Today’s Slashdot tells us that Physicists Discover Geometry Underlying Particle Physics, a story that is based on an excellent article, A Jewel at the Heart of Quantum Physics, by Natalie Wolchover at the new Quanta Magazine sponsored by the Simons Foundation.
As you might suspect, the Slashdot headline is simply nonsense. What’s really going on here is some new progress on computing scattering amplitudes in a very special conformally-invariant QFT, one not known to “underly particle physics”. This is a long story, one going back to Roger Penrose’s work on twistors from the late 1960s. In recent years this has been a very active and successful field of mathematical physics research, with a large group last year putting out Scattering Amplitudes and the Positive Grassmanian, which showed how to express some amplitudes to all loops in terms of volumes of geometric objects defined as subspaces of a Grassmanian. Mathematicians who want to see some speculation about the relation of this to other areas of mathematics should take a look at section 15 of that paper.
The more recent news is that Nima Arkani-Hamed and his ex-student Jaroslav Trnka now have an improvement on that calculational method, which uses the volume of a particular such geometric object they call the “Amplituhedron”. There’s no paper yet, but you can watch recent Arkani-Hamed talks about this here or here (the last from yesterday). How this ended up with the ridiculous Slashdot headline is pretty clear, as Arkani-Hamed with his trademark enthusiasm promotes this work as a road to revolutionizing physics, getting rid of locality and unitarity as fundamental principles, finding emergent space-time, maybe emergent quantum mechanics, etc (while admitting that what has been accomplished is just step 0 of step 1 of a multi-step program). From this, one gets to the rather excessive Quanta headline about a “jewel at the heart of quantum mechanics”, ensuring that the next stage of publicity (e.g. Slashdot) will launch the hype level into outer space, escaping any relationship to reality.
For the details of what this really is, the Quanta article gives a good overview, but you need to consult the long paper and recent talks to dig out a non-hyped version of what the real recent advances are. I’m nowhere near expert enough to provide this, hope that if this turns out to be as important as claimed, surely there will soon be lots of expositions of the story from various points of view. In the meantime, best perhaps to pay attention to what Witten has to say on the topic:
The field is still developing very fast, and it is difficult to guess what will happen or what the lessons will turn out to be.
Update: Here are some slides about the Amplituhedron from Trnka (hat-tip to George Ellis).
Update: Scott Aaronson has come up with an even more dramatic advance, the discovery of the Unitarihedron, which includes the Ampltituhedron as a special case, just “a single sparkle on an infinitely greater jewel”. See his posting The Unitarihedron: The Jewel at the Heart of Quantum Computing, where he unveils this new theory.
Update: See comments here by Lance Dixon and this paper for an alternative approach to computing planar amplitudes in this theory, one not using the “amplituhedron”.
Update: Congratulations to Kosower, Dixon and Bern for the award of the Sakurai prize for their work on amplitudes.
Update: Dixon has a guest post about this topic at Sean Carroll’s blog.