Platform Frame (Rest Frame)
Train Frame (Moving Frame)
Scenario
A train moves past a platform at velocity β. Two lamps at the front and rear of the train flash simultaneously in the train's frame.
Watch what happens in both frames!
Watch two flashes that are simultaneous in the train frame occur at different times on the platform—adjust the train speed to see how simultaneity depends on motion
A train moves past a platform at velocity β. Two lamps at the front and rear of the train flash simultaneously in the train's frame.
Watch what happens in both frames!
This is one of the most mind-bending consequences of special relativity: events that are simultaneous in one reference frame are not simultaneous in another. This isn't an optical illusion or a trick of perception — it's a fundamental property of spacetime.
Two lamps at the front and rear of the train flash at exactly the same time. The passengers on the train see both flashes simultaneously (after accounting for light travel time to their eyes). The train is at rest in its own frame, so this is straightforward.
Observers on the platform see something different: the rear lamp flashes before the front lamp! This isn't because of light travel time — even after accounting for that, the events themselves occurred at different times. The rear event genuinely happened earlier in the platform's frame.
This happens because simultaneity depends on your reference frame. The platform frame's "slices of now" (surfaces of constant time) are tilted relative to the train frame's slices. Events on the same train-slice fall on different platform-slices.
In special relativity, simultaneity is defined using synchronized clocks and light signals. Two events are simultaneous if light signals from them reach a midpoint observer at the same time. But because the train is moving, the midpoint in the train frame is moving relative to the platform frame.
From the platform's perspective, the train's midpoint observer is moving toward the rear flash and away from the front flash. For both signals to reach this moving observer simultaneously, the rear flash must happen earlier. That's not a coincidence — it's exactly what the Lorentz transformation predicts.
The time difference between events that are simultaneous in the moving frame but separated by distance Δx is:
Δt = -γβΔx
For a train of length L moving at β=0.6 (γ≈1.25), events at the two ends that are simultaneous in the train frame are separated by Δt ≈ 0.75L in the platform frame. The faster the train, the larger the effect.
Slow Down the Train: Reduce β toward zero. Notice how the time difference between flashes in the platform frame shrinks. At β=0, both frames agree — simultaneity is absolute at low speeds (which is why we never notice this in daily life).
Speed Up the Train: Increase β toward 0.95. The time difference grows dramatically. At very high speeds, events that seem simultaneous in one frame can be separated by huge time intervals in another.
Watch the Spacetime Diagram: The diagram at the bottom shows the worldlines of the train's endpoints and the flash events. Notice how the horizontal line (simultaneous in platform frame) and the tilted line (simultaneous in train frame) intersect the worldlines at different events. Different frames slice spacetime differently.
Consider a Longer Train: Imagine the train were twice as long. The time difference would double (Δt ∝ Δx). Simultaneity disagreements grow with spatial separation.
The relativity of simultaneity is why faster-than-light travel would violate causality. If you could send a signal faster than light, different observers would disagree on whether the signal was sent before or after it was received. Some would see effects preceding causes!
It's also why "now" has no absolute meaning for distant events. When you look at a star 100 light-years away, you see it as it was 100 years ago. But you can't meaningfully ask "what is happening there right now" because the answer depends on your reference frame. An observer moving relative to you would have a completely different "now" at that star.
This isn't philosophy — it's physics. GPS satellites must account for this effect (along with gravitational time dilation) or they'd accumulate errors of several kilometers per day.