Online research in philosophy

A major problem facing no-collapse interpretations of quantum mechanics in the tradition of Everett is how to understand the probabilistic axiom of quantum mechanics (the Born rule) in the context of a deterministic theory in which every outcome of a measurement occurs. Deutsch claims to derive a decision-theoretic analogue of the Born rule from the non-probabilistic part of quantum mechanics and some non-probabilistic axioms of classical decision theory, and hence concludes that no probabilistic axiom is needed. I argue that Deutsch’s derivation begs the question.

We propose a definition of physical objects that aims to clarify some interpretational issues in quantum mechanics. We claim that the transformations generated by the objective properties of a physical system must be strictly interpreted as gauge transformations. We will argue that the uncertainty principle is a consequence of the mutual intertwining between objective properties and gauge-dependant properties. The proposed definition implies that in classical mechanics gauge-dependant properties are wrongly considered objective. We will conclude that, unlike classical mechanics, quantum mechanics provides a complete objective description of physical systems.

The purpose of the paper is to explore different aspects of the covariance of (mostly) non-relativistic quantum mechanics. First, doubts are expressed concerning the claim that gauge fields can be 'generated' by way of imposition of (local) gauge covariance of the single-particle wave equation. Then a brief review is given of Galilean covariance in the general case of external fields, and the connection between Galilean boosts and gauge transformations. Under time-dependent translations (and hence non-instantaneous boosts) the geometric phase associated with Schrödinger evolution is non-invariant, and the significance of this result is briefly analysed. The covariance properties of Schrödinger dynamics are then brought to bear on certain versions of the modal interpretation of quantum mechanics. The conclusion that it is only relational properties that can be considered coordinate- or gauge-independent elements of reality is reinforced by appeal to the theory of quantum reference frames due to Aharonov and Kauffher. (This paper appeared in "From Physics to Philosophy", J. Butterfield and C. Pagonis (eds.), Cambridge University Press (1999); pp. 45-70.).

The standard mathematical formulation of quantum mechanics is specified. Bohm's ontological interpretation of quantum mechanics is then shown to be incapable of providing a suitable interpretation of that formulation. It is also shown that Bohm's interpretation may well be viable for two alternative mathematical formulations of quantum mechanics, meaning that the negative result is a significant though not a devastating criticism of Bohm's interpretation. A preliminary case is made for preferring one alternative formulation over the other.

This thesis is a contribution to the debate on the implications of quantum information theory for the foundations of quantum mechanics. In Part 1, the logical and conceptual status of various notions of information is assessed. It is emphasized that the everyday notion of information is to be firmly distinguished from the technical notions arising in information theory; however it is maintained that in both settings `information' functions as an abstract noun, hence does not refer to a particular or substance (the worth of this point is illustrated in application to quantum teleportation). The claim that `Information is Physical' is assessed and argued to face a destructive dilemma. Accordingly, the slogan may not be understood as an ontological claim, but at best, as a methodological one. The reflections of Bruckner and Zeilinger (2001) and Deutsch and Hayden (2000) on the nature of information in quantum mechanics are critically assessed and some results presented on the characterization of entanglement in the Deutsch-Hayden formalism. Some philosophical aspects of quantum computation are discussed and general morals drawn concerning the nature of quantum information theory. In Part II, following some preliminary remarks, two particular information-theoretic approaches to the foundations of quantum mechanics are assessed in detail. It is argued that Zeilinger's (1999) Foundational Principle is unsuccessful as a foundational principle for quantum mechanics. The information-theoretic characterization theorem of Clifton, Bub and Halvorson (2003) is assessed more favourably, but the generality of the approach is questioned and it is argued that the implications of the theorem for the traditional foundational problems in quantum mechanics remains obscure.

Bohmian mechanics is an alternative interpretation of quantum mechanics. We outline the main characteristics of its non-relativistic formulation. Most notably it does provide a simple solution to the infamous measurement problem of quantum mechanics. Presumably the most common objection against Bohmian mechanics is based on its non-locality and its apparent conflict with relativity and quantum field theory. However, several models for a quantum field theoretical generalization do exist. We give a non-technical account of some of these models.

We analyze the geometric foundations of classical Yang-Mills theory by studying the relationships between internal relativity, locality, global/local invariance, and relationalism. Using the fiber bundle formulation of Yang-Mills theory, a precise definition of locality is proposed. We show that local gauge invariance -heuristically implemented by means of the gauge argument- is a necessary but not sufficient condition for establishing a relational theory of local internal motion. Finally, we analyze the conceptual meaning of BRST symmetry in terms of the invariance of the gauge fixed theory under general local gauge transformations.

An epistemological interpretation of quantum mechanics hinges on the claim that the distinctive features of quantum mechanics can be derived from some distinctive features of an observational basis. Old and new variations of this theme are listed. The program has a limited success in non-relativistic quantum mechanics. The crucial issue is how far it can be extended to quantum field theory without introducing significant ontological postulates. A C*-formulation covers algebraic quantum field theory, but not the standard model. Julian Schwinger’s anabatic methodology extended a strict measurement-based formulation of quantum mechanics through field theory. His extension also excluded the quark hypothesis and the standard model. Quarks and local gauge invariance are postulates that go beyond the limits of an epistemological interpretation of quantum mechanics. The ontological significance ascribed to these advances depends on the role accorded ontology.

This paper shows how the study of surpluses of structure is an interesting philosophical task. In particular I explore how local gauge symmetry in quantized Yang-Mills theories is the by-product of the specific dynamical structure of interaction. It is shown how in non relativistic quantum mechanics gauge symmetry corresponds to the freedom to locally define global features of gauge potentials. Also discussed is how in quantum field theory local gauge symmetry is replaced by BRST symmetry. This last symmetry is apparently the result of the fact that we do not know how to define quantum Yang-Mills theories without unphysical gauge boson states. Since Yang-Mills theories describe successfully three of the four fundamental interactions the elucidation of this symmetry is a pressing philosophical question.

Deutsch and Hayden claim to have provided an account of quantum mechanics which is particularly local, and which clarifies the nature of information transmission in entangled quantum systems. In this paper, a perspicuous description of their formalism is offered and their claim assessed. It proves essential to distinguish, as Deutsch and Hayden do not, between two ways of interpreting the formalism. On the first, conservative, interpretation, no benefits with respect to locality accrue that are not already available on either an Everettian or a statistical interpretation; and the conclusions regarding information flow are equivocal. The second, ontological, interpretation, offers a framework with the novel feature that global properties of quantum systems are reduced to local ones; but no conclusions follow concerning information flow in more standard quantum mechanics.