Jonathan Bain
Dept. of Technology, Culture and Society
Tandon School of Engineering, New York University


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Publications
2018.
'Non-Locality in Instrinsic Topologically Ordered Systems'
Intrinsic topologically ordered (ITO) condensed matter systems are claimed to exhibit two types of non-locality: one type associated with topological properties, and the other associated with quantum entanglement. This is supposed to allow ITO systems to encode information in the form of quantum entangled states in a topologically non-local way that protects it against local errors. This is a Big Deal, since it could make possible topological quantum computation. But topological non-locality is very different conceptually from quantum entanglement non-locality. Is the Big Deal based on a misunderstanding of these two senses of non-locality? Mathematicians seem to realize the importance of the distinction, but it's unclear if condensed matter physicists do, too.
2017.
'Topological Order and Emergence'
Topologically ordered systems play a prominent role in current research in condensed matter physics (examples include integer and fractional quantum Hall systems, topological insulators, and topological superconductors). These systems cannot be characterized by the standard Landau-Ginsburg theory of phase transitions that has informed much of the discussion, in both the physics and the philosophical literature, of emergence in condensed matter systems.  Nevertheless many authors claim topologically ordered systems exhibit emergence. This essay tries to make sense of these claims.
2016.
'Emergence and Mechanism in the Fractional Quantum Hall Effect'
A fractional quantum Hall (FQH) system can be described in at least four distinct ways: (i) as a system of strongly coupled electrons in the presence of an external magnetic field; (ii) as a system of weakly coupled composite fermions (electrons with an even number of attached magnetic fluxes) in the presence of a modified external magnetic field; (iii) as a system of composite bosons (electrons with an odd number of attached magnetic fluxes) in the absence of an external magnetic field; or even (iv) as a system of strongly correlated electrons in "long-range entangled" states. These alternative formulations can be viewed as providing the bases of four distinct mechanistic explanations of the FQH effect. Many authors have claimed that FQH systems exhibit emergence. Taking them seriously, it seems to me, makes trouble for "mechanism-centric" accounts of emergence that require the specification of a unique causal mechanism. My preference is for a "law-centric" account of emergence in which novel emergent behavior is underwritten by distinct, dynamically robust laws (as opposed to causal mechanisms). I think such a "law-centric" account of emergence does just fine in explainging emergent behavior associated with the FQH effect.
2015.
'Pragmatists and Purists on CPT Invariance in RQFTs'
Greenberg (2002) claims 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 Greenberg's 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.
2014.
'Three Principles of Quantum Gravity in the Condensed Matter Approach'
Research on quantum gravity (QG) has historically relied on appeals to guiding principles. This essay frames three such principles within the context of the condensed matter approach to QG.  I first identity two distinct versions of this approach, and then consider the extent to which the principles of asymptotic safety, relative locality, and holography are supported by these versions. The general hope is that a focus on distinct versions of a single approach may provide insight into the conceptual and foundational significance of these principles.
2013e.
'Emergence in Effective Field Theories'
This essay considers the extent to which a concept of emergence can be associated with effective field theories (EFTs). I suggest that such a concept can be characterized by microphysicalism and novelty underwritten by the elimination of degrees of freedom from a high-energy theory, and argue that this makes emergence in EFTs distinct from other concepts of emergence in physics that have appeared in the recent philosophical literature.
2013d.
'CPT Invariance, the Spin-Statistics Connection, and the Ontology of RQFTs'
CPT invariance and the spin-statistics connection are typically taken to be essential properties in relativistic quantum field theories (RQFTs), insofar as the CPT and Spin-Statistics theorems entail that any state characterized by an RQFT must possess these properties. Moreover, in the physics literature, they are typically taken to be properties of particles. But there is a Received View among philosophers that RQFTs cannot fundamentally be about particles. This essay considers what proofs of the CPT and Spin-Statistics theorems suggest about the ontology of RQFTs, and the extent to which this is compatible with the Received View.
2013c.
'The Emergence of Spacetime in Condensed Matter Approaches to Quantum Gravity'
Condensed matter approaches to quantum gravity suggest that spacetime emerges in the low-energy sector of a fundamental condensate.  This essay investigates what could be meant by this claim. In particular, I offer an account of low-energy emergence that is appropriate to effective field theories in general, and consider the extent to which it underwrites claims about the emergence of spacetime in effective field theories of condensed matter sysrtems of the type that are relevant to quantum gravity.
2013b.
'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.
2013a.
'Effective Field Theory'
An effective field theory (EFT) of a physical system is a theory of the dynamics of the system at energies small compared to a given cutoff. For some systems, low-energy states with respect to this cutoff are effectively independent of ("decoupled from") states at high energies. Hence you can study the low-energy sector fo the theory without the need for a detailed description of the high-energy sector (this makes calculations easier, plus you don't have to worry about thorny issues like renormalizability). Many physicists currently think that the Standard Model of particle physics is an example of an EFT of an, as yet, unknown high-energy theory. This essay is a general review of EFTs; in particular, it identifies two conceptually distinct types ("Wilsonian" and "continuum"), and considers how they might be interpreted, and alos what they say (and do not say) about the notion of emergence.
2011.
'QFTs in Classical Spacetimes and Particles'
According to a Received View among philosophers, relativistic quantum field theories (RQFTs) do not admit particle interpretations. This view requires that particles be localizable and countable, and that these characteristics be given mathematical expression in the forms of local and total number operators. Various results (the Reeh-Schlieder theorem, the Unruh Effect, Haag's theorem) then indicate that formulations of RQFTs do not support such operators. These mathematical results, however, don't hold for non-relativistic QFTs (NQFTs).  I point out that this is due to the absolute temporal structure of the classical spacetimes associated with NQFTs. This seems to suggest that the choices that the Received View makes in mathematically representing its intuitions about the nature of particles are (implicitly) informed by non-relativistic intuitions.
2010.
'Relativity and Quantum Field Theory'
Relativistic quantum field theories (RQFTs) are invariant under the action of the symmetry group of a Lorentzian spacetime--a spacetime that admits a Lorentzian (i.e. "relativistic") metric.  Non-relativistic quantum field theories (NQFTs) are invariant under the action of a symmetry group of a classical spacetime--a spacetime that minimally admits separate absolute spatial and temporal metrics. This essay is concerned with cashing out two impliciations of this basic difference. First, it suggests that a Received View that claims RQFTs cannot support particle interpretations is perhaps implicitly biased with non-relativistic intuitions (this is argued for in more detail in 2011). Second, the relations between RQFTs and NQFTs also suggest that routes to quantum gravity are more varied than is typically acknowledged. In particular, they suggest it should be conceptually possible to construct a quantum theory of gravity by taking the "thermodynamic limit" of a relativistic "particle" (i.e. finite degrees of freedom) theory of gravity (although I have no idea how this might be made more precise).
2008.
'Condensed Matter Physics and the Nature of Spacetime'
Some condensed matter systems exhibit low-energy behavior that can be described by effective field theories that are formally similar to field theories that appear in other areas of physics. The "acoustic" spacetime research programme, for instance, is based on modeling general relativity by teh low-energy behavior of superfluid Helium 4 (and similar systems). Aspects of the Standard Model of particle physics can be modeled by the low-energy behavior of superfluid Helium 3-A, and aspects of conformal field theories (for which twistors come in handy) can be modeled by the low-energy behavior of the edge of 4-dim quantum Hall liquids. This paper evaluates such examples and considers what they have to tell us about the nature of spacetime; in particular, how they might impact the debate between substantivalists and relationalists.
2006.
'Spacetime Structuralism'
This paper goes hog-wild with a number of different mathematical formalisms (twistors, Einstein algebras, geometric algebra) that can be used to formulate classical field theories. The point is to indicate that if you're predisposed to read ontology off of your formalism, then you'd be advised to dig deep and go for some notion of structure, seeing as how alternative formalisms can be very different beasts, indeed.
2004.
'Theories of Newtonian Gravity and Empirical Indistinguishability'
There's not just one, but many theories of Newtonian gravity.  Some are in flat spactimes, others are in curved spacetimes. Are they really different theories, or just different ways of formulating the same basic theory? Inquiring minds want to know...
2003.
'Einstein Algebras and the Hole Argument'
Einstein algebras are abstract algebras that encode the essential structure associated with general relativity (GR). They've been suggested, and rejected, as a way to avoid the Infamous Hole Argument against one way of interpreting GR. This paper points out that some physicists are trying to use them to construct theories of quantum gravity, and that this gives them a bit more respectability than they've typically been afforded.
2001.
'What Should Philosophers of Science Learn from the History of the Electron?' (with John Norton)
That it's structure that's retained across theory change, and that structure is kinda hard to define in a precise way (although we do make an effort).
2000b.
'The Coordinate-Independent 2-Component Spinor Formalism and the Conventionality of Simultaneity'
Some philosophers of spacetime have claimed that the structure associated with half-integer-spin (fermionic) fields can settle the debate over the conventionality of simultaneity. This paper disputes this claim, in particular by calling attention to how fermionic fields can be represented in a manifestly coordinate-independent way.
2000a.
'Against Particle/Field Duality:  Asymptotic Particle States and Interpolating Fields in Interacting QFT (or:  Who's Afraid of Haag's Theorem?)'
This paper tries to indicate how the LSZ formalism that's used by practicing physicists suggests ways of interpreting fuzzy concepts like "particle" and "localization" in quantum field theory (as well as dealing with Haag's theorem). And that these ways are to be preferred to the ways suggested by more abstract (and expressively incomplete) formalisms (like the algebraic formalism).
1999.
'Weinberg on QFT:  Demonstrative Induction and Underdetermination'
This paper reviews an argument by Steven Weinberg that seeks to establish a particular formulation of quantum field theory as the only type of quantum theory in accord with the relevant evidence and satisfying two basic physical principles. The paper reconstructs Weinberg's argument as a demonstrative induction and indicates it's role as a (potential) foil to the underdetermination argument in the debate over scientific realism.
1998.
'Whitehead's Theory of Gravity'
Everything you ever wanted to know about Whitehead's theory of gravity...

Drafts
Front-burner
1.
'Holographic Spacetime and Quantum Error Correction Codes', in preparation.
This essay seeks to understand recent proposals that link aspects of the AdS/CFT correspondence with quantum error correction codes (QECCs). The AdS/CFT correspondence is a dictionary that relates aspects of a (d+1)-dim "bulk" gravitational theory to a d-dim "boundary" quantum field theory. One apparent problem with this dictionary is called the "bulk locality paradox": A standard way of representing a bulk field in terms of boundary fields (the AdS-Rindler representation) seems to entail that any given boundary field must be a multiple of the identity. This is very similar to a necessary and sufficient condition for QECCs, and this has motivated some authors to suggest we view the bulk theory as a code subspace that protects quantum information in the boundary from erasure. What in the world could this mean?
2.
'Why Be Natural?', in submission.
Only because naturalness underwrites a non-trivial notion of emergence for effective quantum field theories (and, arguably, not because it's empirically warranted, or more probable, or underwrites a central dogma of effective field theories)...
3.
'What Explains the Spin-Statistics Connection?', draft.
The spin-statistics connection plays an essential role in explanations of non-relativistic phenomena associated with both field-theorertic and non-field-theoretic systems (for instance, it explains the electronic structure of solids and the behavior of Einstein-Bose condensates and superconductors). However, it is only derivable within the context of relativistic quantum field theory (RQFT) in the form of the Spin-Statistics theorem; and moreover, there are multiple, mutually incompatible ways of deriving this theorem. This essay attempts to determine the sense in which the spin-statistics connection can be said to be an essential property in RQFT, and how it is that an essential property of one type of theory can figure into fundamental explanations offered by other, inherently distinct theories.

Back-burner
1.
'Pragmatists and Purists on CPT Invariance in RQFTs, Version 1'
The bloated companion to (2015).  Includes a discussion of causal perturbation theory.
2.
'Interpreting Effective Field Theories'
A condensed version of (2013a).
3.
'Motivating Structural Realist Intepretations of Spacetime'
Motivated by examples from general relativity and Newtonian gravitation, this essay attempts to distinguish between the dynamical structure associated with a theory in physics, and its kinematical structure. This enables a distinction to be made between a structural realist interpretation of a theory bvased on its dynamical structure, and a structural realist interpretation of spacetime, as described by a theory, based on its kinematical structure. I offer category-theoretic formulations of dynamical and kinematical structure, and indicate the extent to which such formulations deflect recent criticism of the radical ontic structural realist's conception of structure as "relations devoid of relata".
4.
'Condensed Matter Physics and the Nature of Spacetime, Version 1'
The bloated companion to (2008).  Includes reviews of some 2-dim EFTs in condensed matter systems.
5.
'Algebraic Substantivalism and the Hole Argument'
The bloated companion to (2003).
6.
'Towards Structural Realism'
A paper that's been stewing in its own juices for a while.  It suggests an epistemological leg for structural realism to stand on, based on formal learning theory.