Interpretations of the quantum theory

Benjamin Liebowitz

Richard Healey

This chapter begins the project of interpreting quantum gauge field theories. It rejects an interesting recent interpretation and explains why it is so difficult to arrive at a better one. The difficulty stems from the problems of interpreting any quantum field theory. Even the non-relativistic quantum mechanics of particles is a theory whose interpretation remains at best controversial, and at worst simply lacking. Interpretations of quantum field theory face the additional hurdle that it is not clear what the theory is about: neither a field nor a particle ontology is readily squared with the mathematics of the theory. The chapter explores the status of loop representations in several approaches toward the interpretation of quantum field theory.

Johanna Wolff

Quantum mechanics is a paradigmatic example of a scientific theory seemingly demanding ‘an interpretation’. What is it to ‘interpret’ a physical theory? Bas van Fraassen has recently argued that the attitude towards the task of interpreting science can be used to demarcate two otherwise similar epistemic stances: empiricism and naturalism. He claims that while empiricists are committed to the task of interpretation, naturalists cannot make sense of interpretation from outside the scientific theory. Naturalists, it seems, would have to be quietists about interpretation. Chapter 6 investigates in what form, if any, naturalists can make sense of the task of interpretation in the case of quantum mechanics. Doing so will shed light on the question whether interpretation of physical theories is a distinctively philosophical task, and what its purpose might be. It suggests that the aim of interpreting theories is to enhance our understanding, and that this task is not exclusively philosophical.

Philip Goyal

For a century, quantum theory has posed a fundamental challenge to philosophical thinking. On its face, it repudiates many of the key features of the mechanical conception of physical reality. However, the challenge of developing a precise, coherent alternative to that conception has yet to be met. Here, I argue that a major hindrance to the project of quantum interpretation is its existing interpretative methodologies, which suffer from a lack of systematicity in their judgements about what aspects of the theory are interpretational relevant. In particular, I argue that current interpretations tend to marginalize the informal part of the theory in favour of its formal part, and place inappropriate emphasis on the natural language component of the formalism over its detailed mathematical structure. To counterbalance these biases, I propose that an interpretation-free zone be constructed around the theory, wherein an interpreter initially adopt a descriptive stance which considers all parts of the theory, and that the results of this deliberation~(and the judgements about what facts are interpretationally relevant) are reported as part of their interpretation. I argue that the interpretation of quantum theory poses special challenges and difficulties which necessitate this interpretation-free zone, and that existing interpretative methodologies are insufficient to address them. Further, I argue that a reconstructive interpretative methodology, which harnesses the recent results of the quantum reconstruction program, provides a powerful means to identify almost all facts that could be interpretationally relevant, and naturally meets these challenges and difficulties. Moreover, I argue that the quantum reconstruction program offers a powerful way to discover new physical principles, and offers a systematic pathway to build a rich, coherent conception of quantum reality.

Ward Struyve

In this thesis we study the de Broglie-Bohm pilot-wave interpretation of quantum theory. We consider the domain of non-relativistic quantum theory, relativistic quantum theory and quantum field theory, and in each domain we consider the possibility of formulating a pilot-wave interpretation. For non-relativistic quantum theory a pilot-wave interpretation in terms of particle beables can readily be formulated. But this interpretation can in general not straightforwardly be generalized to relativistic wave equations. The problems which prevent us from devising a pilot-wave interpretation for relativistic wave equations also plague the standard quantum mechanical interpretation, where these problems led to the conception of quantum field theory. Therefore most of our attention is focussed on the construction of a pilot-wave interpretation for quantum field theory. We thereby favour the field beable approach, developed amongst others by Bohm, Hiley, Holland, Kaloyerou and Valentini. Although the field beable approach can be successfully applied to bosonic quantum field theory, it seems not straightforward to do so for fermionic quantum field theory.