Minkowski diagram with two inertial frames · click to place events
β = 0.50, γ = 1.155
γ = 1.155
Time dilation: Δt' = γΔt = 1.155×Δt
Length contraction: L' = L/γ = L/1.155
Rel. of simultaneity: Δt' = -γβΔx
Lorentz transformation: ct' = γ(ct − βx), x' = γ(x − βct), γ = 1/√(1−β²).
In a Minkowski diagram, S' axes are sheared: x' axis has slope β (in ct-x plane), ct' axis has slope 1/β. Relativity of simultaneity: events with Δt=0 in S have Δt'=−γβΔx≠0 in S'. Light cone is invariant — all frames agree on causal structure. Click to place spacetime events.