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 $\Delta$ of $\sin^2(\theta_W/2)$ (where $\theta_W$ 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 $\Delta>0$; the Yu-Oh set loses contextuality between $\Delta\approx0.008$ and $0.016$, with state independence going first; the Peres-Mermin square loses contextuality at $\Delta\approx0.059$ or $0.074$ by orientation; singlet CHSH loses nonlocality for $\Delta\geq0.159$; and a GHZ-state OR gate loses Raussendorf's contextuality certificate at $\Delta\approx0.206$. 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.

Quantum Physics (quant-ph); Optics (physics.optics)

arXiv:2610.00274 [quant-ph]

(or arXiv:2610.00274v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.00274 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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