134 research outputs found
Spacetime and Physical Equivalence
In this essay I begin to lay out a conceptual scheme for: (i) analysing
dualities as cases of theoretical equivalence; (ii) 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: (iii) the nature of spacetime in quantum
gravity; (iv) broader philosophical and physical discussions of spacetime.
(i)-(ii) proceed by analysing duality through four contrasts. A duality will be
a suitable isomorphism between models: and the four relevant contrasts are as
follows:
(a) 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.
(b) Extendable vs. unextendable theories: which can, respectively cannot, be
extended as regards their domains of application.
(c) External vs. internal intepretations: which are constructed,
respectively, by coupling the theory to another interpreted theory vs. from
within the theory itself.
(d) Theoretical vs. physical equivalence: which contrasts formal equivalence
with the equivalence of fully interpreted theories.
I apply this scheme to answering questions (iii)-(iv) for gauge/gravity
dualities. I 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.Comment: 25 pages. Winner of the essay contest "Space and Time After Quantum
Gravity" of the University of Illinois at Chicago and the University of
Genev
Spacetime and Physical Equivalence
In this essay I begin to lay out a conceptual scheme for: (i) analysing dualities as cases of theoretical equivalence; (ii) 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: (iii) the nature of spacetime in quantum gravity; (iv) broader philosophical and physical discussions of spacetime.
(i)-(ii) proceed by analysing duality through four contrasts. A duality will be a suitable isomorphism between models: and the four relevant contrasts are as follows:
(a) 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.
(b) Extendable vs. unextendable theories: which can, respectively cannot, be extended as regards their domains of application.
(c) External vs. internal intepretations: which are constructed, respectively, by coupling the theory to another interpreted theory vs. from within the theory itself.
(d) Theoretical vs. physical equivalence: which contrasts formal equivalence with the equivalence of fully interpreted theories.
I will apply this scheme to answering questions (iii)-(iv) 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 (the dimension of spacetime, tensor fields, Lie groups), 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
Planckian Scattering and Black Holes
Recently, 't Hooft's S-matrix for black hole evaporation, obtained from the
gravitational interactions between the in-falling particles and Hawking
radiation, has been generalised to include transverse effects. The action
describing the collision turned out to be a string theory action with an
antisymmetric tensor background. In this article we show that the model
reproduces both the correct longitudinal and transverse dynamics, even when one
goes beyond the eikonal approximation or particles collide at nonvanishing
incidence angles. It also gives the correct momentum tranfer that takes place
in the process. Including a curvature on the horizon provides the action with
an extra term, which can be interpreted as a dilaton contribution. The
amplitude of the scattering is seen to reproduce the Veneziano amplitude in a
certain limit, as in earlier work by 't Hooft. The theory resembles a
"holographic" field theory, in the sense that it only depends on the horizon
degrees of freedom, and the in- and out-Hilbert spaces are the same. The
operators representing the coordinates of in- and out-going particles are
non-commuting, and Heisenberg's uncertainty principle must be corrected by a
term proportional to the ratio of the ingoing momentum to the impact parameter,
times Newton's constant. Reducing to 2+1 dimensions, we find that the
coordinates satisfy an SO(2,1) algebra
The Heuristic Function of Duality
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', vs. suggesting 'new physics'. I dub these the 'theoretical' vs. 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
Book Review: Visual Representations in Science
Review of Nicola Möβner’s 'Visual Representations in Science. Concept and Epistemology'. Forthcoming in Grazer Philosophische Studien
Book Review: Visual Representations in Science
Review of Nicola Möβner’s 'Visual Representations in Science. Concept and Epistemology'. Forthcoming in Grazer Philosophische Studien
The Empirical Under-determination Argument Against Scientific Realism for Dual Theories
This paper explores the options available to the anti-realist to defend a
Quinean empirical under-determination thesis using examples of dualities. I
first explicate a version of the empirical under-determination thesis that can
be brought to bear on theories of contemporary physics. Then I identify a class
of examples of dualities that lead to empirical under-determination. But I
argue that the resulting under-determination is benign, and is not a threat to
a cautious scientific realism. Thus dualities are not new ammunition for the
anti-realist. The paper also shows how the number of possible interpretative
options about dualities that have been considered in the literature can be
reduced, and suggests a general approach to scientific realism that one may
take dualities to favour.Comment: 31 pages, 3 figure
On Empirical Equivalence and Duality
I argue that, on a judicious reading of two existing criteria--one syntactic and the other semantic--dual theories can be taken to be empirically equivalent. The judicious reading is straightforward, but leads to the surprising conclusion that very different-looking theories can have equivalent empirical content. And thus it shows how a widespread scientific practice, of interpreting duals as empirically equivalent, can be understood by a thus-far unnoticed feature of existing accounts of empirical equivalence
- …