The Penrose Diagram
1963 CE
A Finite Map of an Infinite Spacetime
Ordinary spacetime diagrams break down when you try to include infinity. The axes stretch off the page, the interesting parts disappear, and it becomes hard to see what can actually influence what. A Penrose diagram solves this by using a conformal transformation, a kind of mathematical lens that compresses infinite distances into a finite shape without changing which events can send light to which others.
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Ordinary spacetime diagrams break down when you try to include infinity. The axes stretch off the page, the interesting parts disappear, and it becomes hard to see what can actually influence what. A Penrose diagram solves this by using a , a kind of mathematical lens that compresses infinite distances into a finite shape without changing which events can send light to which others.
On a Penrose diagram, light rays always travel along forty-five degree lines, and the edges of the diagram represent different kinds of infinity. Future infinity, past infinity, and spatial infinity all appear as reachable boundaries of the picture. The result is a compact map of an entire universe.