This paper examines the logical and metaphysical consequences of denying Leibniz's Law, the principle that if t1= t2, then φ(t1) if and only if φ(t2). Recently, Caie, Goodman, and Lederman (2020) and Bacon and Russell (2019) have proposed sophisticated logical systems permitting violations of Leibniz's Law. We show that their systems conflict with widely held, attractive principles concerning the metaphysics of individuals. Only by adopting a highly revisionary picture, on which there is no finest-grained equivalence relation, can a well-motivated metaphysics (...) for rejecting Leibniz's Law be developed. We sketch one such picture—a metaphysics of stuff. Stuff ontologies can be initially motivated through ordinary language: stuff stands to mass nouns as objects stand to count nouns. The stuff ontology we propose takes stuff to be fundamental and views the world as composed of an infinite descending hierarchy of kinds and portions of stuff. We defend the coherence of this picture and offer a model theory demonstrating that it can be consistently formalized. (shrink)

There is debate as to whether quantum field theory is, at bottom, a quantum theory of fields or particles. One can take a field approach to the theory, using wave functionals over field configurations, or a particle approach, using wave functions over particle configurations. This article argues for a field approach, presenting three advantages over a particle approach: particle wave functions are not available for photons, a classical field model of the electron gives a superior account of both spin and (...) self-interaction as compared to a classical particle model, and the space of field wave functionals appears to be larger than the space of particle wave functions. The article also describes two important tasks facing proponents of a field approach: legitimize or excise the use of Grassmann numbers for fermionic field values and in wave functional amplitudes, and describe how quantum fields give rise to particle-like behavior. (shrink)

Distance, it is often argued, is the only coherent and empirically adequate world-making relation that can glue together the elements of the world. This paper offers entanglement as an alternative world-making relation. Entanglement is interesting since it is consistent even with quantum gravity theories that do not feature space at the fundamental level. The paper thereby defends the metaphysical salience of such non-spatial theories. An account of distance is the predominant problem of empirical adequacy facing entanglement as a world-making relation. (...) A resolution of this obstacle utilizes insights from the Ryu–Takayanagi formula and Susskind and Maldacena’s related ER = EPR conjecture. Together these indicate how distance can be recovered from entanglement and thus carves the way for entanglement fundamentalism. (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 number of arguments purport to show that quantum field theory cannot be given an interpretation in terms of localizable particles. We show, in light of such arguments, that the classical ħ→0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbar \rightarrow 0$$\end{document} limit can aid our understanding of the particle content of quantum field theories. In particular, we demonstrate that for the massive Klein–Gordon field, the classical limits of number operators can be understood to encode local information about particles (...) in the corresponding classical field theory. (shrink)

One can interpret the Dirac equation either as giving the dynamics for a classical field or a quantum wave function. Here I examine whether Maxwell’s equations, which are standardly interpreted as giving the dynamics for the classical electromagnetic field, can alternatively be interpreted as giving the dynamics for the photon’s quantum wave function. I explain why this quantum interpretation would only be viable if the electromagnetic field were sufficiently weak, then motivate a particular approach to introducing a wave function for (...) the photon :1914–1919, 1957). This wave function ultimately turns out to be unsatisfactory because the probabilities derived from it do not always transform properly under Lorentz transformations. The fact that such a quantum interpretation of Maxwell’s equations is unsatisfactory suggests that the electromagnetic field is more fundamental than the photon. (shrink)

It has been widely thought that the ontology of quantum mechanics is real, physical fields. In this paper, I will present a new argument against the field ontology of quantum mechanics by analyzing one-body systems such as an electron. First, I argue that if the physical entity described by the wave function of an electron is a field, then this field is massive and charged. Next, I argue that if a field is massive and charged, then any two parts of (...) the field in space will have gravitational and electromagnetic interactions, while the existence of such self-interactions for an electron contradicts quantum mechanics and experimental observations. This poses a serious difficulty for the field ontology of quantum mechanics. Third, I argue that a particle ontological interpretation of the wave function may avoid the difficulty by providing a plausible explanation of the non-existence of self-interactions. According to this explanation, the wave function of an electron is a description of the state of the random motion of the electron as a particle, and in particular, the modulus squared of the wave function gives the probability density that the electron appears in every possible position in space. Finally, I answer a major objection to the explanation of the non-existence of self-interactions in terms of particle ontology. (shrink)

I give an introduction to the conceptual structure of quantum field theory as it is used in mainstream theoretical physics today, aimed at non-specialists. My main focuses in the article are the common structure of quantum field theory as it is applied in solid-state physics and as it is applied in high-energy physics; the modern theory of renormalisation.

According to spacetime state realism, the fundamental ontology of a quantum mechanical world consists of a state-valued field evolving in four-dimensional spacetime. One chief advantage it claims over rival wave-function realist views is its natural compatibility with relativistic quantum field theory. I argue that the original density operator formulation of SSR cannot be extended to QFTs where the local observables form type III von Neumann algebras. Instead, I propose a new formulation of SSR in terms of a presheaf of local (...) state spaces dual to the net of local observables studied by algebraic QFT. 1Introduction2Spacetime State Realism in Quantum Field Theory 2.1Equivalence thesis3Entanglement and the Type III Property 3.1No-Go Lemma 13.2No-Go Lemma 24State Space Axioms for Quantum Field Theory 4.1Revised equivalence thesis5Discussion. (shrink)