Ramanujan’s formulae for pi has a connection to modern high energy physics
IISc researchers reveal connections between Ramanujan's pi formulae and modern high-energy physics, enhancing calculations in turbulence and black hole theories.
Physicists from the Indian Institute of Science (IISc) have found that pure mathematical formulae used to calculate the value of pi 100 years ago by Indian mathematician Srinivasa Ramanujan has connections to fundamental physics of today – showing up in theoretical models of percolation, turbulence, and certain aspects of black holes.
The IISc, in a release, said that in 1914, just before he sailed from Madras to Cambridge, Ramanujan published a paper listing 17 mathematical formulae to calculate pi. They were highly efficient and helped compute pi faster than other methods at the time.
It said that even with very few mathematical terms in them, the formulae still yielded many correct decimal digits of pi. The formulae were so foundational that they form the basis for modern computational and mathematical techniques- even the ones used by supercomputers- to compute digits of pi.
Chudnovsky algorithm
“Scientists have computed pi up to 200 trillion digits using an algorithm called the Chudnovsky algorithm. These algorithms are actually based on Ramanujan’s work,” said Aninda Sinha, professor at Centre for High Energy Physics (CHEP) and senior author of the new study.
Prof. Sinha and Faizan Bhat, first author and former IISc PhD student, found that Ramanujan’s formulae naturally come up within a broad class of theories called conformal field theories, specifically within logarithmic conformal field theories.
The researchers found that the mathematical structure underlying the starting point of Ramanujan’s formulae also comes up in the mathematics underlying these logarithmic conformal field theories. Using this connection, they could efficiently calculate certain quantities in these theories- ones that could potentially help them understand phenomena like turbulence or percolation better. This is similar to Ramanujan going from the starting point of his formulae and efficiently deriving pi.
Wider implications
“[In] any piece of beautiful mathematics, you almost always find that there is a physical system which actually mirrors the mathematics. Ramanujan’s motivation might have been very mathematical, but without his knowledge, he was also studying black holes, turbulence, percolation, all sorts of things,” Bhat said.
The IISc said that the study shows that Ramanujan’s century-old formulae have a hitherto hidden application in making current high-energy physics calculations faster and more tractable.
