PreprintCC BY 4.0arXiv
Complete Relational Description of Spin in a Quantum Background
Abstract
The standard description of the state of a spin in quantum mechanics presupposes externally fixed directions -- a classical background. Can a spin be fully described instead in relation to other quantum mechanical systems? Poulin suggested twenty years ago group averaging over rotations the joint state of a fundamental spin and a reference spin with large angular momentum which, however, yields a classical bit in a probabilistic mixture. We revisit this idea and show that when the quantum reference system is augmented to \emph{two} large spins, the standard quantum mechanical description of a spin is recovered in the limit of large quantum numbers for the reference system.
Related
- Relational background field formulation of discrete quantum gravity models: The case of O(N) vector models in zero dimensions
- Can a Local Quantum-Mechanical Description of Physical Reality Be Considered Complete?
- Complete Modified Logarithmic Sobolev Inequalities for one-dimensional quantum Spin Chain
- Functional Renormalization for Random Matrix Theory: The relational background field method
- Non-Abelian Dirac oscillator in a uniform Yang--Mills background: spin--isospin mixing and singlet--triplet splitting
BibTeX
@misc{troger2026complete,
title = {{Complete Relational Description of Spin in a Quantum Background}},
author = {Hannah Troger and Ofek Bengyat and Thomas D. Galley and Marios Christodoulou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.15873},
eprint = {2606.15873},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.15873},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Complete Relational Description of Spin in a Quantum Background
AU - Hannah Troger
AU - Ofek Bengyat
AU - Thomas D. Galley
AU - Marios Christodoulou
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2606.15873
UR - https://arxiv.org/abs/2606.15873
AB - The standard description of the state of a spin in quantum mechanics presupposes externally fixed directions -- a classical background. Can a spin be fully described instead in relation to other quantum mechanical systems? Poulin suggested twenty years ago group averaging over rotations the joint state of a fundamental spin and a reference spin with large angular momentum which, however, yields a classical bit in a probabilistic mixture. We revisit this idea and show that when the quantum reference system is augmented to \emph{two} large spins, the standard quantum mechanical description of a spin is recovered in the limit of large quantum numbers for the reference system.
ER -