Is the Universe an Amplituhedron… ?

Yeah, whatever that is:

Physicists have discovered a jewel-like geometric object that dramatically simplifies calculations of particle interactions and challenges the notion that space and time are fundamental components of reality.

“This is completely new and very much simpler than anything that has been done before,” said Andrew Hodges, a mathematical physicist at Oxford University who has been following the work.

Also some good stuff at the HN discussion.

The idea is that physicists (starting with Feynman) have been using some incredibly complicated math to calculate the scattering pattern of particles after a collision. These initial calculations started out with Feynman drawing a picture of what the scatter pattern might look like then calculating its likelihood. Then draws another one and calculates that likelihood. Thousands of times. 500 pages of algebra, we’re told.

And now some physicists have figured out a standardized shape whose volume calculation replaces those 500 pages of algebra with a single step.

Using geometric objects to simplify very complicated calculations is an old and breathtaking trick. I first came across it studying the probability of events under constrained uniform distributions. I can trade in a triple integral for drawing a couple rectangles and a trapezoid? Deal.

Calculus is painful, drawing pictures is not. And yet they’re the same thing. Which is mind-blowing, and shows that math really can (should!) be simple.

Anyway, the fact that the amplituhedron works so well has all kinds of wacky implications for physics that I don’t really understand, and that even the real experts can only speculate about. My take-away is how neat it is that a visual metaphor can drastically reduce the apparent complexity of some physical phenomenon.

Social scientists everywhere sigh with envy.

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