This paper argues that ground is irreducibly plural: a group of facts can be grounded together, as a collective, even though no member of the group has a ground on its own. This kind of plural grounding is applied to the metaphysics of individuals and quantities, yielding a “structuralist” view in each case. Some more general implications of plural grounding are also discussed.

This paper sets out a moderate version of metaphysical structural realism that stands in contrast to both the epistemic structural realism of Worrall and the—radical—ontic structural realism of French and Ladyman. According to moderate structural realism, objects and relations (structure) are on the same ontological footing, with the objects being characterized only by the relations in which they stand. We show how this position fares well as regards philosophical arguments, avoiding the objections against the other two versions of structural realism. (...) In particular, we set out how this position can be applied to space-time, providing for a convincing understanding of space-time points in the standard tensor formulation of general relativity as well as in the fibre bundle formulation. (shrink)

I argue that a criterion of theoretical equivalence due to Glymour :227–251, 1977) does not capture an important sense in which two theories may be equivalent. I then motivate and state an alternative criterion that does capture the sense of equivalence I have in mind. The principal claim of the paper is that relative to this second criterion, the answer to the question posed in the title is “yes”, at least on one natural understanding of Newtonian gravitation.

Suppose that one thinks that certain symmetries of a theory reveal “surplus structure”. What would a formalism without that surplus structure look like? The conventional answer is that it would be a reduced theory: a theory which traffics only in structures invariant under the relevant symmetry. In this paper, I argue that there is a neglected alternative: one can work with a sophisticated version of the theory, in which the symmetries act as isomorphisms.

It is shown that the Hilbert-Bernays-Quine principle of identity of indiscernibles applies uniformly to all the contentious cases of symmetries in physics, including permutation symmetry in classical and quantum mechanics. It follows that there is no special problem with the notion of objecthood in physics. Leibniz's principle of sufficient reason is considered as well; this too applies uniformly. But given the new principle of identity, it no longer implies that space, or atoms, are unreal.

This paper investigates the significance of T-duality in string theory: the indistinguisha- bility with respect to all observables, of models attributing radically different radii to space – larger than the observable universe, or far smaller than the Planck length, say. Two interpretational branch points are identified and discussed. First, whether duals are physically equivalent or not: by considering a duality of the familiar simple harmonic oscillator, I argue that they are. Unlike the oscillator, there are no measurements ‘outside’ string theory (...) that could distinguish the duals. Second, whether duals agree or disagree on the radius of ‘target space’, the space in which strings evolve according to string theory. I argue for the latter position, because the alternative leaves it unknown what the radius is. Since duals are physically equivalent yet disagree on the radius of target space, it follows that the radius is indeterminate between them. Using an analysis of Brandenberger and Vafa (1989), I explain why – even so – space is observed to have a determinate, large radius. The conclusion is that observed, ‘phenomenal’ space is not target space, since a space cannot have both a determinate and indeterminate radius: instead phenomenal space must be a higher-level phenomenon, not fundamental. (shrink)

There exists a common view that for theories related by a ‘duality’, dual models typically may be taken ab initio to represent the same physical state of affairs, i.e. to correspond to the same possible world. We question this view, by drawing a parallel with the distinction between ‘interpretational’ and ‘motivational’ approaches to symmetries.

I consider two usages of the expression "gauge theory". On one, a gauge theory is a theory with excess structure; on the other, a gauge theory is any theory appropriately related to classical electromagnetism. I make precise one sense in which one formulation of electromagnetism, the paradigmatic gauge theory on both usages, may be understood to have excess structure, and then argue that gauge theories on the second usage, including Yang-Mills theory and general relativity, do not generally have excess structure (...) in this sense. (shrink)

According to 'Ontic Structural Realism' (OSR), physical objects—qua metaphysical entities—should be reconceptualised, or, more strongly, eliminated in favour of the relevant structures. In this paper I shall attempt to articulate the relationship between these putative objects and structures in terms of certain accounts of metaphysical dependence currently available. This will allow me to articulate the differences between the different forms of OSR and to argue in favour of the 'eliminativist' version. A useful context is provided by Floridi's account of the (...) relationship between 'ontic' and 'epistemic' structural realisms and I shall conclude with some brief remarks on possible extensions of OSR into other scientific domains. (shrink)

In this paper I develop a framework for relating dualities and emergence: two notions that are close to each other but also exclude one another. I adopt the conception of duality as 'isomorphism', from the physics literature, cashing it out in terms of three conditions. These three conditions prompt two conceptually different ways in which a duality can be modified to make room for emergence; and I argue that this exhausts the possibilities for combining dualities and emergence. I apply this (...) framework to gauge/gravity dualities, considering in detail three examples: AdS/CFT, Verlinde's scheme, and black holes. My main point about gauge/gravity dualities is that the theories involved, qua theories of gravity, must be background-independent. I distinguish two senses of background-independence: minimalistic and extended. I argue that the former is sufficiently strong to allow for a consistent theory of quantum gravity; and that AdS/CFT is background-independent on this account; while Verlinde's scheme best fits the extended sense of background-independence. I argue that this extended sense should be applied with some caution: on pain of throwing the baby out with the bath-water. Nevertheless, it is an interesting and potentially fruitful heuristic principle for quantum gravity theory construction. It suggests some directions for possible generalisations of gauge/gravity dualities. The interpretation of dualities is discussed; and the so-called 'internal' vs. 'external' viewpoints are articulated in terms of: epistemic and metaphysical commitments; parts vs. wholes. I then analyse the emergence of gravity in gauge/gravity dualities in terms of the two available conceptualisations of emergence; and I show how emergence in AdS/CFT and in Verlinde's scenario differ from each other. Finally, I give a novel derivation of the Bekenstein-Hawking black hole entropy formula based on Verlinde's scheme; the derivation sheds light on several aspects of Verlinde's scheme and how it compares to Bekenstein's original calculation. (shrink)

String theory promises to be able to provide us with a working theory of quantum gravity and a unified description of all fundamental forces. In string theory there are so called ‘dualities’; i.e. different theoretical formulations that are physically equivalent. In this article these dualities are investigated from a philosophical point of view. Semantic and epistemic questions relating to the problem of underdetermination of theories by data and the debate on realism concerning scientific theories are discussed. Depending on ones views (...) on semantic issues and realism different interpretations are possible of the dualities. (shrink)

In this article I assess the Invariance Principle, which states that only quantities that are invariant under the symmetries of our theories are physically real. I argue, contrary to current orthodoxy, that the variance of a quantity under a theory’s symmetries is not a sufficient basis for interpreting that theory as being uncommitted to the reality of that quantity. Rather, I argue, the variance of a quantity under symmetries only ever serves as a motivation to refrain from any commitment to (...) the quantity in question. (shrink)

This paper argues that much of the literature on interpreting scientific theories presupposes a certain picture of what interpretation involves: a picture according to which interpreting a theory is like translating from one language to another. In place of this “external” approach to interpretation, this paper proposes an “internal” approach, according to which interpretation is more concerned with delineating a theory’s internal semantic architecture.

'Holographic' relations between theories have become a main theme in quantum gravity research. These relations entail that a theory without gravity is equivalent to a gravitational theory with an extra spatial dimension. The idea of holography was first proposed in 1993 by Gerard 't Hooft on the basis of his studies of evaporating black holes. Soon afterwards the holographic 'AdS/CFT' duality was introduced, which since has been heavily studied in the string theory community and beyond. Recently, Erik Verlinde has proposed (...) that even Newton's law of gravitation can be related holographically to the thermodynamics of information on screens. We discuss inter-theoretical relations in these scenarios: what is the status of the holographic relation in them and in what sense is gravity, or spacetime, emergent? (shrink)

Weyl symmetry of the classical bosonic string Lagrangian is broken by quantization, with profound consequences described here. Reimposing symmetry requires that the background space-time satisfy the equations of general relativity: general relativity, hence classical space-time as we know it, arises from string theory. We investigate the logical role of Weyl symmetry in this explanation of general relativity: it is not an independent physical postulate but required in quantum string theory, so from a certain point of view it plays only a (...) formal role in the explanation. (shrink)

In this essay I begin to lay out a conceptual scheme for: analysing dualities as cases of theoretical equivalence; assessing when cases of theoretical equivalence are also cases of physical equivalence. The scheme is applied to gauge/gravity dualities. I expound what I argue to be their contribution to questions about: the nature of spacetime in quantum gravity; broader philosophical and physical discussions of spacetime. - proceed by analysing duality through four contrasts. A duality will be a suitable isomorphism between models: (...) and the four relevant contrasts are as follows: Bare theory: a triple of states, quantities, and dynamics endowed with appropriate structures and symmetries; vs. interpreted theory: which is endowed with, in addition, a suitable pair of interpretative maps. Extendable vs. unextendable theories: which can, respectively cannot, be extended as regards their domains of application. External vs. internal intepretations: which are constructed, respectively, by coupling the theory to another interpreted theory vs. from within the theory itself. Theoretical vs. physical equivalence: which contrasts formal equivalence with the equivalence of fully interpreted theories. I will apply this scheme to answering questions - for gauge/gravity dualities. I will argue that the things that are physically relevant are those that stand in a bijective correspondence under duality: the common core of the two models. I therefore conclude that most of the mathematical and physical structures that we are familiar with, in these models, are largely, though crucially never entirely, not part of that common core. Thus, the interpretation of dualities for theories of quantum gravity compels us to rethink the roles that spacetime, and many other tools in theoretical physics, play in theories of spacetime. (shrink)

We analyse the possibility that string-theoretic dualities present a genuine case of strong underdetermination of theory by evidence. Drawing on the parallel discussion of the hole argument, we assess the possible interpretations of dualities. We conclude that there exist at least two defensible interpretations on which dualities do not present a worrying case of underdetermination per se.

I argue that, under the glitz, dual theories are examples of theoretically equivalent descriptions of the same underlying physical content: I distinguish them from cases of genuine underdetermination on the grounds that there is no real incompatibility involved between the descriptions. The incompatibility is at the level of unphysical structure. I argue that dual pairs are in fact very strongly analogous to gauge- related solutions even for dual pairs that look the most radically distinct, such as AdS/CFT.

In this paper we present a schema for describing dualities between physical theories, and illustrate it in detail with the example of bosonization: a boson-fermion duality in two-dimensional quantum field theory. The schema develops proposals in De Haro : these proposals include construals of notions related to duality, like representation, model, symmetry and interpretation. The aim of the schema is to give a more precise criterion for duality than has so far been considered. The bosonization example, or boson-fermion duality, has (...) the feature of being simple, yet rich enough, to illustrate the most relevant aspects of our schema, which also apply to more sophisticated dualities. The richness of the example consists, mainly, in its concern with two non-trivial quantum field theories: including massive Thirring-sine-Gordon duality, and non-abelian bosonization. This prompts two comparisons with the recent philosophical literature on dualities:--- Unlike the standard cases of duality in quantum field theory and string theory, where only specific simplifying limits of the theories are explicitly known, the boson-fermion duality is known to hold {\it exactly}. This exactness can be exhibited explicitly. The bosonization example illustrates both the cases of isomorphic and {\it non-isomorphic} models: which we believe the literature on dualities has not so far discussed. (shrink)

In this paper, I discuss one form of the idea that spacetime and gravity might ‘emerge’ from quantum theory, i.e. via a holographic duality, and in particular via AdS/CFT duality. I begin by giving a survey of the general notion of duality, as well as its connection to emergence. I then review the AdS/CFT duality and proceed to discuss emergence in this context. We will see that it is difficult to find compelling arguments for the emergence of full quantum gravity (...) from gauge theory via AdS/CFT, i.e. for the boundary theory's being metaphysically more fundamental than the bulk theory. (shrink)

The AdS/CFT duality has been a source of several strong conceptual claims in the physics literature that have yet to be explored by philosophers. In this paper I focus on one of these: the extent to which spacetime geometry and locality can be said to emerge from this duality, so that neither is fundamental. I argue: that the kind of emergence in question is relatively weak, involving one kind of spacetime emerging from another kind of spacetime; inasmuch as there is (...) something conceptually interesting to say about the emergence of spacetime and locality , it is no different from that already well known to those within canonical quantum gravity; that at the core of AdS/CFT is an issue of representation and redundancy in representation. (shrink)

The idea that gauge theory has `surplus' structure poses a puzzle: in one much discussed sense, this structure is redundant; but on the other hand, it is also widely held to play an essential role in the theory. In this paper, we employ category-theoretic tools to illuminate an aspect of this puzzle. We precisify what is meant by `surplus' structure by means of functorial comparisons with equivalence classes of gauge fields, and then show that such structure is essential for any (...) theory that represents a rich collection of physically relevant fields which are `local' in nature. (shrink)

The problem of finding a covariant expression for the distribution and conservation of gravitational energy-momentum dates to the 1910s. A suitably covariant infinite-component localization is displayed, reflecting Bergmann's realization that there are infinitely many gravitational energy-momenta. Initially use is made of a flat background metric (or rather, all of them) or connection, because the desired gauge invariance properties are obvious. Partial gauge-fixing then yields an appropriate covariant quantity without any background metric or connection; one version is the collection of pseudotensors (...) of a given type, such as the Einstein pseudotensor, in _every_ coordinate system. This solution to the gauge covariance problem is easily adapted to any pseudotensorial expression (Landau-Lifshitz, Goldberg, Papapetrou or the like) or to any tensorial expression built with a background metric or connection. Thus the specific functional form can be chosen on technical grounds such as relating to Noether's theorem and yielding expected values of conserved quantities in certain contexts and then rendered covariant using the procedure described here. The application to angular momentum localization is straightforward. Traditional objections to pseudotensors are based largely on the false assumption that there is only one gravitational energy rather than infinitely many. (shrink)

The author endeavours to show two things: first, that Schrödingers (and Eckarts) demonstration in March (September) 1926 of the equivalence of matrix mechanics, as created by Heisenberg, Born, Jordan and Dirac in 1925, and wave mechanics, as created by Schrödinger in 1926, is not foolproof; and second, that it could not have been foolproof, because at the time matrix mechanics and wave mechanics were neither mathematically nor empirically equivalent. That they were is the Equivalence Myth. In order to make the (...) theories equivalent and to prove this, one has to leave the historical scene of 1926 and wait until 1932, when von Neumann finished his magisterial edifice. During the period 1926–1932 the original families of mathematical structures of matrix mechanics and of wave mechanics were stretched, parts were chopped off and novel structures were added. To Procrustean places we go, where we can demonstrate the mathematical, empirical and ontological equivalence of ‘the final versions of’ matrix mechanics and wave mechanics. -/- The present paper claims to be a comprehensive analysis of one of the pivotal papers in the history of quantum mechanics: Schrödingers equivalence paper. Since the analysis is performed from the perspective of Suppes structural view (‘semantic view’) of physical theories, the present paper can be regarded not only as a morsel of the internal history of quantum mechanics, but also as a morsel of applied philosophy of science. The paper is self-contained and presupposes only basic knowledge of quantum mechanics. For reasons of length, the paper is published in two parts; Part I appeared in the previous issue of this journal. Section 1 contains, besides an introduction, also the papers five claims and a preview of the arguments supporting these claims; so Part I, Section 1 may serve as a summary of the paper for those readers who are not interested in the detailed arguments. (shrink)

The dominance of string theory in the research landscape of quantum gravity physics (despite any direct experimental evidence) can, I think, be justified in a variety of ways. Here I focus on an argument from mathematical fertility, broadly similar to Hilary Putnam’s ‘no miracles argument’ that, I argue, many string theorists in fact espouse in some form or other. String theory has generated many surprising, useful, and well-confirmed mathematical ‘predictions’—here I focus on mirror symmetry and the mirror theorem. These predictions (...) were made on the basis of general physical principles entering into string theory. The success of the mathematical predictions are then seen as evidence for the framework that generated them. I shall attempt to defend this argument, but there are nonetheless some serious objections to be faced. These objections can only be evaded at a considerably high (philosophical) price. (shrink)

Does the need to find a quantum theory of gravity imply that the gravitational field must be quantized? Physicists working in quantum gravity routinely assume an affirmative answer, often without being aware of the metaphysical commitments that tend to underlie this assumption. The ambition of this article is to probe these commitments and to analyze some recently adduced arguments pertinent to the issue of quantization. While there exist good reasons to quantize gravity, as this analysis will show, alternative approaches to (...) gravity challenge the received wisdom. These renegade approaches do not regard gravity as a fundamental force, but rather as effective, i.e. as merely supervening on fundamental physics. I will urge that these alternative accounts at least prove the tenability of an opposition to quantization. (shrink)

I conceptualise the role of dualities in quantum gravity, in terms of their functions for theory construction. I distinguish between two functions of duality in physical practice: namely, discovering and describing ‘equivalent physics’, versus suggesting ‘new physics’. I dub these the ‘theoretical’ versus the ‘heuristic’ functions of dualities. The distinction seems to have gone largely unnoticed in the philosophical literature: and it exists both for dualities, and for the more general relation of theoretical equivalence. The paper develops the heuristic function (...) of dualities: illustrating how they can be used, if one has any luck, to find and formulate new theories. I also point to the different physical commitments about the theories in question that underlie these two functions. I show how a recently developed schema for dualities articulates the differences between the two functions. (shrink)

Richard Healey argues that the Aharonov- Bohm effect demands the recognition of either nonlocal or nonseparable physics in much the way that violations of Bell's inequality do. A careful examination of the effect and the arguments, though, shows that Healey's interpretation of the Aharonov- Bohm effect depends critically on his interpretation of gauge theories, and that the analogy with violations of Bell's inequalities fails.

The author endeavours to show two things: first, that Schrödingers (and Eckarts) demonstration in March (September) 1926 of the equivalence of matrix mechanics, as created by Heisenberg, Born, Jordan and Dirac in 1925, and wave mechanics, as created by Schrödinger in 1926, is not foolproof; and second, that it could not have been foolproof, because at the time matrix mechanics and wave mechanics were neither mathematically nor empirically equivalent. That they were is the Equivalence Myth. In order to make the (...) theories equivalent and to prove this, one has to leave the historical scene of 1926 and wait until 1932, when von Neumann finished his magisterial edifice. During the period 1926–1932 the original families of mathematical structures of matrix mechanics and of wave mechanics were stretched, parts were chopped off and novel structures were added. To Procrustean places we go, where we can demonstrate the mathematical, empirical and ontological equivalence of ‘the final versions of’ matrix mechanics and wave mechanics. -/- The present paper claims to be a comprehensive analysis of one of the pivotal papers in the history of quantum mechanics: Schrödingers equivalence paper. Since the analysis is performed from the perspective of Suppes structural view (‘semantic view’) of physical theories, the present paper can be regarded not only as a morsel of the internal history of quantum mechanics, but also as a morsel of applied philosophy of science. The paper is self-contained and presupposes only basic knowledge of quantum mechanics. For reasons of length, the paper is published in two parts; Part I appeared in the previous issue of this journal. Section 1 contains, besides an introduction, also the papers five claims and a preview of the arguments supporting these claims; so Part I, Section 1 may serve as a summary of the paper for those readers who are not interested in the detailed arguments. (shrink)

In the literature over the Ramsey-sentence approach to structural realism, there is often debate over whether structural realists can legitimately restrict the range of the second-order quantifiers, in order to avoid the Newman problem. In this paper, I argue that even if they are allowed to, it won’t help: even if the Ramsey sentence is interpreted using such restricted quantifiers, it is still an implausible candidate to capture a theory’s structural content. To do so, I use the following observation: if (...) a Ramsey sentence did encode a theory’s structural content, then two theories would be structurally equivalent just in case they have logically equivalent Ramsey sentences. I then argue that this criterion for structural equivalence is implausible, even where frame or Henkin semantics are used. (shrink)

This is a nontechnical overview of how various approaches to quantum gravity suggest modifications to the way we conceptualize space and time. A theory of quantum gravity is needed to reconcile quantum physics with general relativity, our best theory for gravity. The most popular approaches to quantum gravity are string theory and loop quantum gravity. So far, no approach has been empirically successful, and there is no commonly accepted theory. Thus, the conclusions presented here are tentative. Many approaches suggest that (...) space and time—or perhaps, it is better to talk about spacetime—might not be fundamental. Various views on how to think about time in quantum gravity are briefly presented. (shrink)

The quantum gravity program seeks a theory that handles quantum matter fields and gravity consistently. But is such a theory really required and must it involve quantizing the gravitational field? We give reasons for a positive answer to the first question, but dispute a widespread contention that it is inconsistent for the gravitational field to be classical while matter is quantum. In particular, we show how a popular argument (Eppley and Hannah 1997) falls short of a no-go theorem, and discuss (...) possible counterexamples. Important issues in the foundations of physics are shown to bear crucially on all these considerations. (shrink)

The quantum gravity program seeks a theory that handles quantum matter fields and gravity consistently. But is such a theory really required and must it involve quantizing the gravitational field? We give reasons for a positive answer to the first question, but dispute a widespread contention that it is inconsistent for the gravitational field to be classical while matter is quantum. In particular, we show how a popular argument falls short of a no-go theorem, and discuss possible counterexamples. Important issues (...) in the foundations of physics are shown to bear crucially on all these considerations. (shrink)

In this paper, some conceptual issues are addressed in order to make sense of what string theory is supposed to tell us about spacetime. The dualities in string theory are used as a starting point for our argumentation. We explore the consequences of a standard view towards these dualities, namely that the dual descriptions represent the same physical situation. Given this view, one has to understand string theory in a manner such that what counts as physical spacetime is based only (...) on the shared physical content—or common core—of the dual descriptions. In general such a spatiotemporal picture does not have to agree with, or be similar to, any of the ones suggested by naïve readings of the dual descriptions. However, in certain regimes or limits, one or the other of the initial dual descriptions may give a good effective description of physical spacetime. (shrink)

Foundations of Space-Time Theories, by Michael Friedman, falls naturally into two parts. In the first, he presents the general framework within which he will characterize and discuss space-time theories, and then he devotes a chapter each to Newtonian physics, special relativity, and general relativity. Although there is some rich philosophical discussion along the way, these chapters are, of necessity, somewhat technical expositions of the general framework in action. It is in the second part, consisting of two substantial chapters, one on (...) relationalism, the other on conventionalism, that more general philosophical issues are addressed. (shrink)