Frame dependence of Kochen-Specker contextuality for relativistic spin systems
Abstract
We ask whether Kochen-Specker contextuality is Lorentz invariant. On the full Hilbert space, it is, since boosts act unitarily. Restricted to spin, it is not: momentum acts as an environment applying momentum-dependent Wigner rotations, leaving spin observables unsharp and breaking the operator identities behind state-independent contextuality. For spin 1/2 one scalar governs the loss, the packet average Δ of sin2(θW/2) (where θW is the Wigner angle); for any spin, a ray degrades at a rate set by its spin variance transverse to the boost. In the spin-only account, the Free Will Theorem's SPIN axiom fails for every Δ>0; the Yu-Oh set loses contextuality between Δ≈0.008 and $0.016$, with state independence going first; the Peres-Mermin square loses contextuality at Δ≈0.059 or $0.074$ by orientation; singlet CHSH loses nonlocality for Δ≥0.159; and a GHZ-state OR gate loses Raussendorf's contextuality certificate at Δ≈0.206. A q-plate implements the channel exactly on photon polarisation, with a retardation in place of the rapidity, so the nonlocality, GHZ and aimed-source results are testable without motion.
Related
- Automated search for highly contextual Kochen-Specker proofs
- Nonrelativistic expansions of Dirac-Coulomb energy and first order relativistic Breit potential corrections for light Atomic and molecular systems
- Einstein--Langevin source correlations in closed non-relativistic systems
- Bath-state (In)dependence of Non-Markovianity Measures in Quadratic Open Systems
- ConteXtuAlity: an open source Python package for contextuality
BibTeX
@misc{hance2026frame,
title = {{Frame dependence of Kochen-Specker contextuality for relativistic spin systems}},
author = {Jonte R. Hance and Ruben Campos Delgado},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00274},
eprint = {2610.00274},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00274},
}
RIS
TY - UNPB
TI - Frame dependence of Kochen-Specker contextuality for relativistic spin systems
AU - Jonte R. Hance
AU - Ruben Campos Delgado
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00274
UR - https://arxiv.org/abs/2610.00274
AB - We ask whether Kochen-Specker contextuality is Lorentz invariant. On the full Hilbert space, it is, since boosts act unitarily. Restricted to spin, it is not: momentum acts as an environment applying momentum-dependent Wigner rotations, leaving spin observables unsharp and breaking the operator identities behind state-independent contextuality. For spin 1/2 one scalar governs the loss, the packet average Δ of sin^2(θ_W/2) (where θ_W is the Wigner angle); for any spin, a ray degrades at a rate set by its spin variance transverse to the boost. In the spin-only account, the Free Will Theorem's SPIN axiom fails for every Δ>0; the Yu-Oh set loses contextuality between Δ≈0.008 and $0.016$, with state independence going first; the Peres-Mermin square loses contextuality at Δ≈0.059 or $0.074$ by orientation; singlet CHSH loses nonlocality for Δ≥0.159; and a GHZ-state OR gate loses Raussendorf's contextuality certificate at Δ≈0.206. A q-plate implements the channel exactly on photon polarisation, with a retardation in place of the rapidity, so the nonlocality, GHZ and aimed-source results are testable without motion.
ER -