Dennis Lehmkuhl

We discuss three philosophically interesting epistemic peculiarities of black hole astrophysics: (1) issues concerning whether and in what sense black holes do exist; (2) how to best approach multiplicity of available definitions of black holes; (3) short (i.e., accessible within an individual human lifespan) dynamical timescales present in many of the recent, as well as prospective, observations involving black holes. In each case we argue that the prospects for our epistemic situation are optimistic.

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.

This paper pushes back against the Democritean-Newtonian tradition of assuming a strict conceptual dichotomy between spacetime and matter. Our approach proceeds via the more narrow distinction between modified gravity/spacetime and dark matter. A prequel paper argued that the novel field Φ postulated by Berezhiani and Khoury's 'superfluid dark matter theory' is as much matter as anything could possibly be, but also below the critical temperature for superfluidity as much spacetime as anything could possibly be. Here we introduce and critically evaluate three groups of interpretations that one should consider for such Janus-faced theories. The consubstantiality interpretation holds that Φ is both matter and a modification of spacetime, analogously to the sense in which Jesus is both human and god. The fundamendalist interpretations consider for each of these roles whether they are instantiated fundamentally or emergently. The breakdown interpretations focus on the question of whether Φ signals the breakdown, in some sense to be specified, of the MG-DM dichotomy and perhaps even the broader spacetime–matter distinction. More generally, it is argued that hybrid theories urge a move towards a single space of theories, rather than two separate spaces of spacetime theories and matter theories, respectively.

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.

We approach the physics of \emph{minimal coupling} in general relativity, demonstrating that in certain circumstances this leads to violations of the \emph{strong equivalence principle}, which states that, in general relativity, the dynamical laws of special relativity can be recovered at a point. We then assess the consequences of this result for the \emph{dynamical perspective on relativity}, finding that potential difficulties presented by such apparent violations of the strong equivalence principle can be overcome. Next, we draw upon our discussion of the dynamical perspective in order to make explicit two `miracles' in the foundations of relativity theory. We close by arguing that the above results afford us insights into the nature of special relativity, and its relation to general relativity.

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.

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

This contributed volume is the result of a July 2010 workshop at the University of Wuppertal Interdisciplinary Centre for Science and Technology Studies which brought together world-wide experts from physics, philosophy and history, in order to address a set of questions first posed in the 1950s: How do we compare spacetime theories? How do we judge, objectively, which is the “best” theory? Is there even a unique answer to this question? The goal of the workshop, and of this book, is to contribute to the development of a meta-theory of spacetime theories. Such a meta-theory would reveal insights about specific spacetime theories by distilling their essential similarities and differences, deliver a framework for a class of theories that could be helpful as a blueprint to build other meta-theories, and provide a higher-level viewpoint for judging which theory most accurately describes nature. But rather than drawing a map in broad strokes, the focus is on particularly rich regions in the “space of spacetime theories.” This work will be of interest to physicists, as well as philosophers and historians of science working with or interested in General Relativity and/or Space, Time and Gravitation more generally.

I describe how relativistic field theory generalizes the paradigm property of material systems, the possession of mass, to the requirement that they have a mass–energy–momentum density tensor T µ associated with them. I argue that T µ does not represent an intrinsic property of matter. For it will become evident that the definition of T µ depends on the metric field g µ in a variety of ways. Accordingly, since g µ represents the geometry of spacetime itself, the properties of mass, stress, energy, and momentum should not be seen as intrinsic properties of matter, but as relational properties that material systems have only in virtue of their relation to spacetime structure

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.

I argue that, contrary to folklore, Einstein never really cared for geometrizing the gravitational or the electromagnetic field; indeed, he thought that the very statement that General Relativity geometrizes gravity "is not saying anything at all". Instead, I shall show that Einstein saw the "unification" of inertia and gravity as one of the major achievements of General Relativity. Interestingly, Einstein did not locate this unification in the field equations but in his interpretation of the geodesic equation, the law of motion of test particles.

It is often claimed that relativity theory falls short of giving an account of 'the flow of time' and 'the arrow of time'. Some claim that hence either one or both of these concepts do not correspond to objective reality, others infer that relativity theory is wrongfully 'spatialising' time. I investigate of our normal conception of time is enduring in relativity, even in the absence of a clear representation of flow. It is shown that the conformal structure of spacetime allows for a clear distinction between past, present and future, and that the class of temporally orientable spacetimes allows for an 'arrow of time'. Finally, I briefly discuss the class of Friedmann universes, to which our universe seems to belong, and which is indeed temporally orientable. German Es wird häufig behauptet, dass die Relativitätstheorie keine adäquate Beschreibung des , Zeitflusses' und des , Zeitpfeils' enthalte. Einige ziehen daraus die Schlussfolgerung, dass beiden Konzepten nichts in der objektiven Realität entspreche, andere ziehen den Schluss, dass die Relativitätstheorie die Zeit fälschlicherweise , verräumliche'. Ich untersuche, wie viel von unserer althergebrachten Zeitvorstellung in der Relativitätstheorie überdauert, selbst in der Abwesenheit einer klaren Repräsentation von , Zeitfluss'. Ich zeige, dass die konforme Struktur der Raumzeit eine klare Unterscheidung von Vergangenheit, Gegenwart und Zukunft erlaubt, und dass die Klasse der zeitlich orientierbaren Raumzeiten die Repräsentation einer , Zeitpfeils' durchaus erlaubt. Schließlich diskutiere ich kurz die Klasse der Friedmann Raumzeiten, zu welcher unser Universum zu gehören scheint, und welches tatsächlich zeitlich orientierbar ist