Answer: it can give some qualitative intuition on what is larger/smaller happens before/after based only on arguably more intuitive geometric considerations, without requiring you to do any calculations, see e.g. Figure "Spacetime diagram illustrating how faster-than-light travel implies time travel".
The key insights that it gives are:
- future and past are well defined: every reference frame sees your future in your future cone, and your past in your past coneOtherwise causality could be violated, and then things would go really bad, you could tell your past self to tell your past self to tell your past self to do something.
- every other event (to right and left, known as spacelike-separated events) can be measured to happen before or after your current spacetime event by different observers.
Animation showing how space-separated events can be observed to happen in different orders by observers in different frames of reference
. Source. The opposite of spacelike-separated events.
Mathematically, we can decide if two events are timelike-separated or spacelike-separated by just looking at the sign of the spacetime interval between them.
Different observers might not agree on the order of two spacelike-separated events.
Further discussion at Section "Light cone".
The opposite of those events are timelike-separated events.
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A spacetime diagram represents events using spatial and time coordinates, often with horizontal and vertical . A particle's world line records successive events on its trajectory; lines describing the propagation of light define the light cone.
The axis convention matters when reading a slope. With vertical, a constant-velocity trajectory has , so the drawn vertical-to-horizontal slope is . Light rays then lie at when the two axes use equal length scales. A stationary object has a vertical world line.
Such a diagram makes special relativity geometric: changing an inertial frame changes how events are assigned spatial positions and times, while causal relations remain constrained by light propagation. A diagram showing only one spatial coordinate suppresses other motion rather than proving it absent.
