## High Energy Particle Physics   ## Standard Model and Gravity from Tetrahedra

Authors: Frank Dodd Tony Smith Jr

E8 Physics (viXra 1405.0030) at high energies has Octonionic 8-dim Spacetime that is fundamentally a superposition of E8 Lattices each of which has vertices surrounded by the 240-vertex E8 Root Vector Polytope. At lower energies Octonionic symmetry is broken to Quaternionic symmetry in accord with E8 = H4 + H4 so that the 240-vertex E8 Polytope is decomposed into two copies of the Quaternionic 4-dim 120-vertex 600-cell whose relative size is the Golden Ratio. If you give one copy a rational number size, then the size of the other will be in a Golden Ratio Algebraic Extension space. Let the Rational Number 600-cell be the Vertex Polytope for 4-dim M4 Physical Spacetime of M4 x CP2 Kaluza-Klein and the Algebraic Extension 600-cell be the Vertex Polytope for 4-dim CP2 Internal Symmetry Space of M4 x CP2 Kaluza-Klein. Look at the 4-dim Physical Spacetime 600-cell. It has 120 vertices and 600 tetrahedra. 20 x 24 = 480 of the 600 tetrahedra are in 24 icosahedra within the 600-cell. 5 x 24 = 120 of the 600 tetrahedra are, 5 in each, connected to each of the 24 icosahedra to form 24 octahedra. The 24 octahedra form a 4-dim 24-cell, the Vertex Polytope of the 4-dim Feynman Checkerboard. 24 of the 120 vertices correspond to vertices of the 24-cell and 96 of the 120 vertices correspond to Golden Ratio points, arranged in one of the two possible consistent ways, on the 96 edges of the 24-cell dual to the original 24-cell. Even though 3-dim simplex tetrahedra cannot tile flat 3-dim space, they can combine to form curved 3-dim subspaces in 4-dim space, so that 3-dim simplex tetrahedra can be used as building blocks to construct E8 Physics by taking 1200 of them to make two 600-cells, each in its own 4-dim space, and then combining the two 600-cells and their two 4-dim spaces to make 8-dim E8 Root Vector Polytopes, and then to make E8 Lattices whose E8 Lie Algebra lives in Cl(16) Clifford Algebras whose completion of union of all tensor products form a generalized hyperfinite II1 von Neumann factor AQFT (Algebraic Quantum Field Theory) based on the realistic E8 Physics Lagrangian and corresponding to a realistic 4-dim Feynman Checkerboard.

### Submission history

[v1] 2015-01-06 14:22:52
[v2] 2015-03-20 10:51:09
[v3] 2015-03-28 16:24:24
[v4] 2015-06-29 08:25:50