Unified Field TheoryTheory of everything, unifying all forces, matter & spacetime.
First we have to ask, what does the mathematical process of divivision by \infin or multiplation by \infin do to real numbers and how we would perceive this in relation to physics. How does this then require the use of complex numbers.
The multiplication by \infin either doubles the number of dimensions, for example the formula b = a \times \infin if a \subset \RR would either create a 2D area or redefine the scalar length of a. This is because \infin can either be a linear or angular transform. The only solution if by angular transform creating a 2D area, is for \infin to be imaginary as defined by the Hodge Star operation. If \infin is real then it can only redefine the scale of a. For the angular form we should think of this as outward curl.
Division by \infin is the recyprocal of that, it halves the number of dimensions if imaginary, or inward curl. So if we start with \HH spacetime, we see the \CC quarks, electrons and vector bosons that comprise the communication between them. If we start with \CC spacetime of each particle, we would see the inner \RR scalar field that creates both angular and linear momentum, as is the case of the Higgs mechanism. There is no way to reduct \RR further. The linear form is to reduce scale.
- \CC Spacetime of a single particles has Spin 0 : \RR inward curl that defines scalar bosons, and Spin 1 : \HH outward curl that defines the real and virtual vector bosons connectivity equivalent to \HH = \CC + \star\CC.
- \HH Spacetime of atoms has Spin 1 : \CC inward curl of real and virtual vector bosons, and Spin 2 : \OO = \HH + \star\HH outward curl that defines the real and virtual tensor bosons connectivity.
- \OO Spacetime of universes has Spin 2 : \HH inward curl of real and virtual tensor bosons, and Spin 3 : \SS = \OO + \star\OO outward curl that defines the real and virtual bosons connectivity.
Standard Model: Ring Groups
Simply put \infin like 0 is where positive and negative, as well as real and imaginary scales must cross. Thus equating both division by 0 or multiplication by \infin as outward curl, and multiplication by 0 or division by \infin as the reciprocal inward curl. These curls being definable as \pi/2 rotations. Thus the flat spacetime of special relativity defines the current perspective, and the inward and outward curl defined by what we call quantum mechanics and general relativity.
So we now have equated multiplication of \infin to the Cayley-Dickson construction process and division by \infin to the Cayley-Diskson destruction process. This explains perfectly why we go from Spin 0 scalar \RR boson, Spin 1 \CC vector boson, Spin 2 \HH tensor boson and beyond. Further explaining why particles, fields and spacetime must follow the same rules of complex numbers. One side effect being, \CC vector bosons are commutative which allows for things like time reversal, however \HH and higher bosons are not and as such are not easilly reversable, leading to a flow of time in general relativity but not with quantum mechanics. Thus \HH spacetime is what connects the \CC spacetime interconnectivity of quantime mechanics, and the \OO spacetime interconnectivity required to describe gravity. We have unified the desription of all bosons as rotations, however the number of dimensions they operate on is directly related to the spin of the boson, and what rotations are allowed by the same rules that govern hypercomplex numbers.
So we can now define all bosons, from \RR scalar bosons, \CC vector bosons, \HH tensor bosons and beyond. Everything larger than \RR must have real/linear and virtual/angular form. This is because the initial construction from \RR to \CC creates the separation of space and time, and thus energy and momentum or charge and spin. Mass being defined as the net radius as shown in the special relativity section.
From \CC spacetime and up, real transforms translate to stretching and linear transformation such as increasing momentum energy in the photoelectric effect. Virtual transforms likewise translates to angular transformations, such as required for neutron decay to proton, electron and anti-neutrino. So all bosons going forward must have real linear form, and virtual angular form.
We can now further explain \HH tensor bosons using the same rules, with gravitons as being the 4D equivalent to 2D gluons and strong force being noncommutative and multicoloured in nature. With tachyons being 4D equivalent to the 2D photon and electromagnetic force, being commutative and uncoloured in nature. We now must also have an equivalent 4D \zeta^0, \omega^\pm bosons to mirror the 2D weak force Z^0, W^\pm 2D bosons. Again all 4D tensor bosons having real time-like linear form, and virtual space-like angular form.
Now we can explain both dark matter and dark energy as originating from \pm\star\HH spacetime, dark matter being how we describe 4D angular rotations, and dark energy how we describe linear stretching of the 4D spacetime we are in. There is one way matter can transform to dark matter, and that is for it to gain 4D angular energy to curve spacetime 90 degrees, as in supernova explosions. However it is likely this process also creates dark energy as being the 4D linear energy that pushes spacetime beyond the speed of light. So the process of supernova, not only stretches spacetime as a whole, but also doubles the complexity of remnants of the original star. Ergo stella black holes are likely 8D \HH in nature, and supermassive black holes likely 16D \SS or greater in nature. Just like the weak boson intermediary between the strong and electromagnetic forces, the 4D variant would be the intermediary between dark matter and dark energy, which neatly describes Hawking radiation.
So for example, what we would describe as black hole decay, would be the 4D equivilent of an electron and anti-neutrino being emitted from a free neutron. Only now the mass is now transfered from 8D matter, to 4D linear and angular forms. Just as atoms only self decay once they reach a specific size, black holes like only decay once they reach the equivilent stage to matter fissioning, releasing 4D angular and linear energy seen as frame dragging and dark energy, not as particles within 4D spacetime we could measure but rather how they curve or stretch spacetime around them.