MinkowskiRaums

MinkowskiRaums, commonly referred to in English as Minkowski space, denote a four-dimensional real vector space equipped with a Minkowski metric. This structure provides the mathematical setting for special relativity and serves as the standard model of spacetime in flat, non-curved geometry.

Formally, a MinkowskiRaums is a real vector space V of dimension four endowed with a nondegenerate, symmetric bilinear form g of signature (1,3) or (3,1). In standard inertial coordinates (ct, x, y, z), the spacetime interval (line element) is ds^2 = c^2 dt^2 - dx^2 - dy^2 - dz^2, with a common alternative sign convention. The inner product defined by g classifies separations as timelike, lightlike (null), or spacelike, depending on the sign of ds^2.

A central feature is Lorentz invariance: transformations that preserve ds^2 form the Lorentz group O(1,3) (or O(3,1) in the opposite sign convention). These transformations mix space and time coordinates in a way consistent with the constancy of the speed of light. Vectors in MinkowskiRaums can be timelike, spacelike, or null, and worldlines of free particles are represented by straight lines, with inertial motion corresponding to constant four-velocity.

Historically, MinkowskiRaums were introduced by Hermann Minkowski in 1908 to unify space and time into a single geometric framework, clarifying the geometric structure underlying special relativity. In physics, the concept underpins quantum field theory and the standard formulation of relativistic kinematics. In general relativity, the Minkowski model serves as the local, flat approximation to curved spacetime.

Terminology varies by language; in English, "Minkowski space" is standard, while "MinkowskiRaums" may appear in German-language or translated texts to denote the family of such flat spacetime geometries.