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.

The revelation that particle interactions, the most basic events in nature, may be consequences of geometry significantly advances a decades-long effort to reformulate quantum field theory, the body of laws describing elementary particles and their interactions. Interactions that were previously calculated with mathematical formulas thousands of terms long can now be described by computing the volume of the corresponding jewel-like “amplituhedron,” which yields an equivalent one-term expression.

“The degree of efficiency is mind-boggling,” said Jacob Bourjaily, a theoretical physicist at Harvard University and one of the researchers who developed the new idea. “You can easily do, on paper, computations that were infeasible even with a computer before.”

The new geometric version of quantum field theory could also facilitate the search for a theory of quantum gravity that would seamlessly connect the large- and small-scale pictures of the universe. Attempts thus far to incorporate gravity into the laws of physics at the quantum scale have run up against nonsensical infinities and deep paradoxes. The amplituhedron, or a similar geometric object, could help by removing two deeply rooted principles of physics: locality and unitarity.

Thus far, Sean Carroll has not told me what I should think of this finding. But perhaps he will sometime soon.

There is an old parable — not sure if it comes from someone famous I should be citing, or whether I read it in some obscure book years ago — about a lexicographer who was tasked with defining the word “taxi.” Thing is, she lived and worked in a country where every single taxi was yellow, and every single non-taxi car was blue. Makes for an extremely simple definition, she concluded: “Taxis are yellow cars.”

Hopefully the problem is obvious. While that definition suffices to demarcate the differences between taxis and non-taxis in that particular country, it doesn’t actually capture the essence of what makes something a taxi at all. The situation was exacerbated when loyal readers of her dictionary visited another country, in which taxis were green. “Outrageous,” they said. “Everyone knows taxis aren’t green. You people are completely wrong.”

The taxis represent Science.

(It’s usually wise not to explain your parables too explicitly; it cuts down on the possibilities of interpretation, which limits the size of your following. Jesus knew better. But as Bob Dylan said in a related context, “You’re not Him.”)

Defining the concept of “science” is a notoriously tricky business. In particular, there is long-running debate over the demarcation problem, which asks where we should draw the line between science and non-science. I won’t be providing final any final answers to this question here. But I do believe that we can parcel out the difficulties into certain distinct classes, based on a simple scheme for describing how science works. Essentially, science consists of the following three-part process:

Think of every possible way the world could be. Label each way an “hypothesis.”
Look at how the world actually is. Call what you see “data” (or “evidence”).
Where possible, choose the hypothesis that provides the best fit to the data.

--Sean Carroll.