One-Way Light Relay

A synchrony convention is only a relabelling of time, t′ = t + φ(x): the same events keep the same straight-line paths, but get different time stamps, so the one-way speed becomes 1/(1 + ∇φ·n̂) — infinite in one direction if you want it to be. Because space itself is untouched, every pulse below still flies in a straight line; only the clock labels move. Around any closed path the relabelling cancels exactly, which is why a round trip always measures c and no one-way convention can be tested on its own. Earth here records one real number: Δ, the gap on a single Earth clock between the supernova's direct light and the relayed signal that came by way of JWST. Drag Earth, JWST and Supernova, switch conventions, and watch Δ: no genuine convention may move it, while the two controls — fields that are not the gradient of any φ — do move it, which is exactly what a physically real anisotropy would do.

t′ = 0.000000 s

Supernova Earth JWST relay JWST → Earth slowness s = 0 (∞) · 1 (c) · 2 (c/2) ticks = equal steps of t′

Numbers

Leg	Length (ls)	Time (s)	Avg speed (c)

Earth direct

—

JWST arrival

—

Earth relayed

—

Δ = relayed − direct

—

Δ under Isotropic—

Δ under ——

difference— —

Model

Conventions (relabellings of t) Isotropic (Einstein)φ = 0 Constant vector κφ = κ·x Earth-centred ASC (Lisle)φ = |x − x_E| JWST-centred ASCφ = |x − x_JWST|

Controls (not conventions) Curl fieldg = k·θ̂ about Earth Additive speedc′ = 1 + κ·n̂

Scene

zoom4.4 px/ls

relay τ (s)

steps N

Show ∇φ direction field

Drag Supernova, Earth or JWST to move them; drag empty space to pan. Times come from the midpoint-rule integral of the local slowness along each straight leg — never from a closed form, and never by dividing by a speed.