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)

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)

'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)

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)

We discuss some aspects of the relation between dualities and gauge symmetries. Both of these ideas are of course multi-faceted, and we confine ourselves to making two points. Both points are about dualities in string theory, and both have the ‘flavour’ that two dual theories are ‘closer in content’ than you might think. For both points, we adopt a simple conception of a duality as an ‘isomorphism’ between theories: more precisely, as appropriate bijections between the two theories’ sets of states (...) and sets of quantities. The first point is that this conception of duality meshes with two dual theories being ‘gauge related’ in the general philosophical sense of being physically equivalent. For a string duality, such as T-duality and gauge/gravity duality, this means taking such features as the radius of a compact dimension, and the dimensionality of spacetime, to be ‘gauge’. The second point is much more specific. We give a result about gauge/gravity duality that shows its relation to gauge symmetries to be subtler than you might expect. For gauge theories, you might expect that the duality bijections relate only gauge-invariant quantities and states, in the sense that gauge symmetries in one theory will be unrelated to any symmetries in the other theory. This may be so in general; and indeed, it is suggested by discussions of Polchinski and Horowitz. But we show that in gauge/gravity duality, each of a certain class of gauge symmetries in the gravity/bulk theory, viz. diffeomorphisms, is related by the duality to a position-dependent symmetry of the gauge/boundary theory. (shrink)

In this paper we have two aims: first, to draw attention to the close connexion between interpretation and scientific understanding; second, to give a detailed account of how theories without a spacetime can be interpreted, and so of how they can be understood. In order to do so, we of course need an account of what is meant by a theory ‘without a spacetime’: which we also provide in this paper. We describe three tools, used by physicists, aimed at constructing (...) interpretations which are adequate for the goal of understanding. We analyse examples from high-energy physics illustrating how physicists use these tools to construct interpretations and thereby attain understanding. The examples are: the ’t Hooft approximation of gauge theories, random matrix models, causal sets, loop quantum gravity, and group field theory. (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)

We advocate an account of dualities between physical theories: the basic idea is that dual theories are isomorphic representations of a common core. We defend and illustrate this account, which we call a Schema, in relation to symmetries. Overall, the account meshes well with standard treatments of symmetries. But the distinction between the common core and the dual theories prompts a distinction between three kinds of symmetry: which we call `stipulated', `accidental' and `proper'.

We give an introductory review of gauge/gravity duality, and associated ideas of holography, emphasising the conceptual aspects. The opening sections gather the ingredients, viz. anti-de Sitter spacetime, conformal field theory and string theory, that we need for presenting, in Sect. 5, the central and original example: Maldacena’s AdS/CFT correspondence. Sections 6 and 7 develop the ideas of this example, also in applications to condensed matter systems, QCD, and hydrodynamics. Sections 8 and 9 discuss the possible extensions of holographic ideas to (...) de Sitter spacetime and to black holes. Section 10 discusses the bearing of gauge/gravity duality on two philosophical topics: the equivalence of physical theories, and the idea that spacetime, or some features of it, are emergent. (shrink)

I examine the relationship between \\)-dimensional Poincaré metrics and d-dimensional conformal manifolds, from both mathematical and physical perspectives. The results have a bearing on several conceptual issues relating to asymptotic symmetries in general relativity and in gauge–gravity duality, as follows: I draw from the remarkable work by Fefferman and Graham on conformal geometry, in order to prove two propositions and a theorem that characterise which classes of diffeomorphisms qualify as gravity-invisible. I define natural notions of gravity-invisibility that apply to the (...) diffeomorphisms of Poincaré metrics in any dimension. I apply the notions of invisibility, developed in, to gauge–gravity dualities: which, roughly, relate Poincaré metrics in \ dimensions to QFTs in d dimensions. I contrast QFT-visible versus QFT-invisible diffeomorphisms: those gravity diffeomorphisms that can, respectively cannot, be seen from the QFT. The QFT-invisible diffeomorphisms are the ones which are relevant to the hole argument in Einstein spaces. The results on dualities are surprising, because the class of QFT-visible diffeomorphisms is larger than expected, and the class of QFT-invisible ones is smaller than expected, or usually believed, i.e. larger than the PBH diffeomorphisms in Imbimbo et al. :1129, 2000, Eq. 2.6). I also give a general derivation of the asymptotic conformal Killing equation, which has not appeared in the literature before. (shrink)

While the relation between visualization and scientific understanding has been a topic of long-standing discussion, recent developments in physics have pushed the boundaries of this debate to new and still unexplored realms. For it is claimed that, in certain theories of quantum gravity, spacetime ‘disappears’: and this suggests that one may have sensible physical theories in which spacetime is completely absent. This makes the philosophical question whether such theories are intelligible, even more pressing. And if such theories are intelligible, the (...) question then is how they manage to do so. In this paper, we adapt the contextual theory of scientific understanding, developed by one of us, to fit the novel challenges posed by physical theories without spacetime. We construe understanding as a matter of skill rather than just knowledge. The appeal is thus to understanding, rather than explanation, because we will be concerned with the tools that scientists have at their disposal for understanding these theories. Our central thesis is that such physical theories can provide scientific understanding, and that such understanding does not require spacetimes of any sort. Our argument consists of four consecutive steps: We argue, from the general theory of scientific understanding, that although visualization is an oft-used tool for understanding, it is not a necessary condition for it; we criticise certain metaphysical preconceptions which can stand in the way of recognising how intelligibility without spacetime can be had; we catalogue tools for rendering theories without a spacetime intelligible; and we give examples of cases in which understanding is attained without a spacetime, and explain what kind of understanding these examples provide. (shrink)

We make two points about dualities in string theory. The first point is that the conception of duality, which we will discuss, meshes with two dual theories being ‘gauge related’ in the general philosophical sense of being physically equivalent. The second point is a result about gauge/gravity duality that shows its relation to gauge symmetries to be subtler than one might expect: each of a certain class of gauge symmetries in the gravity theory, that is, diffeomorphisms, is related to a (...) position-dependent symmetry of the gauge theory. (shrink)

I begin to develop a framework for emergence in the physical sciences. Namely, I propose to explicate ontological emergence in terms of the notion of ‘novel reference’, and of an account of interpretation as a map from theory to world. I then construe ontological emergence as the “failure of the interpretation to mesh” with an appropriate linkage map between theories. Ontological emergence can obtain between theories that have the same extension but different intensions, and between theories that have both different (...) extensions and intensions. I illustrate the framework in three examples: the emergence of spontaneous magnetisation in a ferromagnet, the emergence of masslessness, and the emergence of space, in specific models of physics. The account explains why ontological emergence is independent of reduction: namely, because emergence is primarily concerned with adequate interpretation, while the sense of reduction that is relevant here is concerned with inter-theoretic relations between uninterpreted theories. (shrink)

In this paper I review the problematic relationship between science and philosophy; in particular, I will address the question of whether science needs philosophy, and I will offer some positive perspectives that should be helpful in developing a synergetic relationship between the two. I will review three lines of reasoning often employed in arguing that philosophy is useless for science: philosophy’s death diagnosis ; the historic-agnostic argument/challenge “show me examples where philosophy has been useful for science, for I don’t know (...) of any”; the division of property argument. These arguments will be countered with three contentions to the effect that the natural sciences need philosophy. I will: point to the fallacy of anti-philosophicalism and examine the role of paradigms and presuppositions ; point out why the historical argument fails ; briefly sketch some domains of intersection of science and philosophy and how the two can have mutual synergy. I will conclude with some implications of this synergetic relationship between science and philosophy for the liberal arts and sciences. (shrink)

In this paper I analyse two closely related examples of duality and of emergence of gravity, namely AdS/CFT and Verlinde's scheme. Based on the notion of duality introduced in Dieks et al., I here elaborate on the conditions necessary for AdS/CFT to be a duality, in particular the condition of completeness. I also address what is usually seen as a desideratum for any candidate theory of quantum gravity: the background-independence of the theory and the diffeomorphism invariance of the observables. Then (...) I discuss Verlinde's scheme and the extent to which it gives a clear case of emergence of gravity. Finally, I give a novel derivation of the Bekenstein-Hawking black hole entropy formula based on Verlinde's scheme. (shrink)

We argue that dualities offer new possibilities for relating fundamentality, levels, and emergence. Namely, dualities often relate two theories whose hierarchies of levels are inverted relative to each other, and so allow for new fundamentality relations, as well as for epistemic emergence. We find that the direction of emergence typically found in these cases is opposite to the direction of emergence followed in the standard accounts. Namely, the standard emergence direction is that of decreasing fundamentality: there is emergence of less (...) fundamental, high-level entities, out of more fundamental, low-level entities. But in cases of duality, a more fundamental entity can emerge out of a less fundamental one. This possibility can be traced back to the existence of different classical limits in quantum field theories and string theories. (shrink)

The book Hidden Harmony—The Connected Worlds of Physics and Art by J.R. Leibowitz is critically reviewed. The book is intended for a general audience and does not assume prior knowledge of physics or the arts.

This essay, written on the occasion of the 10th anniversary of Mariano Artigas’s death, examines Artigas’s engagement with analytic philosophy in his philosophy of science. I argue that, overall, Artigas’s project in the philosophy of science is one of—using his own metaphor—‘building bridges’ between distinct areas of knowledge. After reviewing the function of Artigas’s philosophy of science as a bridge between science and philosophy, I analyse how he moved from classical to analytic philosophy. I then assess the extent to which (...) Artigas’s work conforms to reasonable analytic standards of clarity and precision, which can be expected from work in the philosophy of science. I conclude that, while Artigas’s dedication and production were admirable, his work remains essentially unfinished, thus inviting further research that should develop and clarify his conception of science, of its aims, its methods, progress, and of how science leads to knowledge. I attempt to assess Artigas’s philosophy of science from an objective and detached perspective. Thus the essay should be of interest to both scholars in the philosophy of science, as well as to those generally interested in Artigas-scholarship. (shrink)

The Birth of String Theory by Cappelli et al. tells the story of the beginnings of string theory and of the evolutionary process it has undergone from its origins in S-matrix theory to its current status as a candidate unification theory. The book is intended for an audience of students and researchers in physics, as well as historians and philosophers of science with some background in quantum field theory.In the 50s and early 60s, theoretical particle physics focused on formulating a (...) theory to explain the strong interactions. Due to issues with the application of perturbative quantum field theory to the strong interactions, theoretical particle physicists shifted their attention to Heisenberg’s ‘S-matrix’ theory, which focused solely on observable quantities. This endeavour led in 1968 to the breakthrough of the famous ‘Veneziano amplitude’, which along with the Dolen–Horn–Schmid duality between the s- and the t-channels led to the dual resonance model . Following Ve .. (shrink)