The postulates and clock synchronisation

Galilean relativity already said that mechanics cannot tell a uniformly moving cabin from a stationary one. Einstein's first postulate widens that to every law of physics, and the widening is the whole content: Maxwell's equations must hold unchanged in the moving cabin, with the same μ₀ and ε₀, so c = 1/√(μ₀ε₀) = 2.998 × 10⁸ m s⁻¹ must come out as the same number in every inertial frame. That is a promise, not a measurement — it asserts that no experiment whatever, optical or mechanical, will single out a rest frame, which is why a null aether-drift result supports it without proving it. The promise costs something at once: if c is frame-independent while lengths and times behave classically, velocity addition breaks, so something in the kinematics has to give. What gives is the assumption that “now” is the same everywhere.

Speed is distance over elapsed time, and an elapsed time between two places needs two clocks that already agree. Try to make them agree. Set them side by side and carry one to B: transport changes its reading by an amount you can only compute from a theory of moving clocks, which is what you were trying to test. Send a light signal instead: the correction depends on the one-way flight time, the very unknown. Every route closes the same loop. A round trip escapes it, because emission and reception happen at the same place on the same clock, so 2L/(t₂ − t₁) needs no second clock and no convention at all. That asymmetry is why every genuine test in this topic — interferometers, optical resonators, Doppler shifts — is built from closed light paths or from frequency ratios read at one point.

Clock A emits at its own reading t₁ and receives the echo at t₂, so B stands L = c(t₂ − t₁)/2 away, a distance that needs only A's clock. Einstein's instruction is to set B to read t_B = t₁ + ½(t₂ − t₁) at the moment of reflection. Reichenbach's observation is that the ½ is doing work no observation can justify, so write t_B = t₁ + ε(t₂ − t₁) with 0 < ε < 1. The outward speed is then c₊ = L/[ε(t₂ − t₁)] = c/(2ε) and the return is c₋ = c/(2(1 − ε)): ε = 0.9 has light crawling out at 5c/9 and racing back at 5c. Notice what refuses to move: 1/c₊ + 1/c₋ = 2/c for every ε, so the round trip, the only interval one clock can time, is untouched. Einstein's value is chosen because it alone treats every direction alike — B setting A by the same rule agrees with A setting B — and because in the coordinates it defines Maxwell's equations keep their isotropic form.

Michelson–Morley compares two round trips at right angles in one laboratory. Rotating the apparatus should shift the fringes by Δn = 2Lv²/(λc²), which for L = 11.0 m, λ = 589 nm and v = 30.0 km s⁻¹ is 0.374 fringe; nothing moved beyond 0.010. That tests isotropy of the two-way speed and nothing else. Kennedy–Thorndike deliberately makes the arms unequal and watches for months: with ΔL = 16 cm and green light, a change of order (30 km s⁻¹)² in v² as the seasons turn would move the pattern by about 3 × 10⁻³ fringe, and none appeared. It tests whether the two-way speed depends on the frame's velocity. Ives–Stilwell views the light from a fast hydrogen beam head-on and tail-on at once: relativity requires the geometric mean of the two shifted wavelengths to be exactly λ₀, whereas a classical moving-source law returns λ₀/γ. It tests the time-dilation factor on its own.

Put a general test theory between the experiments and the conclusion. Mansouri and Sexl allow a preferred frame and write the transformation with three unknown functions: a time factor a = 1 + αv²/c², a longitudinal length factor b = 1 + βv²/c², and a transverse factor d = 1 + δv²/c², where α, β and δ are coefficients, not velocities. Special relativity is the single point α = −½, β = +½, δ = 0. Michelson–Morley constrains β − δ = ½, Kennedy–Thorndike constrains β − α = 1, and Ives–Stilwell constrains α = −½: three equations, three unknowns, one solution. That is why no single null result establishes relativity — Lorentz's contracted aether satisfies the first and fails the second. And the synchronisation parameter ε appears in none of the three, because every observable in them is a closed path or a frequency ratio read at one place.

Sort your results before quoting them. Anything built from an invariant — proper time along a worldline, the interval, a two-way speed, a Doppler ratio, a measured particle lifetime — carries no trace of ε and is safe to report. Anything that names a time at a distant place — “both ends of the rod at once”, a coordinate one-way speed, which twin is older “right now” — is partly the convention you adopted. Einstein synchrony also has a hard boundary: it is defined for inertial frames only. Carried around a rotating frame it fails to close, and synchronising station to station around the equator accumulates a Sagnac gap 2ωA/c², which for A = πR² = 1.28 × 10¹⁴ m² and ω = 7.29 × 10⁻⁵ rad s⁻¹ is 207 ns, or 62 m of position error. The repair is not a better convention but a single declared coordinate time for the whole rotating system.