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As numbers pbad, familiar real numbers – those found on the numerical line, such as 1, π, and -83.777 – start up. particular way to form "complex numbers", first studied in 16th century Italy, behave as coordinates on a 2D plane, adding, subtracting, multiplying and dividing is like translation and translation positions. rotation around the plane numbers, suitably matched, form "quaternions" in 4D, discovered in 1843 by the Irish mathematician William Rowan Hamilton, who, on e, chiseled the formula in the Dublin Broome Bridge John Graves, a friend advocate of Hamilt It was then shown that pairs of quaternions form octonions: numbers that define coordinates in an eight-dimensional abstract space.
Here the game stops. The evidence surfaced in 1898 that real numbers, complex numbers, quaternions, and octonions are the only kinds of numbers that can be added, subtracted, multiplied, and divided. The first three divisional algebras would soon lay the mathematical foundations of twentieth-century physics, with ubiquitous real numbers, complex numbers providing the mathematics of quantum mechanics and quaternions underlying the theory of special relativity. Albert Einstein. This has led many researchers to question the last and least understood divisional algebra. "The octonions are to physics what sirens were to Ulysses," said Pierre Ramond, particle physicist and string theorist at the University of Florida.
Günaydin, Professor Penn State, was a graduate student at Yale in 1973 when he and his adviser Feza Gürsey found a surprising link between the octonions and the strong force, which links the quarks together in the atomic nuclei. A wave of initial interest in the discovery did not last. At the time, everyone was questioning about the standard model of particle physics – the set of equations describing known elementary particles and their interactions via strong, weak and electromagnetic forces (all fundamental forces except gravity). But rather than looking for mathematical answers to the mysteries of the standard model, most physicists have placed their hopes in high-energy particle colliders and other experiments, waiting to see appearing from behind. other particles and to exceed the standard model. They "imagined that the next progress would come from some new pieces fallen on the table, [rather than] to think harder about the pieces we already have," said Latham Boyle, a theoretical physicist at the Perimeter Institute of Physics Theoretical in Waterloo, Canada
Decades later, no particles beyond those of the standard model were found. Meanwhile, the odd beauty of the octonions continued to attract the occasionally independent researcher, including Furey, the Canadian graduate student who visited Günaydin four years ago. Resembling an interplanetary traveler, with a waved silver fringe that narrows to a point between piercing blue eyes, Furey scribbled esoteric symbols on a painting, trying to explain to Günaydin that she had extended his work and that of Gursey by building an octonionic model of both.
"Communicating details to him turned out to be a little more of a challenge than I had anticipated, while I was fighting for a word on the edge," recalls Furey. Günaydin had continued to study octonions since the 1970s because of their deep links with string theory, M theory and supergravity theories that attempt to unify gravity with other fundamental forces. But his octonionic activities had always been outside the mainstream. He advised Furey to find another research project for his doctorate, because the octonions could close the doors, as he felt for him.
But Furey was not – could not – give up. Driven by a deep intuition that octonions and other divisional algebras underlie the laws of nature, she told a colleague that if she could not find academic work, she planned to take her accordion to New Orleans. Instead, Furey earned a post-doctoral degree from the University of Cambridge in the UK. It has since produced a number of results linking the octonions to the standard model that experts call intriguing, curious, elegant and novel.
"She took significant steps to solve really deep physical puzzles," Shadi Tahvildar-Zadeh said. , a mathematical physicist at Rutgers University who recently visited Furey in Cambridge after watching an online series of conference videos about her work
Furey has not yet built a simple octonionic model of all the particles and forces of the Standard Model in one go. and she did not touch gravity. She points out that the mathematical possibilities are many, and experts say that it is too early to say how to amalgamate octonions and other divisional algebras (if any) will lead to success.
"She found intriguing links" Duff, a pioneering string theorist and professor at Imperial College London, studied the role of octonions in string theory. "In my opinion, it's worth it to be pursued.It's finally the way the standard model is described, it's hard to say.If that was the case, it would be qualified for all the superlatives – revolutionary, and so on. "
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