Spacetime and Physical Equivalence

Abstract

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.

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References found in this work

New Work for a Theory of Universals.David K. Lewis - 1983 - Australasian Journal of Philosophy 61 (4):343-377.
Emergent Spacetime and Empirical (in) Coherence.Nick Huggett & Christian Wüthrich - 2013 - Studies in History and Philosophy of Modern Physics 44 (3):276-285.
Glymour and Quine on Theoretical Equivalence.Thomas William Barrett & Hans Halvorson - 2016 - Journal of Philosophical Logic 45 (5):467-483.
Target Space ≠ Space.Nick Huggett - 2017 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 59:81-88.
Dualities and Emergent Gravity: Gauge/Gravity Duality.Sebastian de Haro - 2017 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 59:109-125.

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Citations of this work

Duality and Ontology.Baptiste Le Bihan & James Read - 2018 - Philosophy Compass 13 (12):e12555.
Motivating Dualities.James Read & Thomas Møller-Nielsen - 2020 - Synthese 197 (1):263-291.
On Dualities and Equivalences Between Physical Theories.Jeremy Butterfield - forthcoming - In Christian Wüthrich, Baptiste Le Bihan & Nick Huggett (eds.), Philosophy Beyond Spacetime. Oxford: Oxford University Press.
On Symmetry and Duality.Sebastian De Haro & Jeremy Butterfield - 2021 - Synthese 198 (4):2973-3013.

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