According to spacetime state realism (SSR), 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 (QFT). 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. 1. Introduction 2. Spacetime State Realism in Quantum Field Theory 2.1. Equivalence thesis 3. Entanglement and the Type III Property 3.1. No-Go Lemma 1 3.2. No-Go Lemma 2 4. State Space Axioms for Quantum Field Theory 4.1. Revised equivalence thesis 5. Discussion
According to spacetime state realism (SSR), 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 (QFT). 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. 1. Introduction 2. Spacetime State Realism in Quantum Field Theory 2.1. Equivalence thesis 3. Entanglement and the Type III Property 3.1. No-Go Lemma 1 3.2. No-Go Lemma 2 4. State Space Axioms for Quantum Field Theory 4.1. Revised equivalence thesis 5. Discussion
The axiomatic formulation of an Algebraic Relativistic Quantum Field Theory leads naturally -via the Haag-Kastler axioms- to the fact that operators representing observables generate a von Neumann algebra localized in a space-time region in which said observations are made. I present and explain the axioms, as well as the mathematical preliminaries needed to understand them and apply them to the so-called causal diamond and Fermi's Two-Atom System. The latter shows the importance of formulating axioms concerning causality that try to make compatible the requirement from Special Relativity according to which no causal influence can travel faster than the speed of light and the quantum mechanical theory of measurement and preparability of states. For a relativistic field-theoretic setting, these concepts must be re-formulated, and this reasoning suggests that the operator algebra must be a type III von Neumann factor. I also introduce some philosophical problems concerning our usual notion of causality from Hume to contemporary theories of counterfactual causation and show how the algebraic structure of the theory is deeply related to the causal one and how this theory can be extended if we change the way we think about causality, measurements, and local preparability of states.
Some skeptical arguments on the physical reality of quantum states are given. First, I argue that the algebraic formalism of quantum field theory in curved spacetime (algebraic QFTCS, AQFTCS) leads to such a skepticism. Of course we have the purely mathematical notion of states on a C∗-algebra A, but usually in non-relativistic quantum mechanics and quantum field theory in Minkowski spacetime (QFTM), not all of them are considered to be physically real; Some of them are physically real (or realizable) states, but others are non-physical ``fictional'' states. Only the states which can be expressed as a density matrix on a fixed ``physical Hilbert space'' (the GNS representation space of A w.r.t. the vacuum) are viewed to be physically real. On the other hand, in QFTCS, there is no distinguished physical Hilbert space; no distinguished vacuum state. Thus we cannot distinguish physically real states from fictional states. The second part of my argument is a counterargument to what I call ``pragmatic realism on quantum states'', which insists as follows: ``We are permitted to regard a quantum state as a physical reality, because the concept of quantum state is indispensable in quantum physics.'' I argue that the concept of quantum state is indeed dispensable in non-relativistic QM, and hence this pragmatic realist thesis is vacuous there. I give a conjecture that it is also dispensable in QFTM and QFTCS, and some preliminary considerations on it.
Entanglement has long been the subject of discussion by philosophers of quantum theory, and has recently come to play an essential role for physicists in their development of quantum information theory. In this paper we show how the formalism of algebraic quantum field theory (AQFT) provides a rigorous framework within which to analyze entanglement in the context of a fully relativistic formulation of quantum theory. What emerges from the analysis are new practical and theoretical limitations on an experimenter’s ability to perform operations on a field in one spacetime region that can disentangle its state from the state of the field in other spacelike-separated regions. These limitations show just how deeply entrenched entanglement is in relativistic quantum field theory, and yield a fresh perspective on the ways in which the theory differs conceptually from both standard nonrelativistic quantum theory and classical relativistic field theory. “...despite its conservative way of dealing with physical principles, algebraic QFT leads to a radical change of paradigm. Instead of the Newtonian view of a space-time filled with a material content one enters the reality of Leibniz created by relation (in particular inclusions) between ‘monads ’ (∼ the hyperfinite type III1 local von Neumann factors A(O) which as single algebras are nearly void of physical meaning) ” Schroer (1998, p. 302).
What ontology does realism about the quantum state suggest? The main extant view in contemporary philosophy of physics is wave-function realism. We elaborate the sense in which wave-function realism does provide an ontological picture, and defend it from certain objections that have been raised against it. However, there are good reasons to be dissatisfied with wave-function realism, as we go on to elaborate. This motivates the development of an opposing picture: what we call spacetime state realism, a view which takes the states associated to spacetime regions as fundamental. This approach enjoys a number of beneficial features, although, unlike wave-function realism, it involves non-separability at the level of fundamental ontology. We investigate the pros and cons of this non-separability, arguing that it is a quite acceptable feature, even one which proves fruitful in the context of relativistic covariance. A companion paper discusses the prospects for combining a spacetime-based ontology with separability, along lines suggested by Deutsch and Hayden. 1 Introduction2 Prolegomena3 Wave-function Realism4 Problems with Wave-function Realism5 Spacetime State Realism6 Locality7 Non-unitary Dynamics on the Spacetime Ontology8 Relativity and Poincaré Covariance9 Finding the Appearances10 Conclusion
Introduction It is not exaggeration to claim that one of the major divides in the foundations of non-relativistic quantum mechanics derives from the way physicists and philosophers understand the status of the wave function. On the instrumentalist side of the camp, the wave function is regarded as a mere instrument to calculate probabilities that have been established by previous measurement outcomes. On the other “realistic” camp, the wave function is regarded as a new physical entity or a physical field of some sort. While both sides agree about the existence of quantum “particles” (the so-called theoretical entities), and therefore reject the radical agnosticism about them preached by van Fraassen (1980), the various “realistic” (and consequently, instrumentalist) philosophies of quantum mechanics are typically formulated in different, logically independent ways, so their implications need to be further investigated. For instance, on the one hand it seems plausible to claim that a realistic stance about the wave function is not the only way to defend “realism” about quantum theory. One can support a “flash” or a “density-of-stuff ” ontology (two variants of GRW), or an ontology of particles with well-defined positions (as in Bohmian mechanics), as primitive ontologies for observer-independent formulations of quantum mechanics (Allori, Goldstein, Tumulka and Zanghí, 2008). “Primitive ontologies”, as here are understood, are not only a fundamental ground for other ontological posits, but also entail a commitment to something concretely existing in spacetime (see also Allori, 2013). On the other hand, however, it is still debated whether such primitive ontologies can be autonomous from some form of realism about the wave function (Albert, 1996). In order to discuss this problem, we begin with a preliminary clarification of the meaning of “realism” and “instrumentalism” in physics, which are often subject to ideological and abstract discussions that often have little to do with the practice of physics (Section 9.2).
The phrase “Wave Function Realism” (WFR) has come to be used for a family of views according to which quantum theory motivates us to think that quantum wave functions are fields on a space of extremely high dimension, which is in some sense more fundamental that ordinary three-dimensional space or four-dimensional spacetime. With an aim at gaining clarity about the nature of the project, I distinguish between varieties of Wave Function Realism that one might hold. I focus on two axes of distinction. One has to do with the nature of the project. Is it an Interpretive project, one of accepting standard quantum theory pretty much as we have it, and exploring its implications for ontology? Or is it a Constructive project, which finds standard quantum theory wanting in crucial aspects, and seeks to construct a new theory that will satisfy some set of metaphysical constraints? The other has to do with how radical the claims are that are made about the nature of spacetime. Does the fundamental space on which the wave functions of WFR are defined have intrinsic structure corresponding to the low-dimensional spacetime structure? I call versions of WFR on which this is so “Mild” versions, as on such a view any sense in which the low-dimensional spatial structure is non-fundamental would be at best a highly attenuated one. A more radical view, which I call “Spicy,” has it that the fundamental space has no intrinsic structure corresponding to our low dimension spacetime, and that such structure is emergent from the structure and evolution of certain sort of wave functions. Judging from what they say about the view, it seems that proponents of WFR intend it to be Interpretive and Spicy. I will argue that there can be no such position. Standard quantum mechanics makes such heavy use of low-dimensional spacetime structure that an Interpretive version of WFR must be Extremely Mild. A Spicy but Constructive version has yet to be formulated.