Minkowski space

Summary

Minkowski space is the four-dimensional real vector space $\R^4$ with the indefinite quadratic form $-(x^0)^2 + (x^1)^2 + (x^2)^2 + (x^3)^2$. It is the arena of special relativity: its points are events, and its symmetries are the Lorentz and Poincaré transformations. It is the flat model of a Lorentzian manifold, as Euclidean space is the flat model of a Riemannian manifold.