where t μ μ = d z μ μ d λ λ is the tangent vector to the affinely parametrized geodesic γ γ ( λ λ ) . That is, σ σ ( x , x ′ ) is half the square of the signed geodesic length from x to x ′ computed along the unique geodesic segment, in U , joining the two points. Synge's world function is well-defined, since the integral above is invariant under reparameterization. In particular, for Minkowski spacetime, the Synge's world function simplifies to half the spacetime interval between the two points: it is globally defined and it takes the form