non-relativistic quantum systems with local interactions still have a speed limit. correlations outside the cone $|x| > vt$ are suppressed exponentially, so an effective light cone emerges from locality alone, with $v$ set by the interaction strength rather than by $c$
observed directly: a quench in a one-dimensional cold-atom lattice spreads correlations along a sharp cone (Cheneau 2012)
its static companion is exponential clustering — a spectral gap forces correlations to decay as $e^{-d/\xi}$ with $\xi$ the correlation length. this is the theorem the cyber locality result restates on a graph: the screened Laplacian has Green's function decaying as $e^{-\sqrt{\mu}\,d}$, so a cyberlink's effect falls below $\varepsilon$ within $O(\log 1/\varepsilon)$ hops and a neuron on a phone can compute its own reward without seeing the whole cybergraph
locality is not an approximation the design chose. it is the same theorem that keeps physics computable
see area law · spectral gap · tri-kernel · physical analogies
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