Thomas Gehrmann recalls One day 20 years ago, a cataclysm of mathematical expressions flooded his computer screen.
He was trying to calculate the probability that three elementary particle jets would erupt from two colliding particles. That’s the kind of bread-and-butter calculation physicists usually do to check if their theory matches the experimental results. However, sharper predictions require longer calculations and Gehrmann will be big.
Using the standard method devised by Richard Feynman more than 70 years ago, he sketched out hundreds of possible ways in which colliding particles could transform and interact before firing three rays. Adding up the individual probabilities of those events produces the overall chance of a triple-reaction outcome.
But Gehrmann needed software just to tally the 35,000 terms in his probability formula. As for calculate it? That’s when “you raise the flag of surrender and talk to your colleagues,” he said.
Fortunately for him, one of those colleagues happened to know of a still-unpublished technique for dramatically shortening this kind of formula. With the new method, Gehrmann saw the terms merge and melt into the thousands. In the remaining 19 computational expressions, he saw the future of particle physics.
Today, the reduction process, known as the Laporta algorithm, has become the primary tool for generating accurate predictions of particle behavior. “It’s ubiquitous,” says Matt von Hippel, a particle physicist at the University of Copenhagen.
Although the algorithm is globally popular, its inventor, Stefano Laporta, remains obscure. He rarely attended conferences and did not command a legion of researchers. “A lot of people just assumed he was dead,” von Hippel said. By contrast, Laporta, who lives in Bologna, Italy, omitted the calculus he was most interested in, the method that spawned his pioneering method: an ever more precise assessment of how electrons move in a magnetic field. .
One, Two, Many
The challenge in making predictions about the subatomic world is that there are a multitude of possibilities. Even an electron that is only interested in its own work can spontaneously emit and then receive a photon in return. And that photon can create additional ephemeral particles in the interim. All these preoccupations interfere slightly with the electron’s activity.
In Calculation diagram of Feynman, particles that exist before and after an interaction become paths in and out of the animated sketch, while particles appear briefly and then disappear forming rings in between. Feynman figured out how to convert these diagrams into mathematical expressions, where the loops become sum functions known as Feynman integrals. Events are more likely to happen than events with fewer loops. But physicists must consider rarer, more repeatable possibilities when making the kinds of precise predictions that can be tested in experiments; only then will they be able to detect subtle signs of elementary particles that might be missing from their calculations. And with more loops the integral is exponentially more.
