Einstein’s Train Paradox

Lightning Strikes and Relativity of Simultaneity

Start Pause Reset Information

Train speed: 0.50 c

Events:
Lightning hits the rear and front of the train at the same time in the ground frame.

Ground observer:
Standing at the midpoint on the ground.

Ground frame S:
Rear strike time: t = 0
Front strike time: t = 0
Therefore: simultaneous

Train frame S′:
Lorentz time:
t′ = γ(t − vx/c²)

Front strike:
t′ (front) = negative
Rear strike:
t′ (rear) = positive

So the train observer says:
front strike happened first.

In the ground frame, the two lightning strikes are simultaneous. But the train observer moves toward the front flash and away from the rear flash, so the front flash reaches the train observer first.