Postulate I

                 What The Mainstream Says:

 The universe is infinitely complicated according to the mainstream (eg.,string theory, dark matter, colors, gauges, infinite mass and charge electrons,….)  but I am finding in contrast that the universe is more and more simple, in fact it is infinitely simple eg.,1. The notion of reducing everything around us to a single thing is the (infinitely) simplest idea I can conceive of. It is ultimate reductionism (eg., of complex z) to a single real number 1So just postulate 1.   

Algebraically define 1,0 from z=zz. Also for 1 (zz-z=0) to be real min(zz-z)>0 : the entire theory 

Appendix B2 defines min and zz-z in a real analysis context.

I wanted to also point out that this is all just elementary algebra  (in contrast to that mainstream multitude of disconnected convoluted assumptions). So
                                         Postulate 1
with 1 (and 0) algebraically defined as                                   
                                                 z=zz                                           (1)
so (given the 0 definition) rewrite equation 1 as
                                         zz-z=0                                       (2)
But in order for 1 to be a real number (so having a Cauchy sequence) we must postulate 1 as:

                                            min(zz-z)>0                                   (3)   which is our entire theory.
 The rest is simple algebra.
Relation  3 can be rewritten as
                                               z=zz+C                                       (4)
                                             δC=0, C<0                                    (5)

real 1
To get that Cauchy sequence and so real 1 plug in the left side z into the zz on the right side of equation 4 and repeat
So iterate z=z1=0  to get zN+1=zNzN+C. Can use dC=0 for some CM to get the Mandelbrot set.

Familiar form for equations 4,5
We need equations 4 and 5 put into familiar forms to recognize the usual physics outcomes(eg.,operator formalism).
So we define dz from z=1+dz and substitute it into equation 4  and get
                           δz+δzδz+C=0                             (6)
 which is a quadratic equation with complex solutions (if C>1/4)
                                                   δz=dr+idt                                (7)
Plug equation 6 back into equation 5 and get
                                                δ(δz+δzδz)=0                             (8)
which I call the amazing equation since it (with eq.7) gives:
real part is special relativity                                (A).    sect.1.1.2
imaginary part is Clifford algebra                     (B)
and these both imply the operator formalism  (C)
(A),(B),(C) here imply the Dirac equation for the electron e and neutrino v.
The Clifford algebra drdt area min also implies a extremum smallest area Mandelbulb and so the Fiegenbaum point. The Fiegenbaum point (fractal) local source and the Dirac equation imply that
                                                         New pde                   (9).  
Given equation 9 the composite e,v give the Standard electroweak Model and the 3e composite the rest of particle physics (partII). The fractalness implies cosmology and gravity. Getting A,B,C out of eq.8 in one step like this is the reason for calling it the amazing equation.The fact that the amazing equation and the Mandelbrot set both came out of min(zz-z)>0 shows we nailed it.

Table Of Contents

       Postulate 1 as min(zz-z)>0 (so 1 is a real number) rewritten as                                

       z=zz+C (1.1.1) , δC=0,C<0 (1.1.2) (the rest is elementary algebra)

Sect.1.1  For example rewrite eq.1.1.1; 1.1.2  in a more familiar form (by defining z=1δz). Get δ(δz+ δzδz)=0 (Amazing equation). 

Sect. 1.2.  eq.1.1.1, 1.1.2 imply 1 is a real # (by plugging left z back in right side zz. Get Mandelbrot set.   So this is all a mere derivation (using elementary algebra) from min(zz-z)>0


Mandelbrot Set But z=zz+C is also a iteration (Just plug the left side z in z=zz+C back into each z on the right side and get z’=z’z’+C since z’=(zz+C)=z.) zN+1=zNzN+CM with δC=δ(zN+1-zNz) =0 implying this sequence is the Mandelbrot set since infinity-infinity cannot be zero starting from our z1=0 solution. The sequence zN generated from this Mandelbrot set provides the Cauchy sequence zN of rational numbers needed to show that 1 is a real number. You then use appendix B2 to define the real number algebra by rigorously defining min and zz-z. But eq.1.1.8 requires the (Mandelbrot set subset real#) Fiegenbaum point CM=mC (sect.1.2 appendix C) to define real#1. So for small δz (in z=1+δz), and C=δz=CM/m and m is big. So z’=z’z’ and z’=real#1   So Postulate 1 as min(zz-z)>0.

Amazing Equation Plugging z=1+δz into zz-z=C (eq.1.1.1) gives the quadratic equation δz+δzδzz=C (1.1.4) with in-general complex number solutions. Plug the solution to eq.1.1.4 into eq.1.1.2 and get δC=δ(δz+δzδz)=0 the amazing equation which splits into real (special relativity) and imaginary (Clifford algebra) components and 4D (and so the Dirac equations of the electron e and the neutrino v (sect.1.1)) which also imply the operator formalism. Also composite e,v gives the Standard electroweak Model (sect.1.2) and composite 3e solves for the rest of particle physics (partII). The Mandelbrot set fractalness gives us cosmology and gravity (section 7.6)  

 Because of the left side δ in eq.1.1.6 we can add arbitrary -K to δz in eq.1.1.4. Here  δ(δz-K)=0 in eq.1.1.6 to initialize to locally flat space as in 1.1.10 (In sect.1.2 K=δz). ( for backups).  The universe indeed is infinitely simple:  Summary: Postulate 1 then min(zz-z)>0 then z-zz=C, δC=0,C<0 then real# & δ(δz+δzδz)=0 & fractal physics So given the fractalness astronomers are observing from the inside of what particle physicists are studying from the outside, that |realz|= ONE unit object we postulated at the beginning, the new pde electron. Contemplate that as you look up at the starry night sky (See, PartI, PartII and PartIII for backups.).

(4) Penrose in a utube video implied that the Mandelbrot set might contain physics. Here we merely showed how to find it. The fractal neighborhood of the Fiegenbaum point is a subset.

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

Section 1.1 Derivation of amazing equation Substitute z=1+δz into z-zz=C (eq.1.1.1) and get 1+δz=(1+δz)(1+δz)+C (1.1.3). Thus    δzδz+δz+C=0   (1.1.4) : Solving eq.1.4:  δz=[-1±sqrt(1-4C)]/2. So for noisy C>¼ in general  δz=dr+idt  (1.1.5)  (So we derived space-time.). eq.1.1.1, 1.1.2 holds only at CM so δ(idt)=0 (1.1.3, stability). So plug eqs.1.1.4, 1.1.5 into eq.1.1.2 to get the amazing equation:  δC =δ(dz)+δ(dzdz)=0 (1.1.6)                                                                                                                       Can add K in 1.1.4 δ(δzK)=0 in eq.1.1.6 to initialize to locally flat space. Results of amazing equation:  δ(δz-K)=0  and eq.1.1.5    δ(δzδz)=δ[(dr+idt)(dr+idt)]= δ(dr2+i(drdt+dtdr)-dt2)=0          (1.1.7)   Then the Imaginary part of eq.1.1.7 is  δ(drdt+dtdr)=0 (1.1.8)         If dr,dt positive then drdt+dtdr=ds3=0 is a minimum. Alternatively if dr,dt is negative then drdt+dtdr=0 is maximum instead for dr-dt solutions. In fact all dr,dt sign cases imply a single invariant extremum:               drdt+dtdr=0   (our 1st invariant, sect.2.5)     (1.1.9)  Since we have two independent variables r,t in relδ(δzδz)=δ(dr2-dt2) =. δdr2-δdt2+δk2=δ(dr2-dt2+k2)=δ(dy2+dz2)=-Realδ(dz) still with two independent variables y,z because we can choose k2 randomly. Thus real eq.1.1.6 Real(δ(dzdz)+δ(dz)=0 becomes δ(dx2+dy2+dz2-dt2)=0 with 1.1.9 still holding(since δ(idt)=0). So we have 2+2=4 dimensions and dr2=dx2+dy2+dz2. Note in general dr,dt could be any two of these 4 independent variables implying eq.1.1.9 defines a Clifford algebra. Next factor the real part of eq.1.1.7 to get (our 4D universal 2nd invariant ds2=dr2-dt2): ds2=dr2-dt2=                                                                                                                                                                                                                     [[δ(dr+dt)](dr – dt))] + [(dr +dt)[d(dr – dt)]] =0. (1.1.10) Solve eq. 1.10 and get     (->±e)   dr+dt=sqrt2ds, dr-dt=sqrt2ds,    (1.1.11)          (->light cone v)    dr+dt=sqrt2ds, dr=-dt,             (1.1.12)               “        “              dr-dt=sqrt2ds,   dr=dt,          (1.1.13)     (->vacuum)            dr=dt,           dr=-dt)          (1.1.14) Equation 1.10 gives Special Relativity ds2=dr2-dt2 (note natural unit constant 12 (=c2) in front of the dt2) and eq.1.1.9 gives the Clifford algebra (sect.2.5). A third invariant in section 1.1.2 changes these operators into derivatives thereby making these Dirac equations. So 1.11-1.13 are (neutrino v &stable electron e) leptons. All the rest are composites* of e,v. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 

*composites of e,v are Bosons (eg.,The SM: Z,W), and composite  3e baryons (eg.,proton), and Fiegenbaum Point fractal e cosmology (GR&gravity).  Excited states of e are u,T in appendix.   We finally do understand.      

 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Appendix z=0 details Rotate z by 45+45 Longer summary of section 2 Thus we rotate this (small C) δz through 2 quadrants: (so S=½±½=integer) from the 4 different axis’ max extreme (of 1.15 and 1.11) branch cuts and so get the 4 results: the Z, +-W, photon Bosons of the Standard Model (We have derived it!) with correct field equations (see A6). This is the mother of all reality checks! Also this rotates SR into GR (So we have derived GR too!!) and 1.1.11 into eq.2. This same rotation also breaks those two 2D degeneracies of eq.1.1.11 creating our 4D. Three eq.9 components in 2P3/2 at r=rH give the baryons (PartII) and the tauon and muon are S½ excited states of eq.2. That 1040X fractal electron scale difference of the rH (so next smaller rH gravity from our SR rotation) in the (eq.1.11) eq.2 is at the Fiegenbaum point where δC=0 (i.e., ground state) even for 4D Large fractal baseline (mixed and pure lepton) metric quantization states are in partIII. Mond is a special case.

Why Is This Important? So we derived both physics and math, the most rational thing we could be doing. 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.1.2.7) we postulated. Try looking up at a starry night sky and contemplating that some time. This illustrates the infinite simplicity of this idea. So by knowing essentially nothing (i.e., ONE) you know everything!  We finally do understand (just postulate 1).

References (1) Penrose recently implied in a Utube video that all of physics might be extracted from the Mandelbrot set.  Here we have merely shown how to do that and why it is important. The Fiegenbaum pt neighborhood is a subset.

Table of Contents

      Postulate 1 


 Part I     1U1 states

Part II    1U1U1 states 

Part III   Mixed State

 Rest       Miscellaneous


Mandelbrot set derivation : Note 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=O→0∪0=0+0 in our whole number algebra.