Postulate 1

Modern fundamental physics theories such as the Standard Model (SM) contain many assumptions(postulates). So where do all these assumptions come from? This is not real understanding. It is curve fitting. So why bother? But what if we can narrow down the number of postulates to one? We then have ultimate understanding! So what is that single simple postulate?

  The fundamental insight that answers this question is that Cantor’s Real Number(eg.,1) requirement of that Cauchy sequence (z1,z2,..zN,..) of rational numbers is here provided by the Mandelbrot set iteration formula (zN+1=zNzN+C) eq.1a ( and 1b) sequence (z1,z2,..zN,…). 

Results

We can then merely postulate 1 (real set) to get eq.1a,1b which (given the  SmallC and BigC consequences of the C in eq.1a) answers the above question. 

Appendix

. . Small C  For C0(i.e., small C) in eq.1a we have only one noniterative equation in eq.1a then 1,0 in z1=zz=zz+C (eq.1). Plug eq.1 C into eq.1b (δC=0 for some C) and, after simple factoring,get Special Relativity  (SR is eq.2A:  dr2-dt2=dsin sect.1 introduction) and with the two eq.2AIs gives two unbroken 2D degeneracies in eq.2B (Clifford algebra, sect.2 for leptons) implying 2AIA and so the math of observables (eq.3.4: (dx/ds)δz=-idδz/dx).

      Large C  (section 4, many small Cs,) Simply Rotates the small C z s.  Note for large C we have to normalize the metric on each (¼)MMandelbulb Reimann surface to get local small C eq.1 so as to obtain an associated local mapping eq.2AIA (observables). Get the 3 Lepton families this way. Next determine what we observe of the next larger and next smaller rH fractal scales.

  • N+1 Fractal scale Cosmological scale (appendix B). We then get new eigenvalues associated with (1040)N Xcosmology. Large fractal self similar baseline CM also turns SR into GR and breaks that 2D degeneracy into 4D Clifford algebra of MandelbulbLeptons (2AI eq.9 e and v ambient metric). Inputs into Kerr (a/r)2 term and ambient metric.
  • Nth Fractal scale Subatomic scale (appendixB) 1040 Xsmaller self similarity (eq.2AI e and v)
    • Many body 3 (2A1) Part II pure state and PartIII mixed state Zo,+W,-W r=rH rotations in last 3 Mandelbulbs (appendix A) and got the Standard Model (SM)

So when you postulate 1 (real set) this is the result (so just postulate 1).

Summary 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. Try looking up at a starry night sky and contemplating that some time.  So by knowing essentially nothing (i.e.,ONE) you know everything!   We finally do understand (just postulate 1)

References

(1)Cantor: Ueber die Ausdehnung eines Satzes aus der Theorie der trigonometrischen Reihen, “Ueber eine elementare Frage der Mannigfaltigkeitslehre” Jahresbericht der Deutschen Mathematiker-Vereinigung.

(2) Penrose recently suggested in a Utube video that all of physics can be extracted from the Mandelbrot set.  Here we have merely shown how to do it and why it is important.

Table of Contents

      Postulate 1 

Introduction

 Part I     1U1 states

Part II    1U1U1 states 

Part III   Mixed State

 Rest       Miscellaneous

Cantor’s Cauchy sequence via iteration: Note for example that Cantor’s Cauchy sequence is generated by iteration 1a: So for any initial rational finite z1 between 1 and -1 in iteration formula 1a gives rational finite odd Z2N+1=1-z2N+1,  even Z2n≡1-z2N both of which together make our Cauchy sequence ZN with limit 1 that we requiredNote also that the Mandelbrot Set is derived uniquely from 1 {real set} In that regard eq.1a is iteration zN+1=zNzN+C and eq.1beq.1b says that for some C that δC=0 allowing eigenvalues (giving eq.2AIA). Note if we solve eq.1a for noise C in δC=0 (1b) we get δ(C)=δ(zN+1-zNzN)=0 implying zN+1 is finite since ∞-∞ cannot equal 0 so that eq.1a,1b defines the Mandelbrot set {CM} since then z∞ cannot be infinity. Note also for limit 1,0 finite zN central limit →0(i.e.,small C) in eq.1a then z1=z=z=zz+C (eq.1). Eq.1 implies(1,0) corresponding to the dichotomy ‘set1 always with subset O’: so{1set,O}(1,0) so OO=O00=0+0 in our whole number algebra. That makes this choice of 1a,1b the only one possible since it implies both the Cauchy seq, and the set 1,0.

  Also we define C from noise C=kδz if k in general arbitrary real. So in eq.1.1 if k is exactly a constant and/or k is small (i.e., k<<δC) then δr and δt in δz are trivially constant. So (in  δC=δ(kδz)=δkδz+kδδz so k=k1δz+k2) δk must be small but not zero here. Indeed δz is order 1 deep inside the Mandelbrot set limacon lobe so δz=0 inside.  But δz is constrained to be small on the edge therefore allowing for a small varying k on the edge of any particular Mandelbrot set lobe (in δkδz>0, eg.,fig.1 eq.2AIA diagonal eq.2AI edge contributions, called Mandelbulbs here). Also large k gives nontrivial results as well and so then δδz is very small. 

Cantor’s Cauchy Sequence via Iteration . In that regard eq.1a is iteration zN+1=zNzN+C and eq.1beq.1b says that for some C that δC=0 allowing eigenvalues (giving eq.2AIA). Note if we solve eq.1a for noise C in δC=0 (1b) we get δ(C)=δ(zN+1-zNzN)=0 implying zN+1 is finite since ∞-∞ cannot equal 0 so that eq.1a,1b defines the Mandelbrot set {CM}. But any initial rational finite z1 between 1 and -1 in iteration formula 1a gives rational finite odd  Z2N+1=1-z2N+1,  even Z2N=1+z2N which both of which together make the Cauchy sequence ZN with limit 1 that we required.

So in that case the 1set in the postulate of 1(1∪1≡1+1)whole numbers rational numbersCauchy sequence ZN of rational numbers(same as eq.1a,1b)real number 1). Eq.1a,1b imply for z1-zfor C0 that z=zz eq.1 so eq.1 implies (1,0) corresponding to the dichotomy ‘1set always contains nullset O‘ so {1set,O}(1,0) so OO=O00=0+0 in our whole number algebra. That makes this choice of 1a,1b the only one possible since it implies both the Cauchy sequence and 1,0. Eq. 1a,1b also implies the math of observables (eq.2AIA). Also this ‘self contained’ circular derivation guarantees we don’t pull in postulates other than