🚂 Relativity of Simultaneity
Two lightning bolts strike the front and back of a moving train at the same time for a platform observer — yet the train observer sees them at different times. Einstein's train thought experiment, brought to life.
What is the Relativity of Simultaneity?
Einstein's 1905 special relativity showed that "simultaneous" is not absolute — it depends on your reference frame. Two events that happen at the same time but different places in one frame are not simultaneous in any other inertial frame moving relative to the first.
In the platform frame: the train moves at speed β·c; both lightning strikes occur at t = 0 (same time). The platform observer M at the midpoint receives both light pulses simultaneously.
In the train frame: using the Lorentz transformation t′ = γ(t − βx/c), the front strike has t′ = −γβL/(2c) < 0 (already happened) and the back strike has t′ = +γβL/(2c) > 0 (not yet happened). The train observer M′ sees the front strike first.
The time gap is Δt′ = γβL/c = β²γL₀/c. For β = 0.6 and L₀ = 160 px, with c = 1 px/unit: Δt′ = 0.6 × 1.25 × 128 = 96 px-units.