Null interval
A separation between two events with invariant interval s² = 0 — meaning a light signal exactly connects them. The world-lines of photons are null curves; the light-cone of any event is the locus of null-separated points; null separations sit on the boundary between timelike and spacelike.
Definition
A null interval is a separation between two events for which the invariant interval s² = c²Δt² − Δx² − Δy² − Δz² is exactly zero. Geometrically, the events lie on each other's light-cone — the boundary between the timelike interior and the spacelike exterior — and a signal travelling at exactly c connects them. The world-line of a massless particle (photon, gluon, hypothetical graviton) is null everywhere, with tangent vector satisfying k^μ k_μ = 0; proper time does not elapse along it, and the affine parameter used to parametrize null curves cannot be the proper time τ but must be some other parameter λ chosen by the four-momentum normalization.
Null intervals are the signature of light propagation and the boundary case of relativistic kinematics. Two events connected by a light flash are null-separated — the propagation delay exactly matches the spatial separation divided by c, by definition of c as the propagation speed. The Lorentz-invariance of the interval means every inertial observer agrees on which separations are null; the light-cone structure is frame-independent, and "speed c" is the same in every inertial frame because the null condition c²dt² = dx² + dy² + dz² transforms into itself. In quantum field theory, null intervals are the support of light-front quantization and the asymptotic regime of S-matrix elements; the geometry of null surfaces is also the natural language for black hole horizons, gravitational waves, and the cosmological causal past.