Masses and the Infinity Options Principle: Can We Explain the 3-Generations and the Quantized Mass Problem?

Abstract
After having found that in spaces or space-times with an infinite number of options the quantized Einstein-Field-Equations take on their simplest (linear) form [A1], we here investigate the problem of how mass could be quantized.
In fact, we will see that, with mass appearing as entanglement of dimensions [A2 – A8], its quantization can be easily achieved.
Along the way we also tried to answer the question why there are just three generations of elementary particles. It was derived that in order to satisfy the necessary outcome for Newton’s gravity law in the far distance, the Ricci curvature has to contain a certain term with a power law r-dependency of the type 1/rі (please note that the exponent is just the number of our ordinary space’ spatial dimensions). Inserting this into the quantum gravity equation, which is resulting from the scaling of any metric solution to the Einstein-Field equations, we found three possible ways for the extraction of the three generations:
A)A simple algebraic equation of third order for the Schwarzschild radius allowing for 3 real solutions.
B)A quantum solution for the wave function f only allowing for certain Schwarzschild radii.
C)Extraction of a wave solution to the metric Dirac equation.

Unfortunately, by sticking to the classical Klein-Gordon or Dirac approaches, we were not able to complete the task, but found many interesting facts along the way. With respect to the 3 generations of elementary particle we might say that in fact we have found a fairly potent way to explain an X-generation problem, only that we don’t really see why X should be restricted to 3. However, in demanding the space-time to be restricted to 4 big-scale dimensions, we found that the product of mass and the quantum gravity wave function occurs in a polynomial of third order, which, as it is well known, can have three solutions.

In the end, a solution to the 3-generations problem, so it seems, can be found by combining the Klein-Gordon and the Dirac approach and excepting the two, respectively their solutions, to exist simultaneously. This then automatically leaves no other choice for the product of mass and quantum gravity wave function but to algebraically fall apart into three different solutions. Most interestingly, it was found that this combined approach favors octonions as a tool (not the only one - as it will be shown here) to solve the subsequent differential equations. Thus, so our current conclusion, the way to solve the 3 generations problem could be outlined here but – so far – this path was not treated in a manner one could call complete.