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FQXI ARTICLE

December 9, 2022

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

September 13, 2009

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

If this octonion stuff

is right, it tells you

uniquely what to do with

the extra-dimensions and

how to handle them.

is right, it tells you

uniquely what to do with

the extra-dimensions and

how to handle them.

- Tevian Dray

"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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STEVE wrote on February 26, 2015

2^0 = Q (Real), 2^1 = C(Complex)I, 2^2 = H(quaternions)IJK, 2^3 = O(octonions )

Is there a next level?

2^4 = Hextonian? 16 dimensions? ijklmnopqrstuvw

15-Point Projective Space?

http://demonstrations.wolfram.com/15PointProjectiveSpace/

2^0 = Q (Real), 2^1 = C(Complex)I, 2^2 = H(quaternions)IJK, 2^3 = O(octonions )

Is there a next level?

2^4 = Hextonian? 16 dimensions? ijklmnopqrstuvw

15-Point Projective Space?

http://demonstrations.wolfram.com/15PointProjectiveSpace/

BASHIR YUSUF wrote on December 14, 2010

dimensions and the shape seems to be a key of understanding of the natures fundamentals

dimensions and the shape seems to be a key of understanding of the natures fundamentals

BASHIR YUSUF wrote on December 13, 2010

The core Idea we postulate it is that the nature has same fundamentals. In this scientific article we

will explore the broad area in physical science in different aspect and compare to existing known

scientific theories. There are no remarkable contradictions with accepted theories, instead

integrates and interprets to a better Unified theory.

Gravity is the basic interaction and the Photon is the ultimate elementary particle that every

thing is made of. Sphere...

The core Idea we postulate it is that the nature has same fundamentals. In this scientific article we

will explore the broad area in physical science in different aspect and compare to existing known

scientific theories. There are no remarkable contradictions with accepted theories, instead

integrates and interprets to a better Unified theory.

Gravity is the basic interaction and the Photon is the ultimate elementary particle that every

thing is made of. Sphere...

read all article comments