Two flashes fire at the same moment in the station frame, one at each end of a flash separation L. In the frame of a train moving along that line they are no longer simultaneous: their emission times differ by Δt′ = −γβL/c. The simulator also tracks when each flash reaches the station and train observers, so you can separate what is emitted simultaneously from what is received simultaneously.
• A moving train, a left flash source, a right flash source, a station observer and a train observer in a single 3D scene. • Sliders for train velocity (0 to 0.8c) and flash separation (2 to 5 light-seconds) in the laboratory frame. • Readouts: right-minus-left emission t′, each emission t′, the station reception time, and the times at which the train receives the right and left flashes. • Two experiments: a stationary train (emissions simultaneous, both observers receive together) and approaching the right flash (right emission earlier in train coordinates, receptions also differ).
The station receives both flashes at t = L/(2c). The train receives the right flash at L/[2c(1 + β)] and the left flash at L/[2c(1 − β)]. Equal detection times and simultaneous emission are different claims: the train observer, after correcting for signal delay, concludes the right flash fired first because the transformed emission times, not the delays alone, say so.
The flash separation is specified in the laboratory, not as the train's proper length. Transformed emission times use synchronized coordinates, not merely signal-delay differences. Scene distances are rescaled so both observers remain visible, and the model is one-dimensional with inertial motion.
No. Detection depends on where the observer stands and how fast they move relative to each source. The simulator reports reception times separately from the transformed emission times so you can see the difference.
For a train moving in the positive direction, the right-hand flash, toward which the train is heading, has the earlier emission time, since Δt′ = −γβL/c is negative for right minus left.
The transformed emissions are simultaneous and both observers receive both flashes together. This is the Stationary train experiment and acts as the control case.
No. The separation is set in the laboratory frame. The train's rest length would be larger by the Lorentz factor, which is a distinct quantity not specified by this control.