I discuss the relationship between different versions of the equivalence principle in general relativity, among them Einstein's equivalence principle, the weak equivalence principle, and the strong equivalence principle. I show that Einstein's version of the equivalence principle is intimately linked to his idea that in GR gravity and inertia are unified to a single field, quite like the electric and magnetic field had been unified in special relativistic electrodynamics. At the same time, what is now often called the strong equivalence (...) principle, related to the local validity of special relativity, can also be found in Einstein's writings, albeit by a different name and clearly separated from what he calls the equivalence principle. I discuss both the development of Einstein's thoughts on the different versions of the equivalence principle, their relationship to the relativity principle, as well as later reflections and variants proposed. (shrink)

Two fundamental errors led Einstein to reject generally covariant gravitational field equations for over two years as he was developing his general theory of relativity. The first is well known in the literature. It was the presumption that weak, static gravitational fields must be spatially flat and a corresponding assumption about his weak field equations. I conjecture that a second hitherto unrecognized error also defeated Einstein's efforts. The same error, months later, allowed the hole argument to convince Einstein that all (...) generally covariant gravitational field equations would be physically uninteresting. (shrink)

We address the problem of observables in generally invariant spacetime theories such as Einstein’s general relativity. Using the refined notion of an event as a “point-coincidence” between scalar fields that completely characterise a spacetime model, we propose a generalisation of the relational local observables that does not require the existence of four everywhere invertible scalar fields. The collection of all point-coincidences forms in generic situations a four-dimensional manifold, that is naturally identified with the physical spacetime.

I argue that the Hole Argument is based on a misleading use of the mathematical formalism of general relativity. If one is attentive to mathematical practice, I will argue, the Hole Argument is blocked.

I argue that the hole argument is based on a misleading use of the mathematical formalism of general relativity. If one is attentive to mathematical practice, I will argue, the hole argument is blocked. _1._ Introduction _2._ A Warmup Exercise _3._ The Hole Argument _4._ An Argument from Classical Spacetime Theory _5._ The Hole Argument Revisited.

This book focuses on Albert Einstein and his interactions with, and responses to, various scientists, both famous and lesser-known. It takes as its starting point that the discussions between Einstein and other scientists all represented a contribution to the edifice of general relativity and relativistic cosmology. These scientists with whom Einstein implicitly or explicitly interacted form a complicated web of collaboration, which this study explores, focusing on their implicit and explicit responses to Einstein s work. This analysis uncovers latent undercurrents, (...) indiscernible to other approaches to tracking the intellectual pathway of Einstein to his general theory of relativity. The interconnections and interactions presented here reveal the central figures who influenced Einstein during this intellectual period. Despite current approaches to history presupposing that the efforts of scientists such as Max Abraham and Gunnar Nordström, which differed from Einstein s own views, be relegated to the background, this book shows that they all had an impact on the development of Einstein s theories, stressing the limits of approaches focusing solely on Einstein. As such, General Relativity Conflict and Rivalries proves that the general theory of relativity was not developed as a single, coherent construction by an isolated, brooding individual, but, rather, that it came to fruition through Einstein's conflicts and interactions with other scientists, and was consolidated by his creative processes during these exchanges. (shrink)

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, 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 Émile Meyerson from the mid 1920s till the early 1930s 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 opposed to the positivistic-operationalist spirit of quantum mechanics. (shrink)

The present paper attempts to show that a 1915 article by Erich Kretschmann must be credited not only for being the source of Einstein’s point-coincidence remark, but also for having anticipated the main lines of the logical-empiricist interpretation of general relativity. Whereas Kretschmann was inspired by the work of Mach and Poincaré, Einstein inserted Kretschmann’s point-coincidence parlance into the context of Ricci and Levi-Civita’s absolute differential calculus. Kretschmann himself realized this and turned the point-coincidence argument against Einstein in his second (...) and more famous 1918 paper. While Einstein had taken nothing from Kretschmann but the expression “point-coincidences”, the logical empiricists, however, instinctively dragged along with it the entire apparatus of Kretschmann’s conventionalism. Disappointingly, in their interpretation of general relativity, the logical empiricists unwittingly replicated some epistemological remarks Kretschmann had written before General Relativity even existed. (shrink)

This paper analyzes correspondence between Reichenbach and Einstein from the spring of 1926, concerning what it means to ‘geometrize’ a physical field. The content of a typewritten note that Reichenbach sent to Einstein on that occasion is reconstructed, showing that it was an early version of §49 of the untranslated Appendix to his Philosophie der Raum-Zeit-Lehre, on which Reichenbach was working at the time. This paper claims that the toy-geometrization of the electromagnetic field that Reichenbach presented in his note should (...) not be regarded as merely a virtuoso mathematical exercise, but as an additional argument supporting the core philosophical message of his 1928 monograph. This paper concludes by suggesting that Reichenbach’s infamous ‘relativization of geometry’ was only a stepping stone on the way to his main concern—the question of the ‘geometrization of gravitation’. (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)

Spacetime substantivalism leads to a radical form of indeterminism within a very broad class of spacetime theories which include our best spacetime theory, general relativity. Extending an argument from Einstein, we show that spacetime substantivalists are committed to very many more distinct physical states than these theories' equations can determine, even with the most extensive boundary conditions.

"This book is a very impressive achievement. Kennefick skillfully introduces readers to some of the most abstruse yet fascinating concepts in modern physics stemming from Einstein's gravitational theory.

Readers of this volume will notice that it contains only a few papers on general relativity. This is because most papers documenting the genesis and early development of general relativity were not published in Annalen der Physik . After Einstein took up his new prestigious position at the Prussian Academy of Sciences in the spring of 1914, the Sitzungsberichte of the Berlin academy almost by default became the main outlet for his scientific production. Two of the more important papers on (...) general relativity, however, did find their way into the pages of the Annalen [35,41]. Although I shall discuss both papers in this essay, the main focus will be on [35], the first systematic exposition of general relativity, submitted in March 1916 and published in May of that year. (shrink)

Substantivalists believe that spacetime and its parts are fundamental constituents of reality. Relationalists deny this, claiming that spacetime enjoys only a derivative existence. I begin by describing how the Galilean symmetries of Newtonian physics tell against both Newton's brand of substantivalism and the most obvious relationalist alternative. I then review the obvious substantivalist response to the problem, which is to ditch substantival space for substantival spacetime. The resulting position has many affinities with what are arguably the most natural interpretations of (...) special and general relativity. I move on to consider and reject two recent antisubstantivalist lines of thought. The interim conclusion is that the best argument for relationalism is an appeal to Ockham's razor. However, for this to be successful there must be genuine relationalist theories that share the theoretical virtues of their substantivalist rivals but without the additional ontological commitment. The bulk of the paper is therefore an investigation of various concrete relationalist proposals. I distinguish three options for the relationalist in the face of the success of Galilean invariant physics and trace how these generalise to relativistic physics. One of the options is particularly promising but, since its basic objects end up being spacetime points, this does not help the prospects of relationalism as traditionally conceived. I end with some reflections on the fate of substantivalism in the aftermath of the Hole Argument, concluding that we have as yet to be given good reasons to abandon the natural, substantivalist interpretation of current physics. (shrink)

The advent of the general theory of relativity was so entirely the work of just one person - Albert Einstein - that we cannot but wonder how long it would have taken without him for the connection between gravitation and spacetime curvature to be discovered. What would have happened if there were no Einstein? Few doubt that a theory much like special relativity would have emerged one way or another from the researchers of Lorentz, Poincaré and others. But where would (...) the problem of relativizing gravitation have led? The saga told here shows how even the most conservative approach to relativizing gravitation theory still did lead out of Minkowski spacetime to connect gravitation to a curved spacetime. Unfortunately we still cannot know if this conclusion would have been drawn rapidly without Einstein's contribution. For what led Nordström to the gravitational field dependence of lengths and times was a very Einsteinian insistence on just the right version of the equality of inertial and gravitational mass. Unceasingly in Nordström's ear was the persistent and uncompromising voice of Einstein himself demanding that Nordström see the most distant consequences of his own theory. © 1992 Springer-Verlag. (shrink)

Einstein insisted throughout his life that the signal achievement of his general theory of relativity was its general covariance. How are we to reconcile this with the now common view that general covariance merely expresses a definition, our freedom to label events with any set of numbers we like? There is, I believe, a natural reading for Einstein's claims that does make perfect sense. It requires us to adopt a physical interpretation of relativity theory that is now no longer popular, (...) so the natural reading will no longer have intrinsic interest. It will, however, allow us to make sense of Einstein's claims and his program. (shrink)

Einstein insisted throughout his life that the signal achievement of his general theory of relativity was its general covariance. How are we to reconcile this with the now common view that general covariance merely expresses a definition, our freedom to label events with any set of numbers we like? There is, I believe, a natural reading for Einstein's claims that does make perfect sense. It requires us to adopt a physical interpretation of relativity theory that is now no longer popular, (...) so the natural reading will no longer have intrinsic interest. It will, however, allow us to make sense of Einstein's claims and his program. (shrink)