The Peculiar Math That Could Underlie the Laws of Nature

["Dave Farber" <farber () gmail com>]

Begin forwarded message:

> From: Dewayne Hendricks <dewayne () warpspeed com>
> Date: August 3, 2018 at 02:23:43 GMT+9
> To: Multiple recipients of Dewayne-Net <dewayne-net () warpspeed com>
> Subject: [Dewayne-Net] The Peculiar Math That Could Underlie the Laws of Nature
> Reply-To: dewayne-net () warpspeed com
>
> [Note:  This item comes from friend Ed DeWath.  DLH]
>
> The Peculiar Math That Could Underlie the Laws of Nature
> New findings are fueling an old suspicion that fundamental particles and forces spring from strange eight-part 
> numbers called “octonions.”
> By Natalie Wolchover
> Jul 20 2018
> <https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/>
>
> In 2014, a graduate student at the University of Waterloo, Canada, named Cohl Furey rented a car and drove six hours 
> south to Pennsylvania State University, eager to talk to a physics professor there named Murat Günaydin. Furey had 
> figured out how to build on a finding of Günaydin’s from 40 years earlier — a largely forgotten result that supported 
> a powerful suspicion about fundamental physics and its relationship to pure math.
>
> The suspicion, harbored by many physicists and mathematicians over the decades but rarely actively pursued, is that 
> the peculiar panoply of forces and particles that comprise reality spring logically from the properties of 
> eight-dimensional numbers called “octonions.”
>
> As numbers go, the familiar real numbers — those found on the number line, like 1, π and -83.777 — just get things 
> started. Real numbers can be paired up in a particular way to form “complex numbers,” first studied in 16th-century 
> Italy, that behave like coordinates on a 2-D plane. Adding, subtracting, multiplying and dividing is like translating 
> and rotating positions around the plane. Complex numbers, suitably paired, form 4-D “quaternions,” discovered in 1843 
> by the Irish mathematician William Rowan Hamilton, who on the spot ecstatically chiseled the formula into Dublin’s 
> Broome Bridge. John Graves, a lawyer friend of Hamilton’s, subsequently showed that pairs of quaternions make 
> octonions: numbers that define coordinates in an abstract 8-D space.
>
> There the game stops. Proof surfaced in 1898 that the reals, complex numbers, quaternions and octonions are the only 
> kinds of numbers that can be added, subtracted, multiplied and divided. The first three of these “division algebras” 
> 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. Might 
> the octonions hold secrets of the universe?
>
> “Octonions are to physics what the Sirens were to Ulysses,” Pierre Ramond, a particle physicist and string theorist 
> at the University of Florida, said in an email.
>
> Günaydin, the Penn State professor, 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. An 
> initial flurry of interest in the finding didn’t last. Everyone at the time was puzzling over the Standard Model of 
> particle physics — the set of equations describing the known elementary particles and their interactions via the 
> strong, weak and electromagnetic forces (all the fundamental forces except gravity). But rather than seek 
> mathematical answers to the Standard Model’s mysteries, most physicists placed their hopes in high-energy particle 
> colliders and other experiments, expecting additional particles to show up and lead the way beyond the Standard Model 
> to a deeper description of reality. They “imagined that the next bit of progress will come from some new pieces being 
> dropped onto the table, [rather than] from thinking harder about the pieces we already have,” said Latham Boyle, a 
> theoretical physicist at the Perimeter Institute of Theoretical Physics in Waterloo, Canada.
>
> Decades on, no particles beyond those of the Standard Model have been found. Meanwhile, the strange beauty of the 
> octonions has continued to attract the occasional independent-minded researcher, including Furey, the Canadian grad 
> student who visited Günaydin four years ago. Looking like an interplanetary traveler, with choppy silver bangs that 
> taper to a point between piercing blue eyes, Furey scrawled esoteric symbols on a blackboard, trying to explain to 
> Günaydin that she had extended his and Gürsey’s work by constructing an octonionic model of both the strong and 
> electromagnetic forces.
>
> “Communicating the details to him turned out to be a bit more of a challenge than I had anticipated, as I struggled 
> to get a word in edgewise,” Furey recalled. Günaydin had continued to study the octonions since the ’70s by way of 
> their deep connections to string theory, M-theory and supergravity — related theories that attempt to unify gravity 
> with the other fundamental forces. But his octonionic pursuits had always been outside the mainstream. He advised 
> Furey to find another research project for her Ph.D., since the octonions might close doors for her, as he felt they 
> had for him.
>
> [snip]
>
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