Frame dependence of Kochen-Specker contextuality for relativistic spin systems

Jonte R. Hance; Ruben Campos Delgado

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arXiv · 2610.00274

Frame dependence of Kochen-Specker contextuality for relativistic spin systems

Jonte R. Hance·Ruben Campos Delgado

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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 $\sin^2(θ_W/2)$ (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 $Δ\approx0.008$ and $0.016$, with state independence going first; the Peres-Mermin square loses contextuality at $Δ\approx0.059$ or $0.074$ by orientation; singlet CHSH loses nonlocality for $Δ\geq0.159$; and a GHZ-state OR gate loses Raussendorf's contextuality certificate at $Δ\approx0.206$. 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.

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Jonte R. Hance, Ruben Campos Delgado. 2026-09-24. Frame dependence of Kochen-Specker contextuality for relativistic spin systems. https://arxiv.org/abs/2610.00274

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