Bengaluru, While investigating how string theory can be used to explain certain physical phenomena, physicists at the Indian Institute of Science (IISc) have stumbled upon a new string representation for the irrational number pi.
It provides a simple way to extract pi from calculations involved in decoding processes such as quantum scattering of high-energy particles, the Bengaluru-based IISc said in a press release.
It says that under certain limits the new formula approaches 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 conducted by post-doctoral researcher Arnab Saha and Professor Aninda Sinha of the Center for High Energy Physics (CHEP), and published in 'Physical Review Letters'.
The release said that although the findings are theoretical at this stage, it is not impossible that they could lead to practical applications in the future.Sinha explains how Paul Dirac worked on the mathematics of the motion and existence of electrons in 1928, but he never imagined that his findings would lead to the later discovery of the positron and the design of the positron emission tomography (PET) that was then used. Will provide clues. Scanning the body for diseases and abnormalities.
“Our efforts in the beginning were never about finding a way to see pi. We were all 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 found a new way to look at Pi,” says Sinha.Sinha's group is interested in string theory – the theoretical framework that posits that all quantum processes in nature use different modes of vibrations pulled on a string.
His work focuses on how high energy particles interact with each other – such as protons bumping together in the Large Hadron Collider – and how we can observe them using as few and simple factors as possible. . This way of representing complex interactions falls into the category of "optimization problems".
Modeling such processes is not easy because it is necessary to take into account many parameters for each moving particle – its mass, its vibration, the degrees of freedom available for its motion, and so on, the release said.
Saha, who is working on the optimization problem, was looking for ways to represent these particle interactions efficiently.To develop an efficient model, he and Sinha decided to club two mathematical tools: the Euler-beta function and the Feynman diagram.
Euler–beta functions are mathematical functions that are used to solve problems in various fields of physics and engineering, including machine learning. The Feynman diagram is a mathematical representation that explains the energy exchange that occurs during the interaction and scattering of two particles.
IISc said 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 pi in its component form.If pie 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 get close to the exact value of pi has been a challenge,'' the release said.
The series that Sinha and Saha worked on combines specific parameters in such a way that scientists can rapidly arrive at a value of pi, which can then be incorporated into calculations, such as for high-energy particles. Involved in understanding scattering.
"Physicists (and mathematicians) have missed it until now because they didn't have the right instruments," Sinha explains, which was only found through work done with collaborators over the past three years. "In the early 1970s, scientists briefly investigated this line of research but quickly abandoned it because it was too complex."
It provides a simple way to extract pi from calculations involved in decoding processes such as quantum scattering of high-energy particles, the Bengaluru-based IISc said in a press release.
It says that under certain limits the new formula approaches 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 conducted by post-doctoral researcher Arnab Saha and Professor Aninda Sinha of the Center for High Energy Physics (CHEP), and published in 'Physical Review Letters'.
The release said that although the findings are theoretical at this stage, it is not impossible that they could lead to practical applications in the future.Sinha explains how Paul Dirac worked on the mathematics of the motion and existence of electrons in 1928, but he never imagined that his findings would lead to the later discovery of the positron and the design of the positron emission tomography (PET) that was then used. Will provide clues. Scanning the body for diseases and abnormalities.
“Our efforts in the beginning were never about finding a way to see pi. We were all 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 found a new way to look at Pi,” says Sinha.Sinha's group is interested in string theory – the theoretical framework that posits that all quantum processes in nature use different modes of vibrations pulled on a string.
His work focuses on how high energy particles interact with each other – such as protons bumping together in the Large Hadron Collider – and how we can observe them using as few and simple factors as possible. . This way of representing complex interactions falls into the category of "optimization problems".
Modeling such processes is not easy because it is necessary to take into account many parameters for each moving particle – its mass, its vibration, the degrees of freedom available for its motion, and so on, the release said.
Saha, who is working on the optimization problem, was looking for ways to represent these particle interactions efficiently.To develop an efficient model, he and Sinha decided to club two mathematical tools: the Euler-beta function and the Feynman diagram.
Euler–beta functions are mathematical functions that are used to solve problems in various fields of physics and engineering, including machine learning. The Feynman diagram is a mathematical representation that explains the energy exchange that occurs during the interaction and scattering of two particles.
IISc said 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 pi in its component form.If pie 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 get close to the exact value of pi has been a challenge,'' the release said.
The series that Sinha and Saha worked on combines specific parameters in such a way that scientists can rapidly arrive at a value of pi, which can then be incorporated into calculations, such as for high-energy particles. Involved in understanding scattering.
"Physicists (and mathematicians) have missed it until now because they didn't have the right instruments," Sinha explains, which was only found through work done with collaborators over the past three years. "In the early 1970s, scientists briefly investigated this line of research but quickly abandoned it because it was too complex."
