Modern fundamental physics theories such as the Standard Model (SM) contain many assumptions. So where do all these assumptions come from? This is not real understanding. It is curve fitting. So why bother? By the way there are many axioms in mathematics also. This theory in contrast has only one simple postulate:
So there is reason to be excited. The 1 in the postulate of 1→(1∪1≡1+1)natural numbers→ rational numbers→Cauchy sequence ZN of rational numbers(same as eq.1a,1b)→real number1). But eq.1a,eq.1b also gives us eigenvalue math(physics): This circular self contained argument therefore implies no added postulates: just postulate 1. You then get both theoretical physics(eg.,SM) and rel#math from one simple postulate, that being the reason for the excitement.
In that regard eq.1a is iteration zN+1=zNzN+C and eq.1b is δC=0 allowing eigenvalues (giving eq.2AIA). Note if we solve eq.1a for noise C in δC=0 (1b) we get δ(zN+1-zNzN) =0 implying zN+1 is finite since ∞-∞ cannot equal 0 so that eq.1a, eq.1b defines the Mandelbrot set. Finite zN+1 implies that as central limit C→0 any initial rational z1 between 1 and -1 gives rational iteration terms ZN=1-zN+1 which also implies that Cauchy sequence ZN with the limit 1 we required. Note also for limit 1 ,C→0, z1=z∞≡z=zz+C (eq.1). C≡kδz. Other ways of getting this Cauchy sequence don’t lead to eigenvalue equation 2AIA and so don’t give observables.
So we proceed to derive observables(2AIA) by plugging eq.1 into eq.1b and along the way get Special Relativity(SR) and a unbroken degeneracy Clifford algebra (sect.2) and eq.2AIA. Note for large C we have to normalize the ambient metric on each (¼)MMandelbulb to obtain eq.1 there and the associated eq.2AIA. We then get new eigenvalues associated with that (1040)NXcosmology (Large CM) and also turn SR into GR and break that 2D degeneracy into a 4D Clifford algebra of Mandelbulbs(eq.9) and associated triplets and singlets (i.e., the SM bosons, sect.4) as eigenvalues of eq.2AIA.
So the fundamental insight of this paper is that Cantor’s Real Number (eg., 1) requirement of that Cauchy sequence (z1,z2,..zN,..) is here provided by the Mandelbrot set iteration formula (zN+1=zNzN+C) eq.1a sequence (z1,z2,..zN,…).
Summary: Postulate of Real 1. That is the whole shebang. So the postulate of 1→( 1U1)natural numbers→rational numbers→ Cauchy sequence of rational numbers(same as eq.1a,1b)→real number 1. with equations 1a,1b giving us eigenvalue math (physics). So merely postulate 1 to get both mathematics and physics.
Also that 4D implies we got not more and not less than the physical universe. Also given the fractalness, astronomers are observing from the inside of what particle physicists are studying from the outside, that ONE thing (eq.9) we postulated. Contemplate that as you look up into the starry night sky! So by knowing essentially nothing (i.e.,ONE) you know everything!
We finally do understand.
Table of Contents
Part III Mixed State