A conference on The Philosophical Foundations of Dualities in Physics (co-organised by Elena Castellani and Dean Rickles) will take place at DILEF (Dipartimento di Lettere e Filosofia), via Bolognese 52, Florence, on the 15 and 16 of September, 2014. The workshop is part of a Studies in the History and Philosophy of Modern Physics special issue project on the foundations of dualities. Here are list of participants and the abstracts of their talks:

# Participants

Peter Bokulich (Boston University)

Elena Castellani (University of Florence)

David Corfield (University of Kent)

Richard Dawid (Munich Centre for Mathematical Philosophy)

Sebastian de Haro (Amsterdam University College)

Doreen Fraser (University of Waterloo)

Nick Huggett (University of Illinois at Chicago)

Eleanor Knox (King’s College London)

Dean Rickles (University of Sydney)

Nic Teh (University of Cambridge)

The following will be contributing to the special issue on dualities, though are unable to speak at the workshop:

Kerry McKenzie (University of California, San Diego) – not speaking at conference

Joe Polchinski (KITP) – not speaking at conference

Tiziana Vistarini (Rutgers) – not speaking at conference

# Abstracts

- Nick Huggett, “T-Duality and the Argument for Spacetime Emergence”:
- T-duality is the simplest duality in string theory; hence

useful for laying out the general issues that arise for any duality.

After explaining the origin and formal meaning of T-duality, this essay

argues for an ontological reading of it: there is no determinate radius

to string spacetime. However, phenomenal spacetime does have a

determinate radius: I explain how these two facts are compatible, the

key consequence being that string and phenomenal spacetime are not

identical. Instead, the latter emerges from the former.

- T-duality is the simplest duality in string theory; hence

- Dean Rickles, “Duality, Equivalence, and Physical Content”:
- A duality expresses a reltionship between a pair of putatively distinct physical theories. Theories are said to be dualwhen they generate “the same physics”, where same physics is parsed in terms of, e.g., having the same amplitudes, expectation values, observable spectra, and so on. Hence, theories related by dualities can look very different while making exactly the same predictions about observable phenomena. Indeed, such theories can look sufficiently different that would-be interpreters would surely consider them to be representations of very different possible worlds. In this talk I will be concerned with the question of whether dualites reflect some deep aspect of reality, or whether they are simply a formal device that aids computations in difficult contexts (functioning in much the same way as a change of variables). This links quite naturally to problems of underdetermination, and also to the issue of what we mean by theory in such contexts. I defend a rather deflationary account fo the philosophical implications of dualities.

- Doreen Fraser, “Mathematical and Physical Equivalence in Two Cases in Modern Physics”:
- This paper presents analytic continuation in quantum field theory (QFT) as a case study to compare and contrast to dualities in string theory. Analytic continuation–a mathematical transformation taking the time variable
*t*to imaginary time*it*–was initially used as a mathematical technique for solving perturbative Feynman diagrams, and was subsequently the basis for the Euclidean field theory program for constructing non-perturbative models of interacting QFTs. At a high level of abstraction, analytic continuation is similar to some dualities in string theory in that both involve mathematical transformations which relate theories taken to be equivalent (in some sense) in virtue of the preservation of expectation values. There are also important differences between analytic continuation and dualities in string theory, the most salient of which is that QFTs are typically not taken to be physically equivalent to their analytically continued counterparts. The hope is that this compare and contrast exercise will shed light on both analytic continuation and dualities in string theory, as well as clarify general issues posed by the relationship between the mathematical equivalence and the physical equivalence of physical theories.

- This paper presents analytic continuation in quantum field theory (QFT) as a case study to compare and contrast to dualities in string theory. Analytic continuation–a mathematical transformation taking the time variable

- Richard Dawid, “String Dualities and Empirical Equivalence”:
- String dualities constitute a specific form of empirical equivalence in

physics. One may argue that, after a century when empirical equivalence

was primarily of interest to philosophy of science, the rise of duality in

string physics marks the first time that empirical equivalence takes

centre stage in physics itself. The paper will make the case, however,

that the philosophical repercussions of string dualities are in fact

directly opposed to the way the significance of empirical equivalence was

understood throughout most of the 20th century in philosophy of science as

well as physics. Comparing the canonical perspective on empirical

equivalence with the role played by duality today provides an interesting

indicator of the way string physics has altered the physicists’

perspective on physical theory building.

- String dualities constitute a specific form of empirical equivalence in

- Sebastian de Haro, “Reduction and Emergence in Holographic Scenarios for Quantum Gravity”:
- Reduction and Emergence in Holographic Scenarios for Quantum Gravity”

‘Holographic’ relations between theories have become a main theme in

quantum gravity research: a theory without gravity is in some way

equivalent to a gravitational theory with an extra dimension. ‘t Hooft

first proposed holography for evaporating black holes in 1993, “AdS/CFT”

duality is a more recent holographic topic of study. Very recently,

Verlinde has proposed that even Newton’s law of gravitation can be

related holographically to a thermodynamics of information on screens. I

discuss theory reduction and spacetime emergence in these scenarios: in

what sense are these theories equivalent or reduce to each other and

when is spacetime emergent?

- Reduction and Emergence in Holographic Scenarios for Quantum Gravity”

- David Corfield, “Duality as a Category-Theoretic Concept”
- In a paper published in 1939, Ernest Nagel described the role

that projective duality had played in the reformulation of mathematical

understanding through the turn of the nineteenth century, claiming that

the discovery of the principle of duality had freed mathematicians from

the belief that their task was to describe intuitive elements. While

instances of duality in mathematics have increased enormously through

the twentieth century, philosophers since Nagel have paid little

attention to the phenomenon. In this paper I will argue that a

reassessment is overdue. Something beyond doubt is that category theory

has an enormous amount to say on the subject, for example, in terms of

arrow reversal, dualizing objects and adjunctions. This is pointing us

to a profound change in the ‘metaphysics’ of mathematics.

- In a paper published in 1939, Ernest Nagel described the role

- Peter Bokulich, “Complementarity, Dualities, and Domains of Applicability”
- Complementarity has frequently, but mistakenly, been conflated with wave-particle duality, and this conflation has led to pervasive misunderstandings of Bohr’s views and several misguided claims of an experimental “disproof” of complementarity. In this paper, I explain what Bohr meant by complementarity, and how this is related to, but distinct from, wave-particle duality. I list a variety of possible meanings of wave-particle duality, and canvass the ways in which they are (or are not) supported by quantum physics and Bohr’s interpretation. I also examine the extent to which wave-particle duality should be viewed as an example of the sort of dualities one finds in, e.g., string theory. I argue that the most fruitful way of reading of Bohr’s account complementarity is by comparing it to current accounts of effective theories with limited domains of applicability. I conclude with some grandiose claims about the epistemological and metaphysical implications of dualities in contemporary physics.

- Nic Teh, “‘Duality’ as an inter-theoretical equivalence between Lagrangian and Hamiltonian mechanics”:
- “Duality” is often described as a form of inter-theoretical equivalence. In this talk (based on joint work with Dimitris Tsementzis), I will discuss the case of Hamiltonian and Lagrangian mechanics, and whether (in the hyper-regular scenario) one can formulate an equivalence between these theories. We shall see that this is indeed the case, based on a “symplecticization” of the relevant theories, which leads in turn to a notion of “Morita equivalence” (and indeed inter-definability). I will then compare the framework for this intertheoretic equivalence with some more sophisticated dualities in contemporary physics.

- Eleanor Knox, “The Dimensions of Duality”:
- The AdS/CFT correspondence, and other instances of holographic dualities, raise philosophical puzzles in part because they appear to involve two empirically equivalent descriptions involving spacetimes of different dimensionality. Prima facie, this raises questions about which, if either, description accurately depicts spacetime and is more fundamental. But this is not the first time we’ve encountered equivalent descriptions of different apparent dimensionality; arguments over ‘configuration space realism’ and ‘fibre bundle substantivalism’ can provide instructive examples. I’ll argue that we should divorce questions of fundamentality and questions about spacetime, and that a functionalist approach to thinking about spacetime can make dualities involving differently dimensioned spacetimes a great deal less puzzling than they at first appear.

- Elena Castellani, “Dualities and Ontological Democracy”:
- The paper elaborates on Ashoke Sen’s view that

the discovery of physical dualities in the context of quantum field

theory and string theory has radically changed our understanding of the

ultimate constituents of matter “by bringing in a sort of democracy

between all particles, elementary and composite” (Sen, 1996). I argue

that such apparently puzzling ontological features of dualities can be

better understood by following a structural approach to the objects of

physics. The background is the current discussion on structuralist

stances in physics.

- The paper elaborates on Ashoke Sen’s view that