Octonions -“May Harbor Secrets of the Universe”

Early Cosmos


“The final theory of nature must be octonionic,” observed Michael Atiyah, a British mathematician who united mathematics and physics during the 1960s in a way not seen since the days of Isaac Newton.

“Octonions are to physics what the Sirens were to Ulysses,” Pierre Ramond, a particle physicist and string theorist at the University of Florida, said to Natalie Walchover for Quanta.

Many physicists and mathematicians over the decades suspected that the peculiar panoply of forces and particles that comprise reality spring logically from the properties of eight-dimensional numbers called “octonions.” Proof surfaced in 1898, writes Walchover in Quanta, that the reals, complex numbers, quaternions and octonions are the only kinds of numbers that can be added, subtracted, multiplied and divided.

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The first three of these “division algebras,” Walchover continued, “would soon lay the mathematical foundation for 20th-century physics, with real numbers appearing ubiquitously, complex numbers providing the math of quantum mechanics, and quaternions underlying Albert Einstein’s special theory of relativity. This has led many researchers to wonder about the last and least-understood division algebra.”

Do octonions hold secrets of the universe?

Penn State physicist Murat Günaydin, was a graduate student at Yale in 1973 when he and his advisor Feza Gürsey found a surprising link between the octonions and the strong force, which binds quarks together inside atomic nuclei, but decades that followed, no particles beyond those of the Standard Model have been found.

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Enter Cohl Furey: at the University of Cambridge, driven by a profound intuition that the octonions and other division algebras underlie nature’s laws, the 39-year old physicist produced a number of results connecting the octonions to the Standard Model “that experts are calling intriguing, curious, elegant and novel.”



“She has taken significant steps toward solving some really deep physical puzzles,” said Shadi Tahvildar-Zadeh, a mathematical physicist at Rutgers University.

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Furey has yet to construct a simple octonionic model of all Standard Model particles and forces, and she hasn’t touched on gravity, observes Walchover: “She stresses that the mathematical possibilities are many, and experts say it’s too soon to tell which way of amalgamating the octonions and other division algebras (if any) will lead to success.”

“She has found some intriguing links,” said Michael Duff, a pioneering string theorist and professor at Imperial College London who has studied octonions’ role in string theory. “It’s certainly worth pursuing, in my view. Whether it will ultimately be the way the Standard Model is described, it’s hard to say. If it were, it would qualify for all the superlatives — revolutionary, and so on.”

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“The real theory which we would like to get to,” he said in 2010, “should include gravity with all these theories in such a way that gravity is seen to be a consequence of the octonions and the exceptional groups, said Michael Atiyah. “It will be hard because we know the octonions are hard, but when you’ve found it, it should be a beautiful theory, and it should be unique.”

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The Peculiar Math That Could Underlie the Laws of Nature

The Daily Galaxy, Max Goldberg via Big Think and Quanta 

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