Minkowski geometry

Minkowski space is a four-dimensional space possessing a Minkowski metric, i.e., a metric tensor having the form d τ^2 = - (d x^0)^2 + (d x^1)^2 + (d x^2)^2 + (d x^3)^2. Alternatively (though less desirably), Minkowski space can be considered to have a Euclidean metric with imaginary time coordinate x^0 = i c t where c is the speed of light (by convention c = 1 is normally used) and where i is the imaginary number i = sqrt(-1). Minkowski space unifies Euclidean three-space plus time (the "fourth dimension") in Einstein's theory of special relativity.

Euclidean metric | four-vector | Lorentzian inner product | Lorentz tensor | Lorentz transformation | metric signature | metric tensor | Minkowski metric | positive definite quadratic form | twistor | twistor space