that describe them. The latter do not qualify as proper laws unless they satisfy such constraints. Cassirer pointed out that before and after Kant, the history of physics presents significant instances in which the search for formal conditions that the laws of nature must satisfy preceded and made possible the direct search for such laws. In his earlier years, Cassirer seems to have regarded principles like the energy principle, the relativity principle, the principle of least action, etc., as a constitutive but provisional form of a priori, imposing specific limitations on the form of the allowable laws of nature. Only in his later years, by attributing an autonomous status to these statements of principle, did Cassirer attribute a definitive but merely regulative meaning to the a priori. This does not impose specific requirements on natural laws but only a motivation to search for them

‘Geometrization of Physics’ vs. ‘Physicalization of Geometry.’ The Untranslated Appendix to Reichenbach’s Philosophie der Raum-Zeit-Lehre

This article provides an overview of the Appendix to Reichenbach’s 1928 Philosophie der Raum-Zeit-Lehre, which was not included in the widely read English translation of the book published 30 years later. The Appendix, after a lengthy introduction of the basic concepts of differential geometry and of the problem of the their physical interpretation, presents an intentionally artificial example of geometrization of the electromagnetic field, by allowing spacetime to have torsion, in addition to curvature. At that time, it was a widespread opinion that, after Einstein’s ‘geometrization’ of the gravitational field, the ‘geometrization’ program should be extended to the other known field, the electromagnetic field. However, Reichenbach aimed to prove that dressing a physical field in a geometrical ‘cloak’ is a display of mathematical sophistication, not of physical insight. A geometrical ‘cloak,’ as Reichenbach put it, is useful only if it reveals something new about the shape of the ‘body’ under it, the physical field. The present study, through comparison of Newtonian gravitation (Newton-Cartan theory) with Friedrichs’s geometrization, indicates that Reichenbach’s geometrization attempt was doomed to failure. Nevertheless, it is argued, the philosophical message of the Appendix should be considered an integral part of the line of argument of Philosophie der Raum-Zeit-Lehre, particular its last chapter on general relativity. The book’s main message was that general relativity was not the beginning of the new era of ‘geometrization of physics,’ but the culmination of a historical process of ‘physicalization of geometry

Like Thermodynamics before Boltzmann. On the Emergence of Einstein’s Distinction between Constructive and Principle Theories

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 specific 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 specific 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 effective 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 classification of theories, but also as Einstein’s attempt to formulate a sort of ‘logic of discovery.’ The paper argues that most of Einstein’s scientific successes were obtained by following the principle strategy. Most of his failures happened when he was forced to fall back to the constructive strategy

Nothing but Coincidences: The Point-Coincidence Argument and Einstein’s Struggle with the Meaning of Coordinates in Physics

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 like 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. The 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