Theorem 8: Causal Structure and a Universal Speed c
Nearest‑neighbor ticks define cones; c = Lmin/τ0
Statement
Atomic ticks on a nearest‑neighbor lattice define causal cones; faster‑than‑neighbor propagation breaks ledger order, fixing a maximal speed c = Lmin/τ0.
In plain English
If every tick lets you step only to a neighboring voxel, there’s a built‑in speed limit: one voxel per tick. Try to go faster and the receipts stop making sense—the order of who‑paid‑who breaks. In the smooth limit this becomes light cones and relativity, with c = Lmin/τ0.
- Why inevitable: neighbor‑only updates + order preservation = causal cones with a top speed.
- What it buys: relativity as bookkeeping sanity, not an extra postulate.
Sketch
- The null class consists of one‑voxel‑per‑tick paths.
- Order preservation prohibits super‑neighbor hops.
- Continuum limit induces relativistic kinematics.