An “intrinsically mixed” state is a mixed state of a system that is ‘orthogonal’ to every pure state of that system. Although the presence of such states in the quantum theories of infinite systems is well known to those who work with such theories, intrinsically mixed states are virtually unheralded in the philosophical literature. Rob Clifton was thoroughly familiar with intrinsically mixed states. I aim here to introduce them to a wider audience—and to encourage that audience to cultivate their acquaintance (...) by suggesting that intrinsically mixed states undermine assumptions framing standard discussions of the quantum measurement problem. (shrink)

It has been argued, partly from the lack of any widely accepted solution to the measurement problem, and partly from recent results from quantum information theory, that measurement in quantum theory is best treated as a black box. However, there is a crucial difference between ‘having no account of measurement' and ‘having no solution to the measurement problem'. We know a lot about measurements. Taking into account this knowledge sheds light on quantum theory as a theory of information and computation. (...) In particular, the scheme of ‘one-way quantnum computation' takes on a new character in light of the role that reference frames play in actually carrying out any one-way quantum comptuation. ‡Thanks to audiences at the PSA and the Centre for Time, University of Sydney, for helpful comments and questions. †To contact the author, please write to: Department of Philosophy, University of South Carolina, Columbia, SC 29208; e-mail: [email protected]. (shrink)

As the theory of the atom, quantum mechanics is perhaps the most successful theory in the history of science. It enables physicists, chemists, and technicians to calculate and predict the outcome of a vast number of experiments and to create new and advanced technology based on the insight into the behavior of atomic objects. But it is also a theory that challenges our imagination. It seems to violate some fundamental principles of classical physics, principles that eventually have become a part (...) of western common sense since the rise of the modern worldview in the Renaissance. So the aim of any metaphysical interpretation of quantum mechanics is to account for these violations. (shrink)

There exist well‐known conundrums, such as measure‐theoretic paradoxes and problems of contact, which, within the context of classical physics, can be used to argue against the existence of points in space and space‐time. I examine whether quantum mechanics provides additional reasons for supposing that there are no points in space and space‐time.

This paper provides an algebraic reconstruction of Einstein’s argument for the incompleteness of quantum mechanics, in order to clarify the assumptions that underlie an understanding of Einstein completeness as categoricity.

This book presents a collection of novel contributions and reviews by renowned researchers in the foundations of quantum physics, quantum optics, and neutron physics. It is published in honor of Michael Horne, whose exceptionally clear and groundbreaking work in the foundations of quantum mechanics and interferometry, both of photons and of neutrons, has provided penetrating insight into the implications of modern physics for our understanding of the physical world. He is perhaps best known for the Clauser-Horne-Shimony-Holt (CHSH) inequality. This collection (...) includes an oral history of Michael Horne's contributions to the foundations of physics and his connections to other eminent figures in the history of the subject, among them Clifford Shull and Abner Shimony. Among the editors and contributors are John Clauser and Anton Zeilinger, recipients of the Nobel Prize in Physics 2022. (shrink)

Complementarity can be considered as the weirdest idea associated with quantum mechanics. For Bohr, Complementarity is important in order to be able to convey successfully the non-classical features of quantum mechanics. This paper discusses the epistemic and ontological implications of different new experiments that attempt to detect complementarity. Complementarity has surely survived the attempts to overcome it, yet some of these experiments have led to a more general form of complementarity. Others claim to be able to differentiate among the different (...) interpretations of quantum physics. Nonetheless, such claims have revealed contradictory representations of the ontological picture of the universe. Hence, Bohr’s position is still valid. (shrink)

I argue that philosophical issues concerning reductive explanations help constrain the construction of quantum theories with appropriate state spaces. I illustrate this general proposal with two examples of restricting attention to physical states in quantum theories: regular states and symmetry-invariant states. 1Introduction2Background2.1 Physical states2.2 Reductive explanations3The Proposed ‘Correspondence Principle’4Example: Regularity5Example: Symmetry-Invariance6Conclusion: Heuristics and Discovery.

It is well known that the process of quantization—constructing a quantum theory out of a classical theory—is not in general a uniquely determined procedure. There are many inequivalent methods that lead to different choices for what to use as our quantum theory. In this paper, I show that by requiring a condition of continuity between classical and quantum physics, we constrain and inform the quantum theories that we end up with.

The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, including over 500 references. For example, we sketch how certain intuitive ideas of the founders of quantum theory have fared in the light of current mathematical knowledge. One such idea that has certainly stood the test of time is (...) Heisenberg's `quantum-theoretical Umdeutung (reinterpretation) of classical observables', which lies at the basis of quantization theory. Similarly, Bohr's correspondence principle (in somewhat revised form) and Schroedinger's wave packets (or coherent states) continue to be of great importance in understanding classical behaviour from quantum mechanics. On the other hand, no consensus has been reached on the Copenhagen Interpretation, but in view of the parodies of it one typically finds in the literature we describe it in detail. On the assumption that quantum mechanics is universal and complete, we discuss three ways in which classical physics has so far been believed to emerge from quantum physics, namely in the limit h -> 0 of small Planck's constant (in a finite system), in the limit N goes to infinity of a large system with $N$ degrees of freedom (at fixed h), and through decoherence and consistent histories. The first limit is closely related to modern quantization theory and microlocal analysis, whereas the second involves methods of C*-algebras and the concepts of superselection sectors and macroscopic observables. In these limits, the classical world does not emerge as a sharply defined objective reality, but rather as an approximate appearance relative to certain ``classical" states and observables. Decoherence subsequently clarifies the role of such states, in that they are ``einselected", i.e. robust against coupling to the environment. Furthermore, the nature of classical observables is elucidated by the fact that they typically define (approximately) consistent sets of histories. This combination of ideas and techniques does not quite resolve the measurement problem, but it does make the point that classicality results from the elimination of certain states and observables from quantum theory. Thus the classical world is not created by observation (as Heisenberg once claimed), but rather by the lack of it. (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.

This paper considers states on the Weyl algebra of the canonical commutation relations over the phase space R^{2n}. We show that a state is regular iff its classical limit is a countably additive Borel probability measure on R^{2n}. It follows that one can "reduce" the state space of the Weyl algebra by altering the collection of quantum mechanical observables so that all states are ones whose classical limit is physical.