### Does The Empire Hamiltonian for the QSN Define the Electron, Photon, Neutrino and Quark?

I have realized that the empire Hamiltonian for the Quasicrystalline Spin Network (QSN) may define the electron, along with the photon, neutrino and quark.

For clarification purposes, we call the compound quasicrystal obtained from the Elser-Sloane quasicrystal, a

**Compound Quasicrystal (CQC)**. More on the CQC can be found HERE.
This is a recently sent email to one of our physicists at Quantum Gravity Research, Amrik Sen. I realized this is such a potentially seminal thought (if true) that I need to share it with all our staff and associates interested in discovering if there is a first principles theory based on E8 that can define analytical values for the fundamental constants and particle masses.

Hi, Amrik.

Please journey with me on a gedanken experiment. Others may want to follow along. If you miss full comprehension of any point below, please give me the opportunity to better articulate it.

1. Let us presume spacetime is a superfluid. Here’s an overview article from a few years back on the plausibility of that idea. There are, of course, many papers arguing this.

2. Let us also presume spacetime is discrete. So the superfluid would be made of discrete parts and steps. Rules, syntax, degrees of freedom and the fundamental discrete units of spacetime would each exist in a finite set of possible values, analogous to the finite set of energy values allowed in atomic electrons.

3. Let us presume the discreteness comes in two irreducible fundamental components:

- tetrahedral trits in the E8 derived QSN as legal states of the CQC and
- the discrete quantum of interaction – the empire trit parity and anti-parity values. Empire interactions are the foundational quantum interaction of the superfluid and all its phases.

4. Realize now that there are many legal CQC states allowed on some finite size patch of the QSN, where “legality” means that it corresponds to a discrete shift vector according to the vector algebra that can operate on the E8 lattice.

5. None of these states has anything to do with a discrete superfluid. In fact, the vertex frequency and distribution pattern is virtually identical for any, let us say, 100 unit length (Planck length) cubic volume of the QSN.

6. It’s important to understand that last fact. A single legal selection state of the QSN looks virtually the same as any another. You can develop intuition on this by taking a large Penrose tiling. Select a 100x100 unit length area anywhere. It will look more or less like the same sized area everywhere else. It will contain about the same ratio frequencies of each vertex type and will have about the same geometric pattern and the same symmetry. So how do we get physically realistic microscopic and macro scale differentiation of pattern to describe realistic physics on such a homogenous object? How do we see a hydrogen atom in some frozen state of the CQC?

7. We won’t. It’s a false question because such patterns exist only in the way you order sets of these relatively homogeneous objects to form dynamical animations over the time domain. It is analogous to how one might look at a laser light show as an animation of people and animals walking about simultaneously. Imagine this is a laser show being projected to the spherical surface of a glass sphere. You are in the center of the sphere watching the show. If you freeze any single frame of the laser show, it is simply the same screen with a single static laser point shown somewhere on the surface of the sphere. Only through ordered sets of the static single laser pointer beam that you generate the illusionary information of the people and animals simultaneously walking about.

8. Let us presume we can develop a Hamiltonian using the first principles of empire interactions which describe all physically realistic discretized superfluid phases of the QSN. The only way this can occur is by HOW you order the legal states of the QSN (CQC states). Early universe, turbulence at the cosmic scale can be modeled by randomly ordering some quantity of legal sets. This would be the very high entropy early universe. Things are homogenous. There were no hydrogen atoms. There was little orderly pattern. But, in our model, 1 billion of those frames of the universal frame set would be less orderly than the same billion frames in the current low entropy universe.

9. Now, in this model, where everything is the empire interaction based on ordered sets of QSN state selections behaving as various phases of our quantum superfluid, what are particles?

10. An important thing is that when you get particles out of the high energy near chaotic state, they can get closer and orderly dipole orientation dynamics (such as a spin glass) and certain special ratios of quantum wave function resonance and damping can occur. In the

*emergence theory*view of the QSN ordered states, this level or order where particles can self-organize into patterns like nucleons, etc, are higher ratios of trit-parity verses trit-anti-parity. In other words, more “coherent” or orderly or higher magnitude empire trit synergy.**So, if we allow the QSN Hamiltonian to guide us when it is done, what is the upper limit of this synergy in the simplest case?**It should be the repeating Eulerian circuit of some path of empire trit-parity that is maximally “efficient” where that term is defined by the maximal amount of empire trit-parity that can occur for that simple system over some number of frames that define the full pattern of the quasiparticle particle animation pattern.
11. I suggest that we see if we can exploit the discretized superfluid analogy to get an intuition. Rotating toroids and extruded tori as vortices can be built as patterns created by HOW you order legal states of the CQC upon the QSN. But remember, these must be deeply based on empire interaction, where tri-parity in the empires becomes something the system uses to form very orderly patterns. At the limit of trit-partiy synergy for some small system, we will have a massive fundamental particle as a closed circuit. So imagine something like a 57-group. Imagine it has empire beams as helices of tetrahedra going out infinitely far. What occurs when the empire beam or helix of one particle becomes very close to the empire beam/ray of another 20G? It forms a very small cycling pattern exploiting all three spatial dimensions of the QSN. For example, each 20G has an empire with empire breams. Two 20Gs can connect and share empire breams at any distance. How close? Well, all you have to do is look in the QSN and notice how close you can get two 20Gs. They can get so close they intersect. But let us presume crashing is not allowed in the rules. So in two ordered sets, you can choose one of the intersecting 20s so it does not crash with anything. Then you can select the other one that intersects it in the next frame. This is the notion of the 57-group which is the idea of four 20Gs over four legal frames or selection states. But the visualization to focus on for this email is what empire trit-parity means in the case where these objects (as ordered selection states on the QSN) cycle with a MAXIMALLY efficient trit-parity. The electron is a particle with an infinite half-life. It doesn’t decay. Abdus Salam and Jogesh Pati invented a model that said an electron is not a dimensionless point but instead is composed of multiple dimensionless points called “preons”. In our model, the electron is composed of 20-groups, which is composed of tetrahedra which are composed of dimensionless points. Accordingly, here even at this toy-modeling stage before we have the Hamiltonian, we can envision the pattern of the electron 57-group as a closed circuit. It cannot unwind because it is on a closed Eulerian circuit due to how close and fundamental this pattern of sequential 20-groups is. This is an illustration of approximately what that 57-group looks like over four frames, as three intersecting 20-groups of tetrahedra. Instead of requiring 4 x 20 = 80 tetrahedral trits, it requires only 57, the maximally connected group in the E8 to 4D projection of the Gossett polytope, where a connection can exist at a 0-simplex, 1-simplex or 2-simplex.

12. The toroidal and vortex-like empire field of the 57-group electron is a particular fluidic phase or local discrete fluidic pattern allowed by the empire based Hamiltonian of the QSN. But not just any phase. It’s a special limit for a pattern of 20Gs capable of possessing a circuit that includes a stepwise spherical circuit while at the same time having a stepwise circular forward helical propagation through the QSN. It can have mass and model the inverse proportionality between propagation and time in special relativity. The irreducible first principles of the solutions contained in the empire based Hamiltonian give us particles. Naturally, the math of the gauge symmetries of those particles is based on the vertices of the Gossett polytope because the QSN and its interactions are based on that lattice and algebra, as acted upon algebraically by elements of its D6 subalgebra that are isomorphic to projective actions on the root vectors associated to the angle between 3-simplices of that algebra, i.e., the ArCos ¼ angular relationship of the volume contained in any three root vectors of the Gossett polytope related by ArcCos ½. Again, there are limiting solutions implied by the empire Hamiltonian. Specifically, there are cyclic patterns in certain minimalistic local regions of patterns of ordered sets in the QSN. For example, the tetrahedron unit length is a limit. The 20G is a limit as the vertex with the highest valence rank. Once can ask, “In an ordered set of 4-state selections of a 20 in some local region of the QSN, how close can my four 20Gs be from frame to frame in the animation?” The answer to that would model the electron at rest. Around this object, that cycles in a step-wise spherical pattern to model massive particle clock cycles, there is an “empire wave”, which is the animation created by the empire beams that exist in each frozen state.

13. By way of illustration, this is my blue iPhone charger cable.

It is 4 feet long. In the bottom image, I give an analogy of the electron at rest. Imagine that we discretize my cable into 1 inch unit lengths that are straight lines to model the Planck length of a tetrahedral trit in the QSN with that length. I have 12 x 4 = 48 of these units to play with. And in the QSN model for the electron, I play with them one unit at a time as ordered sets of legal states in the QSN to form a step wise animation of quasiparticle propagation. If I use all of my 48 units to get the maximal number of particle clock cycles, I wind my blue cable 12 times around the pole and it propagates only a small distance. This is a limit, as the electron at rest, where it experiences the greatest mass, least propagation relative to some substructure possibility space, such as the QSN, and it experiences the greatest amount of time or clock cycles. That’s the bottom image. Going up to the middle image, we change the ratio of which of the 48 units are used for clock cycles relative to forward propagation. Now, the electron quasiparticle covers greater distance in exchange for reducing its internal clock cycles by ½ to only 6 windings. Of course, this idea was conceived of by de Broglie in a non-discretized version that had no first principles possibility to ever be mapped to E8 based gauge symmetry unification physics. In the top image, we show the impossible case of the electron acquiring an infinite amount of energy such that it can propagate the maximum possible distance in the QSN relative to the possibility point space. At this limit, its clock cycles slow down to 0 in exchange for the limit of propagation where it behaves like a photon.

14. So we need to put more resources into the Hamiltonian project. It is THE first principles approach that will describe the ordered sets forming various allowed forms of mass energy in some system. It is first principles because it is based on sound mathematical first principles of the irreducible action, as the trit-parity/anti-parity event and the irreducible quantum of the superfluid that defines both spacetime and particle patterns within it – the non-deformable regular tetrahedron, the object which can construct E8. For those of you less familiar with these two elements, two fundamental objects that can construct the entire E8 lattice and, from there, the derivable E8 Lie algebra, are (1) the 3-simplex, a regular tetrahedron and (2) the angle ArcCos ¼. One starts with a single tetrahedron. Clone. Rotate into the 4

^{th}spatial dimension by ArCos ¼. Clone the second one, rotate into the 5^{th}spatial dimension by ArCos ¼ and so on until one iteratively builds out the entire E8 lattice. When we project a slice of E8 to 4D, there is only one hyper package of angles that can transform the E8 slice (and its associated algebra) to the highest regular symmetry in 4D (H4 symmetry). And that is the hypervector based on ArcCos ¼. With this angle, all tetrahedra in the 4D quasicrystal remain regular, as their former positions in the E8 lattice and associated Lie algebra are rearranged in 4D to form 600-cells that intersect in 7 ways and kiss in one way. The algebra here gets transformed as a product of the hyper vector associated algebra and the E8 root vectors to form a subset of the quaternions called the icosians. These are values based on 1 and the golden ratio. Furthermore, where the pre-transformed Lie algebra was commutative and “local”, the transformed richer algebra, as a product algebra of the self-interaction with this D6 associated sub-algebra and the E8 vector algebra, is richer. For example, it is distinctly non-commutative. Any gauge symmetry physics that can be modeled on the E8 Lie algebra and its associated lattice can be recovered in the 4D transformation via the Coxeter H4 folding matrix. From this object, we generate the quasicrystalline spin network (CQC) which also encodes, under transformation, the same realistic gauge symmetry unification physics.
15.

**FINAL OBSERVATION/REALIZATION:**How does the shift vector code that controls the changes in the cut window in the E8 lattice to generate phason quasiparticle dynamics in 4D and from there in the 3D QSN? What is the size of the window? What is the shape of the window? How many windows are there? Is there one window only for each frozen frame of the QSN? It should be a global window. The window can rotate and propagate relative to the vector algebra made non-smooth and discrete by the discretizing quality of operating it according to the E8 lattice. And there should be only one operating at a time. How do we derive the shift vector code?**FROM THE HAMILTONIAN**. For example, we discover a discretized toroidal pattern in the discrete superfluid that enjoys one of the trit-parity limits that I mentioned above. That then maps back to the discrete but non-deterministic projection window shift-vector walk or code in E8. That can then be understood algebraically to describe probability amplitudes, etc.- CLICK HERE FOR MORE VIDEO PRESENTATIONS ON OUR WORK AT QUANTUM GRAVITY RESEARCH
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Thank you so much.

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