Please see Integrated E8, Binary, Octonion for a tutorial that explains the detail of the content of Fano.pdf. It outlines the relationships in the integration of E8 with Octonions, Binary, Particles, NKS, and the Periodic Table of Elements. Other formats are also available (.ppt or .pps and .pdf).
All posts by jgmoxness
Created a simpler Fano plane and cubic .pdf
A simpler version of Fano.pdf is here FanoOnly.pdf (15MB).
Improved complete index of E8, Binary, Octonions, Particles, NKS CA & Periodic Table
The main change was an improved association of the 120 periodic table elements to the 120 root vectors weighted by their simple root grading. See the full 241 page reference here.
Improved the Hasse Visualizations
I’ve added better edge coloring and added edge root vector information (for the added simple root used).
Integration of the Atomic Elements to E8 and Octonions
While it still needs some work – I’ve integrated the atomic elements to the Octonions, E8 and theoretical Lisi eSM model particle assignments (along with Wolfram’s NKS Cellular Automata linked to the Clifford Algebra/Pascal Triangle binary assignments). I have combined all these visualizations with the 2D/3D electron orbitals (based on the symmetry of the {n,l,m,s} quantum numbers (from the Stowe-Janet-Scerri Periodic Table. I totally understand this is not easy to dig into w/o some effort, but … it looks cool 😉
It is shown in an updated version of Fano.pdf. This is a very large and complex 30Mb file – with 241 pages. It shows the Lisi particle assignments, the E8 roots, split real even (SRE) E8 vertex and the Lisi “physics rotation”. It also shows two Fano plane and cubic derived from the symmetries of the E8 particle assignments (and all the relevant construction of it). See the interactive demo or the Mathematica Notebook for a more “navigational look” at the integration.
Created a new 4D Stowe-Janet-Scerri Periodic Table
I’ve replaced the standard periodic table in the 7th “Chemistry Pane” of my E8 visualizer with a 2D/3D/4D Stowe-Janet-Scerri version of the Periodic Table.
Interestingly, it has 120 elements, which is the number of vertices in the 600 Cell or the positive half of the 240 E8 roots. It is integrated into VisibLie_E8 so clicking on an element adds that particular atomic number’s E8 group vertex number to the 3rd E8 visualizer pane.
The code is a revision and extension of Enrique Zeleny’s Wolfram Demonstration
A few screen shots….
2D and 3D electron orbitals for each element
MyToE updated from 2013 Planck Spacecraft and 2012 LHC results
With the recent publication of results for the Planck spacecraft results and the recent LHC Higgs results for the discovery of a 125(+/-1.5)GeV Higgs boson, I thought I would publish the minor tweaks to my PDF ToE summary or see the Mathematica notebook here. Enjoy!
It is interesting to note that my original paper from ’98 (updated ’01) Constants-A_New_Look.pdf contains this new Planck CMB probe result for a Hubble constant of H0=67.133 km/s/Mpc, which is at odds with WMAP, COBE, and prior estimates.
This old paper has a Higgs mH=98.137 GeV, which is around the minima of the ChiSquared value for Higgs. This was quickly excluded by FermiLab results around that time. The basic Higgs prediction relies purely on the dimensionality of the model and the Planck constant. Adding a factor of 2^1/2 gave an aesthetically pleasing mH=147.98 in a ’07 paper here. This was close to a June ’11 FermiLab CDF bump at 148 GeV. Unfortunately D0 at FermiLab didn’t confirm it.
Interestingly between the ’01 and the ’07 papers, one of the Higgs mass models I used 2^1/4 (not 2^1/2) and puts mH=124.43 GeV – right where LHC ATLAS and CMS seem to have found it. This same model also (fairly) accurately integrates this to the Fermi Constant and vacuum expecation (VEV).
The bottom line, my model describes results that are within the most current and accurate experimentally measured data, including the LHC Higgs and Planck CMB probes.
ToE Summary
Octonion Math Notebook
In responding to a query on StackExchange, I created a small notebook that includes a Cayley-Dickson doubling of the built-in Mathematica quaternions to perform general octonion math. It is the foundation for some of the visualizations used here.
The 480 octonions, their Fano planes and multiplication tables
I am pleased to announce the availability of Fano.pdf, a 241 page pdf file with the 480 octonion permutations (with Fano planes and multiplication tables). These are organized into “flipped” and “non-flipped” pairs associated with the 240 assigned particles to E8 vertices (sorted by Fano plane index or fPi). For each split real even E8 vertex, the algebra root, weight and height are listed along with the Clifford/Pascal binary and physics rotation coordinates. On each page, the E8 particle number, symbol, and assigned 2D/3D shape are shown along with the (a)nti, (p)Type, (s)pin, (c)olor, (g)eneration bitwise quantum assignments. Also included is the particle experimental mass and lifetime along with my ToE theoretically calculated mass. (30MB)
I believe this is the only comprehensive presentation of all 480 Fano planes with their multiplication tables available.
Update: Quaternions, Octonions, Time, Particle Mass/Charge and Reality
I am improving and tightening the octonion to E8 to particle symmetry assignments which should inform the particle mass/charge assignment (prediction).
Keep looking at the .CDF .NB or interactive pages – it is always up to date.
I am thinking about how the quaternion trialities within the non-associative algebra of octonions relate to time (and differentiate particles). So it is less about E8 and more about how octonions (linked to E8) affect our 4D reality.