Origami Patterns Solve a Major Physics Riddle

Summary

The amplituhedron is a geometric shape with an almost mystical quality: Compute its volume, and you get the answer to a central calculation in physics about how particles interact. Now, a young mathematician at Cornell University named Pavel (Pasha) Galashin has found that the amplituhedron is also mysteriously connected to another completely unrelated subject: origami, the art of paper folding. In a proof posted in October 2024, he showed that patterns that arise in origami can be translated into a set of points that together form the amplituhedron. Somehow, the way paper folds and the way particles collide produce the same geometric shape. “Pasha has done some brilliant work related to the amplituhedron before,” said Nima Arkani-Hamed, a physicist at the Institute for Advanced Study who introduced the amplituhedron in 2013 with his graduate student at the time, Jaroslav Trnka. “But this is next-level stuff for me.” By drawing on this new link to origami, Galashin was also able to resolve an open conjecture about the amplituhedron, one that physicists had long assumed to be true but hadn’t been able to rigorously prove: that the shape really can be cut up into simpler building blocks that correspond to the calculations physicists want to make. In other words, the pieces of the amplituhedron really do fit together the way they’re supposed to. The result doesn’t just build a bridge between two seemingly disparate areas of study. Galashin and other mathematicians are already exploring what else that bridge can tell them. They’re using it to better understand the amplituhedron — and to answer other questions in a far broader range of settings. Explosive Computations Physicists want to predict what will happen when fundamental particles interact. Say two subatomic particles called gluons collide. They might bounce off each other unchanged, or transform into a set of four gluons, or do something else entirely. Each outcome occurs with a certain probability, which is repr...