I consider what non-relativistic quantum field theories (NQFTs) suggest about the intertheoretic relations between classical and quantum theories of particles and fields, both in the presence and in the absence of gravitational effects. In the absence of gravity, interacting NQFTs exist for which Haag’s theorem, the CPT theorem, and the Spin Statistics theorem all do not apply; and while the Reeh-Schlieder theorem is valid, it does not have the same implications that it does in the relativistic context. Moreover, a consistent NQFT exists that includes gravitational effects. This “Newtonian” quantum theory of gravity is an example of an NQFT in a classical curved spacetime, and is not afflicted by the conceptual problems surrounding relativistic QFTs in curved spacetimes. These examples provide clues to how the fundamental theories in physics relate to each other and to the quest of formulating a fully relativistic quantum theory of gravity.

The phenomenon of broken spacetime symmetry in the quantum theory of infinite systems may force 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 survey the options for understanding the nature of the wave-function in the setting of the relativistic collapse models recently developed by Tumulka. Some of the options involve surprising features, such as backwards causation or locality.

The importance of the Unruh effect lies in the fact that, together with the related (but distinct) Hawking effect, it serves to link the three main branches of modern physics: thermal/statistical physics, relativity theory/gravitation, and quantum physics. However, different researchers can have in mind different phenomena when they speak of “the Unruh effect” in flat spacetime and its generalization to curved spacetimes. Three different approaches are reviewed here. They are shown to yield results that are sometimes concordant and sometimes discordant. The discordance is disconcerting only if one insists on taking literally the definite article in “the Unruh effect.” It is argued that the role of linking different branches of physics is better served by taking “the Unruh effect” to designate of family of related phenomena. The relation between the Hawking effect and the generalized Unruh effect for curved spacetimes is briefly discussed.

There is persistent heterodoxy in the physics literature concerning the proper treatment of those quantons that are unstable against decay. Following a brief litany of this heterodoxy, I develop some of the consequences of assuming that such quantons can exist, undecayed and isolated, at definite times and that their treatment can be carried out within a standard quantum theoretic state space. This assumption requires hyperplane dependence for the unstable quanton states and leads to clarification of some recent results concerning deviations from relativistic time dilation of decay lifetimes. In the course of the discussion I make some observations on the relationship of unstable quantons to quantum fields.

I have defended the view that an interpretation of QFT should be based on a rigorous axiomatic variant of the theory. There are two significant objections to this position: (1) that no realistic model of any set of axioms has ever been constructed (i.e., not for any interacting system in four spacetime dimensions) and (2) that there is nothing to be gained from pursuing the axiomatic program for QFT. In the course of defending myself from these objections, I will discuss some of the recent literature on constructing models for interacting systems.

The CPT theorem states that any relativistic QFT must also be invariant under CPT, the composition of charge conjugation, parity reversal and time reversal. This paper sketches a puzzle that arises when one puts the existence of this theorem alongside a standard way of thinking about symmetries, according to which spacetime symmetries are associated with features of the spacetime structure. The puzzle is that the existence of a CPT theorem seems to show that it is not possible for a well- formulated theory that does not make use of a preferred frame or foliation to make use of a temporal orientation. Since a manifold with only a Lorentzian metric can be temporally orientable, this is an odd sort of necessary connection between distinct existences. The paper then suggests a solution to the puzzle: the CPT theorem arises because temporal orientation is unlike other pieces of spacetime structure, in that one cannot represent it by a tensor field.

Recently, Simon Saunders has applied Quine’s account of discernibility to the theory of identical particles, ultimately to argue (with Muller) that quanta (bosons and fermions) can be weakly discernible. I want to expand on this work along two axes. First, to explain how the results apply to higher kinds of statistics – ‘quarticles’. Second, to dispute the claim that quanta are weakly discernible: I question whether the operators used to discern the particles do not represent the properties that they are claimed to.

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: (1) 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; (2) our best accounts of state preparation don’t work for the preparation of non-normal states; (3) there is a sense in which non-normal states fail to instantiate the laws of quantum mechanics.

The working assumption amongst most philosophers of QFT appears to be that algebraic QFT (AQFT), and not the “Lagrangian” QFT of the working physicist, is the proper object of philosophical and foundational study. I argue that this assumption is unmotivated, and fails to take into account important features of the post-1960s development of Lagrangian QFT. From a modern perspective the two forms of QFT are better seen as rival research programs than as variant formulations of one theory; furthermore, the Lagrangian research program is overwhelmingly supported by experiment.

We consider the claim that decoherence explains the emergence of classicality in quantum systems, and conclude that it cannot. We show that, given a universe composed of a variety of subsystems, some of which are macroscopic and subject to decoherence-inducing interactions, and some of which are microscopic, the macroscopic subsystems do not display any distinctively classical behavior. Therefore, a universe in which macroscopic and microscopic do display distinct behavior must be in a very special, highly nongeneric quantum state.