Our favorite mathematical constant, pi (π), describing the ratio between the circumference of a circle and its diameter, took on a new meaning.
The new representation is based on the twists and turns of string theory and two mathematicians’ attempts to better describe particle collisions.
“Our effort, initially, was never to find a way to look at pi,” says Aninda Sinha of the Indian Institute of Science (IISc), who co-authored the new work with fellow IISc mathematician Arnab Priya Saha.
“All we were doing was studying high-energy physics in quantum theory and trying to develop a model with fewer and more accurate parameters to understand how particles interact. We were excited when we got a new way to look at pi.”
Because it is a mathematical constant, the value of pi has not changed, however irrational the number; over time we just got more accurate images of its exact value, hitting 105 trillion digits at last count.
This new work by Saha and Sinha posits a new serial representation of pi, which they say provides an easier way to extract pi from calculations used to decipher the quantum scattering of high-energy particles scattered in particle accelerators.
In mathematics, a series sets out the components of a parameter such as pi, so mathematicians can quickly arrive at the value of pi from its component parts. It’s like following a recipe, adding each ingredient in the right amount and order to make a delicious dish.
Unless you have the recipe, then you don’t know what ingredients a dish is made of or how much to add and when.
Finding the right number and combination of components to represent pi has puzzled researchers since the early 1970s, when they first tried to represent pi this way, “but quickly abandoned it because it was too complicated Sinha explains.
Sinha’s group was looking at something else entirely: ways to mathematically represent the interactions of subatomic particles using as few and as simple factors as possible.
Saha, a postdoctoral fellow in the group, tackled this so-called “optimization problem” by trying to describe these interactions—which give off all sorts of strange and hard-to-spot particles—based on various combinations of the particle’s mass, vibrations, and broad spectrum from their erratic movements, among other things.
What helped unlock the problem was a tool called a Feynman diagram, which represents the mathematical expressions describing the energy exchanged between two interacting and scattering particles.
Not only did this lead to an efficient model of particle interactions that captures “all the key filamentary features up to some energy,” it also produced a new formula for pi that closely resembles the first-ever serial representation of pi in recorded history, forward by the Indian mathematician Sangamagrama Madhava in the 15th century.
The findings are purely theoretical at this stage, but could have some practical applications.
“One of the most exciting prospects of the new representations in this paper is to use suitable modifications of them to reexamine experimental hadron scattering data,” Saha and Sinha wrote in their published paper.
“Our new representation will also be useful in connecting to celestial holography,” the pair added, referring to an intriguing but still hypothetical paradigm that seeks to reconcile quantum mechanics with general relativity through holographic projections of spacetime .
For the rest of us, we can be satisfied knowing that researchers can more accurately describe what exactly makes up the famous irrational number.
The study was published in Physical examination letters.
