Visualizing events, worldlines, and causality in 2D spacetime
A spacetime diagram puts time up the page and space across it. Draw on one and you can see which events can affect which, and why travelers age differently.
Click to place events and see their light cones, then read the causal relationships below. Two events are causally connected only if one lies inside the other's light cone.
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.
Set the traveler's speed and press Animate. Compare the proper times at the end: the twin whose worldline bends at the turnaround ages less.
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
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.
Click to place points and build a worldline, then read its total proper time. Compare a straight path with a zigzag between the same endpoints: the straighter one accumulates more.
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.
All of flat spacetime squeezed into one diamond. Find the labeled infinities on its edges and notice that light still travels at 45°.
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
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.
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