Spacetime interval

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Invariant between events.

Key relations² = c²t² − x²

s² = c²Δt² − Δx² − Δy² − Δz² is the same in all frames. Timelike (s² > 0), spacelike (< 0) or lightlike (= 0) classify event separation.

Worked example

Two events 5 s apart and 1 light-second away have s² > 0.

Common mistake

Time and space mix, but the interval doesn't.

In more detail

The spacetime interval s² = c²Δt² − Δx² is the same for all inertial observers. It classifies separations as timelike, spacelike or lightlike.

The interval is the invariant used in relativistic physics.
Particle physicists use it to characterise decays.
Physicists use the spacetime interval to decide whether two events could be connected by a signal.

Is the interval the same for all observers?

Yes, that is why it is called invariant.

What is a timelike interval?

One where the time separation is larger than the spatial distance in units of c.

Is the interval the same in all frames?

Yes. The spacetime interval is invariant, so all inertial observers agree on it even though they disagree on the separate times and distances.