★★☆ Moderate

⬦ Minkowski Spacetime Diagram

Drag the velocity slider to Lorentz-boost the moving frame. See world lines tilt, the light cone stay fixed at 45°, and simultaneity lines rotate.

Rest frame (S) axes Moving frame (S′) axes Light cone (c = 1) Simultaneity lines World lines

β = v/c = 0.00

γ = 1.000 Time dilation: Δτ′ = Δt/1.000 Length contraction: L′ = L/1.000

β = 0.00 | γ = 1/(√1−β²) = 1.000

Minkowski Spacetime

In a Minkowski diagram the vertical axis is time (ct) and the horizontal axis is space (x). An object at rest traces a vertical world line; a moving object tilts toward the light cone. The light cone (45° lines) is frame-independent — light always travels at c.

A Lorentz boost at velocity β = v/c rotates both the ct′ axis and the x′ axis symmetrically around the light cone. Events that appear simultaneous in S (same ct) are not simultaneous in S′ (same ct′), and vice versa.