Spacetime & four-vectors

Minkowski spacetime

Minkowski spacetime is the four-dimensional stage on which special relativity plays out: three dimensions of space woven together with one of time into a single fabric. Instead of treating 'where' and 'when' as separate questions, it asks only 'which event' — a point labelled by a time and a place at once. Hermann Minkowski introduced this picture in 1908, recasting Einstein's algebra of moving clocks and rulers as the geometry of a new kind of space.

What makes this geometry peculiar is how it measures distance. In ordinary space you add the squares of the gaps in each direction; in spacetime you instead subtract the time part from the space part, so the 'separation' between two events can come out positive, negative, or zero. This 'indefinite' rule is exactly what makes the speed of light the same for everyone and lets different observers disagree about durations and lengths while still agreeing on the underlying geometry.

Think of it as a map of all of history laid out at once — every event that ever happens or will happen is a dot on this map, and an object's life is a curve threading through it. The map is flat, meaning gravity is switched off; it is the arena of special relativity. When mass and energy bend this arena, you cross over into general relativity and curved spacetime.

s^2 = (c t)^2 - x^2 - y^2 - z^2

The spacetime separation between two events: note the minus signs that distinguish time from space.

Minkowski spacetime is flat — it describes a universe with no gravity. Real gravity curves spacetime, which is the subject of general relativity, not special relativity.

Also called
flat spacetimeMinkowski space平直时空