Special Relativity (Introduction)

the relativity of simultaneity

Ask 'did these two things happen at the same time?' and it feels like a question with one true answer. The relativity of simultaneity says it does not: whether two events at different places happen 'at the same moment' depends on who is asking — specifically, on how fast the asker is moving. Two flashes that are perfectly simultaneous for you can be one-after-the-other for someone gliding past, and there is no experiment that crowns one of you correct.

Here is why, using Einstein's own train. Stand at the exact middle of a moving carriage and set off a flash; because light travels at the same speed c in both directions, the light reaches the front and back walls at the same instant in your frame. But to someone standing on the platform, the carriage moves while the light is in flight: the back wall rushes toward the flash and the front wall runs away from it, so in the platform frame the light hits the back first. Same two events, different time-order — because both observers must measure light at the identical speed c, and something has to give. The word for two events happening at the same time is 'simultaneous', and simultaneity, it turns out, is frame-dependent, not absolute.

This is the deepest and most disorienting idea in special relativity, and the root of the others. Because moving observers disagree about which distant events are simultaneous, they slice up 'now' differently, and that disagreement is exactly what shows up as time dilation and length contraction. There is no universal, ticking 'now' spread across the cosmos — only each frame's own way of matching clocks.

Lightning strikes both ends of a fast train at once according to a platform observer standing at the midpoint. To a passenger sitting at the train's midpoint, the front strike is seen first — for her the two bolts were not simultaneous at all.

Simultaneous in one frame, sequential in another: 'now' is not shared across frames.

Simultaneity only goes relative for events separated in space. Two things happening at the very same place and time coincide for everyone, and cause always precedes effect in every frame — relativity reshuffles distant clocks, but never lets an effect outrun its cause.

Also called
failure of absolute simultaneity同時性的相對性