Special Relativity · Clock Synchronization
How do distant clocks
agree on a time?
A signal goes out, bounces off a distant clock, and comes back. Splitting the round-trip time in half is Einstein's stated procedure for giving a time to something far away — a stated agreement, not an independent measurement of the two one-way travel times.
Ideal model, host calculation
SR-01: Clock synchronization with the event ledger
To give a time to something happening far away, you send a signal out, wait for it to bounce back, and split the difference. Clocks that ride along together while moving turn out not to agree once someone else compares them.
| Event | Kind | Clock | Clock's own reading (s) | Coordinate time (s) | Coordinate position (ls) |
|---|---|---|---|---|---|
| emission-a | emission | A | 0 | 0 | 0 |
| reflection-b | reflection | B | 10 | 10 | 10 |
| reception-a | reception | A | 20 | 20 | 0 |
- Assigned remote time (stated procedure)
- 10 s
- Round-trip speed
- 1 ls/s
- Criterion check (declared clock B)
- synchronized by definition
- Section 2 rod chase: outbound / return legs
- 10 s / 10 s
- Desynchronization of the moving pair (platform frame)
- 6 s
- One-way light speed
- not applicable (The model defines the one-way light speed by convention (Einstein's synchronization procedure), rather than measuring it independently.)
- Three-station transitivity (A, B, C, mutually at rest)
- transitive
Predict before changing the moving pair's velocity:
A pair of clocks rides past at a steady speed, and the riders set their clocks with the same light-signal rule. Judged by our clocks, what do theirs show?
Show the reference code & kernel bindings
Reference evaluator: src/physics/reference/events.ts
// desynchronizationObserved
const signed = kinematicDesynchronization(properSeparationLs, beta, 1 /* c, ls/s */);
const verdict = beta === 0 ? "they-agree" : beta > 0 ? "trailing-clock-ahead" : "leading-clock-ahead";
// synchronizationRound (Einstein's midpoint rule)
const assignedRemoteTime = (emissionTimeA + receptionTimeA) / 2;
const roundTripSpeedLsPerS = (2 * separationLs) / (receptionTimeA - emissionTimeA);The two one-way transit times of the synchronizing signal are set equal by definition, not measured: Einstein's stated procedure (paper 3, section 1). Alternative: slow clock transport -- Requires a dynamical assumption about how a clock's rate depends on its motion, not merely a convention about signals. In the limit of vanishingly slow transport, within one inertial frame, it agrees with the light convention; at any finite transport speed the two differ by an amount that goes to zero with the transport speed. This is a limiting statement, never an exact equivalence at finite speed.
Open the derivation
Einstein's criterion
A signal leaves clock A at time t_A, reflects at the distant clock B, and returns to A at t'_A. The paper does not measure B's reading at reflection; it assigns it by definition as the midpoint:
t_B = (t_A + t'_A) / 2
The round-trip speed 2·AB / (t'_A - t_A) then equals c in the frame where the procedure is applied — not because the speed of light was measured this way, but because the procedure was built to make it come out that way.
Section 2: the moving rod
Running the same procedure on the two ends of a moving rod gives two different leg times in the stationary frame: an outbound leg r_AB / (c - u) and a return leg r_AB / (c + u), because the receiving end has moved during the light's travel. For observers moving with the rod, the criterion that held for the stationary observer fails.
Clocks that move disagree, once you compare them
A pair of clocks synchronized this way in their own rest frame, but moving together at speed v, is found out of step by vL/c² in the platform frame — with the trailing clock ahead. Try the moving-pair preset above and predict the answer before revealing it.
Light is not the only way
The paper chooses light because it makes the assumption it is making visible, not because light is the only possible way to compare distant clocks. Slow clock transport is a coherent alternative: carry a clock, synchronized side by side with another, out to the distant station. It requires its own assumption — how a clock's rate depends on its motion — and agrees with the light convention only in the limit of vanishingly slow transport.