Manuscript En05-B@1 · En05-B.tex · corollary · 8b626460

Corollary: Operational spacelike no-signalling

Continuum no-signalling and sharp operational speed · lines 1697–1713 · proof included or linked

En05-B@1#cor:NS

For two compact operation/readout regions satisfying

∥ x_{p} - x_{q} ∥_{2} \geq c ∣ t_{p} - t_{q} ∣ + η (p \in K_{1}, q \in K_{2})

for some $η > 0$ , a matched local replacement in either region does not change the other's unconditioned complete joint record law.

Proof. Compactness and the positive margin separate each region from the causal past of every point in the other. Apply Theorem thm:DOD to the other region's full finite record set.

Displayed formulas in this passage

unlabeled · line 1700
$∥ x_{p} - x_{q} ∥_{2} \geq c ∣ t_{p} - t_{q} ∣ + η (p \in K_{1}, q \in K_{2})$

Nearby in this section

theorem: Theorem: Matched continuum domain of dependence
section: Continuum no-signalling and sharp operational speed
corollary: Corollary: Sharp isotropic continuum maximal speed