Jonathan Bain

Category-theoretic structure and radical ontic structural realism

Radical ontic structural realism (ROSR) claims that structure exists independently of objects that may instantiate it. Critics of ROSR contend that this claim is conceptually incoherent, insofar as, (i) it entails there can be relations without relata, and (ii) there is a conceptual dependence between relations and relata. In this essay I suggest that (ii) is motivated by a set-theoretic formulation of structure, and that adopting a category-theoretic formulation may provide ROSR with more support. In particular, I consider how a category-theoretic formulation of structure can be developed that denies (ii), and can be made to do work in the context of formulating theories in physics.

Against particle/field duality : Asymptotic particle states and interpolating fields in interacting QFT (or : Who's afraid of Haag's theorem?)

This essay touches on a number of topics in philosophy of quantum field theory from the point of view of the LSZ asymptotic approach to scattering theory. First, particle/field duality is seen to be a property of free field theory and not of interacting QFT. Second, it is demonstrated how LSZ side-steps the implicationsof Haags theorem. Finally, a recent argument due to Redhead (1995), Malament (1996) and Arageorgis (1995) against the concept of localized particle states is addressed. Briefly, the argument observes thatthe Reeh–Schlieder theorem entails that correlations between spacelike separatedvacuum expectation values of local field operators are always present,and this, according to the above authors, dictates against the notion of a localizedparticle state. I claim that this moral is excessive and that a coherentnotion of localized particles is given by the LSZ approach. The underlyingmoral to be drawn from this analysis is that questions concerning theontology of interacting QFT cannot be appropriately addressed if one restrictsoneself to the free theory.

Weinberg on QFT: Demonstrative Induction and Underdetermination

In this essay I examine a recent argument by Steven Weinberg that seeks to establish local quantum field theory as the only type of quantum theory in accord with the relevent evidence and satisfying two basic physical principles. I reconstruct the argument as a demonstrative induction and indicate its role as a foil to the underdetermination argument in the debate over scientific realism.

Einstein Algebras and the Hole Argument

Einstein algebras have been suggested (Earman 1989) and rejected (Rynasiewicz 1992) as a way to avoid the hole argument against spacetime substantivalism. In this article, I debate their merits and faults. In particular, I suggest that a gauge‐invariant interpretation of Einstein algebras that avoids the hole argument can be associated with one approach to quantizing gravity, and, for this reason, is at least as well motivated as sophisticated substantivalist and relationalist interpretations of the standard tensor formalism.

Chapter 3: Spacetime Structuralism

Abstract In this essay, I consider the ontological status of spacetime from the points of view of the standard tensor formalism and three alternatives: twistor theory, Einstein algebras, and geometric algebra. I briefly review how classical field theories can be formulated in each of these formalisms, and indicate how this suggests a structural realist interpretation of spacetime.

The Coordinate-Independent 2-Component Spinor Formalism and the Conventionality of Simultaneity

Abstract In recent articles, Zangari (1994) and Karakostas (1997) observe that while an e-extended version of the proper orthochronous Lorentz group O↑+ (1,3) exists for values of e not equal to zero, no similar e-extended version of its double covering group SL(2, C) exists (where e=1−2eR, with eR the non-standard simultaneity parameter of Reichenbach). Thus, they maintain, since SL(2, C) is essential in describing the rotational behaviour of half-integer spin fields, and since there is empirical evidence for such behaviour, e-coordinate transformations for any value of e≠0 are ruled out empirically. In this article, I make two observations: (a) There is an isomorphism between even-indexed 2-spinor fields and Minkowski world-tensors which can be exploited to obtain generally covariant expressions of such spinor fields. (b) There is a 2-1 isomorphism between odd-indexed 2-spinor fields and Minkowski world-tensors which can be exploited to obtain generally covariant expressions for such spinor fields up to a sign. Evidence that the components of such fields do take unique values is not decisive in favour of the realist in the debate over the conventionality of simultaneity in so far as such fields do not play a role in clock synchrony experiments in general, and determinations of the one-way speed of light in particular. I claim that these observations are made clear when one considers the coordinate-independent 2-spinor formalism. They are less evident if one restricts oneself to earlier coordinate-dependent formalisms. I end by distinguishing these conclusions from those drawn by the critique of Zangari given by Gunn and Vetharaniam (1995).

Chapter 16 Condensed Matter Physics and the Nature of Spacetime

Abstract This essay considers the prospects of modeling spacetime as a phenomenon that emerges in the low-energy limit of a quantum liquid. It evaluates three examples of spacetime analogues in condensed matter systems that have appeared in the recent physics literature, indicating the extent to which they are viable, and considers what they suggest about the nature of spacetime.

Pragmatists and Purists on CPT Invariance in Relativistic Quantum Field Theories

An influential claim in the physics literature states that the violation of CPT invariance in an interacting RQFT entails the violation of Lorentz invariance. This claim is surprising since standard proofs of the CPT theorem require more assumptions than Lorentz invariance, and are restricted to non-interacting, or at best, unrealistic interacting theories. This essay analyzes this claim in the context of the debate between pragmatist approaches to RQFTs, which trade mathematical rigor for the ability to derive predictions from realistic interacting theories, and purist approaches, which trade the ability to formulate realistic interacting theories for mathematical rigor.

Relativity and quantum field theory

Relativistic quantum field theories (RQFTs) are invariant under the action of the Poincare group, the symmetry group of Minkowski spacetime. Non-relativistic quantum field theories (NQFTs) are invariant under the action of the symmetry group of a classical spacetime; i.e., a spacetime that minimally admits absolute spatial and temporal metrics. This essay is concerned with cashing out two implications of this basic difference. First, under a Received View, RQFTs do not admit particle interpretations. I will argue that the concept of particle that informs this view is motivated by non-relativistic intuitions associated with the structure of classical spacetimes, and hence should be abandoned. Second, the relations between RQFTs and NQFTs also suggest that routes to quantum gravity are more varied than is typically acknowledged. The second half of this essay is concerned with mapping out some of this conceptual space.