A lamp at the centre of a moving train fires light to both ends. In the train’s own frame both ends light up at the same instant. But to a platform observer the train rushes forward while the light crawls at the same c both ways — so the rear end races to meet its pulse and is struck first. Simultaneity is not absolute; it depends on your frame. Speed the train up and watch the gap open.
Bench · platform frame · flash from the centre
train speed v{{ simBetaPct }}% c
platform frame
rear struck first
Δt = L₀ vc²· leading clocks lag
In the train’s own frame the flash reaches both ends together — the disagreement is real, not an illusion of signal delay.
§01
The light-clock & the γ dial
Bounce a photon between two mirrors and call each round trip a tick. In the clock's own frame the light goes straight up and down — that's the shortest, proper tick. But to someone watching it fly past, the same photon must travel a longer diagonal at the same speed c, so its tick takes longer: Δt = γΔt₀. Nothing about the clock changed — only the geometry of the path. Slide v toward c and watch the diagonal — and the tick — stretch out.