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Quantamagazine |  Furey has gone further. In her most recent published paper, which appeared in May in The European Physical Journal C, she consolidated several findings to construct the full Standard Model symmetry group, SU(3) × SU(2) × U(1), for a single generation of particles, with the math producing the correct array of electric charges and other attributes for an electron, neutrino, three up quarks, three down quarks and their anti-particles. The math also suggests a reason why electric charge is quantized in discrete units — essentially, because whole numbers are.

However, in that model’s way of arranging particles, it’s unclear how to naturally extend the model to cover the full three particle generations that exist in nature. But in another new paper that’s now circulating among experts and under review by Physical Letters B, Furey uses C⊗O to construct the Standard Model’s two unbroken symmetries, SU(3) and U(1). (In nature, SU(2) × U(1) is broken down into U(1) by the Higgs mechanism, a process that imbues particles with mass.) In this case, the symmetries act on all three particle generations and also allow for the existence of particles called sterile neutrinos — candidates for dark matter that physicists are actively searching for now. “The three-generation model only has SU(3) × U(1), so it’s more rudimentary,” Furey told me, pen poised at a whiteboard. “The question is, is there an obvious way to go from the one-generation picture to the three-generation picture? I think there is.”

This is the main question she’s after now. The mathematical physicists Michel Dubois-Violette, Ivan Todorov and Svetla Drenska are also trying to model the three particle generations using a structure that incorporates octonions called the exceptional Jordan algebra. After years of working solo, Furey is beginning to collaborate with researchers who take different approaches, but she prefers to stick with the product of the four division algebras, R⊗C⊗H⊗O, acting on itself. It’s complicated enough and provides flexibility in the many ways it can be chopped up. Furey’s goal is to find the model that, in hindsight, feels inevitable and that includes mass, the Higgs mechanism, gravity and space-time.

Already, there’s a sense of space-time in the math. She finds that all multiplicative chains of elements of R⊗C⊗H⊗O can be generated by 10 matrices called “generators.” Nine of the generators act like spatial dimensions, and the 10th, which has the opposite sign, behaves like time. String theory also predicts 10 space-time dimensions — and the octonions are involved there as well. Whether or how Furey’s work connects to string theory remains to be puzzled out.

So does her future. She’s looking for a faculty job now, but failing that, there’s always the ski slopes or the accordion. “Accordions are the octonions of the music world,” she said — “tragically misunderstood.” She added, “Even if I pursued that, I would always be working on this project.”