# Zenith Grant Awardee

## Dr. Tevian Dray

### Oregon State University

Co-Investigators

Corinne A. Manogue, <i>Department of Physics, Oregon State University</i>

Project Title

Using Octonionic Cayley Spinors to Describe Fundamental Particles

Project Summary

How many dimensions are there in the universe? Could any "extra" dimensions represent the Standard Model? An underlying principle is needed to answer these and similar questions. We believe the key is to reformulate existing theory in terms of two special mathematical structures: the octonions — the largest division algebra, and the exceptional Jordan algebra — the largest reasonable matrix algebra over the octonions. For 20 years, we have been carefully examining how to rewrite certain pieces of fundamental physical theories in terms of these structures. It turns out that this can be done only in special cases. For example, Lorentz transformations exist in any dimension, but only in ten dimensions do they fit naturally inside the exceptional Jordan algebra. Every time we have used the octonions to guide our choices, we have discovered new features of these special cases. Instead of being inputs to the theory, motivated by experiment, these facts emerge naturally as consequences of the special properties of these mathematical structures. We plan to explore the tantalizing evidence that these mathematical structures can be used to give a unified theory of fundamental particles and their interactions.

Technical Abstract

In previous work, we showed how to rewrite the massless Dirac equation in ten dimensions in terms of an octonionic generalization of the two-component Penrose spinors of relativity. The resulting description has several remarkable properties:

An underlying complex structure naturally selects four preferred space-time dimensions, leading to an interpretation in terms of both massive and massless particles;

Each solution can be identified with a classical solution of the four-dimensional Dirac equation, with the correct number of spin states for precisely three generations of fermions, with single-helicity, massless neutrinos.

Our earlier work can be expressed in terms of the ten-dimensional Lorentz group in the form S L(2, O), acting separately on vectors and spinors. This formalism admits a natural extension to an action of E6 ≈ S L(3, O) on the exceptional Jordan algebra that incorporates vectors and spinors in a single framework. We propose here to first extend our two-component description of fermions to a three-component description of all the (free) fundamental particles, then attempt to describe particle interactions in this language.

## QSpace Latest

PressRelease: *Shining a light on the roots of plant “intelligence”*

All living organisms emit a low level of light radiation, but the origin and function of these ‘biophotons’ are not yet fully understood. An international team of physicists, funded by the Foundational Questions Institute, FQxI, has proposed a new approach for investigating this phenomenon based on statistical analyses of this emission. Their aim is to test whether biophotons can play a role in the transport of information within and between living organisms, and whether monitoring biophotons could contribute to the development of medical techniques for the early diagnosis of various diseases. Their analyses of the measurements of the faint glow emitted by lentil seeds support models for the emergence of a kind of plant ‘intelligence,’ in which the biophotonic emission carries information and may thus be used by plants as a means to communicate. The team reported this and reviewed the history of biophotons in an article in the journal Applied Sciences in June 2024.