Light cone and spacetime diagram simulator
A light cone shows every place a flash of light from one event can reach. Anything inside the future cone can be caused by the event; anything outside can never be influenced by it, no matter how fast you travel. This simulation lets you drag a second event around and watch the classification change.
Interactive, free and runs in your browser. Part of the Special Relativity simulations.
What you will see
A glowing double cone opens from the origin event, with light fronts racing outward and photons riding its surface. A gem marks your event. Pink dashed axes show how an observer moving at speed β slices spacetime, and a dashed hyperbola marks every position the event can take for any observer, because the interval s² = (ct)² − x² is the same in every frame.
Try this
- Drag the gem onto the 45° edge of the cone and watch the label turn lightlike.
- Raise β to 0.9 and watch the moving axes close in on the light cone like scissors.
- Put the event just outside the cone, then change β until the moving frame’s time coordinate turns negative: the order of the two events flips.
Common misconception
Faster observers do not simply see "more time". For spacelike-separated events they can disagree about which happened first, but for timelike events every observer agrees on the order, so cause still comes before effect.
Exam-style question
Event B happens 3 light-seconds from event A and 2 seconds after it. Can A cause B?
Use s² = (ct)² − x² = (2)² − (3)² = −5 light-seconds². The interval is negative, so B is spacelike-separated from A: no signal, even light, can get from A to B in time. A cannot cause B.
Key equations
s² = (ct)² − x²x′ = γ(x − vt)t′ = γ(t − vx/c²)
Curriculum
AQA A-level physics (turning points), IB Physics A.5.