Hans Halvorson

According to the semantic view of scientific theories, theories are classes of models. I show that this view -- if taken seriously as a formal explication -- leads to absurdities. In particular, this view equates theories that are truly distinct, and it distinguishes theories that are truly equivalent. Furthermore, the semantic view lacks the resources to explicate interesting theoretical relations, such as embeddability of one theory into another. The untenability of the semantic view -- as currently formulated -- threatens to undermine scientific structuralism.

I look at the distinction between between realist and antirealist views of the quantum state. I argue that this binary classification should be reconceived as a continuum of different views about which properties of the quantum state are representationally significant. What's more, the extreme cases -- all or none --- are simply absurd, and should be rejected by all parties. In other words, no sane person should advocate extreme realism or antirealism about the quantum state. And if we focus on the reasonable views, it's no longer clear who counts as a realist, and who counts as an antirealist. Among those taking a more reasonable intermediate view, we find figures such as Bohr and Carnap -- in stark opposition to the stories we've been told.

Kierkegaard's Either-Or is a book about the choice between aesthetic, ethical, and religious approaches to life. I show that Either-Or also contains a proposal for philosophy of science, and in particular, about the ideal epistemic state for human beings. Whereas the Cartesian-Hegelian tradition conceived of the ideal state as one of detached deliberation -- i.e. "seeing the world as it is in itself" -- Kierkegaard envisions the ideal state as the achievement of equilibrium between the "spectator" and "actor" aspects of the human being. Kierkegaard's proposal thus sets the stage for Niels Bohr's "epistemological lesson of quantum mechanics".

Physical cosmology purports to establish precise and testable claims about the origin of the universe. Thus, cosmology bears directly on traditional metaphysical claims -- in particular, claims about whether the universe has a creator (i.e. God). What is the upshot of cosmology for the claims of theism? Does big-bang cosmology support theism? Do recent developments in quantum and string cosmology undermine theism? We discuss the relations between physical cosmology to theism from both historical and systematic points of view.

Within the traditional Hilbert space formalism of quantum mechanics, it is not possible to describe a particle as possessing, simultaneously, a sharp position value and a sharp momentum value. Is it possible, though, to describe a particle as possessing just a sharp position value (or just a sharp momentum value)? Some, such as Teller, have thought that the answer to this question is No - that the status of individual continuous quantities is very different in quantum mechanics than in classical mechanics. On the contrary, I shall show that the same subtle issues arise with respect to continuous quantities in classical and quantum mechanics; and that it is, after all, possible to describe a particle as possessing a sharp position value without altering the standard formalism of quantum mechanics

I argue against the claim -- advocated by Albert Einstein, Bernard Williams, and Ted Sider, among others -- that a description is objective only if it says how the world is in itself. Instead, I argue for the claim -- inspired by comments of Niels Bohr -- that a family of descriptions is objective only if they co-vary with their respective descriptive contexts. Moreover, I claim that "there is a shared objective reality" simply means that it is possible to satisfy this kind of covariance requirement.

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.

According to the premises of the fine-tuning argument, most nomologically possible universes lack intelligent life; and the fact that ours has intelligent life is best explained by supposing it was created. However, if our universe was created, then the creator chose the laws of nature, and hence chose in favor of lifeless universes. In other words, the fine-tuning argument shows that God prefers universes without intelligent life; and the fact that our universe has intelligent life provides no new evidence for God's existence.

The nature of antimatter is examined in the context of algebraic quantum field theory. It is shown that the notion of antimatter is more general than that of antiparticles. Properly speaking, then, antimatter is not matter made up of antiparticles—rather, antiparticles are particles made up of antimatter. We go on to discuss whether the notion of antimatter is itself completely general in quantum field theory. Does the matter–antimatter distinction apply to all field theoretic systems? The answer depends on which of several possible criteria we should impose on the space of physical states.

Nature seems to be such that we can describe it accurately with quantum theories of bosons and fermions alone, without resort to parastatistics. This has been seen as a deep mystery: paraparticles make perfect physical sense, so why don’t we see them in nature? We consider one potential answer: every paraparticle theory is physically equivalent to some theory of bosons or fermions, making the absence of paraparticles in our theories a matter of convention rather than a mysterious empirical discovery. We argue that this equivalence thesis holds in all physically admissible quantum field theories falling under the domain of the rigorous Doplicher–Haag–Roberts approach to superselection rules. Inadmissible parastatistical theories are ruled out by a locality-inspired principle we call charge recombination. 1 Introduction2 Paraparticles in Quantum Theory3 Theoretical Equivalence3.1 Field systems in algebraic quantum field theory3.2 Equivalence of field systems4 A Brief History of the Equivalence Thesis4.1 The Green decomposition4.2 Klein transformations4.3 The argument of Drühl, Haag, and Roberts4.4 The Doplicher–Roberts reconstruction theorem5 Sharpening the Thesis6 Discussion6.1 Interpretations of Quantum Mechanics6.2 Structuralism and haecceities6.3 Paraquark theories.

David Malament (1996) has recently argued that there can be no relativistic quantum theory of (localizable) particles. We consider and rebut several objections that have been made against the soundness of Malament’s argument. We then consider some further objections that might be made against the generality of Malament’s conclusion, and we supply three no‐go theorems to counter these objections. Finally, we dispel potential worries about the counterintuitive nature of these results by showing that relativistic quantum field theory itself explains the appearance of “particle detections.”.

Philosophical reflection on quantum field theory has tended to focus on how it revises our conception of what a particle is. However, there has been relatively little discussion of the threat to the "reality" of particles posed by the possibility of inequivalent quantizations of a classical field theory, i.e., inequivalent representations of the algebra of observables of the field in terms of operators on a Hilbert space. The threat is that each representation embodies its own distinctive conception of what a particle is, and how a "particle" will respond to a suitably operated detector. Our main goal is to clarify the subtle relationship between inequivalent representations of a field theory and their associated particle concepts. We also have a particular interest in the Minkowski versus Rindler quantizations of a free Boson field, because they respectively entail two radically different descriptions of the particle content of the field in the *very same* region of spacetime. We shall defend the idea that these representations provide *complementary descriptions* of the same state of the field against the claim that they embody completely *incommensurable theories* of the field.

Quine often argued for a simple, untyped system of logic rather than the typed systems that were championed by Russell and Carnap, among others. He claimed that nothing important would be lost by eliminating sorts, and the result would be additional simplicity and elegance. In support of this claim, Quine conjectured that every many-sorted theory is equivalent to a single-sorted theory. We make this conjecture precise, and prove that it is true, at least according to one reasonable notion of theoretical equivalence. Our clarification of Quine’s conjecture, however, exposes the shortcomings of his argument against many-sorted logic

We show that three fundamental information-theoretic constraints -- the impossibility of superluminal information transfer between two physical systems by performing measurements on one of them, the impossibility of broadcasting the information contained in an unknown physical state, and the impossibility of unconditionally secure bit commitment -- suffice to entail that the observables and state space of a physical theory are quantum-mechanical. We demonstrate the converse derivation in part, and consider the implications of alternative answers to a remaining open question about nonlocality and bit commitment.

We show that Bohr's principle of complementarity between position and momentum descriptions can be formulated rigorously as a claim about the existence of representations of the canonical commutation relations. In particular, in any representation where the position operator has eigenstates, there is no momentum operator, and vice versa. Equivalently, if there are nonzero projections corresponding to sharp position values, all spectral projections of the momentum operator map onto the zero element.

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 analyse 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 non-relativistic quantum theory and classical relativistic field theory.