This is constructed from VisibLie_E8 and uses the Mathematica package Mathgroup. A comprehensive PowerPoint/PDF that gives an overview of the underlying theory and VisibLie_E8 tool capability is in this post.
Greg Moxness, Tucson AZ
The cloud deployments don’t have all the needed features as the fully licensed Mathematica notebooks, so I included a few of the panes that seem to work for the most part. Some 3D and animation features won’t work, but it is a start. Bear in mind that the response time is slow.
A Theory of Everything Visualizer, with links to free Cloud based Interactive Demonstrations:
10) Chemistry: Atomic Elements: 4D Periodic Table Element Select
11) Chemistry: Molecular Crystallography: 4D Molecule Visualization Select
13) Biology: Human Neurology: OrchOR Quantum Consciousness
14) Psychology: Music Theory & Cognition: Chords, Lambdoma, CA MIDI,& Tori
15) Sociology: Theological Number Theory: Ancient Sacred Text Gematria
17) CompSci: Artificial Intelligence: 3D Conway’s Game Of Life
18) CompSci: Human/Machine Interfaces: nD Human Machine Interface
The newer version of the VisibLieE8-NewDemo-v13.nb (130 Mb) will work with those who have a full Mathematica v13 license. It is backward compatible to earlier versions. There are a few bug fixes from the older version of ToE_Demonstration.nb (130 Mb), which should work on v13 and older versions as well.
For more detail on the modules, see this blog post.
Please be patient, it is very large and can take 10 minutes to load, depending on your Internet connection, memory and CPU speed.
I’ve updated an analysis I did on the work of Cohl Furey’s papers from several years ago. Since then, she added another paper: https://arxiv.org/abs/1910.08395v1
The short pdf version of my analysis (with some detail cells collapsed) is here (34 pages), and a longer version is here (no collapsed cells and 51 pages). These pdf’s are a direct output from my Mathematica (MTM) Notebook. I will follow up with a LaTex paper on the topic soon.
This notebook has code built in to operate symbolically on native MTM reals, complexes, and quaternionic forms, as well as my custom code to handle the octonions, and now the bi-octonions (which doesn’t assign the octonion e1 to be equivalent to the complex imaginary (I)). That change also applies to the native quaternion assignments where of e1=I, e2=J, and e3=K in order to work with quater-octonions. This was a fairly trivial change to make since it simply involves removing the conversion of complex (and quaternion) operators from being involved in the octonionic multiplication.
Please note that my previous analysis here (from Feb. 2019) made the mistake of not commenting out these operations. As such, it was operating on octonions (not complexified bi-octonions), so some of my concerns were resolved based on correcting that error.
The bottom line is that I did validate much of the work presented in the referenced papers, with the exception of some 3 generation SM charge (Q) assignments in that latest paper (Oct. 2019).
I am very interested here in the suggestion at the very end of that paper  in the Addendum Section IX(B/C) on Multi-actions splitting spinor spaces, Lie algebras/groups, and Jordan algebras. I suspect having the ability to create a machine (i.e. a symbolic engine such as MTM) to operate on and visualize these structures as hyper-dimensional physical elements is critical to making progress in understanding our Universe more thoroughly.
While I have had some success in replicating quark color exchange, as well as flavor changes (e.g. green u2 to d3 quark exchange using g13), there doesn’t seem to be a complete description of how to construct each of those color and flavor exchange actions from the examples given. So for reference I present all possible combinations of these actions across the particle/anti-particle definitions (see the image linked in the last paragraph of this post). This comment about limited examples also applies to replicating the 3 generation charge (Q) calculation using the sS constructs mentioned above.
I welcome any help or advice or additional examples.
Below is an example image of the 3 generation SM from the 2019 paper built from bi-octonions (with my octonion multiplication table reductions applied. The anti-particles (not shown) are simply the complex-conjugate of these. While I show in string form of Q, I am not showing the commutations based evaluations for them due to the questions / issues I have on how to get it to work.
The image below shows more detail of the 3 generation SM from 2014 with my code implementing the reductions. This leaves off the charge (Q) which was not defined as above in 2014 (AFAIK).
The image below shows a simple construction of the 0-V to 6-V splitting of the Mf Clifford algebraic structures, which I generated using MTM Subsets:
The rather large (long) image here checks all SM particle color and flavor changing actions and includes the anti-particles. The output is extensive and given my open questions on the formalism presented, the accuracy likely deviates from the intent of , but it is interesting to show how everything transforms. If no transform is found for a particular action, it outputs an * for that action. If a color or flavor changing transformation action is found, it identifies that action with the list of particles to which the transformation applies. Note: it only identifies a transformed particle if the source particle has a non-zero reduced value and the resulting match is exact (red) or a +/- integer factor of that particle (blue).
Please see the latest in .nb, .cdf demonstrations files and web interactive pages.
|Latest: 08/15/2016 (10 Mb). This is a lite version of the full Mathematica version 11 demonstration in .CDF below (or as an interactive-Lite web page) (4 Mb). It only loads the first 8 panes and the last UI pane which doesn’t require the larger file and load times. It requires the free Mathematica CDF plugin.
This version of the ToE_Demonstration-Lite.nb (13 Mb) 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.
|Latest: 08/15/2016 (110 Mb). This is a Mathematica version 11 demonstration in .CDF (or as an interactive web page) (130 Mb) takes you on an integrated visual journey from the abstract elements of hyper-dimensional geometry, algebra, particle and nuclear physics, Computational Fluid Dynamics (CFD) in Chaos Theory and Fractals, quantum relativistic cosmological N-Body simulations, and on to the atomic elements of chemistry (visualized as a 4D periodic table arranged by quantum numbers). It requires the free Mathematica CDF plugin.
This version of the ToE_Demonstration.nb (140 Mb) 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.
(The CDF player from Wolfram.com is still at v. 10.4.1, so still exhibits the bug I discovered related to clipping planes/slicing of 3D models).
An interesting post re:qualifications for a ToE prompted me to jot down my initial list of requirements. A ToE should inform, expand on, or rationalize, in a mathematically self consistent and rigorous way, the state of the current SM & GR confirmed experimental data:
1) Prescription (aka prediction, retrodiction or specific rationalization) for 3 generations of fundamental fermion and boson particles (and their resulting composite particles), including: charge, spin, color, mass, lifetime, branching ratio, and scattering amplitudes (aka. S-Matrix)
2) Prescription for CKM and PMNS unitary matrices and CPT conservation
3) Framework for the integration of QM and GR, including e/m, weak, strong and gravitational forces
4) Explanation for dark energy and dark matter in proportion to visible matter
5) Solution to the hierarchy problem
6) Provide a realistic computational model based on the above for the evolution of the Universe from BB to present
7) Explain an arrow of time that is consistent with GR and QM CPT conservation symmetries
Non-specific general appeals to the anthropic principle, landscapes, and/or multiverses tend to excuse or avoid prescription and thus become a benign point (or possibly even meta-physical or philosophical), such that they are not considered supportive of an actually verifiable (aka. scientific) theory.
If the theory says “we can’t know” or “we can’t measure” or “it just is that way” – it isn’t science or part of a ToE. again – my opinion and definition of “science”.
There is redundancy in this list, that is expected (even required). Of course, the beauty of the theory would be in conclusively demonstrating that throughout!
Until we can study an actual ToE that is put on the table – the list is only a guide to what might be needed. I am working on a ToE, but it doesn’t yet meet all the criteria (it’s hard work 😉
IF we have a ToE and really understand it, we should, as Feynman suggested, be able to explain it in plain language to anyone. But in the current state of physics, a completed ToE does not yet exist.
IMO, a ToE is about knowing the Universal Laws of Physics (ULPs). It isn’t, in detail, involved in knowing the Universal Initial Conditions UICs).
If you believe that the laws of “climate science” are known (don’t get me started…), then the only problem with predicting the weather is not so much about NOT knowing the laws – it is about not knowing with sufficient accuracy the initial conditions (location & momentum) of enough particles in the system. We’re missing the “butterfly flapping its wings in the Pacific” data points.
The Copenhagen interpretation of QM suggests that is impossible in principle to know any quantum system ICs (vs. the deterministic formulation of QM by DeBroglie-Bohm). Either way, my view is ToE=ULP.s w/o UICs. So prediction of all long term events specifically (like what I will think about next) is NOT the goal.
We just need enough of an idea about the UICs to initiate the computer model so it comes out close enough to get Earth like planets with weather and life forms thinking about this topic.
Easier, but NOT easy!
I’ve added more features to the Universal History N-Body Gravity OpenCL GPU Simulation. Here are a few snapshots…
Inflationary Epoch(s) w/Pre & Post (These are built into my ToE as an accelerating space-time, varying FineStructure, c and hBar)
CMS closes major chapter of Higgs measurements
Glad to see the more accurate CMS (as well as ATLAS’) Higgs mass homing in on my prediction of 124.443…GeV/c^2 (see http://theoryofeverything.org/TOE/JGM/ToEsummary.pdf).
Can’t wait for more data next year. Of course, validation that the theoretical model works as expected is as important as the experimental verification.
I cleaned up some of the N-Body physics screens, and created a few animation sequences showing the simulation runs available (if you have Mathematica and source code (available upon request and appropriate use-case)).
This is a video of a preliminary Galaxy formation in N-Body gravitational physics.
This is a video of the solar system (not yet using the OpenCL N-Body code for GPU parallelism).
This is a video of the Compton Effect in 3D, which I plan on using to show how Big Bang Inflationary Quantum effects are explained.
I’ve also improved the capabilities of the other demonstrations.