Quantum reference frames: derivation of perspective-dependent descriptions via a perspective-neutral structure

TL;DR

This paper develops a symmetry-inspired framework for describing quantum reference frames, deriving perspective-dependent descriptions and transformations from a perspective-neutral structure, with implications for constrained quantum systems.

Contribution

It introduces a unifying approach to derive and transform perspective-dependent quantum descriptions using a perspective-neutral structure, advancing understanding of quantum reference frames.

Findings

Derived a broad class of perspective-dependent descriptions

Identified Hamiltonian structure with non-commuting constraints

Constructed a quantum perspective-neutral framework

Abstract

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.