In this paper, I reconstruct an argument of Aristidis Arageorgis against empirical underdetermination of the state of a physical system in a C*-algebraic setting and explore its soundness. The argument, aiming against algebraic imperialism, the operationalist attitude which characterized the first steps of Algebraic Quantum Field Theory, is based on two topological properties of the state space: being T1 and being first countable in the weak*-topology. The first property is possessed trivially by the state space while the latter is highly (...) non-trivial, and it can be derived from the assumption of the algebra of observables’ separability. I present some cases of classical and of quantum systems which satisfy the separability condition, and others which do not, and relate these facts to the dimension of the algebra and to whether it is a von Neumann algebra. Namely, I show that while in the case of finite-dimensional algebras of observables the argument is conclusive, in the case of infinite-dimensional von Neumann algebras it is not. In addition, there are cases of infinite-dimensional quasilocal algebras in which the argument is conclusive. Finally, I discuss Porrmann's construction of a net of local separable algebras in Minkowski spacetime which satisfies the basic postulates of Algebraic Quantum Field Theory. (shrink)

A normal state on a von Neumann algebra defines a countably additive probability measure over its projection lattice. The von Neumann algebras familiar from ordinary QM are algebras of all the bounded operators on a Hilbert space H, aka Type I factor von Neumann algebras. Their normal states are density operator states, and can be pure or mixed. In QFT and the thermodynamic limit of QSM, von Neumann algebras of more exotic types abound. Type III von Neumann algebras, for instance, (...) have no pure normal states; the pure states they do have fail to be countably additive. I will catalog a number of temptations to accord physical significance to non-normal states, and then give some reasons to resist these temptations: pure though they may be, non-normal states on non-Type I factor von Neumann algebras can't do the interpretive work we've come to expect from pure states on Type I factors; our best accounts of state preparation don't work for the preparation of non-normal states; there is a sense in which non-normal states fail to instantiate the laws of quantum mechanics. (shrink)

In a previous article, I argued that some recent philosophical work on the use of fictions in science is, while illuminating about some aspects of current scientific practice, unduly limited to cases of well-established fictions. In other words, this earlier work contended, a philosophical account of scientific fictions can do more than merely describe scientific practices, but can aid in the resolution of disputes about the proper interpretation of scientific theories and the epistemic status of some scientific models. In the (...) present paper, I expand upon the variational account of fictions and idealizations... (shrink)

This paper explores the argument structure of the concept of spontaneous symmetry breaking in the electroweak gauge theory of the Standard Model: the so-called Higgs mechanism. As commonly understood, the Higgs argument is designed to introduce the masses of the gauge bosons by a spontaneous breaking of the gauge symmetry of an additional field, the Higgs field. The technical derivation of the Higgs mechanism, however, consists in a mere reshuffling of degrees of freedom by transforming the Higgs Lagrangian in a (...) gauge-invariant manner. This already raises serious doubts about the adequacy of the entire manoeuvre. It will be shown that no straightforward ontic interpretation of the Higgs mechanism is tenable, since gauge transformations possess no real instantiations. In addition, the explanatory value of the Higgs argument will be critically examined. (shrink)

The paper addresses a problem for the unification of quantum physics with the new Aristotelianism: the identification of the members of the category of substance. I outline briefly the role that substance plays in Aristotelian metaphysics, leading to the postulating of the Tiling Constraint. I then turn to the question of which entities in quantum physics can qualify as Aristotelian substances. I offer an answer: the theory of thermal substances, and I construct a fivefold case for thermal substances, based on (...) the irreversibility of time, the definition of thermodynamic concepts, spontaneous symmetry breaking, phase transitions, and chemical form. (shrink)

An Aristotelian philosophy of nature rejects the modern prejudice in favor of the microscopic, a rejection that is crucial if we are to penetrate the mysteries of the quantum world. I defend an Aristotelian model by drawing on both quantum chemistry and recent work on the measurement problem. By building on the work of Hans Primas, using the distinction between quantum and classical properties that emerges in quantum chemistry at the thermodynamic or continuum limit, I develop a new version of (...) the Copenhagen interpretation, a version that is realist, holistic, and hylomorphic in character, allowing for the attribution of fundamental causal powers to human observers and their instruments. I conclude with a critique of non-hylomorphic theories of primitive ontology, including Bohmian mechanics, Everettianism, and GRW mass-density. (shrink)

Ruetsche ([2011]) argues that the occurrence of unitarily inequivalent representations in quantum theories with infinitely many degrees of freedom poses a novel interpretational problem. According to Ruetsche, such theories compel us to reject the so-called ideal of pristine interpretation; she puts forward the ‘coalescence approach’ as an alternative. In this paper I offer a novel defence of the coalescence approach. The defence rests on the claim that the ideal of pristine interpretation already fails before one considers the peculiarities of QM∞: (...) there are pre-QM∞ parallels to coalescence. Despite this departure from pristinism, the ‘modest’ view that emerges poses no threat to scientific realism. (shrink)

A closer look at some proposed Gedanken-experiments on BECs promises to shed light on several aspects of reduction and emergence in physics. These include the relations between classical descriptions and different quantum treatments of macroscopic systems, and the emergence of new properties and even new objects as a result of spontaneous symmetry breaking.

Ruetsche argues that a problem of unitarily inequivalent representations arises in quantum theories with infinitely many degrees of freedom. I provide an algebraic formulation of classical field theories and show that unitarily inequivalent representations arise there as well. I argue that the classical case helps us rule out one possible response to the problem of unitarily inequivalent representations called Hilbert Space Conservatism.

Ruetsche claims that an abstract C*-algebra of observables will not contain all of the physically significant observables for a quantum system with infinitely many degrees of freedom. This would signal that in addition to the abstract algebra, one must use Hilbert space representations for some purposes. I argue to the contrary that there is a way to recover all of the physically significant observables by purely algebraic methods. 1 Introduction2 Preliminaries3 Three Extremist Interpretations3.1 Algebraic imperialism3.2 Hilbert space conservatism3.3 Universalism4 Parochial (...) Observables4.1 Parochial observables for the imperialist4.2 Parochial observables for the universalist5 Conclusion. (shrink)

ABSTRACT Ruetsche claims that an abstract C*-algebra of observables will not contain all of the physically significant observables for a quantum system with infinitely many degrees of freedom. This would signal that in addition to the abstract algebra, one must use Hilbert space representations for some purposes. I argue to the contrary that there is a way to recover all of the physically significant observables by purely algebraic methods. 1Introduction 2Preliminaries 3Three Extremist Interpretations 3.1Algebraic imperialism 3.2Hilbert space conservatism 3.3Universalism 4Parochial (...) Observables 4.1Parochial observables for the imperialist 4.2Parochial observables for the universalist 5Conclusion. (shrink)

In this article, I examine the relationship between physical quantities and physical states in quantum theories. I argue against the claim made by Arageorgis that the approach to interpreting quantum theories known as Algebraic Imperialism allows for “too many states.” I prove a result establishing that the Algebraic Imperialist has very general resources that she can employ to change her abstract algebra of quantities in order to rule out unphysical states.

We pose and resolve a puzzle about spontaneous symmetry breaking in the quantum theory of infinite systems. For a symmetry to be spontaneously broken, it must not be implementable by a unitary operator in a ground state's GNS representation. But Wigner's theorem guarantees that any symmetry's action on states is given by a unitary operator. How can this unitary operator fail to implement the symmetry in the GNS representation? We show how it is possible for a unitary operator of this (...) sort to connect the folia of unitarily inequivalent representations. This result undermines interpretations of quantum theory that hold unitary equivalence to be necessary for physical equivalence. (shrink)

The phenomenon of broken spacetime symmetry in the quantum theory of infinite systems forces us to adopt an unorthodox ontology. We must abandon the standard conception of the physical meaning of these symmetries, or else deny the attractive “liberal” notion of which physical quantities are significant. A third option, more attractive but less well understood, is to abandon the existing (Halvorson-Clifton) notion of intertranslatability for quantum theories.

I examine some problems standing in the way of a successful `field interpretation' of quantum field theory. The most popular extant proposal depends on the Hilbert space of `wavefunctionals.' But since wavefunctional space is unitarily equivalent to many-particle Fock space, two of the most powerful arguments against particle interpretations also undermine this form of field interpretation. IntroductionField Interpretations and Field OperatorsThe Wavefunctional InterpretationFields and Inequivalent Representations 4.1. The Rindler representation 4.2. Spontaneous symmetry breaking 4.3. Coherent representations The Fate of Fields (...) in Interacting QFTConclusions. (shrink)

Spontaneous symmetry breaking in quantum systems, such as ferromagnets, is normally described as degeneracy of the ground state; however, it is well established that this degeneracy only occurs in spatially infinite systems, and even better established that ferromagnets are not spatially infinite. I review this well-known paradox, and consider a popular solution where the symmetry is explicitly broken by some external field which goes to zero in the infinite-volume limit; although this is formally satisfactory, I argue that it must be (...) rejected as a physical explanation of SSB since it fails to reproduce some important features of the phenomenology. Motivated by considerations from the analogous classical system, I argue that SSB in finite systems should be understood in terms of the approximate decoupling of the system's state space into dynamically-isolated sectors, related by a symmetry transformation; I use the formalism of decoherent histories to make this more precise and to quantify the effect, showing that it is more than sufficient to explain SSB in realistic systems and that it goes over in a smooth and natural way to the infinite limit. (shrink)

This paper attempts to make sense of a notion of ``approximation on certain scales'' in physical theories. I use this notion to understand the classical limit of ordinary quantum mechanics as a kind of scaling limit, showing that the mathematical tools of strict quantization allow one to make the notion of approximation precise. I then compare this example with the scaling limits involved in renormalization procedures for effective field theories. I argue that one does not yet have the mathematical tools (...) to make a notion of ``approximation on certain scales" precise in extant mathematical formulations of effective field theories. This provides guidance on the kind of further work that is needed for an adequate interpretation of quantum field theory. (shrink)

This essay expounds the algebraic framework describing general physical theories, within which the phenomenon of spontaneous symmetry breaking makes its appearance in infinite quantum systems. This is in contrast with the fact that a large class of theories - both classical and quantum, finite and infinite - are termed, in the conventional account of classical and quantum mechanics, as exhibiting SSB. This discrepancy will be understood in the light of an interpretation that finds the symmetry breaking to be in some (...) respects stronger in the algebraic account than is generally the case in the conventional picture. The case of SSB in the standard account of quantum field theory will then be discussed, and it will be argued that, although one would expect a connection with the algebraic account to be possible, this turns out to be problematic. Finally the role of the idealisation of infinite systems, crucial to algebraic SSB, will be discussed. (shrink)