The task of quantizing general relativity raises serious questions about the meaning of the present formulation and interpretation of quantum mechanics when applied to so fundamental a structure as the space-time geometry itself. This paper seeks to clarify the foundations of quantum mechanics. It presents a reformulation of quantum theory in a form believed suitable for application to general relativity. The aim is not to deny or contradict the conventional formulation of quantum theory, which has demonstrated its usefulness in an overwhelming variety of problems, but rather to supply a new, more general and complete formulation, from which the conventional interpretation can be deduced. The relationship of this new formulation to the older formulation is therefore that of a metatheory to a theory, that is, it is an underlying theory in which the nature and consistency, as well as the realm of applicability, of the older theory can be investigated and clarified.

"relative State" Formulation of Quantum Mechanics

Environment-induced decoherence and superselection have been a subject of intensive research over the past two decades, yet their implications for the foundational problems of quantum mechanics, most notably the quantum measurement problem, have remained a matter of great controversy. This paper is intended to clarify key features of the decoherence program, including its more recent results, and to investigate their application and consequences in the context of the main interpretive approaches of quantum mechanics.

http://faculty.up.edu/schlosshauer/publications/RevModPhys_76_001267.pdf

Decoherence, the measurement problem, and interpretations of quantum mechanics

Quantum theory: Concepts and methods

http://www.math.pitt.edu/~troy/vlad/cooper.pdf

Dynamical reduction models

We present a toy theory that is based on a simple principle: the number of questions about the physical state of a system that are answered must always be equal to the number that are unanswered in a state of maximal knowledge. Many quantum phenomena are found to have analogues within this toy theory. These include the noncommutativity of measurements, interference, the multiplicity of convex decompositions of a mixed state, the impossibility of discriminating nonorthogonal states, the impossibility of a universal state inverter, the distinction between bipartite and tripartite entanglement, the monogamy of pure entanglement, no cloning, no broadcasting, remote steering, teleportation, entanglement swapping, dense coding, mutually unbiased bases, and many others. The diversity and quality of these analogies is taken as evidence for the view that quantum states are states of incomplete knowledge rather than states of reality. A consideration of the phenomena that the toy theory fails to reproduce, notably, violations of Bell inequalities and the existence of a Kochen-Specker theorem, provides clues for how to proceed with this research program.

https://arxiv.org/pdf/quant-ph/0401052.pdf

Evidence for the epistemic view of quantum states: A toy theory

Preface Introduction 1. Overview 2. Dynamical states 3. Measurement and quantum states 4. Coupled systems 5. Metaphysical aspects 6. Alternatives compared 7. Open questions Appendix Selected bibliography Index.

The philosophy of quantum mechanics : an interactive interpretation

Holism and Nonseparability

Gauging what's real

While its applications have made quantum theory arguably the most successful theory in physics, its interpretation continues to be the subject of lively debate within the community of physicists and philosophers concerned with conceptual foundations. This situation poses a problem for a pragmatist for whom meaning derives from use. While disputes about how to use quantum theory have arisen from time to time, they have typically been quickly resolved, and consensus reached, within the relevant scientific sub-community. Yet rival accounts of the meaning of quantum theory continue to proliferate . In this article I offer a diagnosis of this situation and outline a pragmatist solution to the problem it poses, leaving further details for subsequent articles.

Quantum Theory: a Pragmatist Approach

Introduction 1. What is a Gauge Theory? 2. The Aharonov-Bohm E[currency]ect 3. Classical Gauge Theories 4. Interpreting Classical Gauge Theories 5. Quantized Yang-Mills Gauge Theories 6. The Empirical Import of Gauge Symmetry 7. Loop Representations 8. Interpreting Quantized Yang-Mills Gauge Theories 9. Conclusions

Richard Healey

Papers

The philosophy of quantum mechanics : an interactive interpretation

Holism and Nonseparability

Gauging what's real

Quantum Theory: a Pragmatist Approach

Gauging what's real : the conceptual foundations of contemporary gauge theories