One of the things that made physicist Richard Feynman famous was his invention of the Feynman diagram. Feynman diagrams provide a method for understanding the interactions between sub-atomic particles. Here, for example, is a diagram that represents the collision of an electron and a positron, resulting in the creation of two photons:
Using Feynman diagrams to describe certain interactions turns out to be extremely challenging, however. The collision of two gluons, resulting in the creation of four less energetic gluons, requires 220 diagrams. Some calculations based on this methodology cannot be done without the aid of a powerful computer, since they require thousands, millions and even billions of mathematical terms.
Over the years, various physicists and mathematicians have found ways to simplify these calculations. Recently, in fact, physicists have discovered a new geometrical object, the use of which simplifies the calculations to an amazing degree. They call the new structure an “amplituhedron”:
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, … one of the researchers who developed the new idea. “You can easily do, on paper, computations that weren’t feasible even with a computer before.”
For example, calculating the volume of the amplituhedron in this diagram, which represents the interaction of 8 gluons, provides the same result as 500 pages of algebra based on Feynman diagrams:
I learned about this latest development in an article called “A Jewel at the Heart of Physics”, which can be found here:
The article suggests that the discovery of the amplituhedron might one day lead to major consequences for our understanding of the universe: “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 is not built out of space-time and probabilities; these properties merely arise as consequences of the jewel’s geometry. The usual picture of space and time, and particles moving around in them, is a construct.
If two methods give the same results, the simpler method is clearly preferable from a pragmatic point of view. In fact, it’s likely in such a case that the simpler method better reflects the way the universe works. Perhaps the simplicity of this new method indicates that fundamental reality is simpler than previously believed:
Beyond making calculations easier or possibly leading the way to quantum gravity, the discovery of the amplituhedron could cause an even more profound shift, [physicist Nima] Arkani-Hamed said. That is, giving up space and time as fundamental constituents of nature and figuring out how the Big Bang and cosmological evolution of the universe arose out of pure geometry.
“In a sense, we would see that change arises from the structure of the object,” he said. “But it’s not from the object changing. The object is basically timeless.”
None of this means that there are tiny amplituhedrons underlying the universe, floating around outside space and time (whatever that would mean). It’s not even clear (to me anyway) what “pure geometry” is, since the geometry of an object, whether real or imagined, usually refers to its spatial characteristics.
Nevertheless, this latest labor-saving device may help physicists get closer to the bottom of things, assuming there is a bottom to get to.