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)

We have two aims. The main one is to expound the idea of renormalization in quantum field theory, with no technical prerequisites. Our motivation is that renormalization is undoubtedly one of the great ideas—and great successes--of twentieth-century physics. Also it has strongly influenced in diverse ways, how physicists conceive of physical theories. So it is of considerable philosophical interest. Second, we will briefly relate renormalization to Ernest Nagel's account of inter-theoretic relations, especially reduction. One theme will be a contrast between (...) two approaches to renormalization. The old approach, which prevailed from ca. 1945 to 1970, treated renormalizability as a necessary condition for being an acceptable quantum field theory. On this approach, it is a piece of great good fortune that high energy physicists can formulate renormalizable quantum field theories that are so empirically successful. But the new approach to renormalization explains why the phenomena we see, at the energies we can access in our particle accelerators, are described by a renormalizable quantum field theory. For whatever non-renormalizable interactions may occur at yet higher energies, they are insignificant at accessible energies. Thus the new approach explains why our best fundamental theories have a feature, viz. renormalizability, which the old approach treated as a selection principle for theories. That is worth saying since philosophers tend to think of scientific explanation as only explaining an individual event, or perhaps a single law, or at most deducing one theory as a special case of another. Here we see a framework in which there is a space of theories. And this framework is powerful enough to deduce that what seemed “manna from heaven” is to be expected: the good fortune is generic. We also maintain that universality, a concept stressed in renormalization theory, is essentially the familiar philosophical idea of multiple realizability; and that it causes no problems for reductions of a Nagelian kind. (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)

This is a companion to another paper. Together they rebut two widespread philosophical doctrines about emergence. The first, and main, doctrine is that emergence is incompatible with reduction. The second is that emergence is supervenience; or more exactly, supervenience without reduction.In the other paper, I develop these rebuttals in general terms, emphasising the second rebuttal. Here I discuss the situation in physics, emphasising the first rebuttal. I focus on limiting relations between theories and illustrate my claims with four examples, each (...) of them a model or a framework for modelling, from well-established mathematics or physics.I take emergence as behaviour that is novel and robust relative to some comparison class. I take reduction as, essentially, deduction. The main idea of my first rebuttal will be to perform the deduction after taking a limit of some parameter. Thus my first main claim will be that in my four examples (and many others), we can deduce a novel and robust behaviour, by taking the limit N→∞ of a parameter N.But on the other hand, this does not show that the N=∞ limit is “physically real”, as some authors have alleged. For my second main claim is that in these same examples, there is a weaker, yet still vivid, novel and robust behaviour that occurs before we get to the limit, i.e. for finite N. And it is this weaker behaviour which is physically real.My examples are: the method of arbitrary functions (in probability theory); fractals (in geometry); superselection for infinite systems (in quantum theory); and phase transitions for infinite systems (in statistical mechanics). (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)

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)

This is one of two papers about emergence, reduction and supervenience. It expounds these notions and analyses the general relations between them. The companion paper analyses the situation in physics, especially limiting relations between physical theories. I shall take emergence as behaviour that is novel and robust relative to some comparison class. I shall take reduction as deduction using appropriate auxiliary definitions. And I shall take supervenience as a weakening of reduction, viz. to allow infinitely long definitions. The overall claim (...) of this paper will be that emergence is logically independent both of reduction and of supervenience. In particular, one can have emergence with reduction, as well as without it; and emergence without supervenience, as well as with it. Of the subsidiary claims, the four main ones are: : I defend the traditional Nagelian conception of reduction ; : I deny that the multiple realizability argument causes trouble for reductions, or ``reductionism'' ; : I stress the collapse of supervenience into deduction via Beth's theorem ; : I adapt some examples already in the literature to show supervenience without emergence and vice versa. (shrink)

String theory currently is the only viable candidate for a unified description of all known natural forces. This article tries to demonstrate that the fundamental structural and methodological differences that set string theory apart from other physical theories have important philosophical consequences. Focussing on implications for the realism debate in philosophy of science, it is argued that both poles of that debate face new problems in the context of string theory. On the one hand, the claim of underdetermination of scientific (...) theory by the available empirical data, which is a pivotal element of empiricism, loses much of its plausibility. On the other hand, the dissolution of any meaningful notion of an external ontological object destroys the basis for conventional versions of scientific realism. String theory seems to suggest an intermediate position akin to Structural Realism that is based on a newly emerging principle, to be called the principle of theoretical uniqueness. (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 previous work, I described several examples combining reduction and emergence: where reduction is understood a la Ernest Nagel, and emergence is understood as behaviour that is novel. Here, my aim is again to reconcile reduction and emergence, for a case which is apparently more problematic than those I treated before: renormalization. My main point is that renormalizability being a generic feature at accessible energies gives us a conceptually unified family of Nagelian reductions. That is worth saying since philosophers tend (...) to think of scientific explanation as only explaining an individual event, or perhaps a single law, or at most deducing one theory as a special case of another. Here we see a framework in which there is a space of theories endowed with enough structure that it provides a family of reductions. (shrink)

Intuitively, a classical field theory is background-in- dependent if the structure required to make sense of its equations is itself subject to dynamical evolution, rather than being imposed ab initio. The aim of this paper is to provide an explication of this intuitive notion. Background-independence is not a not formal property of theories: the question whether a theory is background-independent depends upon how the theory is interpreted. Under the approach proposed here, a theory is fully background-independent relative to an interpretation (...) if each physical possibility corresponds to a distinct spacetime geometry; and it falls short of full background-independence to the extent that this condition fails. (shrink)

Superstring theory is an extension of conventional quantum field theory that allows for stringlike and branelike material objects besides pointlike particles. The basic foundations on which the theory is built are amazingly shaky, and, equally amazingly, it seems to be this lack of solid foundations to which the theory owes its strength. We emphasize that such a situation is legitimate only in the development phases of a new doctrine. Eventually, a more solidly founded structure must be sought.Although it is advertised (...) as a “candidate theory of quantum gravity”, we claim that string theory may not be exactly that. Rather, just like quantum field theory itself, it is a general mathematical framework for a class of theories. Its major flaw could be that it still embraces a Copenhagen view on the relation between quantum mechanics and reality, while any “theory of everything”, that is, a theory for the entire cosmos, should do better than that. (shrink)

Emergence develops a novel account of diachronic ontological emergence called transformational emergence and locates it in an established historical framework. The author shows how many problems affecting ontological emergence result from a dominant but inappropriate metaphysical tradition and provides a comprehensive assessment of current theories of emergence.

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.

This is the first of two papers concerned with the philosophical significance of dualities as applied in recent fundamental physics. The general idea is that, for its peculiarity, this ‘new’ ingredient in theory construction can open unexpected perspectives in the current philosophical reflection on contemporary physics. In particular, today’s physical dualities represent an unusual type of intertheory relation, the meaning of which deserves to be investigated. The aim is to show how discussing this point brings into play, at the same (...) time, what is intended by a 'theory’ and in which sense dualities are to be considered 'symmetries'. This paper is introductory and focusses on the first form of duality explicitly applied in twentieth century physics, that is electromagnetic duality as discussed in Dirac’s theory of magnetic poles. The extension of electromagnetic duality in the context of quantum field theory and string theory is explored in a forthcoming companion paper. (shrink)