Simplify the Universe

Particle interactions calculated with a single term all done by hand?! That’s crazy. In case you have nothing to base calculating particle interactions in quantum field theory on, just imagine having thousands of puzzle pieces scattered everywhere to suddenly, without all the pesky pieces, having a single, unified picture. All it takes is some new thinking and a little geometry.

In this new model, physicists describe the universe by an amplituhedron, an infinite-dimensional geometric object. The volume of this object is equal to the scattering amplitude—the holy grail of particle physics—which physicists at the Large Hadron Collider use to describe particle interactions. In some amplituhedrons the amplitudes can be calculated directly. In others diagrams called “twistors” are needed.

What’s more, they’ve found the solution to everything. The volume of an infinite-sided “master amplituhedron” represents the amplitudes of all physical processes. The italics are supposed to impress you. Interactions between a finite number of processes, what us humans normally consider, are contained on various faces. Interesting to me, but probably not to anyone else, is that the master amplituhedron simplifies to a circle in 2D.


Amplituhedron representing an 8-gluon particle interaction, which normally needs ~500 pages of algebra.

The amplituhedron removes locality and unitarity. Particles that aren’t near either other in space or time can interact (what?) and the sum of the probabilities for all possible particle positions doesn’t have to be 1 (what?!). That works out for gravity though, which explodes—yes, explodes—in equations with locality and unitarity. Connecting gravity to particle physics is a big deal—no one’s been able to do it yet. Jacob Bourjaily, one of the researchers, described this method as “a starting point to ultimately describing a quantum theory of gravity.”

Nima Arkani-Hamed, the lead author (the main man, the head honcho), gave a talk about amplituhedrons at the SUSY 2013 conference, which is posted online. Warning: the talk is very technical, but interesting nonetheless (if only to watch a man in shorts and a shirt two sizes too large give a spitfire professional talk). Although, in the talk he says amplituhedrons can be “explained to a smart junior high school student,” which left me feeling like a stupid graduate student.

Shut up and calculate!

Quantum mechanics is confusing. Little by little you wrap your head around the math, just going with the assumption that objects are simultaneously particles and waves, until you feel like maybe there’s something to all those wavefunctions and probabilities. Then you ask what it all means. The confusion rushes back as your professor shrugs.

In the 1920s, the founders of quantum mechanics gathered together in Copenhagen, Denmark to discuss what their math said about the physical universe. In the end, they decided there are fundamental limits to what we can know. They came up with the Copenhagen Interpretation, which according to physicist David Mermin of Cornell University means “shut up and calculate!”

Everyone accepted the Copenhagen Interpretation—if the inventors of the theory aren’t quite sure what it means, how are you supposed to know?! But a small group of scientists aren’t content with the ambiguity of quantum mechanics. With the right perspective, they argue, the meaning will become clear.

The Perimeter Institute for Theoretical Physics is hoping to find clarity. As Christopher Fuchs, one of the Institute’s researchers, says the right perspective will “write a story—literally a story, all in plain words—so compelling and so masterful in its imagery that the mathematics of quantum mechanics in all its exact technical detail will fall out as a matter of course.”

Fuchs is proposing the probabilities inherent in quantum mechanics come from the viewer, not from the object itself. He’s designed a new approach called QBism that, using a type of statistics called Bayesian inference, gets rid of the wavefunctions, amplitudes, and Hilbert-space operators—all necessary in quantum mechanics—and replaces them with simple probabilities.

All in all it’s pretty exciting. I’ve been interested in quantum mechanics and what it really means since I was old enough to realize that we, as scientists, don’t really know everything about the universe. It will be a good day when we can explain the meaning of quantum mechanics to elementary school students in an interesting and understandable story. Maybe QBism will give us that story.