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.”
