A brief flash is set off at the middle of a carriage of length . The light spreads forward and backward at the same speed .
The front wall and the rear wall are both from the middle, so the light reaches each of them after the flash.
The light reaching the rear wall, and the light reaching the front wall: for the passenger these two events happen at the same time.
Now watch the same flash from the ground. The light spreads out from where it was emitted, still at speed ; the speed of the carriage is not added.
While the light spreads, the carriage moves to the right. The rear wall moves toward the light, and the front wall moves away in the same direction as the light.
If the ground measures the carriage's length as , the light takes to reach the rear wall and to reach the front wall. For the observer on the ground the rear wall is lit first and the front wall later.
The two times differ by . For a m carriage at km/h this is about seconds, far too small to notice in daily life.
The upper row shows the flash from the carriage, the lower row from the ground. Neither is an illusion; the passenger and the observer on the ground each measure correctly in their own frame.
What differs is the set of clocks used to read the times. The passenger reads the arrival times on clocks set out and synchronized in the carriage, the observer on clocks set out and synchronized on the ground.
Whether two events are simultaneous is settled only once you choose the frame to measure from. This is the relativity of simultaneity.
Plot position across and up the page, and you have a spacetime diagram. Using rather than for the vertical axis makes the path of light a line at exactly degrees.
Events simultaneous for the ground lie on a horizontal line. Such a line is called a line of simultaneity.
Now place on the diagram the two events that were simultaneous in the carriage. During the time difference the carriage moves , so the two points are apart.
The line joining them has slope . The line of simultaneity for the carriage is a line of slope .
The figure tilts the line of simultaneity from horizontal up to slope . When the line is horizontal the two points sit at different heights; at slope they fall on the same line.
No frame moves faster than , so the slope of a line of simultaneity is always less than . Every line of simultaneity is closer to horizontal than the degree line.
Events that can be reached from the origin by light, or by anything slower, lie in the shaded region. This is the inside of the light cone, and events there come after the origin whichever frame's line of simultaneity you use.
The events whose order depends on the frame are only those in the unshaded region, too far away for even light to reach in time.
Between two events that light cannot connect, neither can influence the other. So the order of cause and effect is the same in every frame.