Special Relativity

The shape of spacetime and connectivity between all particles within it.
This view here show two parallel universes, one for matter and one for antimatter. Beyond the \pm \infin points both light-like and vacuum-like must lie hyperbolic spacetimes, which by nature can only stretch or curve our spacetime from the outside and have no direct connection to matter or antimatter.

One major change with this view of spacetime, is that it has no definitive start or end point, but just like energy and momentum can be viewed both as point-like or wave-like. Mathematically this is known as having a smooth manifold, or that there are no sharp edges, which is the one major sticking points of general relativity in its current form, along with that of definitions of dark matter and dark energy. Singularities only seem strange as we can't see past them.

One other major improvement with this view, is it clearly defines what is a spatial dimension, and what is a temporal dimension, based on duality (Hodge Star) between light and vacuum energy, which are the two light-like events that all matter must be encapsulated by.

This now shows why the neutron decay process n \to p^+ + e^- + \bar{\nu_e} must emit both electron, anti-neutrino and be colour neutral. As the anti-neutrino represents the light-like rotation (vrgb), and electron the vacuum-like rotation (wrgb).

We can see the universe is mathematically quaternion in nature, with quarks being dualistic to electrons. We can create this 4D nature, by utilizing the Cayley-Dickson construction from 1D scalar field (Real, \RR), through 2D vector particles (Complex, \CC) finally to 4D (Quaternion \HH) tensor spacetime of atoms.

*Spacetime: Energy*

*Spacetime: Tesseract*

While the tesseract portrays a 4D object, I have shown here how it can also describe a psudo 10D object, with 6D spatial dimensions (3D \CC) and 4D temporal dimensions (1D \HH). This is due to using the Cayley-Dickson construction and Hodge duality. Mass is easy to visualise as residing at the vertices, and light-like events the edges that connect them.

One thing to notice is the electron and positron have no direct connectivity, and the electron (e :- ww) has light-like connectivity to the anti-quarks (qqq :- cc + mm + yy), and the positron (p :- vv) to the quarks (qqq :- rr + gg + bb).

This explains why the quarks appear far heavier than electrons, as they represent the connectivity between the positive matter universe and negative antimatter universe. Electrons and positrons instead represent the seperation between the two. Quarks and strong force being closely connected to the dimensions of space, the electron and electromagnetism to the dimension of time. The weak force being the light-like or vacuum-like events that connects the electron and quark particles together, and strong force being light-like or vacuum-like events connecting quarks together, shown as the edges.

The imaginary numbered momentum portion between electrons and quarks, explains why the weak force bosons must be virtual between like for like matter and real between matter and antimatter. The lack of interaction between the electromagnetic force and strong force is because they always act orthogonal to each other, so must always have zero inner product. The strong force shown by real dimensions of space, weak force by imaginary dimensions of space and electromagnetism as real numbered dimension of time.

As well as the time-like real particles shown, we also have space-like or virtual electron (e :- ww) with vacuum-like connectivity to the virtual quarks (qqq :- rr + gg + bb), and the positron (p :- vv) with vacuum-like connectivity to the virtual antiquarks (qqq :- cc + mm + yy). Each real and virtual particle pair creating its own ring group consisting of two time-like real forms, and two space-like virtual forms. The virtual forms are denoted by using a bar over the symbol.

One easy way to visualize the difference between real and virtual particles, is the real particle is akin to inner product, and the virtual particles are akin to the outer product. Real particles are inside the light cone with real mass (time-like), virtual particles are outside with imaginary mass (space-like). Both separated by (light-like) events with zero mass.

One major difference with this notation from accepted standard model, is here we use the bar notation to denote virtual particles, not anti-particles which would be denoted by the minus sign (or as above the anti-colour) instead. Any process that transfers mass, must have some combination of real, linear and virtual, angular components, to satisfy energy equivalence. You can visualize this in the first image as all rotations between quarks and electrons as being centred around the T^0 point in the centre. All special relativistic transfers of energy are shown as 2D angular rotations or linear stretching, this specifically does not include gravity, dark matter or dark energy as these are representative of 4D angular rotations or linear stretching instead.