Does the gravitational field described in general relativity possess genuine stress-energy? We answer this question in the affirmative, in a weak sense applicable in a certain class of frames of a certain class of models of the theory, and arguably also in a strong sense, applicable in all frames of all models of the theory. In addition, we argue that one can be a realist about gravitational stress-energy in general relativity even if one is a relationist about spacetime ontology. In (...) each case, our reasoning rests upon a functionalist approach to the definition of physical quantities. (shrink)

Ott (2009) identifies two kinds of philosophical theories about laws: top-down, and bottom-up. An influential top-down reading, exemplified by Ernst Cassirer, emphasized the ‘mere form of law’. Recent bottom-up accounts emphasize the mind-independent natures of objects as the basis of laws of nature. Stang and Pollok in turn focus on the transcendental idealist elements of Kant’s theory of matter, which leads to the question: is the essence of Kantian matter that it obeys the form of law? I argue that Kant (...) has an independent theory of matter in the Metaphysical Foundations of Natural Science, one that gives what Kant himself calls a ‘real definition’ of matter as a theory-independent (if not mind-independent) entity. I argue that this matter theory underpins physical arguments about inertia and impenetrability, which resemble Einstein’s arguments about the unification of fields in general relativity. (shrink)

The General Relativity understands gravity like inertial movement of the free fall of the bodies in curved spacetime of Lorentz. The law of inertia of Newton would be particular case of the inertial movement of the bodies in the spacetime flat of Euclid. But, in the step, from general to particular, breaks the law of inertia of Galilei since recovers apparently the rectilinear uniform movement but not the repose state, unless the bodies have undergone their collapse, although, the curved spacetime (...) becomes flat and the curved geodesies becomes straight lines. For General Relativity is a natural law, within of a gravitational field, the accelerated movement of the bodies, that leads to that a geometric curvature puts out to the bodies in such geodesic movement. In this paper this error of General Relativity, like generalization of the law of inertia of Galilei, is examined and it is found that it is caused by suppression of mass and force that allows conceiving acceleration like property of spacetime. This is a mathematical and non-ontological result. Indeed, mass and force are the fundament that the gravitational acceleration is independent of the magnitude of mass of the bodies but gravity not of the mass and the gravitational force. The action of the gravity force, on inertial and gravitational masses of a body, produces mutual cancellation during its free fallen but too its weight when this cease. By means of the third law of Newton it shows that gravity is a force since weight is caused by gravity. (shrink)

Recent decades have seen a revived interest in super-substantivalism, the idea that spacetime is the only fundamental substance and matter some kind of aspect, property or consequence of spacetime structure. However, the metaphysical debate so far has misidentified a particular variant of super-substantivalism with the position per se. I distinguish between a super-substantival core commitment and different ways of fleshing it out. I then investigate how general relativity and alternative spacetime theories square with the different variants of super-substantivalism.

The General Relativity understands gravity like inertial movement of the free fall of the bodies in curved spacetime of Lorentz. The law of inertia of Newton would be particular case of the inertial movement of the bodies in the spacetime flat of Euclid. But, in the step, of the particular to the general, breaks the law of inertia of Galilei since recovers the rectilinear uniform movement but not the repose state, unless the bodies have undergone their union, although, the curved (...) spacetime becomes flat and the curved geodesies becomes straight lines. For General Relativity is a natural law, within of a gravitational field, the uniform accelerated movement of the bodies, that leads to that a geometric curvature puts out to the bodies of the repose state for animate them of the movement of free fallen. In this paper this error of General Relativity, like generalization of the law of inertia of Galilei, is examined and it is found that it is caused by suppression of mass and force that allows conceiving acceleration like property of spacetime. This is a mathematical and non-ontological result. Indeed, mass and force are the fundament that the gravitational acceleration is a constant value for all the bodies, independently of the magnitude of mass but not of the mass and the gravitational force. The action of the gravity force, on inertial and gravitational masses of a body, produces mutual cancellation during its free fallen. In addition, by means of the third law of Newton it demonstrates that gravity is a force since weight is caused by gravity force. (shrink)

The history of the theory of general relativity presents unique features. After its discovery, the theory was immediately confirmed and rapidly changed established notions of space and time. The further implications of general relativity, however, remained largely unexplored until the mid 1950s, when it came into focus as a physical theory and gradually returned to the mainstream of physics. This essay presents a historiographical framework for assessing the history of general relativity by taking into account in an integrated narrative intellectual (...) developments, epistemological problems, and technological advances; the characteristics of post–World War II and Cold War science; and newly emerging institutional settings. It argues that such a framework can help us understand this renaissance of general relativity as a result of two main factors: the recognition of the untapped potential of general relativity and an explicit effort at community building, which allowed this formerly disparate and dispersed field to benefit from the postwar changes in the scientific landscape. (shrink)

We discuss what we take to be three possible misconceptions in the foundations of general relativity, relating to: the interpretation of the weak equivalence principle and the relationship between gravity and inertia; the connection between gravitational redshift results and spacetime curvature; and the Einstein equivalence principle and the ability to ``transform away" gravity in local inertial coordinate systems.

We analyse the various conceptual notions that go under the umbrella “relationalism/substantivalism”. Our focus will be on evaluating the ontological status of spacetime in General Relativity. To this end we systematically develop the ontological framework that implicitly underlies the traditional debate and common understanding of physics. We submit that spacetime with its chronogeometric and inertial structure, represented by the triple of the bare manifold, the metric and the affine structure, is best construed as the totality of possible and actual spatiotemporal (...) relations of events. This can explain the non-fundamentality of general relativistic gravitational energy and suggests a non-causal, non-interactional understanding of the interdependence of matter in spacetime in GR. (shrink)

We highlight and resolve what we take to be three common misconceptions in general relativity, relating to the interpretation of the weak equivalence principle and the relationship between gravity and inertia; the connection between gravitational redshift results and spacetime curvature; and the strong equivalence principle and the local recovery of special relativity in curved, dynamical spacetime.

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)

Einstein regarded as one of the triumphs of his 1915 theory of gravity - the general theory of relativity - that it vindicated the action-reaction principle, while Newtonian mechanics as well as his 1905 special theory of relativity supposedly violated it. In this paper we examine why Einstein came to emphasise this position several years after the development of general relativity. Several key considerations are relevant to the story: the connection Einstein originally saw between Mach's analysis of inertia and both (...) the equivalence principle and the principle of general covariance, the waning of Mach's influence owing to de Sitter's 1917 results, and Einstein's detailed correspondence with Moritz Schlick in 1920. (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)

The paper considers the "GR-desideratum", that is, the way general relativity implements general covariance, diffeomorphism invariance, and background independence. Two cases are discussed where 5-dimensional generalizations of general relativity run into interpretational troubles when the GR-desideratum is forced upon them. It is shown how the conceptual problems dissolve when such a desideratum is relaxed. In the end, it is suggested that a similar strategy might mitigate some major issues such as the problem of time or the embedding of quantum non-locality (...) into relativistic spacetimes. (shrink)

I argue that the best interpretation of the general theory of relativity has need of a causal entity, and causal structure that is not reducible to light cone structure. I suggest that this causal interpretation of GTR helps defeat a key premise in one of the most popular arguments for causal reductionism, viz., the argument from physics.

We study the possible interpretation of the "universal constants" by the classification of J.-M. Lévy-Leblond. The Planck constant and the speed of light in vacuum are the most common examples of constants of this type. Using Fock’s principle of the relativity w.r.t. observation means, we show that these two constants can be viewed as manifestations of certain relativity. We also show that there is a possibility to interpret the Boltzmann constant in a similar way, and make some comments about the (...) relativistic interpretation of the constant spacetime curvature and gravitational constant G. (shrink)

The equivalence principle has constituted one of the cornerstones of discussions in the foundations of spacetime theories over the past century. However, up to this point the principle has been considered overwhelmingly only within the context of relativistic physics. In this article, we demonstrate that the principle has much broader, super-theoretic significance: to do so, we present a unified framework for understanding the principle in its various guises, applicable to both relativistic and Newtonian contexts. We thereby deepen significantly our understanding (...) of the role played by the equivalence principle in a broad class of spacetime theories. (shrink)

The arguments are exhibited in favour of the necessity to modify the history of the genesis and advancement of general relativity (GR). I demonstrate that the dynamic creation of GR had been continually governed by internal tensions between two research traditions, that of special relativity and Newton’s gravity. The encounter of the traditions and their interpenetration entailed construction of the hybrid domain at first with an irregular set of theoretical models. Step by step, on eliminating the contradictions between the models (...) contrived, the hybrid set was put into order. It is contended that the main reason of the GR victory over the rival programmes of Abraham and Nordström was a synthetic character of Einstein’s programme. Einstein had put forward as a basic synthetic principle the principle of equivalence that radically differed from that of rival approaches by its open, flexible and contra-ontological character. (shrink)

This paper scrutinises the tenability of a strict conceptual distinction between space and matter via the lens of the debate between modified gravity and dark matter. In particular, we consider Berezhiani and Khoury's novel 'superfluid dark matter theory' as a case study. Two families of criteria for being matter and being spacetime, respectively, are extracted from the literature. Evaluation of the new scalar field postulated by SFDM according to these criteria reveals that it is as much matter as anything could (...) possibly be, but alsoꟷbelow the critical temperature for superfluidityꟷas much spacetime as anything could possibly be. A sequel paper examines possible interpretations of SFDM in light of this result, as well as the consequences for our understanding of the modified gravity/ dark matter distinction and the broader spacetime–matter distinction. (shrink)

In this article, we explore the heuristic power of the theoretical distinction between framework and interaction theories applied to the case of General Relativity. According to the distinction, theories and theoretical elements can be classified into two different groups, each with clear ontological, epistemic and functional content. Being so, to identify the group to which a theory belongs would suffice to know a priori its prospects and limitations in these areas without going into a detailed technical analysis. We make the (...) exercise here with General Relativity, anticipate its ontological, epistemic and functional content and show afterwords that such expectations are justified in this case, being consistent with formal issues of General Relativity. With this, we attempt to make a case for the use of the distinction as a powerful tool for scientific and philosophical analysis. (shrink)

The problem of motion in general relativity is about how exactly the gravitational field equations, the Einstein equations, are related to the equations of motion of material bodies subject to gravitational fields. This article compares two approaches to derive the geodesic motion of matter from the field equations: the ‘T approach’ and the ‘vacuum approach’. The latter approach has been dismissed by philosophers of physics because it apparently represents material bodies by singularities. I argue that a careful interpretation of the (...) approach shows that it does not depend on introducing singularities at all and that it holds at least as much promise as the T approach. (shrink)

Supposing that one is already familiar with special relativistic physics, what constitutes the best route via which to arrive at the architecture of the general theory of relativity? Although the later Einstein would stress the significance of mathematical and theoretical principles in answering this question, in this article we follow the lead of the earlier Einstein (circa 1916) and stress instead how one can go a long way to arriving at the general theory via inductive and empirical principles, without invoking (...) presumptions concerning the geometrical structure of the final theory. We focus on the construction of the kinematical structure and the terms describing the coupling of matter to gravity. General covariance, understood and employed as a straightforward extrapolation of empirical considerations, is central to our derivation, together with what we dub the `Methodological Equivalence Principle'. We argue that our approach has a number of virtues, both for one's understanding of the general theory of relativity, but also for pedagogy, since it stresses---to the greatest extent possible (a lesson which we inherit from Bell, [1976])---both the methodological precedence of dynamical considerations to interpretative issues and the theoretical continuity between general relativity and its precursors. We conclude by comparing our approach to other philosophical approaches to general relativity and discussing the significance of empirically motivated methodological principles in the philosophy of science. (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)

This study reconstructs the 1928–1929 correspondence between Reichenbach and Einstein about the latter’s latest distant parallelism-unified field theory, which attracted considerable public attention at the end of the 1920s. Reichenbach, who had recently become a Professor in Berlin, had the opportunity to discuss the theory with Einstein and therefore sent him a manuscript with some comments for feedback. The document has been preserved among Einstein’s papers. However, the subsequent correspondence took an unpleasant turn after Reichenbach published a popular article on (...) distant parallelism in a newspaper. Einstein directly wrote to the Editorial Board complaining about Reichenbach’s unfair use of off-the-record information. While Reichenbach’s reply demonstrates a sense of personal betrayal at Einstein’s behavior, his published writings of that period point to a sense of intellectual betrayal of their shared philosophical ideals. In his attempts to unify both electricity and gravitation, Einstein had abandoned the physical heuristic that guided him to the relativity theory, to embrace a more speculative, mathematical heuristic that he and Reichenbach had both previously condemned. A decade-long personal and intellectual friendship grew fainter and then never recovered. This study, relying on archival material, aims to revisit the Reichenbach–Einstein relationship in the late 1920s in light of Reichenbach’s neglected contributions to the epistemology of the unified field theory program. Thereby, it hopes to provide a richer account of Reichenbach’s philosophy of space and time. (shrink)

The paper investigates the status of gravitational energy in Newtonian Gravity, developing upon recent work by Dewar and Weatherall. The latter suggest that gravitational energy is a gauge quantity. This is potentially misleading: its gauge status crucially depends on the spacetime setting one adopts. In line with Møller-Nielsen’s plea for a motivational approach to symmetries, we supplement Dewar and Weatherall’s work by discussing gravitational energy–stress in Newtonian spacetime, Galilean spacetime, Maxwell-Huygens spacetime, and Newton–Cartan Theory. Although we ultimately concur with Dewar (...) and Weatherall that the notion of gravitational energy is problematic in NCT, our analysis goes beyond their work. The absence of an explicit definition of gravitational energy–stress in NCT somewhat detracts from the force of Dewar and Weatherall’s argument. We fill this gap by examining the supposed gauge status of prima facie plausible candidates—NCT analogues of gravitational energy–stress pseudotensors, the Komar mass, and the Bel-Robinson tensor. Our paper further strengthens Dewar and Weatherall’s results. In addition, it sheds more light upon the subtle link between sufficiently rich inertial structure and the definability of gravitational energy in NG. (shrink)

The present paper revisits the debate between realists about gravitational energy in GR and anti-realists/eliminativists. I re-assess the arguments underpinning Hoefer’s seminal eliminativist stance, and those of their realist detractors’ responses. A more circumspect reading of the former is proffered that discloses where the so far not fully appreciated, real challenges lie for realism about gravitational energy. I subsequently turn to Lam and Read’s recent proposals for such a realism. Their arguments are critically examined. Special attention is devoted to the (...) adequacy of Read’s appeals to functionalism, imported from the philosophy of mind. (shrink)

Super-substantivalism (of the type we’ll consider) roughly comprises two core tenets: (1) the physical properties which we attribute to matter (e.g. charge or mass) can be attributed to spacetime directly, with no need for matter as an extraneous carrier “on top of” spacetime; (2) spacetime is more fundamental than (ontologically prior to) matter. In the present paper, we revisit a recent argument in favour of super-substantivalism, based on General Relativity. A critique is offered that highlights the difference between (various accounts (...) of) fundamentality and (various forms of) ontological dependence. This affords a metaphysically more perspicuous view of what super-substantivalism’s tenets actually assert, and how it may be defended. We tentatively propose a re-formulation of the original argument that not only seems to apply to all classical physics, but also chimes with a standard interpretation of spacetime theories in the philosophy of physics. (shrink)

Following the proposal of a new kind of selective structural realism that uses as a basis the distinction between framework and interaction theories, this work discusses relevant applications in fundamental physics. An ontology for the different entities and properties of well-known theories is thus consistently built. The case of classical field theories—including general relativity as a classical theory of gravitation—is examined in detail, as well as the implications of the classification scheme for issues of realism in quantum mechanics. These applications (...) also shed light on the different range of applicability of the ontic and epistemic versions of structural realism. (shrink)

What were the true reasons of the second scientific revolution? – To answer the question, the epistemic model is applied, according to which radical breakthroughs in science were not due to the fanciful excogitation of new ideas ‘ex nihilo’, but rather to the tedious, long-term and troublesome processes of the mutual lapping, reconciliation, interpenetration and intertwinement of ‘old’ research traditions preceding such breaks. It is contended that Einstein's 'annus mirabilis' constituted an acme of the second scientific revolution. To fathom in (...) what felicitous ways Einstein's 1905 writings hang together one is bound to pay special tribute to his longed strive for unity evinced in incessant attempts to coordinate the profound research traditions of classical physics. Though Einstein's efforts sprung out of Max Planck's pioneering attempts to comprehend electromagnetic phenomena through the lenses of conceptual structures of statistical thermodynamics . It was Planck, who clearly realized the cross-contradiction between 'the physics of material bodies’ and ‘the physics of the ether' and outlined the sketch of its withdrawal: the paradigms 'must be modified to remain compatible'. And it was Planck who took the first step in modifying the physics of the ether and contending that 'not only matter itself but also the effects radiated from matter' possess discontinuous properties, which can be characterized by a new natural constant: the elementary quantum of action. Einstein's part consisted in that he took the second step in modifying the second component of the encounter – the physics of material bodies. Einstein’s foolhardy light quanta hypothesis and distinctive special theory of relativity turn out to be mere milestones of the unwinding of Maxwellian electrodynamics and statistical thermodynamics reconcilement research program. The notorious conception of luminiferous ether was a substantial obstacle for Einstein’s wayward statistical thermodynamics in which the pivotal lead was played by flagrant light quanta paper. Einstein was aware that his enticing light quanta hypothesis was too audacious to be taken literally and he laid out his version of 'electrodynamics of moving bodies' in a markedly Machian/ Duhemian, phenomenological way. As a result of the revision of the second scientific revolution key episode, the arguments are exhibited in favor of the necessity to modify the history of the genesis of general relativity; correspondingly, the process of unification of electromagnetic and weak interactions that took place in the second half of the XX-th century is scrutinized. Eventually, the encounter and interpenetration of the two dominating research traditions of modern physics – that of general relativity and quantum field theory – is elicited. (shrink)

Much scholarship has claimed the physics of Emilie du Châtelet’s treatise, Institutions de physique, is Newtonian. I argue against that idea. To do so, I distinguish three strands of meaning for the category ‘Newtonian science,’ and I examine her book against them. I conclude that her physics is not Newtonian in any useful or informative sense. To capture what is specific about it, we need better interpretive categories.

Quantum gravity is expected to require modifications of the notions of space and time. I discuss and clarify how this happens in Loop Quantum Gravity.