Our favorite mathematical constant, pi (π), which describes the relationship between the length and diameter of a circle, has taken on new meaning. The new idea was based on changes in string theory and efforts by two mathematicians to better describe the collision of particles.
“Our initial struggle was to never find a way to look at pi,” says Aninda Sinha of the Indian Institute of Science (IISc), who co-authored the new paper with IISc mathematician Arnab Priya Saha.
“All we did was study high-energy physics in quantum theory and try to develop a model with fewer and more precise parameters to understand how particles interact. We were excited to have a new look at Pi.”
The value of pi, a mathematical constant, did not change no matter how illogical it was; Over time, we have gained more accurate representations of its exact value, reaching 105 trillion at last count.
In this new paper, Sah and Sinha propose a new representation of the pi series; This, they say, provides an easier way to extract pi from calculations used to decipher quantum scattering of high-energy particles flying in particle accelerators.
In mathematics, a series contains the components of a parameter such as pi, so mathematicians can quickly extract the value of pi from its component parts. It’s like following a recipe, adding each ingredient in the right amount, and creating a delicious meal.
Unless you have a recipe, you won’t know what ingredients are in the dish, how much to add, or when to add it. 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 in this way, “but they quickly gave up because it was too complicated,” Sinha explains.
Singh’s group was looking for something completely different: ways to mathematically represent the interaction of subatomic particles using as few and simple factors as possible.
Saha, a postdoctoral researcher in the group, tackled the so-called “optimization problem” by trying to identify these interactions that create a variety of strange and elusive particles based on different combinations of particle mass, vibration, and a broad spectrum. the range of its chaotic movements, among other things.
A tool called the Feynman diagram, which represents mathematical expressions that describe the energy exchanged between two interacting and scattering particles, helped solve the problem.
This not only provided an efficient model of particle interaction that captured “all the fundamental properties of a string containing some energy”, but also produced a new formula for pi that closely resembled the first pi series representation in history. 15th-century Indian mathematician Sangamgrama Madhava. The results at this stage are purely theoretical but may have practical applications.
“One of the most exciting prospects of the new insights in this paper is the use of appropriate modifications of them to revise experimental data on hadron scattering,” Saha and Sinha write in their published paper.
“Our new representation will also be useful in connection with celestial holography,” the duo add, referring to an intriguing but still hypothetical paradigm that aims to reconcile quantum mechanics with general relativity through holographic projections of spacetime.
The rest of us may be pleased that researchers will be able to more precisely define what exactly the famous irrational number consists of. The study was published on: Physical Review Letters.
Source: Port Altele
