Physicists find a new way to represent the number pi

June 18 () –

Investigating how to use string theory to explain physical phenomena, scientists from the Indian Institute of Sciences (IISc) have found a new series representation for the number pi.

It provides a simpler way to extract pi from calculations involved in deciphering processes such as quantum scattering of high-energy particles.

The new formula under a certain limit is very close to the representation of pi suggested by the Indian mathematician Sangamagrama Madhava in the 15th century, which was the first series for pi recorded in history.

The study was carried out by Arnab Saha, a postdoc, and Aninda Sinha, a professor at the Center for High Energy Physics (CHEP), and has been published in Physical Review Letters.

“At first, our efforts were not directed at finding a way to analyze pi. All we were doing was studying high-energy physics in quantum theory and trying to develop a model with fewer and more precise parameters to understand how particles interact. We get excited when we find a new way to analyze pi“says Sinha it’s a statement.

Sinha’s group is interested in string theory, the theoretical framework that assumes that all quantum processes in nature simply use different modes of vibration pulsed in a string.

His work focuses on how high-energy particles (such as protons colliding with each other at the Large Hadron Collider) interact with each other and what ways we can analyze them using the fewest and simplest factors possible. This way of representing complex interactions belongs to the category of “optimization problems.”

Modeling these processes is not easy because there are several parameters that must be taken into account for each moving particle (its mass, its vibrations, the degrees of freedom available for its movement, etc.).

Saha, who has been working on the optimization problem, was looking for ways to efficiently represent these particle interactions. To develop an efficient model, he and Sinha decided to combine two mathematical tools: the Euler-Beta function and the Feynman diagram. Euler-Beta functions are mathematical functions used to solve problems in various areas of physics and engineering, including machine learning.

The Feynman diagram is a mathematical representation that explains the energy exchange that occurs when two particles interact and scatter.

What the team found was not only an efficient model that could explain particle interaction, but also a series representation of pi.

In mathematics, a series is used to represent a parameter such as p in its component form. If pi is the “dish”, then the series is the “recipe”. pi can be represented as a combination of many numbers of parameters (or ingredients).

Finding the right number and combination of these parameters to quickly approach the exact value of pi has been a challenge. The series that Sinha and Saha have stumbled upon combines specific parameters in such a way that scientists can quickly arrive at the value of pi, which can then be incorporated into calculations, such as those used to decipher the scattering of high-energy particles.

“Physicists (and mathematicians) have not achieved this until now because they did not have the right tools, which were only found thanks to the work we have been doing with collaborators for the last three years or so,” explains Sinha. “In the early 1970s, scientists briefly examined this line of research, but they quickly abandoned it because it was too complicated.

Although the findings are theoretical at this stage, it is not impossible that they could lead to practical applications in the future. Sinha points out how Paul Dirac worked on the mathematics of the motion and existence of electrons in 1928, but never thought that his findings would later provide clues to the discovery of the positron, and then to the design of Positron Emission Tomography (PET). used to scan the body for diseases and abnormalities.

“Doing this type of work, even if it has no immediate application in daily life, provides the pure pleasure of doing theory for the sake of doing it,” adds Sinha.