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. (shrink)

All physical theories, from classical Newtonian mechanics to relativistic quantum field theory, entail propositions concerning the geometric structure of spacetime. To give an example, the general theory of relativity entails that spacetime is curved, smooth, and four-dimensional. In this dissertation, I take the structural commitments of our theories seriously and ask: how is such structure instantiated in the physical world? Mathematically, a property like 'being curved' is perfectly well-defined insofar as we know what it means for a mathematical space to (...) be curved. But what could it mean to say that the physical world is curved? Call this the problem of physical geometry. The problem of physical geometry is a plea for foundations--a request for fundamental truth conditions for physical-geometric propositions. My chief claim is that only a substantival theory of spacetime--a theory according to which spacetime is an entity in its own right, existing over and above the material content of the world--can supply the necessary truth conditions. (shrink)

I discuss several issues related to "classical" spacetime structure. I review Galilean, Newtonian, and Leibnizian spacetimes, and briefly describe more recent developments. The target audience is undergraduates and early graduate students in philosophy; the presentation avoids mathematical formalism as much as possible.

Suppose all of the particles in the universe should happen to come to rest at the same time, in positions so arranged that all of the forces on every particle balance to zero at that time. What would happen next? Or rather, what does Newtonian mechanics say will happen next? Preface Inertia and Stasis 2.1 Stating the Law of Inertia more precisely 2.2 The stasis scenario Indeterministic Examples 3.1 Abstract example 3.2 Second example Non-Lipschitz Forces and Determinism Beyond the Stasis (...) Scenario CiteULike Connotea Del.icio.us What's this? (shrink)

In this paper, I examine a number of alternative global structures for Newtonian space-time, and corresponding Newtonian theories of mechanics and gravitation. I argue that since these theories differ only with respect to questions concerning the relative distribution of inertial and gravitational forces, the choice between them is a matter of convention. Therefore, the global structure of Newtonian space-time is also a matter of convention. Since this result is based on a consideration of the nature of inertial and gravitational forces, (...) rather than on general reductionist principles, it is a "limited conventionalist" result. (shrink)

A theorem due to Bob Geroch and Pong Soo Jang ["Motion of a Body in General Relativity." Journal of Mathematical Physics 16, ] provides a sense in which the geodesic principle has the status of a theorem in General Relativity. I have recently shown that a similar theorem holds in the context of geometrized Newtonian gravitation [Weatherall, J. O. "The Motion of a Body in Newtonian Theories." Journal of Mathematical Physics 52, ]. Here I compare the interpretations of these two (...) theorems. I argue that despite some apparent differences between the theorems, the status of the geodesic principle in geometrized Newtonian gravitation is, mutatis mutandis, strikingly similar to the relativistic case. (shrink)

As Harvey Brown emphasizes in his book Physical Relativity, inertial motion in general relativity is best understood as a theorem, and not a postulate. Here I discuss the status of the "conservation condition", which states that the energy-momentum tensor associated with non-interacting matter is covariantly divergence-free, in connection with such theorems. I argue that the conservation condition is best understood as a consequence of the differential equations governing the evolution of matter in general relativity and many other theories. I conclude (...) by discussing what it means to posit a certain spacetime geometry and the relationship between that geometry and the dynamical properties of matter. (shrink)

Using as a starting point recent and apparently incompatible conclusions by Saunders and Knox, I revisit the question of the correct spacetime setting for Newtonian physics. I argue that understood correctly, these two versions of Newtonian physics make the same claims both about the background geometry required to define the theory, and about the inertial structure of the theory. In doing so I illustrate and explore in detail the view—espoused by Knox, and also by Brown —that inertial structure is defined (...) by the dynamics governing subsystems of a larger system. This clarifies some interesting features of Newtonian physics, notably the distinction between using the theory to model subsystems of a larger whole and using it to model complete universes, and the scale-relativity of spacetime structure. _1_ Introduction _2_ Newtonian Mechanics and Galilean Spacetime _3_ Vector Relationism and Maxwellian Spacetime _4_ Recovering the Galilei Group: Dynamics of Subsystems _5_ Knox on Inertial Structure _6_ Connections on Maxwellian Spacetime _7_ Knox on Newtonian Gravity _8_ Vector Relationism and Newton–Cartan Theory _9_ Inertial Structure in Newton–Cartan Gravity _10_ Reconciling Knox and Saunders _11_ Conclusions. (shrink)

In "The Epistemology of Geometry" Glymour proposed a necessary structural condition for the synonymy of two space-time theories. David Zaret has recently challenged this proposal, by arguing that Newtonian gravitational theory with a flat, non-dynamic connection (FNGT) is intuitively synonymous with versions of the theory using a curved dynamical connection (CNGT), even though these two theories fail to satisfy Glymour's proposed necessary condition for synonymy. Zaret allowed that if FNGT and CNGT were not equally well (bootstrap) tested by the relevant (...) phenomena, the two theories would in fact not be synonymous. He argued, however, that when electrodynamic phenomena are considered, the two theories are equally well tested. We show that it is not FNGT and CNGT which are equally well tested when the electrodynamic phenomena are considered, but only suitable extensions of FNGT and CNGT. Thus, there is good reason to consider FNGT and CNGT to be non-synonymous. We further show that the two extensions of FNGT and CNGT which are equally well tested when electrodynamic phenomena are considered (and which could be considered intuitively synonymous) not only satisfy Glymour's original proposed necessary condition for the synonymy of space-time theories, they satisfy a plausible stronger condition as well. (shrink)

Bohmian mechanics faces an underdetermination problem: when it comes to solving the measurement problem, alternatives to the Bohmian guidance equation work just as well as the official guidance equation. One way to argue that the guidance equation is superior to its rivals is to use a symmetry argument: of the candidate guidance equations, the official guidance equation is the simplest Galilean-invariant candidate. This symmetry argument---if it worked---would solve the underdetermination problem. But the argument does not work. It fails because it (...) rests on assumptions about how Galilean transformations (especially boosts) act on the wavefunction that are (in this context) unwarranted. My discussion has larger morals about the physical significance of certain mathematical results (like, for example, Wigner's theorem) in non-orthodox interpretations of quantum mechanics. (shrink)

Several variant "Newtonian" theories of inertia and gravitation are described, and their scientific usefulness discussed. An examination of these theories is used to throw light on traditional epistemological and metaphysical questions about space and time. Finally these results are examined in the light of the changes induced by the transition from "Newtonian" to general relativistic spacetime.

Craig Callender, Jonathan Cohen and Markus Schrenk have recently argued for an amended version of the best system account of laws – the better best system account (BBSA). This account of lawhood is supposed to account for laws in the special sciences, among other desiderata. Unlike David Lewis's original best system account of laws, the BBSA does not rely on a privileged class of natural predicates, in terms of which the best system is formulated. According to the BBSA, a contingently (...) true generalization is a law of a special science S iff the generalization is an axiom (or a theorem) of the best system relative to the set of predicates used by special science S. We argue that the BBSA is, at best, an incomplete theory of special science laws, as it does not account for typical features of special science laws, such as attached ceteris paribus conditions and the idealized character of law statements in these disciplines. (shrink)

Classical and quantum field theory provide not only realistic examples of extant notions of empirical equivalence, but also new notions of empirical equivalence, both modal and occurrent. A simple but modern gravitational case goes back to the 1890s, but there has been apparently total neglect of the simplest relativistic analog, with the result that an erroneous claim has taken root that Special Relativity could not have accommodated gravity even if there were no bending of light. The fairly recent acceptance of (...) nonzero neutrino masses shows that widely neglected possibilities for nonzero particle masses have sometimes been vindicated. In the electromagnetic case, there is permanent underdetermination at the classical and quantum levels between Maxwell's theory and the one-parameter family of Proca's electromagnetisms with massive photons, which approximate Maxwell's theory in the limit of zero photon mass. While Yang–Mills theories display similar approximate equivalence classically, quantization typically breaks this equivalence. A possible exception, including unified electroweak theory, might permit a mass term for the photons but not the Yang–Mills vector bosons. Underdetermination between massive and massless (Einstein) gravity even at the classical level is subject to contemporary controversy. (shrink)

One hotly debated philosophical question in the analysis of evolutionary theory concerns whether or not evolution and the various factors which constitute it may profitably be considered as analogous to “forces” in the traditional, Newtonian sense. Several compelling arguments assert that the force picture is incoherent, due to the peculiar nature of genetic drift. I consider two of those arguments here – that drift lacks a predictable direction, and that drift is constitutive of evolutionary systems – and show that they (...) both fail to demonstrate that a view of genetic drift as a force is untenable. I go on to diagnose the reasons for the stubborn persistence of this problem, considering two open philosophical issues and offering some preliminary arguments in support of the force metaphor. (shrink)

Innate cognitive capacities are widely posited in cognitive science, yet both philosophers and scientists have criticized the concept of innateness as being hopelessly confused. Despite a number of recent attempts to define or characterize innateness, critics have charged that it is associated with a diverse set of properties and encourages unwarranted inferences among properties that are frequently unrelated. This criticism can be countered by showing that the properties associated with innateness cluster together in reliable ways, at least in the context (...) of the study of cognition. Even though the causal connections between these cognitive properties are not always strict, they are robust enough to warrant considering innateness to be a natural kind as used in contemporary cognitive science. (shrink)

Newton’s First Law of Motion is typically understood to govern only the motion of force-free bodies. This paper argues on textual and conceptual grounds that it is in fact a stronger, more general principle. The First Law limits the extent to which any body can change its state of motion –– even if that body is subject to impressed forces. The misunderstanding can be traced back to an error in the first English translation of Newton’s Principia, which was published a (...) few years after Newton’s death. (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)

By briefly reviewing three well-known scientific revolutions in fundamental physics (the discovery of inertia, of special relativity and of general relativity), I claim that problems that were supposed to be crying for a dynamical explanation in the old paradigm ended up receiving a structural explanation in the new one. This claim is meant to give more substance to Kuhn’s view that revolutions are accompanied by a shift in what needs to be explained, while suggesting at the same time the existence (...) of a pattern that is common to all of the discussed case-studies. It remains to be seen whether also quantum mechanics, in particular entanglement, conforms to this pattern. (shrink)

The epistemic status of Natural Selection has seemed intriguing to biologists and philosophers since the very beginning of the theory to our present times. One prominent contemporary example is Elliott Sober, who claims that NS, and some other theories in biology, and maybe in economics, are peculiar in including explanatory models/conditionals that are a priori in a sense in which explanatory models/conditionals in Classical Mechanics and most other standard theories are not. Sober’s argument focuses on some “would promote” sentences that (...) according to him, play a central role in NS explanations and are both causal and a priori. Lange and Rosenberg criticize Sober arguing that, though there may be some unspecific a priori causal claims, there are not a priori causal claims that specify particular causal factors. Although we basically agree with Lange and Rosenberg’s criticism, we think it remains silent about a second important element in Sober’s dialectics, namely his claim that, contrary to what happens in mechanics, in NS explanatory conditionals are a priori, and that this is so in quite specific explanatory models. In this paper we criticize this second element of Sober’s argument by analyzing what we take to be the four possible interpretations of Sober’s claim, and argue that, terminological preferences aside, the possible senses in which explanatory models in NS can qualify, or include elements that can qualify, as a priori, also apply to CM and other standard, highly unified theories. We conclude that this second claim is unsound, or at least that more needs to be said in order to sustain that NS explanatory models are a priori in a sense in which CM models are not. (shrink)

Many modern commentators on inertial phenomena hold (or just assume) that there is no "problem of inertia", on the grounds that either (a) no explanation is needed for such phenomena or (b) the explanation is already at hand. My purpose here is to comment on both views, defending the thesis that the problem is real and still unsolved.

In this essay, I examine the curved spacetime formulation of Newtonian gravity known as Newton–Cartan gravity and compare it with flat spacetime formulations. Two versions of Newton–Cartan gravity can be identified in the physics literature—a ‘‘weak’’ version and a ‘‘strong’’ version. The strong version has a constrained Hamiltonian formulation and consequently a well-defined gauge structure, whereas the weak version does not (with some qualifications). Moreover, the strong version is best compared with the structure of what Earman (World enough and spacetime. (...) Cambridge: MIT Press) has dubbed Maxwellian spacetime. This suggests that there are also two versions of Newtonian gravity in flat spacetime—a ‘‘weak’’ version in Maxwellian spacetime, and a ‘‘strong’’ version in Neo-Newtonian spacetime. I conclude by indicating how these alternative formulations of Newtonian gravity impact the notion of empirical indistinguishability and the debate over scientific realism. r 2004 Elsevier Ltd. All rights reserved. (shrink)

According to conventional wisdom, local gauge symmetry is not a symmetry of nature, but an artifact of how our theories represent nature. But a study of the so-called theta-vacuum appears to refute this view. The ground state of a quantized non-Abelian Yang-Mills gauge theory is characterized by a real-valued, dimensionless parameter theta—a fundamental new constant of nature. The structure of this vacuum state is often said to arise from a degeneracy of the vacuum of the corresponding classical theory, which degeneracy (...) allegedly arises from the fact that “large” (but not “small”) local gauge transformations connect physically distinct states of zero field energy. If that is right, then some local gauge transformations do generate empirical symmetries. In defending conventional wisdom against this challenge I hope to clarify the meaning of empirical symmetry while deepening our understanding of gauge transformations. I distinguish empirical from theoretical symmetries. Using Galileo’s ship and Faraday’s cube as illustrations, I say when an empirical symmetry is implied by a theoretical symmetry. I explain how the theta-vacuum arises, and how “large” gauge transformations differ from “small” ones. I then present two analogies from elementary quantum mechanics. By applying my analysis of the relation between empirical and theoretical symmetries, I show which analogy faithfully portrays the character of the vacuum state of a classical non-Abelian Yang-Mills gauge theory. The upshot is that “large” as well as “small” gauge transformations are purely formal symmetries of non-Abelian Yang-Mills gauge theories, whether classical or quantized. It is still worth distinguishing between these kinds of symmetries. An analysis of gauge within the constrained-Hamiltonian formalism yields the result that “large” gauge transformations should not be classified as gauge transformations; indeed, nor should “global” gauge transformations. In a theory in which boundary conditions are modeled dynamically, “global” gauge transformations may be associated with physical symmetries, corresponding to translations of these extra dynamical variables. Such translations are symmetries if and only if charge is conserved. But it is hard to argue that these symmetries are empirical, and in any case they do not correspond to any constant phase change in a quantum state. (shrink)

It is well-known that Newton’s theory of gravity, commonly held to describe a gravitational force, can be recast in a geometrical form: Newton- Cartan theory. It is less well-known that general relativity, an apparently geometrical theory, can be reformulated in such a way that it resembles a force theory; teleparallel gravity does just this. This raises questions. One of these concerns theoretical underdetermination. I argue that these theories do not, in fact, represent cases of worrying underdetermination. On close examination, the (...) alternative formulations are best interpreted as postulating the same spacetime ontology. In accepting this, we see that the ontological commitments of these theories cannot be directly deduced from their mathematical form. The geometrical nature of a gravitational theory is not a straightforward consequence of anything internal to that theory as a theory of gravity. Rather, it essentially relies on the rest of nature (the nongravitational interactions) conspiring to choose the appropriate set of inertial frames. (shrink)