Quantum Reference Frames: Derivation Of Perspective-dependent Descriptions Via A Perspective-neutral Structure

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.

Featured image: The image shows the central idea of the paper: A transformation to relative coordinates $q_i$, rendering the reference frame independence of the toy-model lagrangian $L(x,dot{x}) = frac{1}{2}sum_{i=1}^3 m_idot{x}_i^2-frac{M}{2}dot x^2_{cm}$ explicit. The relative coordinates are invariant under local spatial translations but redundantly defined, meaning that we can always express one $q_i$ by means of the other two. These redudancies are exploited to construct a perspective neutral structure which contains all observer perspectives at once.

► BibTeX data

@article{Zelezny2023quantumreference, doi = {10.22331/q-2023-08-29-1098}, url = {https://doi.org/10.22331/q-2023-08-29-1098}, title = {Quantum reference frames: derivation of perspective-dependent descriptions via a perspective-neutral structure}, author = {Zelezny, Viktor}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {1098}, month = aug, year = {2023}<br /> }

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

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