Spacetime diagrams (introductory)
Foundations · Physics
Study notes
Worked example: On a spacetime diagram, event A is at (x = 0, ct = 0) and event B at (x = 4 light-seconds, ct = 3 light-seconds). Can A influence B? What does a moving observer say about their order? Step 1: Separation: Δx = 4, cΔt = 3. Since Δx > cΔt, a signal from A (max 45°) cannot reach B — the events are spacelike separated. Step 2: The spacetime interval s² = (cΔt)² − (Δx)² = 9 − 16 = −7 < 0 confirms spacelike separation. Step 3: A frame moving at v = 0.5c computes Δt′ = γ(Δt − vΔx/c²) = 1.155(3 − 2) = 1.155 s > 0: still A first. Step 4: But at v = 0.9c: Δt′ = 2.29(3 − 3.6) = −1.37 s < 0: now B first! Conclusion: spacelike events have no absolute time order — exactly what the diagram shows, since a tilted simultaneity slice can put either event 'first'.