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FQXI ARTICLE

February 6, 2023

Taking on String Theory’s 10-D Universe with 8-D Math

A bizarre set of of 8-dimensional numbers could explain how to handle string-theory’s extra dimensions, why elementary particles come in families of three—and maybe even how spacetime emerges in 4-dimensions.

FQXi Awardees: Tevian Dray

November 1, 2011

BALANCING FAMILY AND PHYSICS

Tevian Dray (far left) and Corinne Manogue (far right)

Manogue puts it in context: "Tevian is very much the mathematician and I’m very much the physicist. I have a tendency to see the physics that we are striving for, but through a glass, darkly," she says. "I have some sense of where we want to go, but it is cloudy, and kind of befuddled. The first thing that happens is I say, ’we want to do this.’ His reaction is, ’I have no idea what you are saying.’ And so we go through a very tumultuous period, where he is trying to get me to articulate clearly enough what I mean so that he can do the mathematics. It’s typically a loud and frustrating time. At the dinner table, most often."

Together Dray and Manogue are trying to tackle a profound question in physics: Why is our universe described so well by the standard model of particle physics? The standard model works in four dimensions—three of space and one of time—and has been extremely successful at explaining how elementary particles interact with each other. And yet there are vagaries that the standard model can’t make sense of, such as why these particles have the masses that they do, or why they group together in families of three with similar properties, but different masses. Dray and Manogue, who are both at Oregon State University in Corvallis, are convinced that the answer lies in the mathematics of higher dimensions—no less than 10 dimensions, in fact.

It’s typically loud and

frustrating. At the dinner

table, most often.

frustrating. At the dinner

table, most often.

- Corinne Manogue on working with Dray

Strange Brood

Octonions are a strange brood, forming an eight-dimensional number system (see sidebar: "The Crazy Old Uncle of Algebra."). By contrast, the lovable real numbers that we’re all comfortable with live in one dimension—that is, they can be written out along a one-dimensional number line; while the complex numbers that some of the more mathematically-inclined dabble with, make up a two-dimensional number system.

In the standard model, particles can be split into

SPOT THE QUARK

The geometric structure F

day help us visualize how the eight-dimensional

octonions describe quarks in our 4-D world.

That’s exactly the objection that Fairlie raises about the work. "There is no answer to questions of particle interactions," he says. He points out that the peculiar mathematics of octonions introduces new problems. In particular, octonions are

Despite this stumbling block, Manogue and Dray continue to plug away. They have used their octonions to encode the momentum and spin properties of these particles, explain why neutrinos are "left-handed" (that is, why the neutrinos’ spins are always oriented in one particular sense relative to the direction in which they move and never in the opposite sense), and even provide clues to why the particles cluster into families of three. These properties seem to be inherent in the language of octonions.

Speaking at FQXi’s 2nd international conference in the Ponta Delgada, Azores, Dray described the mathematical connection between octonions and fermions:

"Dray and Manogue are among the few really good physicists who think hard about the octonions and what they might mean for physics," says John Baez, a mathematical physicist at the University of California, Riverside. "As far as I’m concerned, these questions remain mysteries. But Dray and Manogue have found some tantalizing clues."

The next step—using a $51,393 grant from FQXi—is to try to use octonions to identify quarks and also to figure out how particles get their charge. "At that stage we might be able to make some experimentally verifiable predictions, like there is no Higgs," says Manogue.

Collapsing Dimensions

Their ultimate goal is to show that the standard model is just a natural consequence of describing the fundamental particles in 10 dimensions. It if works, octonions could also help solve one of the biggest puzzles facing string theorists: How their hypothetical six extra dimensions of space are folded up so that we only experience four-dimensions in our universe.

This may suggest that

spacetime isn’t a fundamental

property of the universe,

but only emerges in its four-

dimensional description.

spacetime isn’t a fundamental

property of the universe,

but only emerges in its four-

dimensional description.

Octonions may also be hinting at another deep truth about the structure of the universe. In 10 dimensions, octonions can be used to describe a particle’s momentum, but not its position. But after the description is collapsed down from 10 to four dimensions, particles can be described in both ways. This may suggest that spacetime isn’t a fundamental property of the universe, but only emerges in its four-dimensional description. "That would be incredibly profound, I think," says Manogue.

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Please read the important Introduction that governs your participation in this community. Inappropriate language will not be tolerated and posts containing such language will be deleted. Otherwise, this is a free speech Forum and all are welcome!

Recent Comments

VIJAY MOHAN GUPTA wrote on July 14, 2012

PicoPhysics standard model is different. It considers only one particle type called UCO (Photon of mainstream physics) constitutes all matter in the universe. It may be mass-particles, fields, dark-matter or Radiations.

Based on single postulates Space contains Energy (Knergy) it has explaination for importance of number 3 in physics and establishes three dimensions of space from unary law 'Space contains Knergy'. It views universe at 5-Dimensional reality. Please review and comment on...

PicoPhysics standard model is different. It considers only one particle type called UCO (Photon of mainstream physics) constitutes all matter in the universe. It may be mass-particles, fields, dark-matter or Radiations.

Based on single postulates Space contains Energy (Knergy) it has explaination for importance of number 3 in physics and establishes three dimensions of space from unary law 'Space contains Knergy'. It views universe at 5-Dimensional reality. Please review and comment on...

STEVE DUFOURNY wrote on July 11, 2012

Interesting to see how the strategists can insist on the false roads.

In fact the strings theorists fear to be less listened just due to my revolutionary theory.

In fact they confound the computing and the realistic universal sphere in 3D.

The rest is vain.

MIT you know , be rational and less in the subjectivities and less in the business of copycats.

Interesting to see how the strategists can insist on the false roads.

In fact the strings theorists fear to be less listened just due to my revolutionary theory.

In fact they confound the computing and the realistic universal sphere in 3D.

The rest is vain.

MIT you know , be rational and less in the subjectivities and less in the business of copycats.

GEOFFREY DIXON wrote on February 19, 2012

More recent take on $T = C\otimes H \otimes O$, if interested. Cheers.

"Division Algebras, Lattices, Physics, Windmill Tilting".

More recent take on $T = C\otimes H \otimes O$, if interested. Cheers.

"Division Algebras, Lattices, Physics, Windmill Tilting".

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