Spacelike

Two events are spacelike-separated when their invariant interval satisfies s² = c²Δt² − Δx² − Δy² − Δz² < 0 — equivalently, when their spatial separation exceeds what a light signal could traverse in their time difference. No signal travelling at or below c can connect them, so they cannot be in causal contact: neither can affect the other. The proper distance between them — the spatial separation measured in the inertial frame where they are simultaneous — is √(−s²); such a frame always exists for any spacelike separation, and Lorentz boosts can shuffle their temporal order freely.

This frame-dependence of temporal ordering for spacelike-separated events is exactly the relativity of simultaneity. There is no privileged "now" slicing spacetime; instead, every inertial observer carves spacelike hyperplanes orthogonal to their own four-velocity, and rotating between observers tilts the slice. Two spacelike-separated events that are simultaneous in frame S are not simultaneous in any frame S' moving relative to S along the line connecting them, and their order can swap. This is not a paradox — since they cannot causally influence one another, the swap has no observable contradiction. The light-cone of any event partitions the rest of spacetime into the timelike interior (causal contact possible, temporal order absolute) and the spacelike exterior (no causal contact, temporal order frame-dependent).