I'm flattered. What we really need is a professional, like a Broken, but I'll give it a shot.
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Originally Posted by Julie
Abstract: All fields of the standard model and gravity are unified as an E8 principal bundle connection.
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The E8 is a mathematical construct that is stable and uniform across 4 dimensions. "All fields of the standard model " means the following forces:
Electromagnetic Force
Strong Nuclear Force
Weak Nuclear Force
and gravity is, well, the Gravitational Force.
The Absolute Numero Uno of Physics for the last 50 years has been an attempt to define a Grand Unified Theory, or GUT. The idea behind it is that all the 4 known forces above SHOULD be reducable to ONE force definable by ONE set of equations, kindof like the magnetic and electronic forces are related and subsumed under the force of Electromagnetism. It has already been shown that under conditions of sufficient temperature and pressure, the Electromagnetic and Weak Nuclear Forces are "the same". This has buttressed the idea that in the beginning of the Univers, under the incredible temperatures and pressures of the Big Bang, there was only one Force. As things cooled, the Force "split", i.e. different parts became relevant only under certain conditions.
If true, all forces should be related as above. The problem is gravity - no one really knows how it does what it does. Are there gravitons? Is it purely a field phenomenon? We know what gravity DOES, we just don't know HOW. String Theory is one contruct to attempt to arrive at a GUT that combines gravity with the other forces, Branes is another.
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A non-compact real form of the E8 Lie algebra has G2 and F4 subalgebras which break down to strong su(3), electroweak su(2) x u(1), gravitational so(3,1),
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I doubt I could even recognize the symbols in the math he uses, but what it says is that Lisi has derived equations (linear? vector? tensor?) that clearly interrelate the 4 basic forces mentioned above.
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the frame-Higgs, and three generations of fermions related by triality. The interactions and dynamics of these
1-form and Grassmann valued parts of an E8 superconnection are described by the curvature and action over a four dimensional base manifold.
Dale?
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This last part is describing the particles (electrons, protons, neutrons, etc.) and their interactions (electronic charge, spin, etc.) that are predicted by the equations.
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What Lisi had realised was that he could find a way to place the various elementary particles and forces on E8's 248 points. What remained was 20 gaps which he filled with notional particles, for example those that some physicists predict to be associated with gravity.
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In studying this E8 form Lisi was able to locate all known forces and particles in specific locations that "make sense" with respect to the relational equations translated into the E8's specific "points". Since there are a defined number of such "points" and they apparently have local relationships, it helps explain why only certain kinds of particles with certain values and properties exist (i.e. "quanta").
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The crucial test of Lisi's work will come only when he has made testable predictions. Lisi is now calculating the masses that the 20 new particles should have, in the hope that they may be spotted when the Large Hadron Collider starts up.
Maybe an extra dimension? You getting this Dale?
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When he was done he had 20 "points" left over, and this is the important part, he will be able to therefore define the properties of specific particles that have not yet been discovered or observed but that his theory, if correct, "demands" be there. So unlike the other GUT theories, this one is eminently testable - if we never find those particular particles then it's incorrect. This is huge.
There, how's that?
-dale