This is a unique projection of E8 which I discovered using my Mathematica notebook:
Tag Archives: Physics
Added PMNS and CKM particle mixing matrix calculations to ToE_Demonstration.CDF
I’ve improved on a great Wolfram demonstration from Balázs Meszéna on Neutrino Oscillations by adding capabilities to view both the PMNS and CKM unitary triangle matrices, print and reference my ToE Neutrino mass predictions, which now accomodate the Koide relationships in particle masses.
Check out the new demonstrations using free interactive web plugin , .CDF, or .NB (for licensed Mathematica users) and social media integrations for comments, pages and posts.
This new pane (#5) presents the Unitarity of CP=T violations by combining the Lepton (Neutrino) Pontecorvo-Maki-Nakagawa-Sakata matrix (PMNS) with the Quark Cabibbo-Kobayashi-Maskawa (CKM) mixing matrix calculations through the Quark-Lepton Complementarity (QLC).
I am also working to incorporate the Koide particle mass relations to MyToE predictions.
Code snippets showing the CKM and PMNS matrix calculations based on the UI.
New site and demonstration capability added!
Check out the new demonstrations using free interactive web plugin , .CDF, or .NB (for licensed Mathematica users) and social media integrations for comments, pages and posts.
Another look at integrating the Pascal Triangle to Clifford Algebra, E8 Lie Algebra/Groups, Octonions and Particle Physics Standard Model
Modified Lisi split real even E8 particle assignment quantum bit patterns:
Assigning a specific mass, length, time, and charge metrics based on new dimensional relationships and the Planck constant (which defines Higgs mass).
The split real even E8 group used has been determined from this simple root matrix (which gives the Cartan matrix upon dot product with a transpose of itself):
This Dynkin diagram builds the Cartan matrix and determines the root/weight/height with corresponding Hasse diagrams.
More amplituhedron capability (projected hull surface area and volume)
Getting more capability built into ToE_Demonstration.nb where it can now calculate the scattering amplitude by calculating the volume of the projected hull of selected edges in the n-Simplex Amplituhedron (based on a theory by Nima Arkani-Hamed, with some Mathematica code from J. Bourjaily for the positroid diagram). Of course, there is still much work to get this wrapped up…
A few more pics of Positive Grassmannian Amplituhedrons…
This last diagram is obtained using the following amplituhedron0.m as input to the ToE_Demonstration.nb (when using fully licensed Mathematica) as shown below:
* This is an auto generated list from ToE_Demonstration.nb *)
new := {
artPrint=True;
scale=0.1;
cylR=0.018;
range=2.;
pt={-0.3, 0.0, 0.6};
favorite=1;
showAxes=False;
showEdges=True;
showPolySurfaces=True;
eColorPos=False;
dimTrim=5;
ds=6;
pListName=”First8″;
dsName=”nSimplex”;
p3D=” 3D”;
edgeVals={{Sqrt[11/2], 8}, {Sqrt[9/2 – Sqrt[2]], 4}, {Sqrt[9/2 + Sqrt[2]], 4}};
};new;
Positroid Diagrams:
Amplituhedron Visualizations!
Playing around trying to visualize the latest in the theoretical high energy particle physics (HEP/TH) determining how particle masses might be predicted from geometric principles (based on a theory by Nima Arkani-Hamed, with some Mathematica code from J. Bourjaily for the positroid diagram).
Positive Grassmannian Amplituhedrons
Compare this Mathematica(l) basis to the artistic representation by Andy Gilmore 
Positroid Diagrams:
Updated demonstrations now include split octonions
I’ve updated the .NB, .CDF and interactive demonstrations to include the ability to visualize the split octonions.
Klein Quartic Curves
With some Mathematica source from Leon Lampret at math.stackexchange.com, I’ve been trying to understand the link between the bitangents of octonions and the Klein Quartic Curves.
Which seems to be closely related to Greg Egan’s wonderful visualization from
http://www.gregegan.net/SCIENCE/KleinQuartic/KleinQuartic.html
Detail explanation of E8 Integration with Octonions, Particles, and the Periodic Table
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).
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
