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Bulletin of the American Physical Society

Reference Frame Dependence in Ontological Interpretations of Quantum Mechanics

Kevin Daniel Vallejo, Joseph Bernal, Andrew Dynneson

Published Mar 8, 2018• 0 citations
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In General Relativity, relational constructions yield gauge-invariant Dirac observables by expressing physical fields relative to reference frames. This leaves open how the physical situations represented in different frames should be understood. I articulate two ontological interpretations within a common fibre-bundle framework, distinguishing \emph{frame-independence} from \emph{frame-freedom} to clarify appeals to perspective-neutrality. The \emph{View from Nowhere} treats the situations characterised by relational observables as partial aspects of a shared physical situation represented by a frame-free gauge-equivalence class. The \emph{View from Everywhere} takes each relational observable to characterise a comprehensive physical situation in its own right, without commitment to a shared frame-free reality. They articulate a qualified realisation of moderate and strong physical perspectivalism within GR, respectively. Using two GPS reference frames as a working example, I show that a physically constrained, frame-independent inter-frame map supplies a constructive counterexample to the claim that connecting perspectives requires frame-free structures in the ontology. The choice between the two interpretations remains open, with their ontological commitments made explicit. I conclude by outlining possible implications for quantum reference frames and relational quantum mechanics.
Abstract In Chapter 4, the MHI was introduced in terms of interpretative postulates that define the ontological reference of each physical term of quantum mechanics in its standard formulation. On the basis of that presentation, an ontology of properties, framed in the algebraic formalism of quantum mechanics, was proposed. The aim of this chapter is to set out in detail the structure of the ontology proposed by the MHI, now with the technical metaphysical resources developed in the previous chapter. In particular, the nature of the properties that constitute the fundamental ontological items is discussed, and it is argued that quantum systems are not objects at all, but mere collections of properties that do not retain their identity either synchronically or diachronically. More precisely, quantum systems turn out to be non-objectual bundles of properties.
In standard quantum mechanics, reference frames are treated as abstract entities. We can think of them as idealized, infinite-mass subsystems which decouple from the rest of the system. In nature, however, all reference frames are realized through finite-mass systems that are subject to the laws of quantum mechanics and must be included in the dynamical evolution. A fundamental physical theory should take this fact seriously. In this paper, we further develop a symmetry-inspired approach to describe physics from the perspective of quantum reference frames. We find a unifying framework allowing us to systematically derive a broad class of perspective dependent descriptions and the transformations between them. Working with a translational-invariant toy model of three free particles, we discover that the introduction of relative coordinates leads to a Hamiltonian structure with two non-commuting constraints. This structure can be said to contain all observer-perspectives at once, while the redundancies prevent an immediate operational interpretation. We show that the operationally meaningful perspective dependent descriptions are given by Darboux coordinates on the constraint surface and that reference frame transformations correspond to reparametrizations of the constraint surface. We conclude by constructing a quantum perspective neutral structure, via which we can derive and change perspective dependent descriptions without referring to the classical theory. In addition to the physical findings, this work illuminates the interrelation of first and second class constrained systems and their respective quantization procedures.