Postulate 1

Abstract: 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? So what is that single postulate required for complete understanding? Answer: real set1, the rigorous way of just saying postulate 1.

  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,…).  Note then that you merely postulate 1 to get eq.1a,1b. 

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 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 1.                    

So we derive both Rel#mathematics(appendix C)  and theoretical physics from one simple postulate 1 (i.e.,real set1) and so have found our single postulate.

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. Next split up our derivation of observables (i.e., 2AI,2AII 2AIA) into Big C and Small C applications of eq.1a and 1b.

      Small C  (section 1-3, for observables eq.2AIA) Note also for limit1,0  finite zN, central limit kδzC0(i.e.,small C) in eq.1a then z1=zz=zz+C (eq.1).  So we get that (1,0) result and proceed to derive the observables (2AIA) by plugging eq.1 into eq.1b and along the way we get Special Relativity(SR) and a unbroken degeneracy Clifford algebra (sect.2 for e and v) and use them to get 2AIA observables..

      Large C  (section 4, many small Cs,)   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)

So when you postulate real set1 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)

Table of Contents

      Postulate 1 

Introduction

 Part I     1U1 states

Part II    1U1U1 states 

Part III   Mixed State

 Rest       Miscellaneous