An analysis of relational quantum mechanics

Thesis

In this thesis, I argue that no current version of Relational Quantum Mechanics (RQM) both meets its own goals and solves the problem of measurement, and the prospects that any such interpretation could be articulated are not promising.

I offer a clear illustration of the core framework of RQM and I note that all versions of RQM share an ontology of systems and events, where an event consists of a variable of a system taking a value relative to another system. An important difference can be drawn between versions of RQM which take the occurrence of events to be relative and those which take it to be absolute.

I argue that if RQM is to solve the measurement problem, it needs to specify the circumstances in which events occur. The primary literature does not offer such a specification, therefore I endeavour to construct one, accounting for both possibilities of the relative or absolute occurrence of events. I explore two avenues, which are suggested by plausibility as well as remarks in the primary literature.

First, I consider an intuition stated in Rovelli’s original formulation of RQM that the occurrence of an event involving two systems is indicated by the appearance of correlations in the quantum state relative to a third system. Unfortunately, I argue that this intuition fails to provide an adequate specification for the (relative or absolute) occurrence of events.

The failure of the correlation-based intuition suggests a different approach which is more in touch with physical practice and apparently favoured by recent writings on RQM, namely appealing to the structure offered by the dynamics. The development of this approach prompts a much needed discussion of the status of the dynamics in RQM and I argue that, given the basic framework of RMQ, the Hamiltonian must be conceived as relative to a system, just like the quantum state. Unfortunately, I conclude that the dynamics does not offer an adequate principle to specify the circumstances in which events (relatively or absolutely) occur.

Interestingly, some arguments indicate that for the occurrence of events to be absolute, it may be necessary to introduce a global collapse of the wavefunction or many worlds.

The search for a principle which defines the circumstances of events turns out to be mostly divorced from the question of which variable becomes determinate at each event, namely the preferred basis problem. I argue that, under the (unlikely) assumption that a plausible account of the circumstances of events is available, there are hopeful signs that a correlation-based rule coherent with RQM’s framework and aims may be formulated. However, the question of whether the rule picks out empirically adequate bases is not addressed.

Authors: Faglia, P

• DOI: 10.5287/ora-4rrpzv4eg
• Type of award: BPhil
• Level of award: Bachelors
• Awarding institution: University of Oxford
• Language: English
• Keywords: interpretation of quantum mechanics; measurement problem; relational quantum mechanics
• Subjects: Philosophy; Physics