The important mathematical constant Pi (π) describes the ratio of a circle’s circumference to its diameter, and it has now taken on a new meaning.
Two mathematicians, Aninda Sinha and Arnab Priya from the Indian Institute of Science, revealed that they initially did not set out to discover a new significance of Pi. Instead, they were studying high-energy physics in quantum theory and trying to find a model with fewer parameters but greater accuracy to understand the interactions between particles.
The new significance of Pi was serendipitously discovered while the mathematicians were “struggling” with the complexities of string theory to better describe particle collisions.
As a mathematical constant, Pi (π) has a fixed value but is an irrational number. The two scientists found a result that accurately represents the value of this constant, achieving up to 105 trillion digits in their latest count.
Their work presents a new series representation of Pi, making it easier to extract in calculations used to decode quantum scattering of high-energy particles in particle accelerators.
In mathematics, a series represents components of a parameter like Pi so that mathematicians can quickly arrive at its value. This process is akin to following a recipe, gradually adding each ingredient in the correct quantities and order to create a delicious dish.
Without a recipe, you would not know what ingredients to use, in what quantities, and when to cook them to make a tasty meal.
Since the early 1970s, researchers have struggled when they first attempted to present Pi in this way and quickly abandoned the effort due to its complexity.
This time, Sinha’s team investigated a completely different approach: mathematical representations of subatomic particles using as few simple coefficients as possible. They aimed to describe interactions between all types of particles based on combinations of mass, vibrations, and a broad spectrum of their usual movements, among many other factors.
They employed a tool called Feynman diagrams to illustrate mathematical expressions describing the energy exchange between two interacting particles. This not only created an efficient model of particle interactions but also yielded a new formula for Pi.
Although this discovery is currently entirely theoretical, it may have some useful applications.
One potential application of this new representation is to re-evaluate experimental data on hadron scattering. The two scientists noted that this method could also be very useful for connecting three-dimensional images of celestial bodies if it were possible to coordinate quantum mechanics with general relativity through three-dimensional projections of spacetime.
For those not deeply involved in mathematics and physics, we can understand that researchers have provided a more accurate description of what constitutes the famous irrational number Pi.
