What is an event

To talk rigorously about relativity we introduce the concept of an event: any point-like phenomenon in space and time, characterised by coordinates $(t, \vv{s})$. An event has no duration or extent — it is an ideal “here and now” — and it serves precisely because it is the only object all observers can agree on, even while assigning it different numbers.

Principle — Coordinates of an event

A reference frame is a rigid three-dimensional scaffold with a lattice of synchronised clocks. An event $E$ has, in every RF, a quadruple of coordinates $(t_E, x_E, y_E, z_E)$ specifying where and when it happens. But beware: the occurrence of an event is absolute (it happens in every RF), while its coordinates are relative.

This distinction between the occurrence (absolute) and the coordinates (relative) is the key to everything. It is the reason why not every fact we describe in ordinary language deserves the name “event” in the relativistic sense.

What counts as an event?

An event is something that all observers recognise as having occurred at a precise point in space-time, even if they assign it different coordinates.

These are events:

• A bomb going off.
• Traveller $A$ meets traveller $B$.
• A ball bounces off a wall.
• Two balls bounce simultaneously at the same point in space.
• A traveller suddenly changes velocity (the occurrence of the change is absolute, even if by how much it changes depends on the RF).

These are NOT events:

• “Two balls bounce simultaneously at two different points”: spatial simultaneity depends on the RF, so in another RF this “occurrence” might never happen.
• “Traveller $A$ passes through point $(x,y)$ at time $t$” (the RF is not specified).
• “Traveller $A$ increases their velocity by $30$ m/s” (in an RF where $A$ is already moving at $c - 3\;\text{m/s}$, an increase of $30$ m/s would take them past $c$: impossible).

Golden rule

To be an event, the statement must be verifiable in any inertial reference frame.

Links

Topics: Special relativity Concepts: Space-time invariant Methods: Minkowski diagram

Related exercises: Spacelike or timelike · Problem — Particle or photon · Mr Rossi goes to the theatre