All posts by jgmoxness

Physics

I've added an N-Body Gravitational Simulation Pane and enhanced the Composite Quark Hadron Model Pane

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The N-Body Gravitational Simulation (not yet complete) uses Mathematica’s OpenCL GPU computing capability to simulate standard (Solar System), GR (Black Hole Centered Galaxy formation), Large Scale Universal Structure, and Quantum GR (Big Bang Inflationary) physics.

I’ve consolidated the Meson/Baryon panes into a single Hadron pane that now includes the formation of the recently validated TetraQuark Hadrons.

Please see ToE_Demonstration.cdf or as an interactive web page) that takes you on an integrated visual journey from the abstract elements of hyper-dimensional geometry, algebra, particle and nuclear physics, and on to the atomic elements of chemistry. It requires the free Mathematica CDF plugin (25 Mb). ToE_Demonstration.nb is the same as CDF except it includes file I/O capability not available in the free CDF player. This requires a full Mathematica license (25 Mb).

outNBody-1b

outNBody-1a

QM-GR-N-Body

Meson

Baryon

TetraQuark

Physics

Added PMNS and CKM particle mixing matrix calculations to ToE_Demonstration.CDF

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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.

ToE_Demonstration

JGM_ToE-15t

Code snippets showing the CKM and PMNS matrix calculations based on the UI.

JGM_ToE-15v

JGM_ToE-15u

Personal

Avengers Tesseract Cosmic Cube

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I finally got around to watching the Avengers movie and noticed that the Tesseract Cosmic Cube looked much like the hyper-dimensional projections that I make with laser etched optical crystal.

The blue light is projected from a multi-colored LED base.

While I do have tesseract projections, the E8 projection on my home page seems most similar. Here are a few blue crystal photos I’ve taken that are also similar.

DSCN0934

IMG_2011_05_13_1042a

IMG_2011_05_13_1054a

IMG_2011_05_13_1029a

IMG_2011_05_13_1025a

DSCN0994

Physics

E8 folding to H4+H4/φ

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I found the rotation matrix that shows the E8 Dynkin diagram can indeed be folded to H4+H4/φ.

The H4 and its 120 vertices make up the 4D 600 Cell. It is made up of 96 vertices of the Snub 24-Cell and the 24 vertices of the 24-Cell=[16 vertex Tesseract=8-Cell and the 8 vertices of the 4-Orthoplex=16-Cell]).

It can be generated from the 240 split real even E8 vertices using a 4×8 rotation matrix:
x = (1, φ, 0, -1, φ, 0, 0, 0)
y = (φ, 0, 1, φ, 0, -1, 0, 0)
z = (0, 1, φ, 0, -1, φ, 0, 0)
w = (0, 0, 0, 0, 0, 0, φ^2, 1/φ)

where φ=Golden Ratio=(1+Sqrt(5))/2

It is also interesting to note that the x, y, and z vectors project to a hull of the 3D Rhombic Triacontrahedron from the 6D 6 cube Hexaract (which then generates the hull of the Dodecahedron and Icosahedron Platonic solids).

Here’s a look at the Dynkin Diagram folding of E8 to H4+H4/φ:

E8-H4-Fold

I find in folding from 8D to 4D, that the 6720 edge counts split into two sets of 3360 from E8’s 6720 length Sqrt(2), but the combined edges and vertices recreate the E8 petrie diagram perfectly.

Some visualizations of this in 8D:
E8-8D-Polytopes-2

to 4D:
E8-4D-Polychora-2

and also showing the Rhombic Triacontrahedron folding from 6D:
E8-6D-StarPolytopes-2

to 3D:
E8-3D-Platonic-2

Physics

Another look at integrating the Pascal Triangle to Clifford Algebra, E8 Lie Algebra/Groups, Octonions and Particle Physics Standard Model

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Pascal-g

Modified Lisi split real even E8 particle assignment quantum bit patterns:

Lisi_Particle_Assignments

Assigning a specific mass, length, time, and charge metrics based on new dimensional relationships and the Planck constant (which defines Higgs mass).

ToEsummary

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):

DynkinE8Full.svg

This Dynkin diagram builds the Cartan matrix and determines the root/weight/height with corresponding Hasse diagrams.

E8Hasse

E8HassePoset.svg

Physics

More amplituhedron capability (projected hull surface area and volume)

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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…
amplituhedron-0b

amplituhedron-0c
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-0a

Physics

Amplituhedron Visualizations!

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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
amplituhedron-1a

Compare this Mathematica(l) basis to the artistic representation by Andy Gilmore amplituhedron-1a

Positroid Diagrams:
amplituhedron-0a

Personal

Announcing the AI party!

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I am officially announcing a new political party for America! It is the AI party. No, this is not about Artificial Intelligence, but that would be a really cool idea.

This is the Anti-Incumbency party. I am really tired of the crap that the public puts up with due to the legacy of corruption and collusion in the name of consensus building.

Yes, the Tea-Party intended to address this with a different point-of-view (POV), but this splits the conservative base and leaves the liberals cold. Yet, Obama alienates the liberals with a schizophrenic agenda that doesn’t even hold true to his original campaign of hope and change.

So this new party will steadfastly vote against ANY incumbent for 6 years. This will flush the system of all the corrupt bureaucrats (and a few good ones). The good ones are collateral damage in a war against a system of government that has become too accustomed to professional politics.

It is time for all of them to go. Yes, some power is lost- but so is the corruption and inept consensus building with pork and back scratching.

Please join me in the AI party. Vote for ANY party except the incumbent. The AI party.