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 $\Delta \approx 0.008$ and $0.016$, with state independence going first; the Peres-Mermin square loses contextuality at $\Delta \approx 0.059$ or $0.074$ by orientation; singlet CHSH loses nonlocality for $\Delta \ge 0.159$; and a GHZ-state OR gate loses Raussendorf's contextuality certificate at $\Delta \approx 0.206$. 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.

arXiv comment15+3 pages, 10 figures