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Wed 19 Dec, 2007 10:52 am
Understandably, there was much celebration among mathematicians when E8 was finally "solved," as the media puts it. A major computing accomplishment, for sure.
But now, I am reading that a few serious players in the field of particle physics believe that the symmetries of E8 can be used to predict the disposition of the particles next discovered. REALLY?
TCR,
Thank you for the detailed reply. I particularly appreciate your historical perspective.
It seems that E8 may be a case in which something symmetrical and powerfully complex MUST surely have a greater utility. Even if E8 turns out to have no larger usefulness, the map of its root system will still possess wondrous beauty.
I have read in many places (for one, an article in "Brain and Cognition" by Dahlia Zaidel of UCLA) that all of us have a powerful innate attraction to physical symmetry in faces when we are mate-selecting. Perhaps, E8 has a particularly elegant countenance to suitors on an intellectual plane.
Symmetry certainly plays an important role in physics. Many of the conservation laws are believed to come about because of "broken symmetries" of quantum fields. All useful particle models exhibit what is know as the Yang-Mills symmetry. As a matter of fact symmetric properties are powerful mathematic tools used to guide the development of particle physics.
String theory will be testable once the 2 satellites reach the other side of the sun and send test signals to the 2 on the side we see - but it will take years until they're all in place.
However there's a new theory of everything using E8:
http://arxiv.org/abs/0711.0770
and that's a general outline for the non-techies:
http://backreaction.blogspot.com/2007/11/theoretically-simple-exception-of.html
Quote:Each root of the E8 Lie algebra corresponds to an elementary particle field, including the gravitational (green circles), electroweak (yellow circles), and strong gauge fields (blue circles), the frame-Higgs (squares), and three generations of leptons (yellow and gray triangles) and quarks (rbg triangles) related by triality (lines). Spinning this root system in eight dimensions shows the F4 and G2 subalgebras.