The Minkowski Spacetime and Poincaré Group

Spacetime Interval

Just as distance is invariant in 3D space, the spacetime interval is invariant in 4D Minkowski space:

• : Timelike (causally connected, observer can travel between events).

• : Lightlike (connected by a light ray).

• : Spacelike (causally disconnected, order of events depends on observer).

Minkowski Spacetime

The Minkowski spacetime is a flat -dimensional space endowed the metric Physically, is the time coordinate and are the spatial coordinates, and we usually write .