Spacetime · light cones and causal structure

SPACETIME — light cones and the limits of causality

vertical axis is time · horizontal plane is space · light moves at 45°

events inside your light cones are causally connected; events outside them are elsewhere

drag — orbit camera · wheel — zoom · hover an event — see classification

move observer: WASD space · Q/E time · L fire light pulse · R reset · O auto-orbit · space pause

observer at (x,t,z) = (0.0, 0.0, 0.0)

future light cone — events you CAN influence

past light cone — events that CAN have influenced you

elsewhere (spacelike) — no causal connection possible

lightlike — exactly on the cone (photon path)

tachyon worldline — forbidden by relativity (dashed)

HOVER AN EVENT

—

event —

Δx —

Δt —

Δz —

spatial dist. r —

spacetime interval s² —

s² = −(c·Δt)² + Δr²
negative = timelike, zero = lightlike, positive = spacelike

"henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality." — Hermann Minkowski, 1908