Visualizing events, worldlines, and causality in 2D spacetime
Spacetime diagrams are the essential visual tool of relativity. They encode the causal structure of the universe: which events can influence which, what paths are possible for particles and light, and how different observers experience time.
Every event in spacetime has a light cone — the set of all points reachable by light signals. The future light cone contains everything the event can influence; the past light cone contains everything that could have caused it. Nothing outside the light cone can be reached.
Try it: Click to place events and see their light cones. Drag events to check causal connections — two events are causally connected only if one lies inside the other's light cone.
One twin stays on Earth while the other flies to a distant star and returns. When they reunite, the traveler is younger. But wait — from the traveler's perspective, wasn't Earth moving? The resolution lies in the asymmetry: the traveler accelerates (changes frames), breaking the symmetry between the two worldlines.
Proper Times (at journey's end)
Stay Twin
10.00
Travel Twin
8.00
Age Difference
2.00
Lorentz factor gamma = 1.2500 | Travel twin ages 20.0% less
Every object traces a worldline through spacetime. Stationary objects have vertical worldlines; light has 45° worldlines. The proper time experienced along a worldline depends on its shape — straighter worldlines (less acceleration) accumulate the most proper time.
A Penrose diagram conformally compactifies spacetime — mapping infinity to a finite boundary. All of Minkowski spacetime fits in a diamond shape, with light still traveling at 45°. This reveals the global causal structure at a glance.
Conformal Boundaries
i⁺
Future timelike infinity
Where massive particles end up
i⁻
Past timelike infinity
Where massive particles came from
i⁰
Spatial infinity
Where spacelike curves end
ℐ⁺
Future null infinity
Where outgoing light rays end
ℐ⁻
Past null infinity
Where incoming light rays originate