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THE POLYNOMIALS [ n.. Knots–FIGURES ]

  EDGE - POINTS VIBRATION & M-GEOMETRY

BY

Markos   Georgallides

1Larnaca–Cyprus (Expelled from Varosha-Famagusta  town occupied by the Barbaric

  Turks , in Aug - 1974) Cyprus , Civil - Structural O Engineer (NATUA) , Athens .

  Abstract

The Interactions :

One of the most important concept in Geometry is , distance , which is the Quanta in E-

geometry , while in Material-Geometry the composition of Opposite , where the Material -

Point is the Quanta in Chemistry and Physics . As in Algebra Zero ,0, is the Master-key 

number for all Positive and Negative numbers and this because their sum and multiplication 

becomes zero, and the same on any coordinate-System where ± axes pass from zero . In PNS

Space , The Rolling of the Positive ⊕ constituent on the Negative ⊝ constituent , creates

the Neutral Material Point which Equilibrium . Angular-Momentum is identical with Spin and 

consists the First-Discrete-Energy-Monad which occupies , Discrete Value and Direction ,

in contradiction to the Point which is Nothing , Dimensionless and without any Direction .

Quaternions [(+)↻↺(-)] ≡ Box 𝐁 𝐑 =𝐀𝐁 carries the Principal stress 𝛔 𝐀 , 𝛔 𝐁 between Points 

A(+) , B(-)  which σ , as Centripetal-acceleration is the minimum Energy becoming from the 
in-storage AB acceleration and is equal to the Gravity Force g . [108 – 110] . Because of the

Revolving and Periodic acceleration of Gravity  g ≡  σ exists as the First Energy-Box-𝐁 𝐑 ,

while in the Second Box 𝐁𝐏 is followed the Local-Extreme-case where Gravity g ≡  σ ,

and is altered Locally by changing the Principal-stress σ with an Local-uniform-Pressure

  → 𝐠𝐋 ≡ g k = g . [ Force/Area ] = G ← i.e. The minimum  Local - Energy acceleration is the 

known , Universal Gravitational-constant G = g k = 𝐤𝐄 g = 𝐤𝐋 σ , such for Macrocosm and 

for Microcosm , Obeying the Newton`s Laws of motion . G ⏊ σ

This Energy in Hydrogen-Cave as E-M , Conductor ≡ Edge Points Vibration ≡ The Pin of 

Atom → Plug Into their Sockets , which are the Orbit – Bracket–Hooks ≡ The Hands of 

Atoms ←  i.e. The Atoms Plug with their Pins into the other Atoms-Drains = Holes , and 

so Bond and carry Informations .

1

https://doi.org/10.5281/zenodo.16737369

mailto:georgallides.marcos@cytanet.com.cy


  

 

 

 

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

This Resonance frequency of Hydrogen is Common to all Atoms and to all  Compounds in  

this Cosmos . The Energy-Quaternion w ̅̅ ̅, B̅, Monad-Magnitudes exist as DUAL- Nature for 

Any { ⊕ , ⊝ }, { Position , Motion },{ Universe , Black-Holes } , { Gravity ,Antigravity} ,  

{Action → . ← Reaction} ,  Edge Points Vibration creating Electric = [⊕] and Magnetic = 

[⊝] Forces as [⊕↔⊝] ,The Light and others .The STPL- Line Conductors on the [STPL]-

Mechanism , are the Physical-Rotors for the Origination of the Cosmic –Particles which 

transfer Informations as the Signals - Spectrum .[110]     

From Mechanics-Physics , all Systems Possessing Elasticity ≡ motion and Reaction to the  

motion , the called mass , are capable of  free vibration  or vibration ≡  Periodic - motion  

taking Place in the Absence of External Excitation .This Principle issues for Both Systems  

Closed {The Atoms Nucleus} or Open Systems {The Orbitals}. For instance , In order that  

shifting of an  u-d-Quarks from an Anti-Proton into a Proton , the Spin-Pair  requires extra  

input of Energy in (MeV) , so that would the Proton  Paired with a Neutron and be Stable.      

transfer Informations as the Signals . Vibration in a cave  ∆ , means the Wave Pattern .  

Cave–Spin-�̅�  of  PNS Space is  �̅� = r m v and is the first Monad occupying  4-Spaces , i.e.   

                 From Number n , of the Equilibrium number of masses m 𝐧 in  a  System.   

           a.. The n - Spaces of Monad  �̅�  are the Polygons  𝐒 𝐧 with  n = 1 ≈ ∞ Knots ,  

           b.. The n Anti-Spaces of Monad - �̅�  are the Polygons - 𝐒 𝐧 with n =1≈ ∞ Knots , 

           c..  Sub-Spaces of Monad ≡  ± √ �̅�  
𝒏=𝟏−∞

 are the Polygons with  n = 1 ≈ ∞ Knots   

All  n-Regular Polygons End to equations of  n-degree Segment , by finding  a suitable value 

of  the  Segment  , x  ,  That is  we have in the general case to solve one or two equations of  

the form  :  A .R0. xn -  B .R2. xn−2 + C .Rn−6. x³ – D .Rn−4. x² + E .Rn−2.x1– F. Rn. x0 = 0  

     for  The Even Polygons  , and  

A .R 2. xn−2 - B.Rn−2. xn−3 + C.R2(n−4). x³ -D.R2(n−3). x² +E.R2(n−2). x1– F.R2(n−1).x0 = 0          

     for The Odd Polygons  ,     where  A , B , C , D  are constants .  

The  Presented Geometrical method is the solution of the above equation in the general case . 

Because , the  nth - degree - equations  are  → the Vertices (n) and the Sides (𝐚𝐧= 𝛌𝐧)  of the  

n-Polygon in circle ←  number  , π , is their common Mould . [ 62 ] . The Natural Mechanism 

Continuously Originates the Elementary Particles and Compounds , Atoms and Molecules 

with the  One Action from Opposite . Article  [111]  encloses many Paragraphs of [110] , in  

order to Distinguish and Prove the Way of  Energy and the Stresses- Paths in the Spaces .   

For the Regular Polygons is given such the  Geometrical Solution as well the Algebraic .  

[106] = Programming the Atoms and Compounds , is an Program which solves the Problem 

of the n-Knots Figures  and gives the Energy Spectrum of  any Complex-Forced-Vector .  

Article  [114]  an Way of Deceptioning the Cells is prepared .  

 

Keywords  :  The Figure  n-Knots , The Polynomials n-Knots  , Spaces and Figure  n-Knots ,  

                      The  Waves of  Spaces .  

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CONTENT                   

ABSTRACT                                                                                            Page ….................1 ,   

A… THE  STRUCTURE  OF  THE EUCLIDEAN  GEOMETRY    

1a.. :  The Points , Vectors , Lines , Planes , Volumes  , n-Spces            Page ….................4 ,    

2a.. :  The Fundamental  Principles of  E-Geometry                               Page ……….4.Fig-1 ,   

3a.. :  The Quantization of the  Energy – Space – Universe                    Page …………....7 ,   

4a.. :  The Correlation of  Spaces  and  The Primary motion                  Page ………11.Fig-2 ,    

5a.. :  The Figure-eight Knot  &  The Figure  n = 1 ≈ ∞ Knots             Page ………13.Fig-3 ,  

6a.. :  The Origination of  The Primary motion  in Spaces                      Page …… ..21.Fig-4 ,   

7a.. :  The Mechanism and Charges  for the DUAL Originations           Page …...............23 ,  

8a.. :  The Material Geometry E-Geometry Physicks and Chemistry     Page ……....24.Fig-5 ,   

          [a].. The { S TP L }  Natural  Mechanisms                       Page …..26.Fig-6,7.7a,7b,7c ,   

          [b].. The { TVPM }  Natural  Mechanisms                                  Page ... 32.Fig-8a , 8b ,   

          [c].. The { TC I C }  Natural  Mechanisms                       Page ..35.Fig-9,9a,b,9c,9d,9e ,    

          [d].. The { TOBM } Natural  Mechanisms                                   Page ......... 43.Fig-10 ,   

9a.. : The Flow Plan  of  the Space - Energy Universe                           Page ……..45.Fig-11 ,     

10a..:The  E-Spaces and the Energy Regular-Polygons             Page.49.Fig-12a,12b,12c,12d ,   

B… :  GENERAL  :          

1b.. :  The Spaces and the Energy States                                                 Page …... 54.Fig-12- ,           

2b.. :  The Complex Numbers  and  Quaternion.                                     Page …............. 56 , 

3b.. :  The Stability of  Space - Anti-Space , IN  the Neutral-Space       Page …….59.Fig-13 ,   

4b.. :  The Quantum Interference of the Duality-Photon                         Page …….59.Fig-14 ,   

C..  :  THE  ORIGINATION  OF THE  PHYSICAL  LOOPS ≡ CAVES   

1c.. :  The Gravitation Force  G , and the  Kick-Start                              Page ….............. 62 , 

2c.. :  The  United-Coulomb-Newton Law for Interactions                     Page ….............. 69 ,  

3c... : The Origination   of  Photon`s  Light velocity  c                            Page ……..........69 ,    

4c... : The Origination  of  Electron-charge  e̅ ≡ q̅                                    Page ……..........72 ,    

5c... : The  Origination  of  the Hydrogen  Cave H   &  Explanations      Page ……..........73 ,    

6c.:  The  Epilogues of  Prior                                          Page…78.Fig-17a,17b,17c,17d,17e ,   

D... THE ORIGINATION OF THE  FUNDAMENTAL PARTICLES        

1d… : The  Balancing of  the Space and Anti-Space                               Page ……..99.Fig-18- 

2d… : The Vibration of Particles  in all Levels                                        Page ……100.Fig-19- 

5d… : The Natural Electromagnetic E-Tetrahedron , Cube , Spheres     Page …..102.Fig20.b- 

8d..   : The Stability of Fundamental Particles Conductors & Atoms      Page ……108.Fig26 -  

9d..   : The Origination of Proton-Neutron Funta-Particles , Objectivity Page ……110.Fig28 - 

E..  :  REFERENCES                                                                              Page…….……113 ,  

 

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A… THE  STRUCTURE  OF  THE EUCLIDEAN  GEOMETRY . [6 -12 ]      

a1..  Point  is  nothing , has not any Position and  Dimension , and  may be anywhere  in the  

   known Space therefore , the  Primary point  A  ,  being  nothing also  in no Space , it is the    

   Only - Point and   no-where  ( i.e. Primary Point  is the Only Space and  from this all  the    

   others ) . [ 6 ] 

a2..  Straight  line is  0 , Positive , Negative , consisted of ± ∞  Points which are nothing , and   

   since it is  composed of  infinite Points which are filling the line , then nature of line is that  

   of Point i.e. ( the all is one  for Lines and for Points ).  

a3..  Plane  is Positive , Negative , ± Neutral  lines and since Points are Imaginary lines it is    

   composed  of infinite  Straight lines  which  are filling Plane , so then  , nature of  Plane is    

   that  of  Line  and that of  Points  ( i.e.  the all is one  for Planes ,  Lines  and  Points ) . 

a4.. Space  is + Positive , - Negative , ± Neutral Planes and since Points are Imaginary Planes    

   it is composed  of  infinite Planes  which  are filling Space , so then ,  nature  of  Space  is   

   that  of Plane  and that of Points (i.e. the all is one  for Spaces , Planes , Lines and Points) . 

2a… THE  FUNDAMENTAL   PRINCIPLES  OF  E-GEOMETRY .    

2a1.. The first dimensional Unit  AB  is of  two  Points  A , B  not coinciding  which is the   

geometrical Shape that has as Position the Point of direction AB⃗⃗⃗⃗  ⃗ , BA⃖⃗⃗⃗⃗⃗  , and as Magnitude (the  

length |AB|  = 0 → N → ∞ ) . |AB|  is a straight line  through Points  A , B . ( F.1b) , [ 6 ]                

                    ↓                                        A           C          B               A         C               B  

  CA + CB   =  AB      ,  where  ,           ▫            ▫           ▫              —▫—— ▫ ————▫—  

                                                                      F.1(a)                                F.1(b)   

    ds   =  An  Infinitely  small  increment  of  length  AB  in the  direction   AB⃗⃗⃗⃗  ⃗  or  BA⃖⃗⃗⃗⃗⃗  . 

    ∞   =  An  Infinitely  great   magnitude  |AB|   in the directions  AB⃗⃗⃗⃗  ⃗ , BA⃖⃗⃗⃗⃗⃗  ) . Any  Point   

    C  is  on Straight  line  AB , only when  exists the equation  CA + CB  = AB ,        i.e. 

    The  Whole  AB  is  equal  to the  Parts   CA  and  CB . ( as equation F 1.b ) .      

In  case that  CA + CB  >  AB   then  Point  C  is not  on line  AB  ,  and  this  is the  main 

difference  between  Euclidean  and Non-Euclidean  geometries . In Definition 2 ( a line   

AB is breathless length) is altered  as  for any Point  C  on  line AB  exists  CA + CB =AB. 

Edge  Points  A , B   not coinciding on Monad  AB ,  keep  the Properties of  Complex 

numbers with  Imaginary  Part  which  differs  between  the infinite  Point  [11] – [13] 

Unit AB  creates  Spaces  with  two basic  Elements  , The  Position ( which are the three  

directions  AB⃗⃗⃗⃗  ⃗  ,  BA⃖⃗⃗⃗⃗⃗  ,  AB⃖⃗⃗⃗  ⃗  ) and  the  Dimension  ( which  is  the Magnitude  N such that   

N  =  0 → |AB| → ∞)  , and when exists , 

A  =  B         =       The Principle  of  the  Equality .   

A  ≠  B         =       The Principle  of  the  Inequality .     

A→↔← B  =  ∞  The Principle  of  Virtual  Displacements . W = ∫ P.ds = 0 ,  ds = ∂W / ∂P 

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PA⃗⃗⃗⃗  ⃗   +   PB⃖⃗⃗⃗⃗⃗   =  0   The Principle  of  Stability  

 PA⃗⃗⃗⃗  ⃗   +   PB⃖⃗⃗⃗⃗⃗   > <  0   The Principle of  Motion .       

2a2.. The Monads = Quantum =  𝐝𝐬⃗⃗⃗⃗  = AB / ( n  = ∞ → 0 )  =  [ a ± b i ]  =  0 →  ∞ , are 

simultaneously ( Actual Infinity ) and  also  ( Potential  Infinity ) in  Complex number form  

and  this  defines , infinity  which exists  between  all Points which  are not coinciding  and 

where (  ds > 0 ) ,  and  because  ds  comprises  any  two  edge  Points with  Imaginary Part  

then  this  Property  differs  between  the  infinite  Points. The Plank length  is a Monad  ds   

= 1,62 x 𝟏𝟎−𝟑𝟓 m , for the two Points A , B ,  and  for the moment is accepted  as the smallest  

possible size . Monad  is also infinitely divided  because  edge  Points  A , B  are  not      

      coinciding   i.e. ...   ds  =  1x𝟏𝟎−𝑵 <  ∞  ,  where  N  is any number .        

1..  Spaces of  Unit-AB  are (in Plane)  the Infinite (+) Circumscribed-Regular-Polygons   

on the circles with AB  as Side (repetition of  Unit AB) the Nth Space , the Nth Unit Tensor 

of  the  N  equal  finite Elements  ds  , and  for  the  ∞   Spaces ,  the  line AB  ↔ . ( Fig-1 )                 

      The diameter  of  this circles extends  to infinity  ( it  is of  Potential nature ) .  [11]   

2..  Anti - Spaces  of  Unit  AB  are  ( in the three dimensional Space )  the  Symmetrically 

Infinite (-)  Circumscribed- Regular-Polygons on the circles or ( a Solid in Cube in Sphere 

with AB  as side of the Solid ) . The Harmonic Repetition of  Unit BA , symmetrical to AB ) 

is the Nth Anti-Space , the  Nth Unit Tensor of  the N  equal finite Anti - Elements , and  for 

the ∞  Spaces , the Sphere  through  line  BA .The diameter  of  this  Spheres  extends  to the 

infinity  ( it is of  Potential nature )  .  [11]   

3..  Sub- Spaces  of  Unit AB  are ( in Plane) the  Infinite  Inscribed-Regular-Polygons in 

the  circle with  AB  as diameter  ( are the Harmonic Repetition of the Roots  in Unit  AB ) 

and  in Nth  Sub-Space , the  Nth  Unit Tensor  of  the  N finite Roots  and  in case  of the ∞   

Elements  are  the  Points   on the circle , and  for  3D-Space ,  the Points on Sphere  N.AB )  .   

The Superposition of  Spaces , Anti-Spaces  and  Sub-Space  Layers of  Unit  AB  is shown  

in  Figure .   Remark  :   (+)  Spaces  ,  (-) Anti -Spaces  , ( ± )  Sub-Spaces , of  a Unit  AB   

are  between  magnitude  ( Point = 0 = Nothing ) and  the Infinite  magnitude  ( ↔  =  AB = 

 ± ∞  =  Infinite )  which  means  that  All Spaces  exist in One Space only .  

Because  in Spaces  and  Anti-Spaces , the  ∞ Spaces of   Unit AB  is Sector AB  ↔  , and   

in Sub-Spaces  the   ∞  Sub-Spaces  of  Unit AB   are the  Points  on  the circle with  AB  as  

diameter  ,  then  this  ordered  continuum  for Points  on  the  circle  of  Unit   AB   and  on  

 line  AB   shows the correlation  of  Spaces   in Unit  AB .   i.e.    

Monads  ds = 0 → ∞ are Simultaneously, Actual Infinity (because for n = ∞ then  ds  = [ 

AB / n = ∞ ] = 0  , or A Point  )  and , Potential Infinity , ( because for  n =  0  then  ds = [  

AB / n = 0  ]  =  ∞  is  the  straight  line  through  AB . Infinity  exists  between  all  Points 

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which  are not  coinciding , and because Monads  ds  comprises any two Edge-Points with 

Imaginary  Part , then this Property is the difference  between  the infinite  Points .  [11] 

4..  Neutral-Spaces  of  Unit-AB  are ( in Plane) the  Infinite  Circles with AB  as diameter   

( the Harmonic Repetition  of  the Roots  in  Unit - AB ) and  in  Nth  Sub-Space , the  Nth  

Unit Tensor  of  the  N   finite Roots  , and  in case  of  the ∞  Elements  are  the Points  on  

the circle ,  and  for  the 3D-Space ,  the Points on the Unit - Sphere  AB ) .   

      Since  Spaces , Anti – Spaces and  Sub-Spaces  are created  from  Unit  AB , and  

      are  Property  of  this  Unit  only ,  therefore  these are a  Restrained  System ( S )  

Presupposition  for  Unit  |AB| = ds  (displacement  ds)  is Point  A  to move at the New  

Position  B  (A ≡ B)  which  means   an   IMPULSE  ( P )  transfers Point A  to  B . 

Since  in each   Restrained  System  ( S )  the  Work done  ( W)  by  Impulse  ( P ) on  

a Virtual  displacement  ( ds > 0 )  is zero ,  or  W = ∫ 𝑃𝑑𝑠
𝐵

𝐴
 = 0   Therefore  ,   

Each Unit  |AB| = |ds|  > 0  exists , by  this Inner Impulse  ( P ) which means that ,     

The Position and Dimension of all Points which are connected across the Universe and  

that of  Spaces , exist  because  of  this Static Inner Impulse P between A and B , on the  

contrary , should  be one Point only ( Primary-Point = Black-Hole →  ds = 0  → P = ∞)  

         Impulse P =  ∞  ,  and  may be  Vacuum , Momentum  or  Potential or Induced  

         Potential and  it is  a Type  of  Effect  of  Push nature .   

2a3..The Superposition  of  Plane Space  , Anti-Space Layers  and  Sub-Space Layers   

The simultaneously  co-existence  of  Spaces  , Anti-Spaces  and  Sub-Spaces  of  any Unit  

|AB| , Unit  AB  =  0  →  ∞ ,  ( A ≡ B )   i.e. ,  Euclidean , Elliptic , Spherical  , Parabolic , 

Hyperbolic, Geodesics , Metric  and Non-metric geometries , exist  in Euclidean  Model  as  

an  Sub-case within . The  Interconnection  of  Homogeneous and  Heterogeneous  bounded   

Spaces Anti-Spaces  and Subspaces  of  the Universe . The  Unity of  Opposites is also the  

Quantized  Property of  Euclidean  geometry < all is one  > as  it is  Discrete  ( for Monads  

AB ) and  Continuous (for  Points  A , B ) . For Primary Point  A  it is the only Space [17]  

        The Unique  Case  where P = 0  and  Δs > 0  =  AB  → ∞  is the Primary Planck`s     

        Space [ PS ]  The Spherical connection of the same Points in PS , is related on  

        the influence ( P = 0 → AB⃗⃗⃗⃗  ⃗  → ∞)  of  the infinite ( ∞ ) Equilibrium Primary-Spaces     

        and  Anti-Spaces .  For every  Point  in  [ PS ]  exist  the  three  Spatial  dimensions  

         ( x , y , z ) and  the infinite dimensions of the ( i )  Layers  at  this Point existing from  

        the other Layers ( at small scale using coordinate system ) of Primary Anti-Space and   

        Sub-Space  where   i = 1 → ∞  . It  has been also shown that ,    

Every  Point  M  of  Primary Planck`s Space  [ PS ]  exists in this Space  with a deficit  of  

Impulse   P  = 0 → ∞  ,  due  to the influence  of  the other  Equilibrium Primary  Spaces .    

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The Unique  Case  where P = 0  and  Δs = 0 → 0  is the Primary Neutral  Space [ PNS ]  

The ⊕ Material Point ≡ The Space , continually Rotates around The ⊝ Material Point ≡ 

The Anti-Space , on 2R circle . [PNS] Space is a  

This  Property  of  Points  in Neutral  Space  is  the cause of their Continuously  Survive .  

The Quantization  of  Points becomes  through  Vector  Unit  d�̆� = |AB| , and for  Energy is  

done in bound States ( loops ) which withhold  the diffusion ( flow ) .The two  fundamental  

dimensions (Quanta of  Points (ds) and Quanta of  Energy (d P) , are connected on| AB|,  

So  at any  Point  M  exist the Centripetal force of two  Opposite [⊕↻↺⊝] .All  Points  of  

[PNS] are Homogenous  ( i.e. all Points of   PNS  Space  are Equivalent ≡ )  and  Isotropic  

( i.e. all  directions , ⇉ ,  of   AB  are  Equivalent  )  →  [ A ≡ A ] , For the  Primary dipole 

and for Any dipole  Ai-Bi issues , The Position  of Dipole in the  equilibrium Space Anti-

Space creates  charge = momentum  and  Angular momentum  ( Spin = the  intrinsic twist 

of  Space , Anti-Space ) which  inextricably unify Geometry of  Space and motion . [10 ]       

Figure – 1 . The 4-Primary-Spaces of Euclidean-Geometry and the Primary Rotational        

                     Quantized motion ≡ The Unit-Angular-Momentum-Energy in PNS Spaces .  

3a… THE   QUANTIZATION   OF THE → { ENERGY – SPACE  UNIVERSE  } ←   

       In a Conservative System the Total Energy ≡ Motion is constant and the Differential 

equation of motion can be established by the Principle of  Conservation of Energy . For the 

free vibration of an Undamped System , the Energy is Party Kinetic = 𝐄 𝐊 which is stored in 

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

the mass by virtue of its velocity and Party Potential = 𝐄 𝐏 which is stored in the form of 

Strain energy in elastic deformation , or the  Work done in a Forced-Field such as gravity .  

Newton`s second law is the first basis for examining the motion of a Free – Vibration in a  

System . When the Deformation of a Spring in the Static - Equilibrium  Position is Δ  and the 

Spring force  k.Δ equal to the gravitation al force mg , then issues   k.Δ = mg  …. (a) 

Applying Newton`s second law to the mass m , or mass can be replaced by a mass Moment of 

Inertia denoting the Resistance to  motion Δ  , and then  m �̈� = - k x  for an  x – x axis . The  

Natural – Period of the oscillation is established from relation wn T = 2 π  where issues  [7] 

      T = 2 π  √  
m

𝐤 
    ,   𝐟 𝐧 = 1 / T =  

1 

2π
 √  

 k

 𝐦 
    ,   𝐟 𝐧 = 1 / T  =  

1 

2π
 √  

 g

  Δ 
          ….…(b)  

i.e. The Kinetic Energy 𝐄 𝐊  is applicable in a Single - DOF System including Rotation .  

Since Issues E K = E P  so and   E K + E P = constant  . From the theory of Vibrations ,    

{ All Systems possessing mass= m and Elasticity = E = 1 / k  are capable of free vibration in  

the absence of external excitation which is its Natural frequency of vibration = 𝐰 𝐧  and the 

equation of motion is → �̈� + 𝐰 ²𝐧 x = 0 ←where  w ²n= 
k

m
  , Gravitational force  G = m g }   

i.e.  Since the Hydrogen-cave  System H , as E-M  Conductor , Possesses  mass 𝐦 𝐇 ,  and  

       light-velocity c , then vibrates IN – OUT  the Space-Positions (x , y , z)  of all Universe  

      with its Natural frequency  𝐰𝐇 =√
k

𝐦 𝐇 
   . or and frequency  𝐟 𝐇 = 

𝐰 𝐇 

𝟐𝛑
 ,  and is a Wave – 

         function providing the complete Description of the Physical Reality .   

From ,  Work =  W = Force - 𝐅 𝐢,𝐣,𝐤 x Displacement  𝐝𝐬 𝐢,𝐣,𝐤 = ( 𝐅 𝐢,𝐣,𝐤 x  𝐝𝐬 𝐢,𝐣,𝐤 ) = ( F x ds ) ,  

and for the Unit of time  dt ,  →   W / dt =  F x ( ds / dt ) = ( F x �⃡�  i , j , k ) =  Power = P .  

       i.e.  Power ≡ Force x Velocity or  (  P  =  F x �⃡�  )   

      Remarks , from Mechanics - Physics   :   

1…Energy  E = 
1

2
 m H . c ² ,    or  → 2E = 𝐦 𝐇 . c ² ← and  Velocity = The light-velocity c ,  

2…Wave length  λ H = 
𝟐𝛑 𝐜

𝐰 𝐇 
  ,   and  Wave Amplitude  𝐀 𝐇 = 

 λ H

𝟐𝛑
 ,  

3…Hydrogen Power   𝐏 𝐇  =  0,5. 𝐦 𝐇 . [ 𝐀 𝐇 ] ² . [ c ] ²  

4…The Hydrogen Stress-Vector 𝛔 𝐇  is related to  c  as ,  c =  𝚽 . 𝛔 𝐇  

5…Since Hydrogen cave is an  E-M  Conductor then it is a Wave with Natural frequency ,  

      and since occupies the Property of →Atoms-Plug ≡ Pin and Atoms-Drain = Hole so are  

      Bonded ← in a multi-DOF System at the Stationary Conditions . 

6…To find the Eigenvalues and Eigenvectors of a multi-DOF System , Iteration method of        

       motion is formulated by either the Flexibility Matrix [a] or the Stiffness Matrix.   

7…Momentum ≡ ± SPIN ≡ [Gravity and Antigravity] because the light velocity �̅� = [
𝐆 𝚽

𝐀
] ,  

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       and Precedes  that of  A-Momentum  �̅� = r m �̅� . Exists Vector B ⊥  r-c  Plane . 

8…Since Angular-velocity |w̅| , a vector , Rotates in one axis k with respect to one variable  

      only and this happens IN {PNS-Space ,Atoms-Space ,Objective-Reality and in Universe}  

      then Quaternion - Momentum , B̅ & w̅  , and W ≡ Motion are Stabilized in the DUAL – 

      TYPE , such  in Microcosm , as in Macrocosm , or Both as Omnipresent .       

1…The DUAL-Momentum B̅ & w̅, as Real ≡ Existing-Universe , Imaginary≡ Black-Holes  

2…The DUAL - Photon , as Real ≡ Space ≡ Particle and, Imaginary ≡{ E M - Wave }.  

3…The DUAL - Spin  B̅ , as Real ≡ Space ≡ Gravity and, Imaginary ≡ { Anti - Gravity }.   

4…The DUAL – Matter B̅ , as Real ≡ Space ≡ Atoms and, Imaginary ≡{ E M -Wave }.   

5…The DUAL-Refraction of Energy as Real ≡ The Space angle φ , Imaginary ≡ �̅� 1, �̅� 2 

      { The Energy ≡ W from the different velocities , �̅� 1, �̅� 2 }.    

     The Results in  Hydrogen - cave  : 

1…Hydrogen-Cave , IN – OUT Universe occupies mass 𝐦 𝐇 , velocity �⃡�  , and Power  𝐏 𝐇  

2…Electron in Hydrogen-cave Precesses and Nutates due to the Gravitational constant G. 

      The produced Work is stored in form of→ Stress Energy as Hydrogen-Bracket-Hook←  

      The Electron  Precesses from the continuous and immense-communication to gravity, g .  

      Electron-Spin is the Angular-momentum-vector �̅� and rotates according to equation 
dB

dt
 

3…The Stationary → Tetrahedron , In-Sphere , Cube , Ex-Sphere ←construction  

       of Atoms Permits the Space – coordinate - Structure of Atoms , 

      The Wave-eigenfunctions of many non-commuting Physical operators as Momentum  

      Power, from the Quantum-Mechanical description of the Physical-Reality is Complete 

i.e.  IF-known the Physical Operators , their coordinates are simultaneous Physical reality. 

4…The Interactions of Two or more Systems with known Status can be calculated any time 

       by the Bioelectronic-Spectrum of →{ Carrier-Modulating-Modulated , Demodulation  

       Process Mechanism } ←  using Markos Program  < Programming Atoms-Bonding and  

       Their Compounds > SO , Energy ≡ motion is of Wave nature which enters the Energy   

       caves and becomes  a  Particle or Wave or Both . In case of Photons exists this DUAL- 

       Property  , Wave – Particle . Thus The Historical Doubt of Einstein - Podolsky - Rosen  

       for the Q-Mechanics Completion VANISHES  .  [100,104] . 

5… The Programming of Atoms Bonding is the Quantization of Atoms -Wave -Energy to all  

       Possible  Equilibrium Positions of the [⊕↔⊝] constitutes Reactions . The Wave-Energy  

       as Vibration travels at 75-90 % of  the light speed  c , while the Wave-Energy in Black  

       Holes is  n π c times of  the light speed . [100-101]     

6… From all the Possible Reactions in Compounds , the Bonding or the Releasing of energy  

       is the Vital rule of the Theory of Vibrations .The Program  Programming the Atoms and  

       their Compounds , analyses the Interactions of two or more Energy Systems with known 

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Status using the → Carrier–Modulating–Modulated–Demodulation Waves Process ← 

       Some following Wave Properties that are Defined  :  

6a... The Equilibrium  Mode – Shapes , Φ , Diagrams . 

6b1..The Circular – Frequencies , 𝐖 𝐑 , in 1015 Hz ,  

6b2..The  Natural – Frequencies  , 𝐟 𝐑 , in  1015 Hz ,  

6c.. The Resultant Energy – State , 𝐄 𝐑 , in e-Volt , 

6d...The Electric–Magnetic Field  , 𝐄 𝐑 - 𝐌 𝐑 , in 10−12 Ampere -10−6 Tesla , 

6e.. The Intensity of the  λ-Electric–Field  , 𝐈 𝝀 , in 10−12 Ampere , 

6f.. The Intensity of Magnetic–Field  , 𝐌 𝝀 , in 10−6 Tesla , 

6g.. The Wavelength  , λ , in .10−10 meters ,  

6h.. The Wave Velocity  ,  �̅� , in 105 meters / s , 

6i1..The Resultant Voltage at Wavelength-sides , 𝐕 𝝀 , in Volt ,  

6i2..The S-Bands Voltages at Wavelength-sides , 𝐕 𝝀 , in Volt , 

6j.. The Radius of the Helical motion , r = 𝐀 𝐑 in .10−10 meter , 

6k.. The Total  Carrier Power , 𝐏 𝐂𝐓 , in 10−20 Watt , 

6l.. The Total  Side-Bands Power , 𝐏 𝐓 , in 10−20 Watt , 

6m.. The Side-Bands Amplitude , 𝐀 𝐁 , in 10−10 meter , 

6n.. The Side-Bands Coefficients ,  a - m  , in  n-n , 

6o.. The Modulating  Phase Shift  ,  𝛗 , in  Rad /2π ,  

6p.. The Modulating  Factor ,  𝒎 , in  n-n , 

6q.. The Total Energy-Status ,  a - m  , in H-W ,         

       

Figure-2..  The  ± Energy in Hydrogen and Atoms exists from Hydrogen Common-Atom .    

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            The two Hydrogen Bonding   →    H + H = H1
1 + H1

1 = H1
1−1 H1−1

1  = H1
0 + H0

1 = H2  

            Water  H2O = O1 H2= O2
2 H2

2   =  T 4
4 = O2

2−2H2−2
2 = O2

0 H0
2 = ES 2=T/2

2=T/2
  , Still. [102]     

4a.. THE   CORELATIONS  OF SPACES  AND  THE PRIMARY MOTION .   

Euclidean Geometry Spaces occupy Position (x , y , z) and Dimension |⇅| at any Point P, 

Cauchy Stress Tensor defines the State of Stress (σ , τ) to the Traction-Vector (Te= e. σ)  

The Position of Spaces  is defined from any 3-dimension Coordinate (x , y , z)  or from 

        Angular-System ( φ , θ , ω )  or  any other System with axis from any fixed Point O .  

        The Dimension of Spaces is defined as the distance between any two Points O , P ,  

        and from any fixed Point O  the magnitude |OP| = 𝐧 |OP| , where n⃡  is The Unit    

        Line - length direction and is identified by vector  n⃡  ≡  |AB| = The Unity Monad .  

In Fig-1-1 , On AB Diameter = 2R = The Monad of Neutral-circle exist the Spaces with  

       their Sides 𝛌𝐧= 2,√R2 − a²n , and their Critical-sides  𝐚𝐧 = 
1

2
 √4R2 − λ²n , as below  

1… For Spaces , the Polygon Side is   λ n(S) = 2 .√R2 − a²n(S) , 

2… For Anti-Spaces , the Polygon Side is  λ n(AS) = 2 .√R2 − a²n(AS) ,     

3… For Sub-Spaces , the Polygon Side is   λ n(SS) = 2 .√R2 − a²n(SS) ,   

4… For Neutral - Spaces , the Polygon Side is λ n(NS) = 0 , while in Material-Geometry   

      becomes from the Centripetal Force  FC = σ = 
m.v³

r
 = J w² r , where the Unity Monad r  

     ≡ monad R = 
σ

J.w²
 = 

𝛔

�̅� 
 = 

Stress 

Angular−momentum̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅ 
 , and Polygon Side  𝛌 𝐧(𝐍𝐒) = 2 √R2 − a²n , 

     All becoming from Pythagorean relation  [ R ] ² = [ an] ² +  [ 
λn

2
 ] ² . 

In Fig-3 , is shown the Geometrical construction of the Inscribed and the Circumscribed  

           n-Regular Polygons . With 4 , 5 , 6 , different Vibrating masses for each Space and  

by using the Argand Diagram for a Vector of Amplitude AB = 2R = The Monad , then the  

4 - Spaces are measured using the Euler equation for exponential functions  as follows  ,  

On the  SPACES , the Vector of Amplitude can be represented as the Complex quantity  

on  →  S      Z +
 n   = + 2R.𝑒𝑖.𝑛𝜔𝑡 = + 2Rn.[ cosw. t + i. sinw. t ]  = x + i .y 

on  → AS    Z −
 n   =  - 2R.𝑒𝑖.𝑛𝜔𝑡 =  - 2Rn.[ cosw. t + i. sinw. t ]  = x + i .y 

on  → SS    Z ±
1/𝑛

 = ±2R 1/n. ei.θ/n = ± √2R
n  . √[ cosw. t + 𝐢. sinw. t ] n = x + i .y where  

The Space Vector–Amplitude 2R = √ λ n(S)
2 − a²n(S)    ,  for the n-masses .  

The Anti-Space Vector–Amplitude  2R = √ λ n(AS)
2 − a²n(AS) ,  for the n-masses .  

The Sub - Space Vector–Amplitude 2R = √ λ n(SS)
2 − a²n(SS) ,  for the n-masses .   

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       Remarks : 

 a…From Argand Diagram the Vector  Z +
 n =2R.𝑒𝑖.𝑛𝜔𝑡=+2Rn.[cosw. t + i. sinw. t] = x + i .y  

       meaning the Wave Pattern of Spaces in Planck`s cave 10−35 m .The Vector Amplitude  

       𝐀𝐁̅̅ ̅̅  = 2R = The Monad ,is the Complex quantity 𝐀𝐁̅̅ ̅̅  ≡ �̅� ≡ x + i .y , where x = 2R → the  

       Geometry of PNS - Space and  y = 𝑒𝑖.𝑛𝜔𝑡→  the motion in Planck`s Space .      

b…Since Anti-Space Z −
 n  ≡ -  Z +

 n  , means the Conjugate Space to the Space Z +
 n  .   

c…Since from Wave-Action of  Spaces issues   Z −
 n x Z +

 n = [2R] 2n . e i.2nθ , this means  

      that ,The conservation of Energy = Work , between the Spaces and the Anti-Spaces   

      happens by doubling the number , n , of the Vertices of the Regular Polygon .  

d... The Natural frequency of an  x-x  linear vibration , [⊕↔⊝], becomes from 𝐰𝐧= 2π.f n 

       meaning that the infinite frequencies f n are stored in Subspaces by  doubling the  

       number , n , of the Vertices with 2n-Sides to a Regular Polygon of initial  n.Sides .         

e... The Natural frequency of an Rotational ↻ r ↺  DOF vibration System becomes from 

      �̅� = r.m.v n= r.m.v n= r.m.w n.r = m.w n.r ² = m.r².w n , meaning the Natural Identities  

      of the ∞ Monads in our Universe .   

The Equations of motion in a Material Point related to the Inner motion was referred before 

where the In-between-magnitude  Circumscribed – Inscribed Polygon  , The Part , becomes 

the Outer AB  as the ,Whole or the Self-Growth .This Augmentation-Property , of these two 

Golden-Ratios , exists in the Material-Point and on Frequency fn  , which motion ≡ Growth , 

and Spread in Two-Closed-Transverse Planes as is in the Propagating Electromagnetic Wave  

where E ⊥ H . From Planck E = h.fn ≡ [
1+√5

2
] 

hσ

2πr
 = [

nσ

 8 r² 
].B̅  , 𝐟𝐑 ≡ [ f1=N ,f2 ,f3 , f R = w²N ] , 

Euler`s  𝐞−𝐢.𝐀(
𝛑

𝟐
+𝟐𝐤𝛑).𝐛 = e−i.A(

π+4kπ

2
).b = A.cos[

π+4kπ

2
]. b –  i . Asin[

π+4kπ

2
].b ,  L = [ B̅/2].w ,  

so then   w =  √2π. fR = 2L /  B̅  , and the Wave Equation is  y = 2A.sin(
2π.x

λ
 ).cos . wt ....(a)  

f... The Natural frequency of the Unit-Energy-Vectors , �̅�.�̅� = m.r².w ²n =  m.v²n= KE .  

     From Momentum �̅� = r m v = m �̆� r² = ± [ 
𝛑.𝐫𝟐 

𝟐
].�̅� x �̅�  ,  �̅�.�̆� = ± [ 

π.r2 

2
].c̅ ² , c̅ = σ Φ , i.e.   

    The Primary Space is Originated from the Stress   σ , and from the Angular 

    Momentum   �̅� , �̅�  , Produced  from the Two - Opposite  [⊕↔⊝] components.   

g...Since Monads are Complex quantities as  AB ≡ �̅� ≡ x + i. y , then are Quaternions where  

     Material-Points ≡ Quaternions , which  Carry the → Motion ≡ Energy ← from the two  

    Edge-Poinds [ �̅�↔�̅� ] , as this is from Point A , to Point  B circularly . Simultaneousley   

   On AB Conductor is created an Electric Field  𝐄 𝐅  between A–B Points and ⊥ on AB axis  

   directed to the motion , and an Transverse (⊥AB)   Magnetic Field as ,  𝐌 𝐅 ⊥ 𝐀𝐁̅̅ ̅̅  ⊥ 𝐄 𝐅 .  

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5a.. The  Figure-eight Knot  &  The Figure  n = 1 ≈ ∞ Knots :      

Figure -3-  : The Geometrical construction of the 4-Spaces and the , Spaces Waves of PNS .  

       In Argand Diagram  AB = 2R  →  x = -1 , O , +1  , y = i , exist the Vector of Amplitude  

      �̅� ≡ x + i . y , with angle  θ ᶱ  = [ Z – OC] ᶱ ,  [i = √−1] .x . The  Wave's " strength " and  

      " direction ", where x is a number that represents the magnitude or length of the vector z ,  

      and from Definition of the complex Vector Space , is the Set of Vectors of length (the n  

      Vertices which form the n Polygon Sides , or the Norm of  the Complex-Vectors ) 

In  (1) , (2) , are the 4-Geometrical Spaces consisting the Geometrical - Mould .  

In  (2) , are the Vectors of Amplitude ON the 4 -Spaces consisting the E-Form-Mould .     

      It is constructed in Space → The Inscribed and the Circumscribed to the circle  

      of diameter AB , the  →  Regular Tetra Pleuron ←   

      It is constructed in Anti-Space → The Inscribed and the Circumscribed to the circle  

      of  diameter AB , the →  Regular Penta Pleuron ←   

      It is constructed in Sub-Space → The Inscribed and the Circumscribed to the circle  

      of  diameter AB , the →  Regular Hexa Pleuron ←   

In  (3) , are the Norm (magnitudes) of the 4 -Vectors  consisting the  Strength -Mould .   

        In Fig-3 The time-harmonic function �̅� (t)≡Wave , x is the amplitude, w the angular  

        frequency , and Phase of  �̅� (t) to be determined by the number n , n+1 of Vertices .  

       The complex – Vector  ±  �̅� (t) uses the Norm  Iz̅I = 2.R  , and the number n , of the  

       Space which Determines  the Number of Knots and Sides of  Regular Polygons as ,   

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1…The Space is consisted of  4 masses [99] which Produce the Space - Wave = 2R.𝑒𝑖.𝑛𝜔𝑡 , 

2…The Anti-Space is consisted of 5 masses Producing the Anti-Space–Wave= - 2R.𝑒𝑖.𝑛𝜔𝑡   

3…Sub-Space is consisted of 6 masses Producing the Sub-Space–Wave =  ± 2R 1/n. ei.θ/n    

 5a1.. The Physical notion of  the Regular Polygones  :   [ 62 ]  

According to Archimedes ,  Geometric means  , speaking of numbers , whether solid or 

square , observes that , Between Plane  One - mean  suffices , but to connect two solids two – 

means are necessary .This denotes that between two square numbers there is one mean 

proportional number and between two cubes there are two means proportional numbers .  

It was Proved  that  Odd numbers become from any two consequent Even numbers , so  

the sum of two irrationals may be either rational or irrational . The Cattle – Problem of 

Archimedes may be further analyzed reaching to equations of any degree.  

It was shown before that , all  n-Regular Polygons End to equations of  n-degree Segment , by 

finding  a suitable value of  the  Segment  , x  ,  That is  we have in the general case to solve 

one or two equations of  the form  :  

A . R 0. x n -  B . R 2. x  n−2 + C . R n−6. x ³ –  D . R n−4. x ²  +  E . R n−2. x1 – F . R n. x0  =  0  

            for The Even Polygons  , and  

A .R 2. x n−2 - B .R n−2. x n−3 + C .R2(n−4). x ³ - D .R 2(n−3). x ² + E .R 2(n−2). x1 – F .R 2(n−1). 

x0 =  0       for The Odd Polygons  ,                                   where  A , B , C , D  are constants .  

The  Presented Geometrical method is the solution of the above equation in the general case . 

Because , the  nth - degree - equations  are  → the Vertices (n) and the Sides (𝐚𝐧)  of the  n-

Polygon in circle ←  so number  , π , is their Mould . 

The Knot is  a  Closed – Curve in Space ( x , y , z ) , that does not intersect itself .  

A simple Parametric representation of the Figure-eight Knot is as the Set of all ( x , y , z )  

Points where ,  x =  ( 2 + cos 2𝑡 ). cos(3𝑡) , y =  ( 2 + cos 2𝑡 ). sin(3𝑡) ,  z =  sin(3𝑡) ,   

For the Cave-Spin , �̅� = r m v , which is a Monad  and is consisted of 4-Spaces exists   

        → (( The Spaces n.�̅�  Polygons , The Anti-Spaces  - n.�̅�  Polygons ,  

                 The Sub-Spaces  ± √𝐧. �̅�  
𝒏=𝟏−∞

 Polygons )) ← ,  with  n = 1 ≈ ∞ Knots     

It has been Proved [62]  that , Projecting the vertices of  the Regular  n-Polygon on  

any tangent  of  the circle , then  the Sum of  the  heights  𝐲 𝐧  is equal to , n  R .   

  This is a linear relation between  Heights , h , and the radius of the circle , the monad .   

This Property on the circle yields  to the Geometrical construction ( As Resemblance Ratio of 

Areas which is controlled ) and  the Algebraic measuring of the Regular Polygons as follows,                                                                      

when  :   R     =   The radius  of  the circle , with a random diameter  IAB I  .                                 

               𝐚𝐧   =   The side of the  Regular  n -Polygon  inscribed  in the circle     

               n     =    Number of Sides , a , and Knots  of the  n -Polygon  , then exists :                                                    

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         n . R     =   2 . R  + 2 . y1  + 2 . y2  + 2 . y3  +……… 2 . 𝐲𝐧               …………. (n)                                                                                                                                                       

         The heights   yn  are as follows   yB  =  [ 2 . R ]  ,  y1 =  [ 4.R ² - a ² ] /.  ( 2 R) …(y) 

Equation (y) is a Space-Wave depended on 𝐚𝐧 , meaning n Informations  on  𝐲𝐁  Height . 

y2  = [ 4.R4 – 4. R2. a2 +  a4 ]/(2. R3)                                                                                                                                                                      

y3 = [ 8. R6 – 10. R4. a2 + 6 . R2. a4 – a6 ] –a2 . 64. R 8- 96. R6.a²+52. R4. a4 –12.R². a6 +a8    

           ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ 2. R5 ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯       

yn  =  [ …………….. ]  / 2. Rn                                              Figure – 3A-                                                                                                  

In Fig-1-1 , On AB Diameter = 2R = The Monad of Neutral-circle exist 

 the Spaces with  their Sides   𝛌𝐧 =  2,√R2 − a²n , and their Critical-sides  

        𝐚𝐧  =  
1

2
 √4R2 − λ²n  ,  as below  

1… For Spaces , the Polygon Side is   λ n(S) = 2 .√R2 − a²n(S) , 

2… For Anti-Spaces , the Polygon Side is  λ n(AS) = 2 .√R2 − a²n(AS) ,     

3… For Sub-Spaces , the Polygon Side is   λ n(SS) = 2 .√R2 − a²n(SS) ,   

4… For Neutral - Spaces , the Polygon Side is λ n(NS) = 0 , while in Material-Geometry   

      becomes from the Centripetal Force  FC = σ = 
m.v³

r
 = J w² r , where the Unity Monad r  

     ≡ monad R = 
σ

J.w²
 = 

𝛔

�̅� 
 = 

Stress 

Angular−momentum̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅ 
 , and Polygon Side  𝛌 𝐧(𝐍𝐒) = 2 √R2 − a²n , 

     All becoming from Pythagorean relation  [ R ] ² = [ an] ² +  [ 
λn

2
 ] ² . 

5a2 .. The General Equations of motion in a Polygon-Vector–Conductor  d = Side 𝛌 𝐧(𝐍𝐒) 

The Displacement at Point x of a Conductor d , is x + dx and Strain will be u + ( 
∂u

∂t 
 ).dx , and 

the Unit Strain is ( 
∂u

∂x 
 ) . From Hook`s law , σ = E u , The ratio of Unit-Stress to Unit-Strain 

is equal to the `modulus of Elasticity E and A = the cross section area of the Conductor , then 

issues  
∂u

∂t 
 = 

Force

A .E 
 = 

F

A .E 
 and by differentiation becomes → A .E.  

𝛛²𝐮

𝛛𝐱² 
 = 

𝛛𝐄

𝛛𝐱 
   …….(1)  

Applying Newton`s law of motion for the element dx and equate the Unbalance-force 
∂P

∂x 
 , to 

the Product of the mass and acceleration of the elements , and then  
∂E

∂x 
 dx = ρ A dx 

∂²u

∂t² 
  ….(2)   

 

Eliminating  
∂u

∂x 
  then we have The Partial differential equation  

∂²u

∂t² 
  = [

E

ρ 
] 

∂²u

∂ x² 
  .…(3)   and    

𝛛²𝐮

𝛛 𝐱² 
 = [ 

𝛒

𝐄 
 ] . 

𝛛²𝐮

𝛛𝐭² 
 ≡ [ 

𝟏

 𝐜² 
 ] . 

𝛛²𝐮

𝛛 𝐱² 
  …(4)  where �̅� =√ 

E

ρ
 , and it IS The velocity of Propagation of 

the Displacement dx , along the Conductor or → is The Stress–Wave ←   

Applying equation (4) in an Conductor [ d ≡ 𝛌 𝐧(𝐍𝐒) ] of Space Anti-Space Equilibrium  

formation of Polygon STPL line  with both ends Free , then the Natural - frequencies must  

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16 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

be zero because charges ⊕ , ⊝ interchange at both ends , A , KA , and issues  
∂u

∂t 
 = 0   

such at  x = 0 ,  and as at , x = d = λ n(NS) = AKA . The Two equations of the below (5)  

correspond to these ,  Stretched ≡ linear , boundary conditions  which are as follows ,   

        { 
∂U

∂x 
 } 𝑥 =0   =  A 

𝟏

 𝐜 
 [C sin wt + D cos wt ]  =  0       

        { 
∂U

∂x 
 } 𝑥 =0   =  

𝐰

 𝐜 
 .[ A cos |

𝐰 .𝐀𝐊𝐀 

 𝐜 
 | - B sin|

𝐰 .𝐀𝐊𝐀 

 𝐜 
 | ].[ C sin wt + D cos wt ]     …..(5)   

        Equation (5)  must be true for any time  t  , Therefore from the First equation  A = 0 .  

        From the Second equation B must be finite in order to have vibration and is satisfied  

        when , sin |
w .  AKA 

 c 
| = 0 ,  or  , | 

w.n .  AKA 

 c 
| = | 

𝐰 𝐧 𝐝 

 𝐜 
| = 

𝟐.𝐧 �̅�

 𝐜 
 =  π , 2π , 3π , ... nπ , .…(6)   

        where , n = The order of the mode and the equation of motion In Conductor becomes   

        d = λ n(NS) =AKA which is an longitudinal-vibration u = 𝐮𝟎 cos [
𝐧 𝛑

𝐝 
] x sin [

𝐧 𝛑 

𝐝 
].c ..(7)  

        a Cosine-Wave having n nodes in Pipe d .  

The equation of motion for an Longitudinal wave in a Conductor  d = λ n(NS) =AKA is   

→  y(x ,t) = N. sin [ kx - wt + φ ] ← …(8)  where , c = the light velocity-vector , N = the 

amplitude , w = the angular velocity-vector , φ = The Phase angle , and  k = 
2π

λ 
 = 

π

  rL 
 = 

Propagating-Energy Constant =Wave-number , λ =The Wave length , �̅� = 
w

  k 
 = 

λ

  T 
 =√ 

T

m
 =√ 

E

ρ
  

= The light-velocity in Conductors .  

The frequency of the Longitudinal wave is   →  f L = [ n ] 
�̅�

  2λ 
 = 0 ,  

1.c 

 2λ
  ,  

𝟐.c 

 2λ
 ,  

𝟑.c 

 2λ
 …. . .  

𝐧.c 

 2λ
   ,  

The equation of motion of a Standing-Wave in Conductor d = λ n(NS) =AKA  ≡ 2 |rA−K𝐴| ≡ 

r L ≡  λ  is as ,  y(x ,t) = 2N sin[k x].cos [(w =2πc/λ) t] ...(9)  where Longitudinal - frequency 

f L = ( n + 
1

  2 
 ) 

�̅�

  2λ 
  . The Amplitudes become zero at y = 0  when  k x = 0 , which implies  

k x = n π , n = 0 , 1 , 2 , 3 , …n  . and Since the sine-function repeats itself after every 2π  

change in angle which is The Wavelength  λ , of the Wave , and from equation  

→ sin[k x] ≡ sin[k x +2nπ] ≡ sink.[x+ 
2n.π 

 k
] ←  then for n =1 ,   

The wavelength λ = [ 
2.1.π 

 k
 ] = 

2π 

 k
 , and is The-Unit-Energy , The Quantum , k = 

𝟐𝛑 

 𝛌
 .....(10)  

 and Wave-equation → sin[k x] ≡ sin[k x +2nπ] ≡ sink.[x+ 
2n.π 

 k
] ≡ sin[

𝟐𝛑 

 𝛌
].[ x + λπ ]  ....(10a)  

Since , k λ = 2π  constant  and λ , is the displacement for n =1 , then implies that k , is Force  

and because Force x Displacement = Work ≡ Energy ≡ motion , therefore  k λ ≡ E ≡ Constant  

 ≡ The Unit-Energy ≡ Energy- Quantum .  

     In case of Energy Equilibrium, then Frequency in Conductor  d = AKA= λ / 2  and ,  

 f L = (n + 
1

  2 
 )

�̅�

  2λ 
 ≡ 

0,5 c 

    2λ
 ,
1,5.c 

      2λ
 , 

2,5.c 

     2λ
 , 

3,5.c 

       2λ
 ,,,,, 

(2n+1) .c 

        2     2λ
 = 

1

  2 
 [

 c 

2λ
] ,

3

  2 
[
 c 

2λ
] ,

5

2
|

 c 

2λ
| ,,,,,, 

2n+1

  2 
|

 c 

2λ
|  

The Wave is a Force  𝐐 AKA⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗  = F = |⊕ => AKA| , an Energy-Vector | ⊕ 𝐐 ⇉ AKA⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗  |≡| ↔ | that  

Propagates from the Place where it was created , The Point A , so when is found an Obstacle 

at  End-Point 𝐊𝐀  then the Particles of the Conductor medium oscillate Perpendicular |↕|| ,  
because  IT IS THE - ONLY - EXIT , to the direction of the Wave - Propagation , and by this 

Way the  motion continues transverse as Longitudinal Wave in Conductor  d = AKA  as , |⇉ ⇈| 

≡ ® , or  in Conductor d = λ n(NS) =AKA , The two Perpendicular Energy-Vectors , |k 1 x k 2| =  

k 1┴2 = k = 
𝟐𝛑 

 𝛌
=

𝟐𝛑𝐟=𝐰 

 𝐜
 and Longitudinal Wave -Energy → c { k 1 x k 2 } = 2π.f , or  |

𝐤 𝟏 𝐱  𝐤 𝟐

𝟐𝝅
|.c  

= 
𝐜 

𝛌
 = f  .  In Figure  -3 - and -9- 

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17 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

The Obstacle at Edge  𝐊𝐀 Point , is The Presentation of the , ⊕ constituent and The Lack  

of ⊝ constituent .  The Transverse - Propagating-Wave , or the moving Energy -Vector  

|⊕ 𝐐 ⇈ AKA⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗ | = |↕| at node KA , and with the Energy-Vector | ⊕ 𝐐 ⇉ AKA⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗ | ≡ |↔| at node A , 

consist The Electromagnetic - Wave in  d = AKA= 2r  Conductor . The Energy in this 

Stationary Wave  of wavelength  λ = 2d  is ,   

                    E = h f L = h 
2n+1

  2 
|

 c 

2λ
| = 

2n+1

  2 
|
 hc 

2λ
| = | 

 3.h.c 

4λ
|          ……… (11)    

and from relation  λ = c T = 
c

  f 
 = 

2π

  k 
 ,  Then  k = 

2π

λ 
 = 

2πf

  c 
 = 

w

  c 
 = |

 v̅ 

  c 
|.|

1

  r 
| = |

 v̅ 

  c 
|.|

2

  λ 
|   , or  the 

Propagating-Transverse-Wave carries the Standing-Wave-Energy-Constant-magnitude   

                   Constant-motion    k  = 
2π

λ 
 = 

2πf

  c 
 = 

w

  c 
 = |

 v̅ 

  c 
|.[ 

2

r[A−KA]
 ]   .…...(12)      

The two Perpendicular Energy-Vectors , |𝐐 ⇉ AKA⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗  = ↔ | and |𝐐 ⇈ AKA⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗  = ↕ | ,in Conductor  

d ,of this moving Energy FORM The Energy-Square , {| ↔ |.| ↕ |≡|𝐐 ⇉ |}.{| 𝐐 ⇈|} ≡ u0 , on 

Conductors AKA . with Conductors - Pivot-axis Propelled on their  Merging -Resultant -axis  

of direction |⇉ ⇈ ≡ ⤱| .   

In case of an closed Conductor above motion with Energy = k = 
2π

λ 
 = 

2πf

  c 
 = 

w

  c 
 , and with 

velocity �̅� = 
w

  k 
 = 

λ

  T 
 =√ 

T

m
 =√ 

E

ρ
  , consists the Stationary–Energy-Storage with fundamental 

frequency  f 1 = (n + 
1

  2 
 ) 

�̅�

  2λ 
 ≡ 

3.�̅�

 4 λ 
≡

3.𝛔 𝚽

 4 λ 
 ….…(13) . 

The Obstacle at  KA Point is the ⊕ constituent which executes  an Coulomb force  

F [+ ↔ +] =  
[⊕↔⊕]

r²
 = 

[σ.σ]

r²
 = |

σ.

r
|
2
=|

e.

r
|
2
= |

2πf

Φ
|
2
= | 

w

Φ
 |

2
. The Energy k at Point KA is the Total 

mass MT of Conductor d = AKA = r = λ n(NS) equal to the Moment of Inertia  JT = 
m.r²

 3 
 ,where  

m is the stiffness per meter of Conductor r . The Impact of this mass at THE end-Point is the 

Energy = J w and Impact → m v = J w r = [
m.r²

 3 
] . wr , or velocity after impact velocity →  

v = [
r³

 3 
].2πf = [

2πf.r³

 3 
] .......(14)    Coulomb force with fundamental frequency becomes 

F [+↔+] = |
2πf.

Φ
|
2
= [ 

2π

 Φ 
|
3.�̅�

 4 λ 
 |] ² = | 

3πv

2λΦ
 |

2
…….(15) 

Placing velocity after Impact (14) in Equation (15) then the concentrated Energy at Point  

KA is  F [+↔+] = {
3π

 2λΦ 
[
2πf.r³

 3 
]}² = | 

π2r4f

λr.Φ
 |

2
=| 

B=(π2r4f)

λr.Φ
 |

2
=| 

�̅�

λr.Φ
 |

2
≡ Angular-momentum ≡  

SPIN  …...(16)  In Short-distance Conductor d = 6,195543.10−7m , the Magnetic-field  

          B̅ = 
m.v

q̅ r
 = 

9.10−31Kg.2,9979.108 𝑚/𝑠 

1,6.10−19C.[6,195543.10−7]
 = 2,718088.1013 Telsa , which is Perpendicular ,   

                                                                normal , to the Conductor`s axis .  ⇉   i.e.  

In a Closed Energy-Conductor 𝐫 [+↔+] , the fundamental frequency 𝐟 𝟏 becomes the Spin.  

The Energy- Square - Prism , |AKA| .{𝐐 ⇉ AKA⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗  }.{𝐐 ⇈ AKA⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗ } = |Qx.Qy|.|AKA|=kx.ky|.|AKA| 

=  |↔|.|↕|.|AKA| …..(17) , where |↔| = |kx| the Conductor`s Axial-energy , |↕| =| ↺ | the 

Conductor`s  Rotation-Energy = SPIN , and |↔|.|↕| the Conductor`s Resultant-energy-Vector 

is an Cruise-missile . When a Conductor  d = AKA = r = λ n(NS) has a Hole at an Point 𝐀𝐄  

such that AAE= 2 r ,{ A -2r-  𝐀E -r- 𝐊A}= d  then The Energy  k at Point  A E is the Total  

mass MT of Conductor AAE = 2 r  equal to the Moment of Inertia  JT = |
m.4r²

 3 
| , where m is  

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18 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

the stiffness per meter of Conductor 2r .     

From equation (15) Coulomb force F [+↔+] =|
2πf.

Φ
|
2
= [

2π

 Φ 
|
3.�̅�

 4 λ 
 |]² =| 

3πv

2λΦ
 |

2

 becomes as 

F[+⇅ ⇵+] ≡ F[+↔+]  , equal and Perpendicular and {𝐐 ⇉ AAE⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗  } = {𝐐 ⇈ AAE⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗ } , |Qx| = |Qy| , |kx| 

= |ky| , |↔| = |↕|  …....(17a) Transverse motion |↕| , Presupposes an |←| Impact of the mass at  

end-Point A E and is the Energy = - J w  and because lack of Obstacle Impact → mv = - Jw² = 

[ 
m.r²

 3 
].w² , or velocity after impact → v =  - [

2πf.r³

 3 
] = - [

 v.r²

 3 
] ..(14a). Placing velocity after 

Impact (14a) in Equation (15a) then the concentrated Energy at Edge Point KA is  

 F[+↔+] = {
3πw

 2λΦ 
[
−2πf.r²

 3 
]}² = | 

𝑤[π2r4f ]

rλΦ
 |

2
= |

w.B=(π2r4f)

r.λΦ
 |

2
= w².| 

�̅�

rλΦ
 |

2
≡ | 

2L= w.�̅�

rλΦ
 |

2
 

≡ The Total Energy 2L to the Twin circles squared , or to Angular- momentum ≡ SPIN  

    squared …….(16)  ⇉  i.e.  

In an Energy – Slit - Conductor 𝐫 +{ 𝐀 −2r−  𝐀E −r− 𝐊A}= 𝐝 + ,  the fundamental frequency  

𝐟 𝟏  becomes the Spin , Or , The carrier of the Total-Energy 2L of the moving - System .  

At AE Point Energy - Square-Prism is → |AAE|.{𝐐 ⇉ AAE⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗  }.{𝐐 ⇈ AAE⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗ } = |Qx.Qy|.|AE KA |  

= |kx.ky|.|AE KA | = ≡ |↔|.|↕|.|AE KA | .........(18) , where |↔| = |kx| the Conductor`s  

Axial-energy , |↕| = |ky| the Conductor`s . Transverse - Energy , |↺| the Conductor`s 

Rotational-Energy = SPIN , where |kx.ky| = |↔|.|↕| ≡ ⤱ = The Dot-Product = Area of 

Vectors , which is a Scalar magnitude     𝐀 𝐱.𝐲 = |𝐤𝐱|.|𝐤𝐲|.𝐜𝐨𝐬 𝛉 , where  θ , is the angle  

between the two vectors , kx , ky and  ,  The Cross-Product =The Resultant-Vector =®=  

�̅� = 𝐤𝐱 x 𝐤𝐲 which is Perpendicular to kx,kyvectors  where , r =√k²x + k²y , x = r.cos θ ,  

y = r.sin θ , θ = tan−1(
y

 x 
) , and   �̅� = 𝐤𝐱 x 𝐤𝐲 = 

𝐰 

𝐜
 = 

𝟐 𝛑 

𝛌
  

The Conductor`s Resultant-Energy-Vector , ® = �̅� , is as an Non-guided Cruise – missile . 

 From Total Energy relation  2L = B w ≡ E K + E U ≡ |kx|+ |ky| is seen that , kx , ky , consist 

the  2-Line , Plane-Launcher of { Energy ≡ motion- missile } into → Two Perpendicular 

and Equal Conductors , with Conductors-Pivot-axis Propelled ON their Merging-Resultant 

axis of the two  directions ⇉ ⇈ ≡ ⤱ .  In One-Conductor , kx= ZA̅̅̅̅   , k y= 1,MM̅̅ ̅̅ ̅̅ ̅̅  , Resultant 

 R̅ = Z1MO̅̅ ̅̅ ̅̅ ̅̅  , while for (2) → In Two-Conductors , kx= ZB̅̅̅̅  , k y= ZA̅̅̅̅  , R̅ = Z ,1_2_3 , MO̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅ ≡ ⤱    

The Total Energy 2L = B w ≡ E K + E U ≡ |kx|x|ky|x|AKA| ≡ |kx|x|ky|x|λ| ≡ An  Propagating-

Wave in λ ,  i.e.  Energy-Square-Prism is a Moving-Energy-Volume and Because from 

Cauchy equations of Stresses in three dimensions , The Energy Stress remains Flat ONLY 

WHEN the Plane - Section becomes a circle , And Because from Mechanics the  Sphere 

occupies the Least - Resistance to the motion , then the  Square - Prism is altered to the 

Equivalent , Energy-Sphere - Cone → ⸿ = k πr ³ ← Fig-9a ,9b , 9c. 

where the Cube [| ↔ |.| ↕ |.|𝐀𝐊𝐀|] = x ³ becomes an Sphere–Cone ≡ 𝐐.𝐀𝐊𝐀
⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗   | ⇉ | ↑↓

 𝛌 | → 

 k π r³ = x ³   .  From the max-sin |
w .AKA 

 c 
| = 1 , of equation (6)  then   

u = [ C sin wt + D cos wt ].sin|.
𝐰 .𝐀𝐊𝐀 

 𝐜 
| ……..…(14a)   

The condition u = y (AKA , t ) = 0 , leads to the equation →  sin |
𝐰 .𝐀𝐊𝐀 

 𝐜 
| = 0  ,  or to   …(14)    

For the Duality-Photons issues   , v̅ . [ fn̅  + fn ] ≡ | 
𝐯 

𝛑².  𝐫⁴𝐧  
|. B̅n  + | c̅ | fn         ..……...(15a) 

Or         v̅. [ fn̅  ≡ (n + 
1

  2 
 ) 

�̅�

  2.|AKA| 
 ] + [f n ≡ n 

�̅�

  2λ 
 ] ≡ → �̅� { |

�̅�

  𝟐.𝛌 
| (n + 

𝟏

  𝟐 
) + 

𝐧

  𝟐𝛌 
 }  ..........(15) 

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19 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

E-Vectors |𝐐 ⇉ AKA⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗  = ↔| x |𝐐 ⇈ AKA⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗  = ↕ |x|AKA| ≡ |Qx.Qy|.|AKA|  ≡  | ↔ |x| ↕ |y| λ | ≡ k π r³.  

From Wave-Energy-constant k = 
2π

λ 
 = 

2πf

  c 
 = 

w

  c 
 = |

 v̅ 

  c 
|.{

 1 

  r 
=

2

r|A−K𝐴|
}so c= 

w

 k 
 = λ f , or |

�̅�

  𝟐.|𝐀𝐊𝐀| 
|≡ f   

i.e. Frequency f AKA
of Pipe |AKA| is the Stationary-Photon Energy-Storage fn̅  ≡ |

�̅�

  𝟐.|𝐀𝐊𝐀| 
| ≡ 

|
�̅�

  𝛌 
| ...(16) and Photon v̅. [ fn̅  + fn ] ≡ �̅�. { |

�̅�

  𝛌 
| + 𝐟𝐧 } i.e. , as Particle ≡ v̅. |

�̅�

  𝛌 
| ≡ E U ≡ Potential 

Energy , and as Wave ≡ v̅. fn ≡ E K ≡ Kinetic Energy . Since Energy- Constant-magnitude , k , 

denotes the Total motion then needs a Scalar -Magnitude for measurements and a Vector-

Magnitude for Directions .  

In Conductor D = |AKA| ,| D | ≡ The Scalar Magnitude between Points , which gives also the 

direction of motion with Points , A , KA , and  AKA
⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗   vector the Direction which defines the 

Vector AKA
⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗   . The Total Energy k = |

 v̅ 

  c 
|.[

2

r[A−KA]
] of Photon-wave is Split as, E U+ E K= k ≡ 

Potential + Kinetic Energy  where  

E U ≡ v̅. |
�̅�

  𝛌 
| ≡ Particle ≡ �̅� { |

�̅�

  𝟐.𝛌 
| (n + 

𝟏

  𝟐 
) } ≡ | 

𝐯 

𝛑².  𝐫⁴𝐧  
|. B̅n  = | 

𝐯 

𝛑².  𝐫⁴𝐧  
| r².q.B̅M ≡ | 

𝐪.𝐯 

𝛑².  𝐫⁴𝐧  
| x B̅M  

is the Stationary-Storage ≡ Particle ≡ Magnetic-field with velocity , v , in cave  λ = 2r = 2π / k  

and   E K ≡ v̅.fn ≡ Wave ≡ Kinetic Energy = 
2π

λ 
 = 

q

k.A 
 = 

q

k.πr ² 
 = 

σ.Φ

k.3rB̅M  
 = {

σ.Φ

  k.3r 
}

𝟏

   B̅M  
=

𝐜/𝐄

   B̅M  
 , and  

�̅�𝐄 ≡ c�̅�𝐌   , and the moving Electromagnetic-wave is ,  

E̅E = |E̅0|.sine [kz - wt] , B̅M = |B̅0|.sine [kz - wt] , k = 
2π

λ 
 , 

      Motion is kept in Caves as Electric , Magnetic fields and as frequencies and conserved 

in them when the Space-Points become Energy-Conductors . The in caves  Energy-Import  

is shown in Figures . 

      Examples  :         

1..  In an Conductor d =AKA= 2r , with ⊕ obstacle at KA Point occupies zero velocity and  

      ⊕ Charge is accelerated . The Initial light-velocity is accelerated as v² = v̅o²+2a.r , or  

       a = 
−v̅o²

 2.r 
 = 

[2,9979.108]²

2.r
 = 

8,9874044.1016

2.r
 m/s² . For Conductors , r =10−16,100,1016 then ,  

     a1 = 
−v̅o²

 2.r 
 = 

8,9874.1016

2.10−16  = 4,4937.1032 m

 s² 
 , a2 = 

−v̅o²

 2.r 
 = 

8,9874044.1016

2.100  = 4,4937022.1016 m/s²,   

     a3 = 
−v̅o²

 2.r 
 = 

8,9874044.1016

2.1016  = 4,4937022.100 m/s².       

Force on Charge becomes from the Electric field as  F̅K = m.a̅x= q.E̅F =+e. E̅F and E̅F= 
m.a

q = e 
 , 

or      E̅F =  
m.a

e 
 = 

m

e 
 [a] = 

9.10−31

1,6022.10−19 [4,4937022.1032] = 25,242366. 1020 N

C 
  

          E̅F =  
m.a

e 
 = 

m

e 
 [a] = 

9.10−31

1,6022.10−19
 [4,4937022.1016] = 25,242366. 10 4

 N

 C 
  

          E̅F = 
m.a

e 
  = 

m

e 
 [a] = 

9.10−31

1,6022.10−19 [4,4937022.100] = 25,242366. 10−12 N

C 
  

i.e. The ⊕ Charge is accelerated Opposite to initial direction of ⊝ Charge in an  

      Electric-field E̅F . This Property of Acceleration , creates the Magnetic-Fields in  

      Electric Conductors as Atoms are .  

2.. Uniform circular motion of electron in Caves constitutes a current  I = 
e

T 
 = e.f , and T= 

2πr

c 
 ,  

   I = 
e.c

2πr 
 = 

1,6022.10−19.2,9979108.

2π.r
 = 7 ,644811.10−12. [

1

r 
] , and for  r =𝟏𝟎−𝟏𝟔, 𝟏𝟎𝟎, 𝟏𝟎𝟏𝟔 m then   

   I = 
e.c

2πr 
 =7 ,644811.10−12. [

1

r =10−16,
] = 7 ,644811.104 -  7 ,644811.10−12 – and  

                                                                                             7 ,644811.10−28 Ampere.  

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20 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

3.. The Electric-Potential V = 
𝐪

𝐫 
 = 8,99.109 

Nm²

C² 
[
1,602.10−19.

r =  10−16  
]=14,4038.106 =1,44038.107Volt  

     V = 
𝐪

𝐫 
 = 8,99.109 

Nm²

C² 
 [

1,6022.10−19.

r =  100,10 16  
] = 14 ,403778.10−10 V , 14,403778.10−26 V , 

4.. Electric-Field �̅�𝐅 = 
𝚫𝐕

𝐝 
 = [

14,403778.106.

r =10−16,100,,10 16 
] =14,403778.1022, 14,403778.10−10 V 

5.. Force on electron is  F = q .�̅�𝐅 =1,6022.10−19.{14 ,403778.1022}= 23,077733.103 N and   

     F = q .�̅�𝐅 =1,6022.10−19.{14 ,403778.10 6−16}=23,07.10−13 N,23 ,077733.10−35 N , and  

6.. The Produced Work is W = F.ds = F r = 23 ,077733.103.{10−16 } = 23 ,077733.10−13 J .      

    W = F.ds = F r = 23 ,077733.103.{100,1016 } = 23 ,077733.103, 23 ,077733.1019 J .  𝑒 0 

7.. Intensity I E−r is , 𝐈 𝐄−𝐫= 
c.E²

2 
 = [

2,998.108.1,602210−19(14 ,4038.1022)²

2
]=498,26077.1033W/m2  

      𝐈 𝐄−𝟐= 
c.E²

2 
 = 498 ,261.101W= 4,9826077.103W and 𝐈 𝐄−𝟑= 

c.E²

2 
 = 4,9826077.10−29 W/m² 

8.. The Power 𝐏 𝐄−𝐫= 
E²

Z=πr² 
 = 

(14,403778.1022)²

π.(10−16)² 
 = 6,60394.1077W , 6,60394.1057, 6,604.1013W 

9.. Two-Capacitors Conductor of  area A and Charge q  Charge density is on Plates σ = 
q

  A 
  

     and Electric field  E = 
σ

  𝑒 0 
 = 

q

  A 𝑒 0 
  and from Potential difference V= E d then  E =

V

  𝑒 0 
  and  

     
V

  d 
 = 

q

  A 𝑒 0 
 or  V = q.[

d

  A .e 0.
] = 

q

  A 
 = E d . From above → A = 

q.d

  V 
 = [

1,602210−19(10−16)

14,403778.(r=106)
] = m2  

     1,11235.10−42 ,1,11235.10−26,1,11235.10−10 m2 ,Stress σ = 
q

  A 
 = 1,44038.1023 ,7 ,−9 T

m² 
 

Remarks :   1.. The Stress-Strain Relationship , from Static theory of Elasticity solves  

                    the Problem of static Indeterminacy. That is , the Stress Parameters  σ x , σ y ,   
are bound in , (1) By the Stereo static conditions (2) and by the Constraint that the Strain 

accompanying the Stress  s x , s y ,  remains Geometrically Continuous . This Property of  

the Stresses allows .the Transportation of the Informations on Knots to the Polygon-Sides.  

2.. When a Body contains Potential Energy , 

During any Unloading it gives off  Mechanical - Work , since the Points  

of application of the GRADUALLY - withdrawn Loads are Displaced.      

If the Unloading is ABRUPT , then  Kinetic Energy is converted into Potential and after is  

Kinetic , converted back into Kinetic and so on . That is, the body Performs an Oscillating  

motion until the Mechanical Energy is extinguished due to a State of Equilibrium or Alters . 

3.. The Action of the Complex–Vectors create the Waves of Motion ≡ Energy Waves ,  

which are closed curves and Transported . The Pattern of Disturbances with the Informations , 

Propagates from the One-Edge-Point to the other Edge-Point of Conductors , OR  is on the  

[Sub-Units] . Action of Vectors exist on  Polygon–Conductor`s  d = Side λ n(NS) of Polygons.    

 4.. Action of a  SIGNAL which  Strikes the  Tetrahedron–Cube-Spheres  Mechanism . 

Unloading happens on the  three Tetrahedron - Sides which withdrawn Loads are Displaced     On the 

Anti-Parallel-Strand . If the Unloading is ABRUPT, then  Kinetic Energy of 1-Strand  is converted in 

the 2-Strand as Potential and so on . That is , CUBES Perform an Oscillating motion until the 

Mechanical Energy is extinguished to their Vertices , which are the stores of Information . 

5.. The Harmonic  displacement of  Support-Points on a Regular Polygon vertices .  

The Projections of  Heights  y n  of a Regular Polygon  are as  2.y n=  n R , which allows to the 

Vector- Force Polygon to follow the Space-Vector-Wave = 2R.𝑒𝑖.𝑛𝑤𝑡 = 2R.[cos w t + i .sin wt] . 

i.e. Complex frequency Response , Happens on the Regular Polygon Vertices only .  

6a.. THE  ORIGINATION  OF  PRIMARY  MOTION  IN   E - SPACES  .      

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21 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

    The Stress - State (σ , τ)  in Spaces is defined from the Cauchy Stress Tensor where ,   

     Exists at any Point inside a material in the deformed State Placement or Configuration.  

    The second order Tensor consists of nine components and relates a unit length direction  

    vector  𝐧 to the Traction-Vector 𝐓𝐧 across an Imaginary Surface (in M-Geometry is Φ) 

    Perpendicular to n⃡ , Tn⃖  = n⃡ σ , or  Tj
n⃖  = ∑σ i j n i , obeying to the Tensor transformation  

    law for Stress Analysis . A contact Force ∆F exerted at Point P of element area  ∆A , the  

    ratio  ∆F/∆A becomes dF/dA and the couple stress vector ∆M vanishes and prior tensor  

    becomes  Tj
n⃖  = lim

∆S=0
∆Fi/∆S = 

dFi

𝑑𝑆
 . Equation  means that the Stress-Tensor  depends on  

   the Position (location) in  Body and the orientation of the Plane on which it is acting .  

         From Spaces (4) in Material-Geometry of PNS -Space (Fig-1-3) the eternal Rotation  

         of the two  Opposite [⊕↻↺⊝]  constitutes , and because of their in between Stress σ   

         which is equal to the Centripetal-Force then issues  FC = σ = 
𝐦.𝐯³

𝐫
 = J w² r = �̅� r ,where  

         the monad r ≡ monad R = 
σ

J.w²
 = 

𝛔

�̅� 
    i.e.  The Stress σ , which is created between the  

         Opposite [⊕↔⊝] , and  through the only Possible Rotational-motion , Originates the  

         Angular-velocity �̆� = 
𝛔.𝚽

𝐫 
 = 2πr.f  and the Angular Momentum �̅� = 

𝛔.

𝐫 
 = 

𝛔.

𝐑 
 , which when  

         Placed on AB  Diameter = 2R = The Monad  consist the Neutral – Spaces - Energy.  

         The Planck`s cave , 10−35 m , is The Safety-Valve ≡ The Critical State for the Stress  

         Ellipsoids , B̅ w̅, Vectors in order that this Total-Energy to Superflow and be Still into  

         Vacuum ≡ [10−62-10−35m] . This Vacuum between the |Gravity cave - Planck`s cave|  

         CONSISTS  The  BLACK - HOLES - CHAOS , as the Recycling–Energy into which  

                 → The { Energy – Space - Monad  |�̅�| ≡ |AB| } , Decomposes ← {Fig-14}  

         The Rolling of Polhode Unit-Space into the Herpolhode  Space-monad Cone.  

Figure -4- The Central Axial-Ellipsoid of ⊕ constituent Rotating through constant Point O .      

In (1-2) The ⊕ Material Point  OK , {⊕ ≡ O,[OK = R] ≡ The Space}, continually Rotates  

         around The ⊝ Material Point OK, { ⊝ ≡ O , [OK] ≡ The Anti-Space }, on 2R circle .  

Their Common circle center , forms the material angle φ = φP.t = (
vP 

√c²−r² 
).t , which then  

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22 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

 CREATES at any contact Point P  the Centripetal Force  𝐅𝐂 = 
mv²

r
 = 

𝜋r²

2r
[w². r²] = 

𝝅.𝐫³

𝟐
 [w ²].     

The vector �̆� of Angular velocity w , formulates the Polhode Cone of Base-radius a , and of  

OP = S  side forming the 𝐰-angle with z axis , while the vector �̆� of Angular Momentum B ,  

formulates the Herpolhode Cone of Base-radius  r , of  OP = S side and 𝛉-angle with z axis 

In (3) , is the MPMP Space where Time is not existing  t = 0 , and the same for motion also .  

     In PNS-Space the 3-dimension motion of the Primary constituents [⊕↻↺⊝] the time is  

as Period T , and Momentum is the Angular-velocity �̆� and Angular Momentum �̅� , where   

the Momentum �̅� = r m v = m �̆� r² = ± [ 
𝛑.𝐫𝟐 

𝟐
].�̅� x �̅�  and ± [ 

𝛑.𝐫𝟐 

𝟐
] ≡ the Hemi - circle area .  

The Polhode is of radius a , and rotates with an angular velocity w̆ = 2π.fP in the Cone πa².s .  

The Herpolhode is of radius r , and is the Stationary Cone πr².s . with an angular Momentum  

B̆ = r m v = r m (w r) = m �̆�  r²  . The Polhode Cone is rolling on OP and contact common  

line , into the Herpolhode Cone without friction .      i.e.  

    The motion in PNS-Space exists as the Rotation of Space Point P (+) on [ O ,OK ] circle  

    Anti-Point P ` (-) on [ O ,OK ] of Anti-circle and defines The Angular-momentum �̅� , so   

     The Position of Spaces Points P (+) and Points  P (-) and Momentum are simultaneously  

     Determined and measured , consisting  a direct violation of the Uncertainty Principle .   

The Primary - Rigid -Body Analysis  :  

a.. The Position of the Herpolhode Cone is , Fig-4.  

     x = a.sin θ. coswt  ,  y = a.sin θ. sinwt  ,  z =  a - a.cos θ = a.[ 1 - cos θ ] where exists ,  

     a = The Polhode Cone Base-radius , r = The Herpolhode Cone Base-radius [ x , y . z ] =  

     Coordinate System such that  z-axis ⊥ [KOK] line , and angle - 𝛉 between OP , Oz Axis .    

b.. The Energies of the  Polhode - Herpolhode Cones are from Lagrange`s Principle where  

     for any Particle , The Kinetic 𝐄 𝐊 and Potential 𝐄 𝐔 Energy are measured as below , 

𝐄 𝐊 =  
1

2
 m.[ ẋ ² + ẏ ² + ż ² ] = 

1

2
 m a².[ θ̇ ² + w².sin ² θ ] , and  𝐄 𝐔 =  m g z = - m g a.cos θ  

The Lagrangian  𝐋 𝐊𝐔 = m.a².[ 
θ̇ ² 

2
 -  V EFFECTIVE ] , where the Effective Potential  V EFFE is   

V EFFE = -  
1

𝑚,𝑎²
 [ m g a.cos θ + 

1

2
 m a².w².sin ² θ ] = - [ 

g .cosθ 

𝑎
 + 

w².sin ²θ 

𝑎
 ]  …..(e)       

The equation of motion for the Bead becomes from Lagrangian  which is  �̈� = [ 
∂V EFFE

∂θ
 ] ..(b) 

Since θ is constant then issues θ̇ = θ ̈ = 0 , and for the Bead-Herpolhode motion 
∂V EFF

∂θ
= 0 ..(c) 

Equation (c) is Stationary at Positions which satisfy relation  g.𝐬𝐢𝐧𝛉 = a.w².𝐬𝐢𝐧𝛉.𝐜𝐨𝐬 𝛉..(c1) 

1…The Solutions of (c1) are at Position  sin θ = 0   where  issues            𝛉 =  0    

2…The Solutions of (c1) are at Position  sin θ.cos θ = sin 2θ = 0 and is  𝛉 =  π  & 2𝛉 = 2π   

3…The Solutions of (c1) are at Position  cos θ = 
g

a,w ²
  and for θ = 0 then   w ²   =   

𝐠

𝐚
     

Remarks :    

1… Solution (1) for θ = 0  exists always and from Figure-4-(2) the velocity vector �̆�  is  

        applied at the center of mass  𝐊 𝟎 , Anti-clockwise  Spinning .    Fig-4-(3)     

2… Solution (2) for θ = π  exists always and from Figure-4-(2) the velocity vector �̆�  is  

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23 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

        applied at the center of mass  𝐊 𝟎 , Clockwise  Spinning .           Fig-4-(3)          

3… Solution (3) where since θ = 0  exist the Prior and from Figure-4-(2)  velocity vector 

       �̆�  is applied at the center of mass  𝐊 𝟎 , and the  ± Spinning is very fast from the center  

      and is such that  w ²  ≥ 0 , and happening  when { from relation   
g

a
 } the radius a   0 .     

4…The Solution  w ² ≥ 
𝐠

𝐚
  , Determines the Stability of the Polhode System .    

      The Solution  w ² <  
𝐠

𝐚
  and θ = 0 , Determines Stability at Point O Position and−V EFFE.    

      The Solution  w ² <  
𝐠

𝐚
  and θ = π  , Determines Stability at Point O Position and+V EFFE.    

      For Solution  w ² >  
𝐠

𝐚
  and θ = 0  , The Position is Unstable at Point O with  −V EFFE.    

      For Solution  w ² >  
𝐠

𝐚
  and θ = π  , The Position is Unstable at Point O with +V EFFE.     

                                                              Meaning the Black – Holes Origination .  

      From Solutions  w ² =  
𝐠

𝐚
  , the  θ = 0 = π =2π Positions are Unstable and below Point  

      O with+V EFFE. meaning an evolving and Operational Black-Hole Stable Origination.  

5…All above Stable Solutions result to the determination of the two Vector - magnitudes  

      that of Angular-velocity �̆�  and that of Angular Momentum �̅� , differently Black-Hole.  

     -----------------------------------------------------------------------------------------------------------  

     Both magnitudes define the Unit-Energy Vectors  → { Unit-E Vector R = 
σ

J.w²
 = 

𝛔

�̅� 
 } ←  

     When the Unit-E.Vector R is Placed ON [AB≡2R S.Diameter of Spaces-Neutral-circle]  

    Then the Energy-Monad  |�̅�| exists on  Space-Monad |AB| ≡ |�̅�| as {E+S -Monad |�̅�|},  

                    i.e. IS THE { Energy - Space - Monad  |�̅�|  } ,       with   the  magnitudes ,  

      Spaces Sides  𝛌𝐧= 2,√R2 − a²n ,   &  , Quantum Critical-Side  𝐚𝐧 = 
1

2
 √4R2 − λ²n ,   

     ----------------------------------------------------------------------------------------------------------- 

The Quantization of Energy in Spaces , happens when follow the Archimedes formula for 

Doubling the Vertices n , 𝛌𝟐𝐧=√2R2 − R√4R2 − λ²n  & Critical-Sides  𝐚𝟐𝐧= 
1

2
 √4R2 − λ²2n  

where then Energy is divided and spread on the double number of the Polygon Sides .   

Monad R = 
σ

J.w²
 = 

𝛔

�̅� 
  remains the same , while Spaces Sides change as above  𝛌𝟐𝐧 , 𝐚𝟐𝐧 .    

7a.. THE    MECHANISMS  &  CHARGES ,  FOR  DUAL - ORIGINATIONS ,   

       THE NATURAL - Spaces  of AB  Diameter is the { AB̅̅ ̅̅   Unit Complex Vector } .             

1… Spaces  ≡ The Infinite (+) Circumscribed-Regular-Polygons in AB̅̅ ̅̅  . [Fig-1,3].  

2…Anti - Spaces  ≡ The Infinite (-) Circumscribed-Regular-Polygons in AB̅̅ ̅̅  .[Fig-1,3]. 

3…Sub. - Spaces  ≡ The Infinite (+) Inscribed-Regular-Polygons on Diameter AB̅̅ ̅̅ .[F-1,3]. 

4…Neutral-Spaces  ≡ The Infinite Circles on Diameter AB̅̅ ̅̅  .(The Sphere on AB), [Fig-1,3].   

5…{MFMF} ≡ The Gravity cave = 10−62 m .  

6…{ PNS }   ≡ The Planck`s cave Length = 10−35 m .  

7…Vacuum ≡ [ 10−62 -- 10−35m ] = The  in-between distance         

      THE Origination-Mechanisms in Spaces & the Origin of Charges.   

8…Action-Spaces  ≡ The Infinite Quaternion - monads →   �̅� ≡ ( s + v̅.i ) ≡  𝐀𝐁̅̅ ̅̅   ≡  

      ≡  √s2 + [ v̅. i ]² ]  ,  or   �̅� ≡ x + i . y ≡  𝐀𝐁̅̅ ̅̅   ≡  moduli  , r ,  is their magnitude   

      [ r = | r | = √ x2 + y2 ]  , on Unit-Diameter AB̅̅ ̅̅  . The [QMAS] . For Quaternion v = s  

      𝐳  * 𝐳  = (s + v̅.i )² = s² +[v̅]² +2.sv̅.i = s² – v̅ ² ± 2.s v̅ = |s|² -|s̅|² ± 2.|s|.|s̅| , for |v̅| = s  .     

8a.. THE  Material - Geometry ,  E-Geometry , Physics AND  Chemistry .    

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

8..[a].. The { STPL } Mechanisms in Spaces , from Charges in  Under-Planck`s-Length  ≡  

      The Six Triple Points Line Mechanism ≡  The Complex Vector-Spaces  Rotor ,  

      It is a Mechanism on where the Charges of Opposites , [⊕↔⊝] , React as Centrifugal  

      force FC which in turn changes → (Action-Reaction ≡ + Spin – Anti Spin) ←of  [MFMF]  

      Space To Rotational motion Angular-velocity = �̅�  & Angular-Momentum = �̅� . [Fig-6].        

8..[b].. The {TVPM} Mechanisms , from Charges on Two-Perpendicular-Vectors-Edges ≡      

      Markos  Two - Vectors Three - Poles Mechanism .  [Fig-8a , 8b].                      

      In Fig-8|4| , Vector  CP̅̅̅̅  ⏊ CA̅̅̅̅  Vector , which changes the Energy ≡ The Stress  σ  of   

      The  | CP̅̅̅̅  x CA̅̅̅̅  |  Square  , to 2 - Halve  ±  Squares  on Vectors-axis for Equilibrium .  

8..[c].. The { TCIC } Mechanisms , from Charges In Three-Vectors-Conductors-Edges ≡  

      Markos  Tetrahedron Cube Inscribed-Circumscribed Circles Mechanism . [Fig-27-29]. 

      In Fig-6 , The Tetrahedron  Conductors -Vectors  DA̅̅ ̅̅  ⏊ DB̅̅ ̅̅  ⏊ DC̅̅ ̅̅   ,  CARRY  Energy as  

      Electromagnetic-Fields (Forces-Frequencies-Stresses-any motion) TO Inscribed Sphere  

      (Nucleus of Atoms), TO  Cube Vertices (Electrons-Position) ,TO  Circumscribed Sphere  

      (The Electrons Orbits) for Equilibrium and for transferring Information  and Signals . 

8..[d].. The {TOBH} Mechanisms , from Charges In Two-Orbits-Pins & Drain.            

      Markos Atoms Bonding  Bracket - Hook Mechanism .      [Fig-2].         

      In Fig-9 , The ⊝ - Electron  Precesses due to the Gravity and Produces Work which is  

      stored  in a second Orbit . This 2-Orbit  equilibrium exists from the Existing ⊝ -Electron  

      ≡ DRAIN  and from the New  ⊕ -Nucleus ≡ The PIN . The Second -Orbit  called as the  

      Bracket – Hook -Mechanism , with which Atoms and Compounds are Bonded .[99-104]         

     The { LNCS } Mechanisms , from Spaces - Action  ON Quaternion - monads 𝐀𝐁̅̅ ̅̅   is the  

     Lagrange`s  Non Conservative  Systems for generalized coordinates , where the System  

     is subjected to forces that do not have Potential or ,  d (T + U) ≡ δW𝐍𝐏𝐅 = 0 , as  exists in  

     the  Gravitational  Force G  and from which are created  → The Elementary Particles   

     using the STPL – Mechanism , and all Universe using the ISTCCS  – Mechanism ← and   

    The DUAL → The Black - Holes ← as equation δW𝐍𝐏𝐅 =  ∑ Qi. δqiN
i=1  , [Fig-3, 21 , 22]. 

8..[e].. MATERIAL-GEOMETRY  &  E-GEOMETRY IN PHYSICS and  CHEMISTRY               

 

Figure – 5 - : The Relation between The [+] Spaces , [-] Anti-Spaces , [+ -] Sub-Spaces  

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

               of Euclidean & Material-Geometry in a circle (R,OA) of Three-Dimensions.    

  In (1) , The Euclidean Geometry , E-G , is defined upon the Number of Points  

               which can define the  Specific Space  i.e.     

   The → One-Point in E-G  is defining One-Material-Point-Space , the M-P-S .  

   The → Two-Points  are defining the Line-Segment-Space , the   Line-M-P-S . 

   The → Three-Points  are defining the Plane-Triangle-Space , the Plane-M-P-S .. 

   The → Four-Points  are defining the Volume Tetrahedron-Space , the Volume-M-P-S . 

   The → Five-Points are defining the Volume Regular Pentahedron-Space the SV-M-P-S. 

      and so on , representing the Steady-Stable-Regular Geometrical-Formations. 

     The corresponding to the  Material-Geometry-Units  are for :   

1.. One-Point → Two-Units , [⊕],[⊝] with Dimension as , the Material-Vector [⊕→ ⊝]    

2.. Two-Points  → Four-Units , [⊕],[⊝] with  One Dimension as , the Material-Line    

3.. Three-Points → Six-Units ,   [⊕],[⊝] with Two Dimension as , the Material-Plane   

4.. Four-Points → Eight-Units , [⊕],[⊝] with Three Dimension as the Material-Volume  

       Keeping the Property of Edge-Points to be the Vector ⊕ → ⊝ then Bond is the  

        Potential to the Unique-Steady-Stable-Regular Material-Geometry-Formations.   

In (2-3-4-5). All Units in Vectors follow Quaternion  q = [s+v̅.i] = AB̅̅ ̅̅  Properties i.e.  

            [⊕] → the Positive constituent of Quaternion at , Point  A .  

            [⊝] → the Negative constituent of Quaternion at , Point B .  

                        Pythagorean relation  [ R ] ² = [ an] ² +  [ 
λn

2
 ] ² . 

In Euclidean-Geometry E-vector AB̅̅ ̅̅  carries Point A to Point B as , Vector A → B  

In Material-Geometry M-vector AB̅̅ ̅̅  carries Energy , ⊕ , from Point A to ⊝ ,  

Energy of Point B  as , ⊕ moves to ⊝ , which is as The Periodic - Pattern .  

Velocity �̅� = The rate of change  ( m / s ) in AB , Therefore Units are Formatted 

according to the Steady-Material-Geometry-Formations which are  : 

The Line-Vector in cave , r ,which is the Simplest with Double number of 4-Units     

The Plane-Regular-Triangle in Orbits , is the most Stable Shape of 6-Plane-Units  

The Volume-Regular-Tetrahedron in Space is the most Stable Shape of 8-Volume 

Units , the Cube , which are the Crystals . The Regular n-Hedron are for all others .  

This is the Why The Glue-Bond , Bond is the Potential , between the 6-Units formulates 

the Regular-Hexagon as the First Steady - Plane - Formulation in nature as in Fig-18-    

Remark :     

The Constraint , that Strain accompanying the Stresses s x , s y  remains Geometrically  

Continuous is , because  the Material Point is consisted of the two Units  ⊕  ,  ⊝ .only  

 

 

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8..[a].. The { STPL } Physical Mechanisms : The Six Triple Points Line Mechanism .  

 

Figure -6- : The  Physical Three – Phase - Mechanism , Producing  The Fundamental   

       Particles and the Primary Forces IN Absolute System  A ≡ R . γ = R. 𝐬𝐞𝐜𝛗. [97]          

In –Fig. ABC is any Right-angled Triangle at , A = (The-Space) , KAKBKC = Triangle is the  

(Anti-Space) ,, AEBECE = Triangle is the (Sub-Space) respectively.The Instaneous Pole P of  

Rotation is off the Circle of diameter |BC| . The Poles of Rotation lie on{DA- PA} Reference  

System .The Reference System {𝐃𝐀- 𝐏𝐀}≡ [R] (x' , y', z', t') moves with velocity �̅�, Parallel  

to , x - x', Axis with respect to the Fixed  and Absolute System {𝐃𝐀- O} ≡ [S]-(x , y , z , t ) .   

The Geometrical expression of Lorentz  factor γ = 
𝒄

𝒗
 , is the   𝐬𝐞𝐜𝛗 = γ = O𝐃𝐀 : A𝐃𝐀 =  ±  

1 / [ √1– (v/c) ² ] = c / [√c² – v²] , which is the Conchoidal of Nicomedes {s = a + b. secφ}  

         and which acquires the material Angle   ,  φ  =  
𝐯

√c²−r² 
   ,   i.e. issues  |A| ≡ |R| . γ   

[a]-1…The [STPL] line is an Extreme - Spaces–Physical -Originating-Wave  Pattern .  

Extreme-Spaces (are the Extreme Space-Triangles ABC≡ ⊕) meet Anti-Spaces (Extreme 

Anti-Space-Triangles , KAKB KC≡ ⊝ ) through The Only-Gateway which is the Circularly 

Charged + , 0 , - , or [ ⊕    ⊝ ],[ ⊝    ⊕ ],[ ⊕  ⊝   ] Formulation which is a Physical 

Geometrical formation - Mechanism  called The [STPL] line . Figures-[ 6 ,7 ]                                 

          → The [STPL] - line is a Physical – Mechanism as  , In-circle  Triangle   

          Ex-circle    Ex - Triangle consisted from  The Three Spaces , On which the  

          Three Breakages [ s² = ⊕  ,  2s ² =    , - s ² = ⊝ ]  are Circularly- Charged  

          On the Three – Extreme - Triangles {A B C} , {KA KB KC} , {AE  BE  CE} ←     

 Producing The Energy-Quantities ± 𝐐𝐩−𝐩 . This Circular-Charge from Breakages  

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

On The-Three -Triangles is the THRUST upon The Energy-Quantity Produced ,  

for Each needed Circular Charge , To  Shake Off  Quantity 𝐐𝐩−𝐩 . The  3-Circular  

Charges correspond to the 3-Phase Rotors Produce the 3-Phase Physical-Current ,   

        Since Common Circle exists on their Common - Sphere , THEN the Infinite  

        Straight- lines ,  Launch The  E - Quantity 𝐐 𝐩−𝐩  OFF the  Fundamental  

        Particles to all Universe and  INTO  The Planck`s Confinement Only .   

                                                           i.e. 

The Physical-Three-Phase- STPL Mechanism is the only Absolute-System [A] On which  

circularly exist the Relative-System [R] ≡ [ ⊕    ⊝ ] ↻ [ ⊝    ⊕ ] ↻ [ ⊕  ⊝   ] of  

The three constituents [ ⊕    ⊝ ] , which Produces The Fundamental Particles and The  

Existing  Objectivity as  [A] ≡ [R].γ  , where  γ = sec φ = [
𝐎DA

𝐀DA
] = ± [

𝟏

√1−(v/c)² 
] = [

𝐜

√c²−v² 
]  

The material Angle  φ = 
𝐯

√c²−r² 
  ,  and  {A ≡ DA- O}≡{R≡ DA-PA}. γ  , or   |A| ≡ |R| . γ   

        The Euclidean Geometry is the  SPRING  , for the Geometrical  Relative -Velocities .  

When the Points [ A , B , C ] , [𝐀𝐄, 𝐁𝐄, 𝐂𝐄] , [ 𝐊𝐀, 𝐊𝐁 , 𝐊𝐂 ] are Applied on the three lines 

(𝐊𝐀𝐊𝐁  , 𝐊𝐁 𝐊𝐂 ,𝐊𝐂𝐊𝐀) , then the  SIX  Pairs of the corresponding lines , extended are 

concurrent at Points  PA , PB , PC  for the Triple Pairs of lines ( The Pascal`s  Perspectivity of 

Points in Euclidean Geometry ) , [ A𝐀𝐄, 𝐁𝐂𝐄, 𝐂𝐁𝐄 ] , [B𝐁𝐄, 𝐂𝐀𝐄, 𝐀𝐂𝐄] , [C𝐂𝐄, 𝐀𝐁𝐄, 𝐁𝐀𝐄] and 

at Points DA , DB , DC  for the  Triple Pairs of Lines [𝐊𝐁 𝐊𝐂 , BC , 𝐁𝐄𝐂𝐄] , [𝐊𝐀𝐊𝐂 ,AC ,𝐀𝐄𝐂𝐄]  

and  [𝐊𝐀𝐊𝐁 , AB , 𝐀𝐄𝐁𝐄] , ( Desargues`s  Perspectivity of Points  in Euclidean Geometry ) and 

all the  18 common Points  lie on a Straight line The   STPL Mechanism     

      This Mechanism  Stabilizes the Nucleus Forces  for the{ ⊕ - Space [ A B C] }  and for  

      the {⊝ - Anti-Space [ KA  KB  KC ]} and this succeeded by The Pascal`s –launched caves   

      r  through the STPL  Circuit  of the Ptolemy`s  and  the Ceba`s Geometry theorem for  

      The Complex Vector - Forces which are ,  Circularly and  Diagonally Equilibrium .i.e.     

     →  STPL is The In-Sphere , Tetrahedron-Cube , Out-Sphere  Physical Mechanism ←   

     For its  27-Conductors ≡ Electric - Magnetic Fields , Space-Energy CPT is invariant .  

8..[a]-2…The Explanation of  The  Absolute and Relative Motion. . Fig – 6    

Because Properties In and On [STPL] line , are relative to the only one Equilibrium and also  

       Absolute System  ± Λ = r.mv̅ = r.m.w̅.r = mr².w̅ , so exists that what is called Relativity.   

       Absolute System let it be the  [A] ≡ {DA- O} ≡ The STPL mechanism , and as   

       Relative System  ( Reference , Affine ) [R]  ≡ {DA- O}  

The Absolute motion happens on [A] ≡ {DA- O} and on [R] ≡{DA-PA} of  the two Systems . 

It was shown , that in {DA- O}, (x ,y ,z , t ) , System �̅� , �̅� , vectors are isochrones i.e. Period  

T = L / V = 2πR/V = 2π / [c/𝑟𝑐] = 2π/[v/𝑟𝑐] → c/rc = v/rv → c.rv= v. rc , where rv , rc are the 

radius of their intrinsic rolling circles . This relation is Geometrically expressed as ,   

         𝐬𝐞𝐜𝛗 =  O DA  :  A DA = γ =  
𝒄

𝒗
 =  ±  1 / [ √1–(v/c) ²]  = c / [√ c² – v²] ,  and it is a  

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

         Geometrical Cycloid Property equal to Lorentz`s  , γ , factor . The Newton`s laws  

         are true into the Reference System  [R] ≡ {DA- PA}  as follows Proof ,       

         Considering { DA- O},(x ,y ,z , t ) , as the Fixed frame [A]  of the coordinate System  

         in the Gravity cave (d = 2r) , and Point  A= (x, y , z) is fixed on circle (O,OA) which  

         is Rotating with a velocity  v̅ = w ̅̅ ̅r , of angular velocity  w̅ = 2π /T = 2πf  , in where  

        Period of Rotation T , is then also constant .    

         Since the acceleration ,a, for a Quaternion   z = (s + v̅. i)  is  a = [d²z/dt²] = (ds/dt.v̅. i) +  

         s. d(v̅. i)/dt = 0  + s. d(w r)/dt = 0 + 0 , and this because w̅ is constant for both therefore    

         velocity �̅� = constant also , i.e. →  

     The  Centrifugal velocity of the  Absolute System [ A ] is any constant , �̅� , and this  

      because Angular velocity , �̅� ,  is constant also and thus , is not needed to accept   

      A priori this constancy of velocity �̅� = 0 → �̅� → ∞  on circle  (O, OA) and to exist   

      In Frame , ( It has been Proved that this velocity �̅� ≡  σ Φ ) so ,  

Automatically is defined the conversion factor t = time , between the conventional time units  

(second) and the length units (meter = A.DA) or as  c̅. rv = v̅. rc , → c̅ (v)(T/2π) = v̅(c).(T/2π) 

→ c̅(v)/w = v̅(c) / w , which is happening with the same  w , without setting any restrictions ,  

in contradiction to the  General Relativity which is an axiom  a priori . Additional ,  

 This is the why that the conversion factor , t = time , has not any essence in all universe   

 but it is only a meter of changes in all  Relative Systems . STPL Mechanism is the only   

 Absolute System On which circularly exist  [ ⊕    ⊝ ],[ ⊝    ⊕ ],[ ⊕  ⊝   ] , the  

 three constituents , [ ⊕    ⊝ ] , and Originates this Existing - Objective - Cosmos .   

 This circularity of  the constitutes exist because of their Natural frequency of vibrations .  

     Because [STPL] line of the fixed frame becomes from this System [A] , then this relative  

     Frame [R} is common to the fixed one (common DA)  and let it be  [R] ≡ (x' , y' , z' , t') . 

From figure , sin φ = (�̅� / �̅�) , meaning that the Relative System , [R] ≡ (x' , y' , z', t') , ( the  

Affine Frame) is the Projection of Absolute Frame [A] ≡ {DA-O} - (x , y , z , t) where exists 

as the Simultaneity for all motions where issues ,  

                     [R] ≡ {DA- A} ≡  [ (x' , y' , z' , t') ] ,  

                     [A] ≡ {DA- O} ≡  (x , y , z , t) = [R] .γ  ≡ ( x' , y' , z', t' ) . γ    

Considering Point DA as the common center and [STPL] as the x-x axis of the two Systems ,  

then  becomes  DA ( x , y=y ', z = z', t) and for all linear Systems  DA ( x', y'= y ,  z '= z , t' )   

 This Specific state of constancy , i.e., the Centrifugal velocity of Absolute System [A] to  

 be a constant c̅, and the rectilinear motion with respect to one another defines the natural    

 Inertial frames , and because of uniformity of Space and motion , therefore occupies  the  

 same meter for  their changes , (i.e. the Time) .        

 Since also Points O , A  remove to Point DA isochrones by their intrinsic Property motion      

 which are  → their wavelengths are a Stationary wave in cycloid ←  following Lorentz`s    

 factor γ , then this following  happens also to all Frames which make this motion , and so  

 issues for all the System relations  { DA – O } = γ.{ DA – A } . Fig-6       

On this Relative System DA( x', y' = y, z' = z , t`) are conveyed , the Breakages [ ± (wr)² , 

2(wr)² ] of (O,OA) circle after the colliding with the rotating velocity v̅ = w̅.r  of the [A] 

System , and are the Fundamental Particles , Fermions and Bosons, or by escaping consisting 

the Rest Field and Gravity , or Dark matter and Dark Energy as analytically was shown .[39] 

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

The Angular-Momentum Ellipsoid Nibs on →{ Herpolhode and Polhode Ellipsoids}. In any 

Rotational motion , B̅xw̅  are Constants and The Angular-velocity-vector �̅� , describes the 

Ellipsoid of Angular Velocity and its nib describes a Cone of which Plane-Base is Fixed .  

Simultaneously .The Angular-Momentum �̅� describes the Ellipsoid of Angular Momentum 

and  its nib describes a Cone also of which Plane-Base is also Fixed . The Nib of Angular -

velocity-vector , �̅�  , describes on the Tangential-Plane of the Angular-Momentum Ellipsoid , 

the Polhode , while The Nib of Angular-Momentum �̅� , describes on the Tangential-Plane , 

of the Angular – Velocity - Ellipsoid , the Herpolhode . or The Fixed Tangential-Planes  

on �̅� , �̅� nibs which are alternately Perpendicular to  B̅ , and w̅ , common Central Axes of 

Rotation , or The Angular-Momentum  Ellipsoid  Nibs , in Herpolhode and  on Polhode 

Ellipsoids as → Electro magnetic Fields ← and which are Space-Energy CPT invariants .    

     The moving Energy-Vector is  |⊕ 𝐐 ⇈ AKA⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗ | = |↕| →{ The Electron-Unit-Charge }, and    

     since Charges correspond to the 3-Phase Rotors is ,The Unit-Charge Complex-Vector.    

Remarks :  

Material Point A ≡ ± |(w̅.r)²| of the Fixed System {DA- O} travels with velocity v̅ at Point  

DA , so geometrical distance  A.DA  in the Relative System [R] ≡ {DA- PA} is  A.DA = x'+ v̅ t', 

and because of the Isochrones motion in the Fixed System [A] ≡ {DA- O} , then  holds ,  

         x = (x'+ v̅.t') .γ  or    x  = (x'+ v̅.t').γ  ≡  [ x'+ v̅.t'] / [√1-(v/c) ²] ……. (a)  

Inversely , by using (a) , where [A] ≡ { DA-A} ≡ {DA- O}/ γ , then if Material Point A of the 

Fixed - System { DA- O} travels with velocity  v̅  at Point  DA , where then the geometrical 

distance ADA in the Fixed System is ,     

[A] ≡  {DA -  O}  is →   A.DA  =  x - v̅.t   and in the Relative System ,   

[R] ≡ { DA- PA}   is →   x' = (x-v t).γ = [x-v t]  :  [√1 - (v/c)²]  …...(b)   Fig-6      

      An application to Gravity [72]  and Photon [95] ,  

Because Gravitational Force is equal to → the Geometric-Resultant of the light-velocity  

c , acting on Electron-Unit-Charge  �̅�  ← or is ,  G = c √𝟐  �̅� , then Electron - Charge is ,  

q̅ = 
G

c √2 
 = 

6,680561 .10−11 

1,41429.[2,9979346.10 8] 
 = 1,58.10−19 Coulomb , which is the known Coulomb`s   

charge Quantity . From  gL ,kL  Universal constants  the Newton`s Gravitational constant  

Force G ≡ g.kE ≡ g .[gL kL ] ≡ [
T²P 

𝐚³
].[gL kL ] ≡ 9,808238* 6,8116.10−12 ≡ 6,68056.10−11 𝐦³

𝐍𝐬²
 

The in depth Position of electrons allows to the Work Produced in Prior  Phase - Areas  as  

Golden Ratio Pattern , to be Stored in the Next . Energy = motion / T  ≡ (
v

2πr
) . [σ + σ Φ] = 

�̅�  . [ 
𝛔

𝟐𝛑𝐫
 + 

𝛔𝚽

 𝟐𝛑𝐫  
 ] ≡  �̅� . [. fn̅   + 𝐟𝐧 ] ≡ Moving - Storage →[ �̅� . fn̅   ] ← + Moving-Frequency  

→ [ �̅�.𝐟𝐧 ] ←  ≡ The Material-Point . i.e.         

The Energy Produced in Photon-Cave is consisted of  Two-moving-Storages , that travel as  

Wave  [�̅�.𝐟𝐧] →[ �̅� . fn̅   ] → [ �̅� = �̅� = λ
f

Φ
 ] → [ S ≡ EM-R ≡ f1=N , f2 , f3, fD ,,f n= w² ] , and as  

Particle  →[ f1= (E²+H²) = n 
(1+√5)σ 

  2πr 
 = 

 nB̅

π² r⁴ 
] →{W≡EM-R≡ [εE² + μB²] = 2.λc.sin.2φ} and is  

The Duality  of the Energy-Storage  S ≡ { [⊕← 𝐫 →⊝]  + Motion M  . [87-89] .The  three     

elements [Σ = n . h]  [s² = ⊕  , 2s²= , - s² = ⊝] of  This {STPL}-Mechanism formulate 

the 3-Knots Figures  ( n = 3 ) and determinates the Elementary-Particles Vector Mould . 

 

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

8.[a]-3..The circularly existing Unit-Charge Complex-Vector [⊕  ⊝],[⊝  ⊕],[⊕ ⊝ ], 

 

  Figure - 7 -  : The , STPL , Mechanism is the Generator of the Cosmic-Particles . 

                         The Unit-Charge is as Complex-Vector  Velocity Thrust ( v̅ = w̅.r ) ,  

                         with and from the Breakages →  𝐳  * 𝐳   = (s + v̅.i )² = s² + [v̅]² +2.sv̅.i  .  

7-a = The Positive Breakage Quantity  Q ≡ [ ⊕    ⊝ ] , for Leptons and Quarks .    

 

  Figure –7- a  :   The , STPL , Mechanism is the Generator of the Cosmic-Particles . 

                      The Unit-Charge is as Complex-Vector  Velocity Thrust ( v̅ = w̅.r ) , with  

and from the  Breakages →  𝐳  * 𝐳   = (s + v̅.i )² = s² + [v̅]² +2.sv̅.i . V-Trust ≡ [ ⊕    ⊝ ] 

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7-b = The Positive Breakage Quantity  Q ≡ [⊝   ⊕] , for Anti-Leptons , Anti-Quarks .     

  Figure -7- b   :   The , STPL , Mechanism is the Generator of the Cosmic-Particles . 

                      The Unit-Charge is as Complex-Vector  Velocity Thrust ( v̅ = w̅.r ) , with  

and from the  Breakages →  𝐳  * 𝐳   = (s + v̅.i )² = s² + [v̅]² +2.sv̅.i . V - Trust ≡ [⊝   ⊕]  

7-c = The Positive Breakage Quantity  Q ≡ [⊕  ⊝  ] , for Bosons Origination  .     

  Figure -7- c   :   The , STPL , Mechanism is the Generator of the Cosmic-Particles . 

                      The Unit-Charge is as Complex-Vector  Velocity Thrust ( v̅ = w̅.r ) , with  

and from the  Breakages →  𝐳  * 𝐳   = (s + v̅.i )² = s² + [v̅]² +2.sv̅.i . V - Trust ≡ [⊕  ⊝  ] ,  

Since the Primary motion ≡ [PM] exist from the three Breakages only , and STPL is the  

n =3 Mechanism creating Elementary Particles   [n-Knots=3] in  𝐕 GRA = 7,593.1035 V.   

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

8..[b].. The { TVPM }  Physical Mechanisms : Two - Vectors  Three - Poles Mechanism .   

 

  Figure -8- a : The Two-Perpendicular Complex-Vectors , CA ⊥ CP , Slide on (O,OA) circle , and  

                      through the Three  Poles , A , C , P , carry the Stress  σ , of Square , ACPC’, to the Two  

                      Equal and  Opposite Squares |COAB| , |COPB’| for Halve Area - Stress - Conservation  

 b-1...  The Conservation of Energy IN Geometry - Mechanism   :  [62]   

In(1)…On AA` diameter circle (O,OA) exists the Inscribed -Square OA x OA = OA², and the  

Circumscribed  Square CP x CP = CP². Since Vector  CP = [OC= OA].√𝟐 , therefore the Inscribed 

Square is Halve  the  Circumscribed . The same to the Circles  π [
𝐂𝐏

√𝟐
] ² = π [CP] ² = π [OA.√𝟐] ² =  

2.π [OA]² . This Linear Expansion of Archimedes-Circles and Squares Passes from a Point M ,  

such that  π r ² = CMNH Square . [ 47 - 51 ] 

In(2)... On Two-Perpendicular Vectors , CA ⊥ CP , Point C` Slides on (O,OA = OP) circle forming 

the CAC`P to CMNH to CBAO  Squares with Prior of (1) Properties .This Sliding-Rotating Method  

Is the  Markos { 2 -Vectors 3 -Poles Mechanism } which Circles and Squares as Areas Pass from the  

Point M determined by the Position 𝐀 𝐞 , such that   π r ² = CMNH Square .  

The Squaring of the circle  π [
𝐂𝐀

√𝟐
]² =  CM²  . [ 47 - 51 – 98A ]  

In(3)..  If the Two-Perpendicular Vectors Are Conductors with Prior Properties then Square CAC`P   

to CMNH to CBAO  Square , are a Rotating and Changing-Squares-System , CP ² ↑ = |∷| ,↻, →  To 

2-Half and  Equal Area Squares  CB ² = ⤭ =[⊕
∷

2
+⊝

∷

2
] CB`² , by turns in  OABC ⊥ OPB`C Planes  ,  

which Equilibrium and Consist , The Neutral-Space . Placing Stress in Squares becomes the Physical  

World as , Physics Mechanics and Chemistry , by Conservation of Energy as Stresses in Areas .               

As in Electricity , The flow of a current in an Conductor , CA = d , Represents the created around  

the Conductor  by the Circular-Lines of Forces , Magnetic field , The flow of  ⊕→⊝-Charge in d  

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Conductor , is the Torsional Force �̅�𝐅 = v⃗ .r = w⃗⃗⃗ .r ² = 2πf. r ² = σ Φ r …....(1) . Since edge-velocities 

v̅C = v̅A= 0 , therefore CA =d= ½ (aT²)  and Acceleration , a = 2d /T² = 2d.f², and then the velocities  

diagram is Energy-Triangle → v.[Δ-CAP] = v.[½ (2d. |v⃗ |)] = v.[d w r ] = v d.2πf.r = v.[σ Φ d] ..(2)  

The Current flow in Electric-Field  �̅�𝐂𝐀𝐏  of CAP Plane is transported into the Perpendicular to CA  

axis Opposite Magnetic-Field �̅�𝐏𝐀 in PA-Plane due to the Force �̅�𝐅= �⃗� .r = I = 
 𝟐𝛑𝐫

𝛍 
 �̅�𝐏𝐀= σ Φ r .(3)  

Stress  σ = 
𝐅𝐨𝐫𝐜𝐞 

𝐀𝐫𝐞𝐚 
 = 

𝐆

𝐯.𝐯
 = 

G

√2 .c
 = The  �̅� Electron Charge = 

G

√2 .c
 = 

6,6736923 .10−11 

1,41429.2,9979346.108 
 =1,574.10−19 C  

      The Spin of cave , r, is Equal to the Angular-momentum-Vector →  Spin ≡ |�̅�| ≡ r σ Φ  ← 

      which contains and  it is the Golden-Radio-frequency  Φ  as Pressure  , σ , in cave  r .     

i.e.  [a]  The Forces are Spread on Surfaces as Stresses  σ , and in case  of  Area = 0  then are  

      Spread on the Velocity – square – Surfaces , and for the light  c , on Resultant √𝟐.c .  

b-2... For  Conductor-Case which is an Screw-motion where a Torque is created in Perpendicular  

      Plane of Con-axis . Markos { 2-Vector 3-Poles Rotating Mechanism },{
−A ∷ ↻
+𝐂 ↑ [⊕

∷

2
+⊝

∷

2
]𝐏 } 

carries motion (+) → (-)  from Point A through an Perpendicular-Conductor  CA , to Point B , into 

an  Changeable and Rotating-Squares-System , PA ↑ = |∷| ,↻, →  To  2-Half and  equal Area Squares  

CB = ⤭ = [⊕
∷

2
+⊝

∷

2
] CB` , by turns in  OABC ⊥ OPB`C  Planes which Equilibrium [⊕

∷

2
+⊝

∷

2
]=0  

(The Neutral-Space) .  

b-3..For  the motion of the ⊕→⊝-Charge of any Conductor d = CA becomes Stress - σ  in length d 

       Motion is created in Conductors  d ≡ [⊕← 2𝐫 →⊝]   following the [⊕↔⊝] Interactions .This  

Motion is Conserved and kept in Caves as Electric and Magnetic fields and as frequencies which  

are conserved in them when the Space-Points become Energy-Conductors and Energy  k = 
2π

λ 
 = 

2π

d 
 .   

b-4...The in caves Energy Imports are in Squares which equilibrium through  MPM ≡ Markos   

of ⊝ Charge  in an Electric–field  E̅F . For Velocity-Vectors at Point  C issues , CP⃖⃗⃗⃗  = CA⃖⃗⃗⃗   and  CP⃖⃗⃗⃗  ⊥  

CA⃖⃗⃗⃗  and the Resultant is the Velocity-Vector  C⃡C`AP , Electric-Vector = 
 πσΦ

4 
[d]² , Magnetic-Vector =  

 πσΦ

4 
[d]² . Similarly on Material Vector CP⃖⃗⃗⃗  carries the Maximum Conjugate-Force CC`= C⃡KA from 

E-Square  CP² to two Equal and Opposite squares – CB`PO ,+ CBAO from CAC`P ≡ 
+𝐂𝐎𝐀𝐁

−𝐂𝐎𝐏𝐁 `
[⤭] which 

Rest in the Circumscribed circle π.OA² = 2π(
𝐎𝐀 

√𝟐
)², to the Screwdriver Inscribed to , CA⃖⃗⃗⃗  , CD⃖⃗ ⃗⃗  circles ,  

π[
𝐂𝐀²

𝟒
] , π [

𝐂𝐏² 

𝟒
] . Motion to Rest , Before the Halve areas , circles Pass through  the equal to CMNH 

Square where exist Quadrature at Position M and to Half-Area circle  π [
𝐎𝐁

√𝟐
]² = π[

𝐎𝐁 ²

𝟐
] at Position M 

b-5..This Property of Any Two Equal and Perpendicular  Vectors at Point  C , issues for any Point   

       N , which has a Screwdriver –Material - Vector- CN .    

The Quantization of  E-Geometry to its Dimensional-moulds :  

The- One , Two , Three Vectors and Three - Poles Mechanism .        

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

 Figure -8 - b   :   The Quantization of E-Geometry to  its moulds , The Point , the Linear , the  

                     Plane , the Space (volume) Mould for E-geometry Quantization , to Opposite.  

b-6…For (1)  monad  EA , to Antimonad  EC–For (2) AB line to Parallel line MM` - For (3) 

CE  Radius to the  CM  Square Segment - For (4)  KA  Segment  to the  KD  Cube  Segment .  

From (3) the Two-Perpendicular Vectors , CA ⊥ CP , Slide on (O,OA) circle and through  

the Three Poles , A , C , P ,  carry the Stress σ , of Square  ACPC , To the Two Equal and  

Opposite  Squares  |COAB| , |COPB’|  for still  to the  Halve Area - Stress - Conservation .   

      For the Rotating Square  CMNH  exist as Upper-Still-State the Square  CAC`P  

      and  as Lower - Still-State the Square  CBAO , related  [ CAC`P ] = 2.[ CBAO ]  .                      

In(3)..On Two-Perpendicular Vectors , CA ⊥ CP , Point C` Slides on (O,OA = OP) circle  

forming the  CAC`P to CMNH to CBAO  Squares with Prior of (1) Properties .This Sliding 

Rotating Method is Markos { 2-Vectors 3-Poles Mechanism } which Circles and Squares  

as Areas Pass from the Point M determined by Position 𝐀 𝐞 , such that issues  π r ² = CMNH 

Square .The Squaring of the circle is π [
𝐂𝐀

√𝟐
]² = CM² = |CM`|² , Fig-15,  [ 47-51 ] , [62] 

       Remarks :    

1… The Two - Vectors  Three - Poles Mechanism is a Mechanism from Two ⊥ Vectors  

       in Geometry , where the Action of Energy on their Vectors Square and is Conservated .     

2… The Mechanism is a Rotating and Changing-Squares System , on a Circle which  changes  

        The Inscribed to the circle Square , changes to 2 –Halve Opposite and equal Squares .The  

        same Procedure  issues for the Inscribed  and  Circumscribed circles to the Circle .    

3… Since from Wave-Action of  Spaces issues   Z −
 n x Z +

 n = [2R] 2n . e i.2nθ , this means  

      that ,The conservation of Energy = Work , between the Spaces and the Anti-Spaces   

      happens by Doubling the number n , of the Vertices of the Regular Polygon . i.e. The  

     Surplus energy is stored in 2.n vertices , and on  𝛌𝟐𝐧=√2R2 − R√4R2 − λ²n  Sides ,  

     where then Energy is divided and spread on the double number of the Polygon Sides.  

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

8..[c].. The { TCIC } Mechanism : The Tetrahedron , the Cube , and the Inscribed –  

            Circumscribed to the Circle  Mechanism .  

Figure - 9- : The Active-Conductors of Elements and The Space , Anti-Space  formation .  

           In Figure  ZA , ZB , ZC ,  are the three Conductors on  the Three Diagonals of  Cube  

          with 1 , 2 , 3 , 4 , 5 , 6 , 7, 8 , Vertices .  At Point  Z  is Acting a Complex-Vector Z̅ and 

          which transform the Vibration to the three conductors in Space Pattern . It was shown  

          [61]  that The Stresses of Complex-Vectors are Spread in Surfaces only for Still states.   

The number of Moulds of Stationary-States are → 𝟐n=1−4 Points ≡ 2 , 4 ,8 ,16 ≡ 4–Types←       

 (2) = For the Proton = Nucleus , (4) = Tetrahedron , (8) = Cube = The Neutral-caves , (16) =   

The Double Number of Vertices for the 8-Stationary Neutral-caves and called TCIC-Pattern  

            →{  The Sphere – IN TETRAHEDRON – IN Cube , IN External  Sphere }← 

The Active-Conductors of Elements and The Space , Anti-Space  formation .     

Point , in E-geometry is considered nothing , without Position and direction while in , MG ≡  

Material - Geometry [1 Positive ⊕ and 1 Negative ⊝] . From Nothing (i.e. the Point Z ) to 

Existence ( i.e. to be another Spherical Point P ) issues the Zero Virtual work law ,where  

zero Work is the equilibrium of two Equal and Opposite forces on Points and is [⊕ - d - ⊝] . 

Thus Space [S] is Z-Point ⊕ , Anti-space P-Point ⊝ , and  d = ZP = The Conductor of Points  

Since ,The Position and the Number of Points, create  the Spaces so the Only Three elements  

are  → {⊕ , [⊕↔⊝] , ⊝} ≡ [+, 0 , -] ← for  Material Geometry exist linearly in moulds .  

      The Stresses of Complex-Vectors Act on a Surface , A circle of Sphere , between the Sub  

      Units Axially and Rotationally following Ptolemy`s and  Cebas Theorem of Equilibrium.   

      The Space Anti-Space  and , Neutral-Space Conductors are self-Sustaining .  

      Stability   : 

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

The number of Moulds of Stationary-States are as→ 2n=1−4 Points ≡ 2 ,4 ,8 ,16 ≡ 4–Types← 

      i.e. Monads are formed  from the first 4- Moulds as → The 1-Point which is  everywhere,  

      the  2- Points which form Vectors , the 3- Points which form the Planes , the 4 - Points  

      which form the Volumes . For  n > 4 as this is the Atoms Structure, follows the  

      Sustainability of the Spaces and Anti-spaces. Since Space-Energy Structures follow the  

      M-Geometry Stability these follow the Mould of Spaces  2 n = 3 = 8  Elements which is  

      The-Cube as shown before . Instances ,    

1..  In the constant , Hydrogen Conservative-Cave-System , which creates only closed Orbit  

      shapes as Circles , Ellipses and Eight-shape , ∞ , are Placed the above elements , π g ≡  

      Energy ≡ [meter of area * meter of force] ≡ Electrons on Orbits , and also the  

      Unit-Space ≡ Massive-Complex-Unit-Space ≡ →[+�̅�.s²]← jointed through the Neutral  

      Material-Points [ (+) [↔] (-)]  with the Strong-force →  S F = h .fn ≡ h .{ [S ≡ BP ≡  

     EM-R ≡  f1=N , f2 , f3, fD ,,f n ] ≡ h.n 
(1+√5) σ 

  2πr 
  ≡ h [ 

n.B̅

4𝜋2.  r4 
 ] ….(mg)  

     Equations (m) , (mg) are the Energy-Space-constituents in Hydrogen-System .   

c-1.. The Protons and  the Nucleus Structure  :  

       From above MP ≡ [(+)[↔](-)] ≡ Neutral = n , then     

a.. For 1 Proton [(+)[↔](-)]↔(+)  ≡ Neutral                                   →      n = 1 p = 1   

b.. For 2 Proton (+)↔[(-)↔(+)][(+)↔(-)]↔(+)  ≡ Neutral             →      
p n
n p 

c.. For 3 Proton (+)↔[(-)(+)](+)[(-)(+)](+)[(-)(+)] ≡ Neutral         →   [ 
0 0 0

0 2⃡ 0
1e 0 0

 ]     

d.. For 4 Proton (+)↔[(-)(+)](+)[(-)(+)](+)[(-)(+)](+)[(-)(+)]        →   [ 
0 0 0

0 2⃡ 0
1e 1e 0

 ]     

e.. For k Proton (k1)↔[(-)(+)](k2)[(-)(+)](+)[(-)(+)](+)[(-)(𝐡𝐤)] →   [ 
ke ke ke

ke 𝑘 ∶ 8 − 18⃖⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ke
ke ke ke

 ]     

f..  The Inscribed to the Tetrahedron-Sphere consists the Nucleus ≡ The ⊕ Space , and in  
      Circumscribed to the Tetrahedron-Cube  Sphere consists the Orbitals  ≡ The ⊝  Space .    
c-2.. The Annihilation of the Fundamental Particles .  
     Considering the , Matter Antimatter , with the classical known theory of Annihilation as   

     the common Constant Energy then issue for a Force ↔Anti Force , Action ↔Reaction  

     Electron = e−= ⊝→ mass 𝐦𝐞 = 9,11.10−31 Kg → Charge 𝐂𝐞 = 1,602.10−19 eV →  

                                                                                        Cave     a   = 5,0.10−17 m   

1.. Electron - Positron    e−→  e+ ≡ 2 γ  ≠  0  

     The Common Me→p is from relation  
1

MT
 = 

1

me
+

1

mp
 = 

1

me
 +

1

me
 = 

2

me
 = 

2

9,11.10−31 
 = 

1

4,555.10−31 
        

    From energy equation E = 
1

2 
Me→p c² = 

1

2 
 [4,555. 10−31].[2,998. 108]² = 6,827945. 10−15 J 

                                                =     J / (1,6022.10−19 eV) = 4,2616059. 10 4 eV = 42,616059 .KeV  

         The common frequency is  f e→p =  
E

h 
 = 

6,827945.10−15 J

 6.62607.10−34 Js.
 = 1,0304667. 10 19 H    i.e.  𝐟 𝛄    

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

c-3.. The Equilibrium of the Three-Spaces , The Space Anti-Space , Neutral-Space  

The Stability of Elementary Particles , Conductors and the Atoms -Nucleus  : [60]   

   Figure– 9a- : The Electric and Magnetic Field of 3 Conductors On 2 Anti-Parallel-Strands   

   The Waves - Motion ≡ Energy , is Transported and , The Pattern of Disturbances  

    with Informations , Propagates from the One-Edge-Point to the other Edge-Point  

    of  Conductors , OR  is on [ Sub-Units ] .   To Prove the Stability of the System ,      

    The Equations of motion become everywhere from any Opposite Space ≡ ⊕ , Anti- 

    space ≡ ⊝ . During these motions as , ds . is Done a Constant-Work , k , or and from  

    their velocities �̅� and this Work may be Positive or Negative for Equilibrium . In F-23 

    Cycloid Anti-cycloid motion is as , D. The Origination of Gravity g , Antigravity [- g ]  

In Fig-9a , Conductor D = d = AKA where ⊕ constituent attacks ⊝ by a Hook`s law force  

as Stress  σ = E u , and an Coulomb force F [+ ↔ −] = 
[⊕↔⊝ ]

r²
 = 

[2 σ]

r²
 , creating Work ≡ motion  

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

as was shown  It was shown that , The Stability of Nucleus Forces , is succeeded through 

The Pascal`s - Ceba`s  triangle launched caves r , while Leptons from their Anti - Leptons  

existence in the same launched Pascal`s - caves r .  [58] The Equilibrium of the Three-Spaces 

is Done on the three Cyclic-Quadrilaterals (ABEAECE) , (BCEBEAE) , (CAECEBE) ,  of the  6  

Conductors each for ,  [a , b , c , d , p , q ] x [3-ABC] = 18 Conductors .  The Stability is  

1..Linearly  through the Products of the Diagonal - connectors as , → → →   

[AAE].[BECE] = [ACE].[AEBE]+[ABE].[AECE] , [BBE].[CEAE] = [BAE].[BECE]+[BCE].[BEAE] , 

[CCE].[AEBE] = [CAE].[BECE]+[CBE].[CEAE]   and ,  

2..Rotationally through the Ratio of  the Diagonals ≡ The Conductors | 
AKB

AKC
|x| 

BKC

BKA
 |x| 

CKA

CKB
| = 1 

or  Rotational-Equilibrium as ,  [AKB].[CKA].[BKC]=[AKC].[BKA].[CKB], of all Opposites  

 Tangential-Electromotive Forces .  

3.. From Mechanics-Physics , all Systems Possessing Elasticity ≡ motion and Reaction to 

motion , the called mass , are capable of  free vibration  or vibration taking Place in the 

Absence of External Excitation [7] .This Principle issues for Both Closed or Open Systems.  

i.e. Either for the Nucleus where issues The Pascal`s - Ceba`s  triangle  Stability , or for the   

Orbitals where issues  the Tetrahedron-Cube -Sphere-Mould .A  Signal  as the Electric and 

Magnetic Field  IN  3-Conductors Is  transformed  On  the 2 Anti-Parallel – Strands .   

c-4... The Natural Electromagnetic Energy-Tetrahedron and , The  3- Conductors  

          Into The  Energy - Cube  and Spheres  :  [102]    

          In Fig- 9c -  The Electric - Magnetic Field of 3-Conductors which lie on the DABC   

occurs  INTO the {⊝ 8-Anti-Space Cube , [DA1A D1 , B B1CC1]}, and The Positive →  

{ ⊕ 8 - Space – Cube , [DA1A D1 , B B1CC1]} , INTO  The {⊝ 16-Anti-Space [ 1 ,2 ,3 ,4  

 5 , 6, 7, 8 - 9 ,10 ,11, 12 , 13 ,14 , 15, 16] } Sphere Cube on Vertices.= Point [The Point 16  

 ≡ |⇉|Z|] consists the Navel-String  Gate  into the Triangle-Circle-System  {Z-(∆D,ABC),   

 ∆[T1T2 T3]} of the Stationary Bases which Results on the 2 -Anti-Parallel-Strands . 

 The Dual Photon v̅ [
σΦ

 2πr  
 + 

σ

2πr
 ] ≡  v̅.[ fn̅  + fn ] , occupies Stresses = σ and velocities v̅ , in  

     The Tiny-caves r . The Colours in light , are the Still-Sub-Units in Storage →[v̅ . fn̅  ]←  

     and exist  as Frequencies of → Violet , Blue , Green , with their Complementary Colours 

     Yellow , Orange , Red ←  

Every 8-electrons are vibrations on Atoms-Cube-Structure {A Tetrahedron in Cube in a 

Sphere} whether it be Sound or Light . Above Structure is followed by all Compounds. The  

Molecules are Systems consisted of The PERIFERAL ≡ Skeleton  𝐌 𝟏𝟔 and The CENTRAL  

≡ Fittings  𝐌 𝟖 , and  the ACCESSORIES ≡  𝐌 𝟒  or  𝐌 𝟐 , 𝐌 𝟏 . This Property of Atoms and  

of the Compounds is  The Critical - Valve of  Switching the motion  as this happens in the 

Electro-magnetic  Solenoid Valves with High or low Pressure and flow  rates directly or Not . 

Remarks  :    Work of Elastic Deformation . 

Elastic Deformation requires (1) That every New Stress that is applied to a New infinite 

Element is always added to the existing one .(2) Be always Unity Work of Deformation.  

                      When a Body contains Potential Energy , 

During any Unloading it gives off  Mechanical - Work , since the Points of application  

of  the GRADUALLY - withdrawn Loads are Displaced.      

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

If the Unloading is ABRUPT , then  Kinetic Energy is converted into Potential and after is  

Kinetic , converted back into Kinetic and so on . That is, the body Performs an Oscillating  

motion until the Mechanical Energy is extinguished due to a State of Equilibrium or Alters . 

Figure – 9b- :   The Electric - Magnetic Field of 3 - Conductors Results on 2 -Anti-Parallel - 

Strands .The Stability of →{ ⊕ 4-Space [D A B C]} Regular - Tetrahedron , IN {⊝ 8-

Anti-Space Cube , [ DA1B D1 , C C1AB1]}, and The →{ ⊕ 8- Space [ DA1BD1 , CC1AB1]} 

Cube, INTO    The {⊝ 16-Anti-Space [ 1 ,2 ,3 ,4 ,5 , 6, 7, 8 - 9 ,10 ,11, 12 , 13 ,14 , 15, 16]} 

Sphere Cube Vertices . The  Point [16 ≡ | ⇉ |Z|] consists the Navel - String Gate in System .   

and are { Z - (∆D , ABC) , ∆ [ T1 T2 T3 ] } Stationary Bases . The Stability Analysis in [88]  

c-5.. :  The Mater Antimatter 3-D  Origination Mechanism [⊕↔⊝]                                 

Figure – 9c- : The 4-Dimentional Spinning , Tetrahedron - Cube – Spheres - Mould .   

                       The Stationary-States  are  → 2n=1−4 Points ≡ 2 , 4 , 8 , 16 ≡  4–Types ← 

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Figure – 9d.. :The Hydrogen , Carbon , Oxygen , Atoms-Conductors Into the Sphere-Cube- 

               Mould . Deka hexahedron , Octahedron ≡ Cube , Tetrahedron ≡ 4-Points , Triangle .      

               The Nucleus ≡ ( In-Sphere ) , Tetrahedron  ≡  ( D - A.B.C ) ,  

               Cube  ≡ ( O,2,A,4,B,6,C,8 )  , Orbitals ≡ ( Ex-Sphere ) , Mould .  

When  Vector ≡ 2-Points ≡ The Closed-Conductor , 1-Point ≡ The Opened -Conductor ≡  

The Bracket-Hook . Oxygen is the Element which fills 8 - 2 = 6 vertices of Cube as EL →  

{

1𝑒  0𝑒 1𝑒

  1 𝑒 2⃡  0 𝑒
1𝑒 1𝑒 1𝑒

 } ≡   (± 2
2 ) , where ⓪ is the first , Zero-Acting Cube  filled with 1e ,  

              therefore is the only Steady element which occupies the first Energy-Level ①  

              with 2 Electron-Positions as ① = 2e = 2⃡  Positions at 1⃗  , 1⃗⃖    

The Electron being in the Hydrogen  Precesses because of the different axis of Rotation and 

Nutation`s , from the continuous and immense-communication to the effect of gravity g .  

Since Electron is continually oscillating , with the Nutation-frequency 𝐟 𝐍 , so  Produces a  

continuous and oscillating Magnetic-field –M- which in turn is the source of an oscillating  

Electric-field – E - which implies the Regeneration of each other , i.e. it is a Propagating  

Electromagnetic-Wave where E = B c , and with a quantum-Energy E = h fN or  E = 2μ.B ,    

This Energy E consists the Hydrogen Bracket  Hook [HBH] ,  or [BH⃗⃗⃗⃗  ⃗]  and it is the only  

free monad which can Bond to all Energy Structures .     

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The Spheres-Cube-Structure of Atoms In Sphere Center –O- allows The Stability of the 

System, Per–Two electrons in Dipole Positions , 1 ↔ 6 , 2 ↔ 5 , 3 ↔ 8 , 4 ↔7 , consisting  

The-Positive Dipole-[BH⃗⃗⃗⃗  ⃗] , to be able to move → Into-In- Outside it ← and allow the Atoms- 

Bonding as this in  Energy levels .  The  Cube-Structure of Atoms and Orbits in the Out-

Sphere formulates +[BH⃗⃗⃗⃗  ⃗]  to those Dipole Positions which lack of one electron and so can 

PLUG-In the LOOP of the others . The Atoms with Zero Stable State are , 

        The Hydrogen Bracket-Hook Into the Carbon encloses the Inscribed Sphere  

        for the Nucleus , Into the Oxygen for the Orbitals ,  Into the Sulfur enclosed into the  

        Circumscribed Sphere for the Atoms-Conductors Sustains .     

       The  First  4-Dimentional Spinning ,Tetrahedron-Cube–Sphere-Mould are , 9c--2 

1… O-1-3-5-7 -             → The  First Solid Tetrahedron Structure in Nature ,  

2… O-1-2-3-4-5-6-7-8  → The  First Cube  with max. Positions e = 2.n² = 8 ,  

3… R - [ O , A , B , C ] → NUCLEUS IS IN the First Inscribed Sphere into Tetrahedron.     

4… R-O-1, 2, 3, 4, 5, 6, 7, 8 → ORBITS ARE IN Enveloped Cube-Sphere of Tetrahedron.    

Deka Hexahedron , Octahedron ≡ Cubes , Tetrahedron ≡ 4-Points , Triangle ≡ 3-Points ,Vector 

≡ 2-Points ≡ The Closed-Conductor , 1-Point ≡ The Opened -Conductor ≡The Bracket-Hook .  

The Hydrogen Nucleus is kept  in the Inscribed  to the Tetrahedron-Cube-System  where 

exist the Protons and Neutrons , while The Electrons of Hydrogen Orbits  are kept  into the 

Circumscribed , to the Tetrahedron-Cube-System . Both Equilibrium  by following the 

Menelaus - Ceba`s Principles . [70]  

Any Two Perpendicular Energy-Vectors , |𝐐 ⇉ AKA⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗  = ↔ | , |𝐐 ⇈ AKA⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗  = ↕ |  of this  

      Propagating Energy , FORM The Energy-Square , |↔|.|↕|≡|𝐐 ⇉ |.| 𝐐 ⇈| ≡ q0 , on  

     Conductor AKA and Then Energy-Circular-Prism = |AKA| .{𝐐 ⇉ AKA⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗  }.{ 𝐐 ⇈ AKA⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗  } 

     ≡ [�̅�  𝐱�̅�  𝐲].|AKA| = | ↔ |.|↕|.|AKA| ,  i.e.  

     An Energy-Circular-Cone which is a Moving Energy -Volume , and Because from  

      Cauchy equations of Stresses are of three Dimensions , then The Energy Stresses  

      remains Flat  ONLY- WHEN the Plane-Section is a circle [𝐄𝟐 ] and  

     The Square becomes circle, Anti-Quadrature..   

Because from Mechanics , the Hydrogen Nucleus is kept  in the Inscribed  to the 

Tetrahedron-Cube-System  where exist the Protons and Neutrons , while The Electrons  

of Hydrogen Orbits  are kept  into the Circumscribed , to the Tetrahedron–Cube-System .  

Both  Equilibrium  by following the Menelaus-Cebas Principles .  

Oxygen is the Element which fills 8 - 2 = 6 vertices of Cube and for Neon 10 -2 = 8 , as  

Ox → {

1𝑒  0| 0/

  1 𝑒 2|⃖⃗  ⃗/  1 𝑒
1𝑒/ 1𝑒| 1𝑒

 }≡ ( −2
+2 )     ,   ② ≡ 𝐍𝐞 1x8

2⃡  = 2⃡ + 8 =  10     → {

1 1 1

1 2⃡ 1
1 1 1

}, 

The Possible Orbits of Oxygen are two as , → 1e /-- 2⃡/-- / 0 ← and → 1e |-- 2|⃖⃗  ⃗--  0 | ← for all 

the 8-Cube Positions . ⓪ is the first , Zero-Acting Cube and is filled with 1e , therefore is 

the only Steady element which occupies the first Energy-Level ① with 2 Electron-Positions 

as ① = 2e Positions at 1⃗  , 1⃗⃖ . In the same way  ①  is the first One-Acting Cube and is filled  

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

with 2e, and so on , The Electron being in the Hydrogen -cave Precesses because of the 

different axis of Rotation and Nutation`s , from the continuous and immense-communication 

to the gravity g .  Since Electron is continually oscillating with the Nutation-frequency 𝐟 𝐍 so 

Produces a continuous and oscillating Magnetic-field –M- which in turn is the source of an 

oscillating Electric-field – E - which implies the Regeneration of each other , i.e. it is a  

Propagating Electromagnetic-Wave where E = B c  and with a quantum-Energy E = h fN  

or  E = 2μ.B , This Energy E consists the Hydrogen Bracket Hook HBH , or [BH⃗⃗⃗⃗  ⃗]  and it is 

the only free monad which can Bond to all Energy Structures . 

The Sphere-Cube-Tetrahedron Structure of Atoms In Sphere Center –O- allows to issue 

The  Ceba`s Theorem for 6-Stresses  on the Inscribed Tetrahedron which Secure The 

Stability for the Nucleus-System , and for the Outer Electron-System the Stability is Obtained   

Per–Two electrons the Dipole Positions 1 ↔ 6 , 2 ↔ 5 , 3 ↔ 8 , 4 ↔7 , consisting The-

Positive Dipole-[BH⃗⃗⃗⃗  ⃗] , to be able to  move → Into-In- Outside it ← and allow the Atoms-

Bonding as this in  Energy levels . 

The  Cube-Structure of Atoms and Orbits in the Out-Sphere formulates the  +[BH⃗⃗⃗⃗  ⃗] to those  

Dipole Positions which lack of one electron and so can PLUG-In  the LOOP of the others. 

       Conclusion :  

1… The Forces of Atom`s  NUCLEUS , are Holded from   → The Inscribed Sphere   

        In the Tetrahedron  ,  which follows the Ptolemy`s and Ceba`s Vectors Structure .     

2… The Forces of Atom`s  ORBITALS , are Holded from   →   

       The Into  the Cube , Circumscribed–Sphere  Complex Vectors Structure .         

3… The Forces of Atom`s POSITIONS  , are Holded  from →  

       The on Cube  Inscribed  Tetrahedron Complex Vectors Structure .     

4… The Stability of the {TCIC} Mechanism follows the Ptolemy`s & Ceba`s   

       Complex  Vectors  Structure [62]  

The Action of the Complex–Vectors create the Waves of Motion ≡ Energy Waves which are 

closed curves and Transported . The Pattern of Disturbances with the Informations  Propagates 

from the One-Edge-Point to the other Edge-Point of Conductors , OR  is on the [ Sub-Units ] .       

Coulomb force [⊕→⊝] = F [+ ↔ −] = 
[⊕↔⊝ ]

r²
 = 

[ 𝟐 𝛔 ]

𝐫²
 = F = σ .A = [

2πrf

Φ
].A = w r.[ 

𝐀

𝚽
 ] = v .[ 

𝐀

𝚽
 ]  , 

and Acts on a Surface , A , between the Sub-Units Axially and Rotationally following 

Ptolemy`s and  Cebas Theorem of Equilibrium .               Figure –9e-   

Remarks  :  The Work of Elastic Deformation On the { TCIC } Mechanism : 

                  Every New Stress that is Applied to D - Element is always added to the existing  

                  And the Unity Work of Deformation is transformed  to three Tetrahedron Sides.  

                  When  a  SIGNAL  Strikes the  TCIC –  Cube`s  Mechanism . 

The Signal is Energy-Wave carrying motion . Unloading happens on the three Still-Spaces    

in Tetrahedron - Sides  which withdrawn Loads are Displaced   On the Anti-Parallel-Strand . 

If the Unloading is ABRUPT, then  Kinetic Energy of 1-Strand  is converted in the 2-Strand 

as Potential and so on . That is , CUBES Perform an Oscillating motion until the Mechanical 

Energy is extinguished to their Vertices , which are the stores of Information .  

Anti-Parallel-Strand is the Body containing the Potential Energy , During any Unloading on  

CUBES , it gives off  Mechanical-Work , since the Points of application of  the Gradually - 

withdrawn Loads are Displaced . The Stability of Kinetic – Potential Energy is continues .       

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

 

  Figure –10- The Hydrogen  BRACKET – HOOK  of  2 = Orbitals  [ (+) [↔] (-)]   

                     Stationary-State happens as → [⊝] ≡ ORBIT-1  ↔  [⊕] ≡ ORBIT-2  ←  

8..[d].. The { TOBH }  Mechanisms Atoms Bonding  Bracket - Hook Mechanism .       

            d-1.. :  The Precession and Nutation of Electron  :               

Gravitational constant  G ,  is The Pulling and the Cohesive Force on all the Quantized Energy 

Structures which communicates with everything due to the  Periodic excitation  on all Spaces.[84] 

The Newton`s laws issues for the masses and also the same to Electrons in caves as below ,  

      G ≡ g.kE ≡  g .[gL kL ] ≡ [
T²P 

𝐚³
].[gL kL ] ≡ 9,8078925* 6,8116.10−12  ≡  6,68056.10−11  

𝐦³

𝐍𝐬²
    

      The Electron being in Hydrogen-cave Precesses because of the different axis of Rotation   

      and Nutation`s ,  from the continuous and immense-communication  to the gravity , g .  

Electron-Spin is the Angular-momentum-vector B̅ and rotates according to equation  
dB

dt
 = [u̅B̅] =  

u B.[k̅k̅`]  in Gravitational Potential Ug = [ mg] .s.cos θ = - s Q . [k̅k̅`] so the change of angular  

momentum  B̅ is →  
dB

dt
 = u = 

s.Q

B
 = 

s.Q

J3.w3.
 ← and from the 1-degree equation of motion u , become  

�̈� + w ² u = 0 , with solution a Period of Nutation  T =  
2π

u
 = 

2π.J3w  

sQ
 , and its natural Frequency   

f N = 
sQ

2π.J3w 
  ….(1)  with Total Energy of Nutation  E N =  

J1

2
 [w1² + w2²] +  

J3

2
 w3² ….(2)  [70] .    

For Material-Points , the chains of Spins due to Periodic excitation [↔]  is created in Orbit  a  

Magnetic field due to LRC-circuit and which is tuning to the critical Quantum critical-State 𝐠𝐆 .  

The Light velocity vector �̅� = �̅�  , by Acting on cave , r = 𝐋 𝐏  , finds the Impedance m g , and  

becomes the Centrifugal-Force 𝐅𝐠  of  Cave equal to Gravity g . The chains of Spins for the ,  

ONE-WAY Pointy vibrating , is the Resonance – Frequency  fR  =  
(1+ √5 ] ) .σ

4πr
  =  

 σ 𝛷

2πr
  of vectors  

v̅  and  B̅  , of the-Stationary-Photon-cave , where B̅ ≡ S̅ ≡ Spin ,  i.e. The  fR  is common to both .            

The Moving Electron in Orbit of charge  �̅� ≡ ⊝ , energy E  with the Orbit -Velocity - Vector             

�̅� =√ 
2

𝑚
[E − { 

𝐤

𝐫
+

𝐋 𝟐

𝟐𝒎 𝒓𝟐 }] which creates IN Orbit , r , the Varying and Perpendicular Magnetic 

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

Field  �̅� , which in time-turn Creates an Electric-field  �̅� ⊥ �̅� , with the Resultant force F acting  

on Electron Velocity  �̅�  and which is composed of the  𝐕𝐩 , Perpendicular to the Magnetic-circles 

 O ⊥ B , and 𝐕 𝐯 , Parallel to the Magnetic-field-Vector  |�̅�| , is tending in such way that  L ≡ S ≡  

 Spin . The resulting motion of Electron in trajectory is the Helical motion and Work Produced  

during this motion . The Conservation of Energy exist in Orbit between  Protons and Electrons  

[p↔ e] therefore Energy as frequency exists in Orbit only , and differs of those of Energy- levels.  

      Since frequency 𝐟 𝐍 = 𝐟𝐑 = 2, 839845.𝟏𝟎𝟏𝟎 s−1 and exists in all Atoms , due to the Hydrogen  

      first cave ,then  this  𝐟𝐍  is the Resonance - frequency 𝐟𝐑 between all Atoms and Molecules. 

      It was  proved that  → Since  fR  =  
 σ 𝛷

2πr
  and related to Hydrogen cave r and Stress  σ  only ←   

      It is the Unique  Common and Neutral-Monad , in all Chemistry structures and Composites .         

d-2..Energy from equation  E= h.𝐟 𝐍 =  6.62607.10−34 . 2,8398447.1010 = 18,817009.10−24 J /  

         (1,6022. 10−19 ) = 1,174463 .10−4 eV , and conserved as Thermal-Energy 𝐄 𝐓  in kilo Cal  

         and which  is continually increasing as ,  E T = 18,817009. 10−24 J / [(4,19. 103 ) = kcal] =  

         4,49093. 10−27 kcal . Since 1eV =  96,363636 kJ/mol  thermal energy  E T = 4,49093. 10−27  

         kcal / [96,363636.kcal/mol=1eV] = E T = 4,660399.10−29 eV. This happens  because of the  

         closed Energy - Orbit-Rims  r , constant light velocity c , and from Spin equation  S = r m c .  

Taking into consideration the Thermal - Energy of  a Photon when it is Pressing the surface of   

1 m2 for 60s then ,  𝐄 𝐏 = 20  kcal = 20.(4,19. 103 ) = 8,3777.104 J , and the ratio , [ E T / E P] =  

4,49093. 10−27/20 = 2,24546.10−28 , which is a Quantity Not - detected . The Hydrogen caves  

created in the Sun 1 Million Years-ago =106.365.24.3600 =3,1536.1013 sec ,is accumulated  a  

Thermal-Energy of  a magnitude E Therm= 3,1536.1013.4,49093.10−27 = 1,41626.𝟏𝟎−𝟏𝟑 kcal ,  i.e.       

The Stationary Hydrogen-wave–cave needs 1- Quadrillion years to conserve 1-kcal Thermal-Energy . 

For Half-frequency fR / 2 =1,4199223.1010 s−1, the Kinetic Energy is Zero and the Potential-Energy  

is  U = E = h f =  6,62606957.10−34 . 1,4199223.1010 = 9,4085039.10−24 J / (1,6022.10−19 eV) =  

5,8722405.10−6 eV , which agree with  the Bohr-Magneton .           

     Remarks :  

1.. The Real Shear - Stress that exists in the Force – Carriers .  

     From the Static Theory of  Equivalent Tension (Moore's cycle) is  (1) =  

     σ = √(𝛔𝟏 −  𝛔𝟐)² + 𝟒 𝛕𝟏𝟐  , and  σ1,2 = (σ1+σ2 )/2 ± (½)√(σ1 − σ2)² + 4 τyz²  ,  

     instead of the classical case which is  σ = 2.τ max = √σ1
2 + 4. τ ²  ,  . (2) . Because  

     nature always follows the uniform tension so it follows the (1) case. where exist the  

     equation  σ = √(𝛔𝟏 − 𝛔𝟐)² + 𝟒𝛕𝟏𝟐  , and  σ 1,2 = (σ1+σ2) /2 ± (½)√(σ1 − σ2)² + 4τyz²  = 

     
σ

2
 [√5+1 ]  = σ.[ 

√𝟓+𝟏 

𝟐
 ]  , which is the Golden ratio for stresses .  

2.. The Bernoulli Astute about Stresses-Linear-Distribution is equallyTrue for Bending too. 

3.. In the case of concentrated Stresses (such as Closed or Open Conductors) ,the Doubling  

     of the main Stresses Observation is True , and this because of the Golden ratio Pattern.  

 

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

      1d.. The Spaces and the Energy States   :  

       In  Articles  [87-89 ] is Elucidated the Duality-Photon as Particle and as Wave . 

       The Photon`s Charge �̅� Photon = 
v.σΦ

 2πr  
 , Transfers Information`s and Energy-Storage  

       in Nature . In  Articles  [87-88-89-90 ]  are Elucidated The Gravitational constant G ,  

       The Stresses  σ , The Light-velocity  �̅� , The Gravity  �̅�  , The Hydrogen cave H ,  

       The electron - �̅� , The electron-charge  �̅� 𝐞 , The Weak-Forces  �̅� 𝐅 , The Strong –  

       Forces  𝐐𝐓 , and The Uniform-Resonance - Frequencies  𝐟 𝐑 , for Atoms Structure .     

       In  Articles  [91] is Shown How ,The Three Circularly-Placed Physical-Charged- 

       Breakages on The-Three Spaces [⊕ -  - ⊝] , Or on the 3-Extreme -Triangles of   

       STPL- Mechanism  which is The -Thrust  for The-Origination of  all the Cosmic- 

       Particles in Linear & Rotational Conductors Frequencies , either into  the Atoms   

       or to their Compounds [91] .                                 

 9a..  THE   FLOW - PLAN  OF  THE →  SPACE - ENERGY ←  UNIVERSE .    

1.. It was shown in [9-18] what is Primary-Neutral-Space [PNS] as well as what is Infinity 

[15] , and Rotational Energy ≡ Λ ≡ Torque ≡ momentum [22] so [PNS] → [A𝐏𝐀 ↔ 𝐏𝐁 B] 

≡ Work W =|EP |= [ |Λ|.  + Λ x  ] → W = ∫ P.ds = 0 → and  so exists Time T = ds / v = 0 .  

The Cause is , because  Primary  Point , A , is nothing  and then  is Quantized as   →   

an Point B  (which is following  the Principle of  Virtual  Displacements W = ∫ P.ds = 0  =  

Force x Displacement = Energy x Space , and according  to the  ancient  Greek Philosopher  

Anaximander [ The non-existent (  i.e. the  Point A ) , Exist when is Done ,  it  occurs  as   

( Point B )  i.e. ≡ [ Το μη  Ον , Ον γίγνεσθαι ]  =  [ Το Τίποτα υπάρχει Όταν αυτό Γίνεται ] 

Time is Not existing  because ds = ∞ . 0 =  constant  [21-22] .   The relative Range is the 

Displacement AB → which is The Monad-Space as AB = 0 → k → The Infinity Anti-space.     

2..  [PNS] The Energy-Quaternion  [ |Λ|.  + Λ x ] ≡ �̅� ≡ [ λ ± Λ x  ] ≡ |�⃡�𝐨| 𝐰. 𝐞^{ [ �⃗⃖�  i  

      /  √ Λ' �⃗⃖� ] . [Arc Cos (w|λ|/2 . |√ �⃡� `𝐨. �⃡�𝐨|] } which is  the Beyond-gravity Forced - field . 

[25] . As in case  (1) →  there is No change  of  ds →  so Time  T = ds / v = 0  . The Cause is 

the Lever arm moment of the Primary Forces and is Quantised as the Torque , < The Torque 

modelling of microscopic description > , and later the Momentum [19] .  

     The relative Range of the Infinite Points is the Displacement AB = �⃡�  to Infinity  ∞  .  

3.. [PNS] → The Temperature-Quaternion[ λ , ± Λ x  ]  = z o = Λ =  n.R.T / V( λ = C)  →   

     The Gas equation  →  No change of  ds → so Time T = 0 . The Cause is  the  Heat causing  

     vibration  on  molecules and  is  Quantised as   →  Intensity ( Pressure σ  = 
𝟐𝛑𝐫.𝐟

𝚽
 = 

𝟐𝛑𝐫.𝐜

𝚽.𝛌
 =     

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

     
𝟐𝛑𝐫.𝛔

𝛌
) between them . The relative Range of the Infinite Points in Displacement is  

     AB = λ = 𝟐𝛑𝐫 which is the wavelength  λ.  

3.a → k1 ≡  z = |𝑧 0| . e - i. ( 9.π  /2 ).10   = The Energy Under Planck length , The Tank Cavity  

    of  Gravity where  �̅� 𝐄 = 0  and  ET = Λ.v B + Λ x v.�̅� and  is the  accelerating  removing , 

Rotating energy  Λ  to  v�̅� ,  m  =  0  and  ET = Λ.v.B + Λ x v.�̅� and it is the  linearly  

removing ,  Energy  Λ  towards  v B , so No  change  of ds → therefore Time  T = 0 .  

The Cause is the High Heat Conservational Balanced Tank of  gravity  and  is  Quantised   

as  The Fundamental Particles ( Bosons and  Fermions) . [30]   

     The relative Range  is of the Infinite Points in Displacement  |AB|  to  Infinity .       

3.b → k2 ≡  z = |𝑧 0|.𝐞− 𝐢(
𝟓𝛑

𝟐
)𝟏𝟎

 = The Energy In Planck length → ∞  changes of  ds →    

     so Time T = t . Cause are the Infinite changes of  Space and is  Quantised  as → Matter , 

Energy and  the Existent as caves . The Material-Points occupy a relative Range in Planck`s  

length  as   In Fig-1-   

3.c. → k3  ≡  z = |𝑧 0 =Λ|. e - i. ( π  / 2 ) . 10   = The  Black Hole Temperature , Balanced Tank  

Energy length , where  PV = n.R.T  and  ( PA  =  Wd  =  σ.T 4 )  → No change  of ds  →  so 

Time  is  T = Constant . Cause is  the Very high Heat  causing  vibration on  molecules  and  is 

Quantized   as  →  Intensity = ( Pressure  =  Fd =  C. �̅�  =  ± Co .w.[√ A² - x²] )    i.e.   

Cause → (Constant  Co) →  Quantized  as New monad  and relative Range  is Infinity , or    

The meter of Space-Energy- changes is time T , which exists in k2  Quantized-Region only.  

From Quaternion equation  �̅� = [s  �̅�. i] = [s² ±�̅�.s²] = [ �̅�↔�̅� ] = [ +|�̅�|² ↔ - |�̅�|² ] is seen   

         that  motion , +|�̅�|²  at Point  A , is transferred as  motion  - |�̅�|²  at Point B . This issues  

        from Quaternion equation  �̅� = [s  �̅�. i] = [s² ±�̅�.s²] = [�̅�↔�̅�] = [ +|�̅�|² ↔ - |�̅�|² ]. Fig -1-  

 i.e.  The Vectors-Sum of , n , Vectors , either On The  Same  Linear-Direction Or , On Non  

         Linear-Directions Results on The – Resultant - Vector �⃗⃖�   of the Linear-Vibration and   

         between the Quaternion Edge-Poinds [ �̅�↔�̅� ] . 

Conclusions –1- : Energy In Primary-Neutral-Space [PNS] and , In Under Planck1s length ≡ 

The Tank Cavity of  Gravity is an  Standing Wave with NO-Time existing as T = ds / v = 0 .   

Conclusions –2- : Since In Primary-Neutral-Space [PNS] and , In Under Planck1s length ≡  

The Tank Cavity of  Gravity existing as T = ds / v = 0 . the only meter of changes is the Period  

of Rotation  of the  [⊝ ↻ ⊕] as in the next Figure-11 .  

 

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47 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

  

Figure –11-The Rotation of Opposites [⊝ ↻ ⊕] and the How and Why Spin is equal to 1 ,  
𝟏

𝟐
    

In (1). The Glue-Bond-Pair of  Opposites [⊝ σ ⊕]  of the Rectilinear motion for both →  

     Great  circles and  the Small circles , creates on the  Stress-common-curve  Rotation  

     of circle of radius r , the velocity  v̅ = w.r =  
2π

T
.r = 2πr. f = [ 

σ

2
 ].(1+√5) = ± σ.Φ , and the  

     frequency  f = 
(1+ √5 ] ) .  σ

4πr
 = 

σ Φ

2πr
  ,  of a  Period  T =  

4πr

σ(1+√5)
 = 

2πr

σ.Φ
  and , ± σ , where then  

     exist  two equal  and Opposite Forces , →  the  Centripetal , Fp , and the Centrifugal , Ff   

     force . The Produced work as Energy is → E = h f = �̅� = Momentum = r m v = r [
𝜋 𝑟²

2
] w r  

     = [
𝜋 r4

2
]w = [

𝜋 r4

2
] 2πf = π². r4.f = �̅� , where f = 

(1+ √5 ).σ

4πr
 = 

σ.Φ

2πr
  , meaning that the Stress - 

Pointy Rotation creates the Angular – Momentum and momentum as  , �̅� , �̅� , in the  

Zero Wave-note . [70]         

The Glue-Bond Pair of Opposites [⊝ - ⊕] in the  → Left Direction of Small circles creates 

a Rotation on circle of radius , R , with velocity v = w.2r = 
2π

T
.2r  = 4πr. f = [ 

σ

2
 ].(1+√5) , 

where  frequency f = 
(1+ √5 ] ).σ

8πr
 = 

σ Φ

2πr
 , Period T = 

8πr

σ(1+√5)
 = 

2π(2r)

σ.Φ
 , where ± σ are the two 

equal and opposite Centripetal ,Fp , Centrifugal ,Ff  force , with Energy → E = h.f =  
h.σΦ

2πr
 ,  

in One Wave- note.  The Glue-Bond Pair of Opposites [⊝ - ⊕] in the →  Right Direction  

of Small circles creates a Rotation on circle of radius , R = 2 r , with velocity v = w.2r =  
2π

T
.2r = 4πr .f = [ 

σ

2
 ].(1+√5) , where frequency f = 

(1+ √5 ] ) .  σ

8πr
 , Period T = 

 8πr

σ(1+√5)
 = 

4πr

σ.Φ
 and  

the ± σ  are the two equal and Opposite Stresses , Or  Centripetal , Fp, Centrifugal , Ff force .  

      Energy is → E = h f =  
(1+ √5 ] ) .σh

8πr
 =  

σΦh

4πr
  ,  in the One Wave - note . 

In (2) The hollow-Cone of 90ᵒ , between Angular-momentum-vector �̅� and Angular-velocity- 

     vector �̅� when illuminated by a circularly Polarized light beam , then any changes in Spin  

 

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48 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

     ≡  �̅�  of the Polhode Cone POT and the exchange of Linear and Angular Momentum  

between Electromagnetic fields and the material Media are shown as the Profiles of  

the Phase and the Angular-velocity-vector in the  POT- cone cross-sectional Plane , i.e.   

               The Space can be eternally twisted but cannot disappear . [70]    

Measurements of Physical-Properties such as Position , Momentum , Spin and Polarization , 

performed on Entanglement Particles gives rise to seemingly Paradoxical effects considering  

Systems  as a whole  and the  ERP Paradox . The answer is given in Figure 1-(the right-2) 

where is shown each Property of the Material-Point . The Spins [⊝ ↻ ⊕] Presuppose   

[⊝ , ⊕]  Material-Points  which are The caves in PNS Space .   

Conclusions -   

The Energy in Spins , Presuppose that the  Caves to be in  [PNS] Space and in the Under 

Planck1s length . The ± Spin  is created from the Opposite  Centripetal , 𝐅𝐩 , Centrifugal , 

𝐅𝐟 , forces . The Energy  E  is initially absorbed  in [PNS]  and  in all quantized  regions , 

either as momentum (mv)  or as  Rotational Momentum (Λ = r. mv) . From momentum 

relation  �̅� = m r v = m r² w = m r² (2πf)  = 
J.w

2
 = [

πr⁴

4
].[2πf] = 

π ²𝐫⁴f 

2
 , then the Mass of the 

elementary Particles is →  m = 
2π³𝐫⁴,f ²

r²2πf
 = 

𝛑²𝐫²

𝟏
f = [

𝛑𝐫.𝐯

𝟐
]v  ,  Or   𝐦 𝐄𝐏  = 

𝛑.𝐫²

𝟒
 = 

π.(1,07.10−7)²

4
 = 

8,992023.10−15 Kg  , in the min Planck`s cave  𝐝 𝐏𝐜 = 1,07. 10−7 m → which agree with the 

Diffraction Energy mechanism for all Space Levels of quantization and which are the 

Energy Particles only ,where for base e = 2,71828  and k = 0 → 𝐋 𝐯=  e^i.( ± π/2).b  

the Space is   e^ (-15,7079) = 1,78118 .10  ̄ 7  m           

Since velocity v = s / t = distance / time then for constant  s ,  then  v is also constant  and    

t = T , the Period of vibration and  for any  constant momentum   Λ  =   λ2  m2  v²2  / 2  =  

 λ2  m2 [wλ2 ] ² =  4π². m2 . λ³2 .f ² = [4π². m2 . λ³2 ] f ² =  Co. f ² = Λ  ,  i.e.   

            In all Rotational Systems  time T is constant and equal to  the Period of  

            Rotation which is the meter of changes . For monads in  k2 ≡ PNS region 

            ET = [Λ  +Λ x ] = [Λ.M+ΛxM ] = √ m. v²E + [Λ.  vB + Λ 𝐱  vB ]²  =   

             = √ m. v²E + [Λ.  vB + S ² ] ²  = h . f = h / T  =  h .v / λ ,                  i.e.              

In every monad issues  λ.mv/2  =  h f = λ Λ   and Kinetic-energy Λ = h f / λ = Co.f   where the 

constant  𝐂𝐨 = E/ f ²  a gauge magnitude depended  on the angular velocity �̅� , the velocity �̅� , 

and  then wavelength  λ is conserved as momentum  (mv) or angular momentum  ( Λ =  r. mv̅ 

= m. wλ²/4)  or  both . Considering  oscillatory  motion  as  the simplest case of  Energy 

dissipation  , and this because any other motion is not  differently conserved , then The 

Work  embodied  in Dipole  is an  <  Spring-mass  System with viscous dumping  >  

with co variants , energy E , mass  m , velocity �̅� = �̅�E = ẋ  wavelength  λ , and  then Energy 

dissipation  is the damping force  equal   F d = C ẋ  where  C is a constant and ẋ  the velocity.  

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49 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

Following the steady-state of  displacement and velocity then →  x = A. sin(wt - θ) ← and   ẋ 

=  w.A .cos(wt-θ) = w x , where  the Energy dissipated  per cycle is the executed work which 

is , W d  =  F d .dx = ∲ C x̅ dx = ∲ C x̅ ²dt =  π C w A²  =  (π/4) C wλ² =  

[π²/2] C. f . λ²  → The Energy dissipated  per Cycle  Wd   by  the damping Force  𝐅 𝐝  , is  

mapped  by writing velocity ẋ  in the form  ẋ = wA.cos(wt - θ) = ±wA.[√1 − sin²(wt − θ) ]  

=  w . [ √A² − x² ]  where then  the Dumping  force   F d = C. ẋ = ±  Co .w. [ √A² − x²]  and  

by rearranging [ cos²(wt-θ) +sin²(wt-θ) =1]  then is  Fd ² / [ Co .w. A ] ² + x² / A² = 1 , i.e.   

        Energy = motion is mapped as an  Ellipse  with  𝐅 𝐝 ,x  mapped  along  the vertical   

        and  horizontal  axes  respectively and  the Energy Dissipated Per - Cycle is  given  

        by the  area  enclosed  by the above ellipse .   

The Total Energy  E  =  λ2 . Λ  which is embodied in monad AB̅̅ ̅̅   is moving as an Ellipsoid  

in the Configuration  of  co variants  λ , m , v = �̅�E , as  Kinetic ( Energy of motion Ω̅ ) and   

Potential Energy  (The Stored Energy in  λ , m , v) by Rotation  and  Displacement , on  the 

Principal axis  (through the centre of  monad ) , which  is mapped out , as  in Solid material  

configuration by the nib  of  the Rotational-Vector  (Ω̅ ) = δ r̅ c) = [ v̅ c + w̅ . r̅ n] . δt , as the 

Inertia-ellipsoid  [ The  Poinsot's - Ellipsoid of construction ]  in an  Absolute Frame which 

instantaneously Rotates around vector axis w̅ , θ , with the constant  Polar distance w̅.Fd/|Fd|   

and the constant angles ϑs , ϑb , traced on  Reference - Cone [Body Frame] and on [ Absolute  

Frame ]  cone , which are rolling around  the common axis of  , w̅ vector , without slipping ,  

and  if  (Ω̅ ) = Fe , is the Diagonal of  the Energy Cuboid  with the three  dimensions a̅ , b̅ , c̅   

then  follow  Pythagoras  conservation  law , with the three  magnitudes [J,E,B ]  of  Energy- 

State  following  →  Cuboidal  ,  Plane ,  or  the Linear  Diagonal direction . [ 25 - 26 ].   

The Transportation of Energy on Edge - Points  happens in Material Geometry , while  

the Transportation of  the Edge-Points as  , Positions ,  exists in Vector Geometry only.  

Since in Vibrations the Deformation of the Spring  is an equilibrium Position in ∆ , and   

the Spring-Forse  k ∆ = w = m g = Gravitational force w acting on mass m , then exists  →   

m �̈� = ΣF = w = k [ ∆ + x] ….(1) , and because k ∆ = w  we obtain  w ²n = k/m.. (2) and (1)  

becomes →  �̈� + 𝐰 ²𝐧 = 0 ,…(3) ←  i.e.  The Transportation of  Energy is a Harmonic -

Vibration in cave  ∆  , means the Wave Pattern . 

It is shown [92]  that  in PNS-Space the two equal and Opposite Stresses  ± σ , are the Two  

Centripetal , 𝐅𝐩 , Centrifugal , 𝐅𝐟 force  where Energy is → E = h f =  
(1+ √5 ] ) .σh

8πr
 =  

σΦh

4πr
  ,   

in the One Wave - note .and the  frequency f =  
(1+ √5 ] ) .  σ

8πr
  , Period T =  

 8πr

σ(1+√5)
 = 

4πr

σ.Φ
  .     

10.a.. The E-Spaces and the Energy Regular - Polygons  .  

     a.  THE  GEOMETRICAL  SOLUTION  :  

     a.. The  Even  and  Odd   n-Polygons  [ 80 ] :     

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

    

 Figure –12a- An Even and an Odd n-Polygon in circle  O ,OA  with diameters , Ak A2k ,  

         Passing from  Point A2k , as Vertex (apex) of the Polygone , and  diameters  , Ak+2 M1   

         To be  Perpendicular to Side  A1A2 . The Projections of the Heights  𝒉 𝒏 .     

         Let be the n-Polygon    A1 , A2 , A3 , Ak ,  Ak+1 , Ak+2 , A2k ,  in circle  (O , OA1) ,  

(e)  a straight line not intersecting the circle  

d1  , d2  , d2k  ,     The heights of the vertices to (e) line ,  

h1  , h2  , h2k+1  ,  The heights of the midpoints  Mk Mk+1  of the sides to (e) line   

φ  h−λ ,                , The Angle of the vertices and the ( ⏊ ) Semi -Sides , and   

OK  =  h  , The height from the center  O  to  (e) line .  To Proof  :   

In any n - Polygon  ,   The Sum  , Σ = Σ (h) ,  of the Heights  , d1  , d2  , d2k  , of the Vertices   

A1 , A2 , A3 , Ak ,  Ak+1 , Ak+2 , A2k ,  where  n = 2k  , from any straight line  (e)  is equal to  

                              Σ = Σ (h) =  n . OK = n . h    .   The Geometrical Proof in [ 80]   

Remarks :  

1..  In the System of  Regular - Polygons the ,  Interior angles ( w )  and Gradient ( φ ) ,  

      Heights ( h )  and their differences , Δh , – Summation and Subtraction of  Heights  

      are  Interconnected and Intertwined  at the Common Circle  [ A , Δh = 𝐡 𝐀- 𝐡 𝐁 ]  

      Producing  the Common  ( n+1 )  , Odd – Regular - Polygon . This Property allows  

     to refer  the Regular - Polygons to the Tangents of any Triangle A,B,C, as it is the  

     8..[a]   { STPL }  Mechanisms : The Six Triple Points Line Mechanism . i.e.  

                     The Fundamental Particles Origination happens  from The Electric and  

                       Magnetic Field of the 3 Conductors On 2 Anti-Parallel-Strands , Fig– 9a- 

2.. 𝐬𝐢𝐧 𝛗   = (  
𝐡 𝛗  

𝛌 𝛗
 ) ,  is the Harmonic - Mean between [ 𝐡 𝐀 - 𝐡 𝐁 ] , [  

𝟏

𝟐 (𝐫 𝐚 − 𝐫 𝐛)
 ] 

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

The Force Harmonic Vibration & The Unbalance Vibration System :  

 

 Figure –12b- The Complex Frequency Response from the Vector-Force-Polygon is seen 

that the terms of the Forced Harmonic Vibration , ( m ẍ + cẋ + k x ) =  𝐅 𝟎 .sin(w t)  , are 

Perpendicular to the y-y axis .When the force changes to = 𝐅 𝟎 .cos(w t) , then the terms are  

Perpendicular to the  x-x axis , i.e.  Vector-Force is  𝐅 𝟎 .[ cos(w t) + sin(w t) ] = 𝐅 𝟎 .e
 i.[w t]      

     The Rotation  Unbalance Vibration System :  

      For an Unbalance-Rotational System , the Source of vibration excitation IS considered  

an Spring mass System constrained to move  in the vertical dirtection  and is excited by an 

Unbalanced rotation. The Unbalance is represented by an eccentric mass m ,with eccentricity 

e , and Rotates with angular velocity w , on the Nonrotating mass  M - m , with displacement  

x + |
𝐞

√𝟐(𝐧)
 | ,  The equation of motion is , [ M-m] ẍ + m

d²

dt²
 [x +|

e

√2(n)
 |] + c ẋ + kx = 0  , which 

can be rearranged to      →  M ẍ + c ẋ + k x  =  m |
𝐞

√𝟐(𝐧)
 |  ←   …... (c-2) .  as in Fig-12b-2.   

By tuning the System to the frequency of the exciting force  Fo= 1 such that w ² = 
 k 2  

  m 2    
, then 

System  acts as an Vibrator-Absorber and reduces the motion of the main mass  M ≡ m16 ≡  

m1 and  m 8 ,4 ,2 ≡ m2 ≡ m , to Zero . Making the Substitution  , w11² = 
    k 1 

  m1
 , w22² = 

   k  2

  m 2
  , 

and assuming the motion to be Harmonic , then the Steady-State solution is ,  

XS  = 
   m  |

e

√2(n)
| w ²

√(k−Mw2)2+ [cw]2
  , and   tanφ = 

c w 

k−Mw ²
  and so the reduced  to Non-dimensional form 

equation for amplitudes is , X S =  | 
m e

M√2(n)
|.|

  [ 
𝐰

  w n.
  ] ² 

√(1−[
𝐰

  w n.
 ] 2)

2
+ [2𝜁

𝐰

  w n.
 ]
2| , and tanφ = 

    2 ζ .[
𝑤

 w n 
]    

1−(
𝐰

 wn  
)²

 

…... (c-3)  which is  identical with    , m ẍ + c ẋ + k x =   Fo.sin  wt  ….. (b-4)  for  Steady-

State solution . The Resonance frequency  𝐟 𝟏 = 
w1

2π.
 = 1

2π.
√ 

𝑘

𝑚
− 

𝑥²1

2m².
   ,        From (c-3) ,   

a).  Choosing the Damping factor-values  ζ  and the eccentric weight exciter e , is Possible  

      to define  the Resonant amplitude  X = 
1

2 ζ.
 [ 

m e

M
 ] , and  by altering the eccentric mass-m  

      the Prober X = 
m e

M
 .  

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

b).  Above Un balance happens in Rotating machines or wheels , which can be repaired  

       by Adding or Detaching  ± masses , or the opposite ∓ Detaching – Adding masses. 

1). For small values of  ,  
𝐰

 wn  
 << 1 , both the Inertia  m.w².X , and Damping forces  c w X , 

     are small which results in a  small  Phase angle φ . The magnitude of the impressed force  

     F0 , is then nearly equal to the Spring-Force , k X , as in Fig.12.b-2 

2). For value ,  
𝐰

 wn  
 = 1 , the Phase angle  φ = 90 °, as in diagram .The Inertia Force  mw²X ,  

     is larger and  balanced by the Spring force  k X . whereas the impressed force  F0 is  >> 

     the Damping  force . The Amplitude at Resonance is  X = 
F 0

 𝒄.wn  
 = 

F 0

 𝟐𝛇 𝐤  
 , or from diagram.      

3).  For large values ,  
𝐰

 wn  
 >> 1 ,  the Phase angle approaches φ = 180 ° , and the impressed  

      force F0 , is expended almost in overcoming the large Inertia force , mw²X .    

a. THE  NATURAL ANALOGOUS  OF THE ENERGY MOTION  THROUGH THE PATHS . 

            The Propagation Path of Vibrations  & The Vibration-Absorber . 

 

Figure –12c-  The Electromagnetic-Wave {�̅�. fn̅  + �̅�.𝐟𝐧 } into the Atoms-Bracket-axes-Hook. 

                      The Process of  the Photo elastic  Fringe – Pattern  [96A]  

In-1-  The Unloaded  Beam ( F = 0 ) is the Length AB̅̅ ̅̅  .  

In-2-  The Loaded  Beam ( F = F ) is the Deflection-Curve  AB⏟
dh

 , the Strain , where exist ,  

a.. The Shape of the Beam is the Space , the Strain , the Figure of the System ,  

b.. The Shape of the Line-Stresses is the Figure-Fringe  the Path of Energy  .  

c.. The Colure  of  the Figure-Fringe . is the motion = the Energy  the Forced Vector. 

In-3-  The Loaded and Deflected-Beam are  the Spaces = the Figures of System.  

          The Loaded and Deflected-Beam Strain-Lines-Fringes , are the Path of motion ,   

          The Loaded and Deflected-Beam Colure - Fringes , are the kind of Forced Vector,   

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

  The Complex Force – Vector Harmonic - Vibration & The Vibration-Absorber .  

 

Figure –12d- The Complex -Force -Vector is  𝐅 𝟎 .[ cos(w t) + sin(w t) ] = 𝐅 𝟎 .e
 i.[w t]  .  

In-1-  The Terms = ( m ẍ , cẋ , k x ) , of Vector Force Polygon are Perpendicular to y-y axis.  

           In Case of Complex -Force -Vector  the Polygon becomes an Absorber which  

           Reduces  the motion from Kinetic Energy to Potential Energy (a Magnetic Field) .  

In-2-  The 2-DOF System with Vector Force  such that ,  w ²11 =  
k 1

 m1  
 ,  w ²22 =  

k 2

 m2  
 , acts  

           as  an Vibrator Absorber , and reduces the motion of the mass m 1  to zero .The two  

           Natural Frequencies , f 1  , f 2 ,  are Perpendicular [ ⏊ ] each other  as the Diagrams.  

           This happens for every action on the  8.[ a , b , c , d ] Physical - Mechanisms .           

In-3-  The{ STPL } - Six Triple Points Line Mechanism is formed from Three Tangents  

          from  A ,B ,C  Spaces on 2R - Circle . Since Pascal-Desargues lines meet on  Markos 

          STPL Mechanism lines ,Then transfer the Properties & Information ( f 1  , f 2 , ,, f n )  

          From The Complex-Vector-Absorber = 𝟐𝐑̅̅ ̅̅  ,  to The Vector-Force-Polygons  

Remarks :  

1..  The n-Knots Figures is any N-DOF System , which Characteristic equation results to  

      an Algebraic equation of  3-n Degree , with main equation of motion [ λ.M + K ] X = 0  

2..  The n-Knots Figures exist in Figures where the Vector -Force - Polygons have the same  

      number n , as the in Figures . In (3) The Circularly- Charged  Breakages are the three- 3   

      elements [Σ = n . h]  [s² = ⊕  , 2s²= , - s² = ⊝] which formulate the 3-Knots Figures. 

      This {STPL}-Mechanism of 3  elements ( n=3 ) determinates the Mould which denotes  

      the number n , of the Spaces for  Elementary-Particles Vector.  

3..  The case of {TCIC}≡ [ Σ = n . h ]  8 x ①  which is the Physical Mechanism , gives  

       the n-masses of Atom`s &Compounds determining the Atoms Complex-Vector-Response.  

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    B… GENERAL  :                

1.b. The Spaces and the Energy States .  

1…The Objective Reality is composed of  two elements , that of Distance . The Space ds ,   

       and that of Motion , or else the called Energy , and it is the content of all sciences [32]  

2…The Euclidean-Geometry describes the Space only but Not the Energy as is motion [48]  

3...The Solution of all the Unsolved-Ancient-Greek-Problems [50] opened the way to the 

     Material-Geometry [54] which Incorporates the Motion → In-Space as (⊕↔⊝) ≡ 0,[61] 

     The Space exists in Energy - Caves as Energy-Quantum-Quantities  [39] , while Motion  

or  Energy exist in Caves as an Confined - Stationary-wave which is either Static or an 

moving Energy-Storage or an Energy-Box [68] . The Any-Two Opposites (+) , (-) exist in 

Nature and  are found everywhere from → Zero-Point (0) ≡ [+ = -] or as (+ A) + (- A) = 0  

in E-Geometry  and →  [0] = [⊕↔⊝] ≡ f n , [⊕←ds→⊝] ≡ ds in Material-Geometry , to  

     the aperon , ± ∞  where → The Space ≡ ds , is the nodes distance , and motion exist  

     as the Vibration  Type   ← [52]  

4..The Electron-Nutation in Hydrogen cave Produces Energy due to g  effect , as an minimum    

     frequency fn ≡ 2,8398447. 1010 H  and thus exists in all Atoms . This Energy in Hydrogen-   

     Cave is an Electrical -Magnetic Conductor, which is The Pin of Atom-Plug and enters Into  

     the other Atom-Sockets , which are the Orbit-Bracket–Hooks . These are the Hands of    

    Atoms , i.e. → The Atoms-Plug , Placing their Pins into the other Atoms  Drains ≡ Holes ,  

    and so is done  that  what we say the Bonding of Atoms  . 

5.. Because of  the Resonance frequency between all Atoms , and because of  the Common     

     Hydrogen , so Atoms Bond by Pinning and form  Molecules and all Compounds in this  

     Cosmos . This is Possible because the Periodic-System of Atoms is NOW modulated into  

     4 New - Categories with  Only-One New- Criterion which is The Number of (±) Energy  

     Conductors  in Atoms , related to their Stability .  

6..The first Solid (4 Points not coinciding ) is The Tetrahedron , and the first Material Space  

     for the Two elements (+) , (-) , are (4 x 2 = 8 Positions for Electrons )  The-Cube , i.e. the  

    Tetrahedron is Into the Cube and Into  its  Ex - Sphere , and this because all the Circles on 

    Tetrahedron exist on Sphere .  

7.. When 1-8 Electrons ⊝  are Placed  on the Cube's Vertices and into this Onion - System ,  

     then Automatically are formed  the 1- 4 , Energy-Conductors  , where issues [⊕ ↔ ⊝]  

 = [ p ↔ e ] = [Atom-Plug = + Electric Vector ↔ - Magnetic Vector ≡ Drain ≡ Hole ] , and 

are the Actions between Opposite . With this New modulation [ The ,1 , 2 ,3 , 4 , Energy-

Conductors ≡ Atoms-Four Fundamental frequencies] , Conductors exist on System and ARE  

ACTIVE + as → The-Electric-Vectors ← and simultaneously PASSIVE ≡ Drains (-) as → 

The-Magnetic Vectors ≡ Holes ← . The Zero-State Conductors are those whose  8 Cube- 

Positions are all filled with electrons . The Multiple – Plug-Pins Atoms can Plug all the  less 

number Electrons - Atoms and can Be-Plugged from all the greater number Electrons-

Atoms .With these Four modulations are formed all Atoms and their Compounds these  

are the Mechanisms of  , Water , the Cells , RNA , DNA , Cancer ,and everything in this   

    Energy - Space Universe .  

8..In the same way , is that  where an  110 Volt Refrigerator Can’t-Plug into  220 Volt Socket  

and this because are different in construction , the same to Atoms-Plug which differ to the  

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Number and the Length of their Pins . Hydrogen is the Multiple-Plug-Pins Atom which can 

Plug all Atoms and itself.      

9..The New-Atom-Structure is consisted of →  a) The Nucleus IN-Sphere  b) The Dynamic  

Electro-Magnetic -Tetrahedron  ,  c) The N-Outer- Cube  , d) The Orbitals in EX-Sphere. 

10..In the New-Atom-Structure , the Master-Keys - Resonances are the Communications-  

11.. Article [110] is the completion of [72-82] and of Physical interpretation of the three  

      constants of nature , that of Planck constant 𝐋 𝐏 , Newton`s  Gravitational constant  

      G , and the Gravity Constant  g ,with a rigorous Geometrical and Mechanical logic .      

It was shown [33-36]  that Un-clashed Fragments through the center , O , consist the Medium-

Field Material-Fragment → [ ± s² ] = [MFMF] ≡ The Chaos , the Base for all motions ← and 

Gravity which  is a force [ i] while the clashed with the constant velocity , c̅ , consist the 

Dark matter [ ± .c̅.s ] and the Dark Energy [c̅. i]  , so declaring that → Antimatter-Galaxies 

and Antimatter-Asteroids can exist only as Dark-matter or and Dark-Energy and Not as 

Antimatter light , - c . From the velocity Breakages  [ ± s² = ± (w r)²] , [ i = 2(w r)² ] and 

the between instress σ , become the Waves {The distance ds = r =|AAE| which is the Work 

embedded in monads and it is what is vibrated as frequency f } of the Material-Point with  

         their Vibrating  equations of motion and after to become the Waves .  

A → The Particles with Inherent Vibration occupying the Distances r = ds =Positions |AAE|  

         the {Monad = 𝐎𝐊𝟎 = R} ≡ Energy In Vacuum Spaces are the Fundamental Particles ,       

          as [ ± v̅.s²] →  Fermions , Quarks and Leptons , and → [  v̅. i] →  the Bosons , 

B → The Gravity-Antigravity Field-Energy g without Vibration being a Stationary-Rotating  

         Spinning Material Point M-P.  [ ± s² ]   →  The [MFMF] Neutral Field  ≡ The Energy            

         Chaos , and their Negative Energy Binder - Field [ i ] → as ± Positions , 

         For  �̅� = ± �̅�  ,  then  + �̅� = + Gravity – Spin = +   
𝛑.𝐫𝟑𝛔.𝚽

𝟐
       The Gravity Spin      

                                          -  �̅� = -  Gravity – Spin =  -   
𝛑𝐫𝟑𝛔.𝚽

𝟐
      The Antigravity Spin  

C → The Dark-matter and the Dark-Energy constituents are as below ,  

         [ ±c̅.s² ] →  The Dark-matter , and the Binder Gravity-Force  g̅ ≡ [ i] ,  

         [ c̅. i ]  →  The Expanding Dark -Energy , Positive-Energy , which both are   

                             moving with light - velocity , c̅ , causing the Universe to Grow.   

            From above in , A , and ,C, case → Energy as Velocity ,v̅, and , c̅ , exists in the  

           Discrete monads ,± v̅.s² , and  , ±  c̅.s²  only . 

2 ,  The Case of  Transportation of Energy , from Chaos to Stationary-Material-Points .  

       Dark Energy  DE ≡ [ �̅� . i] (©) , Acting  Positive-Energy , on the Five Constituents   

                                      {  [ ( i) , (+s²) , (-s²) , (+cs²) , (-cs²) ]  } then Produces , 

       [ ± s² ]    →   The [MFMF] Field [ ± c̅.s² ] → DM-DE  Field of , DM = Dark matter ,  

                             and  DF = Anti matter = Dark Energy .   

       [ ±v̅.s² ]  →   The PNS  Space , Particles  Fermions , and [ i ] → Gf ≡  Gravity-Force   

                             in  DM-DE  Stationary Rotating = Field .         

       [ v̅. i ]   →   The Bosons ,          

       [ c̅. i ]    ≡    The  DE →   Dark Energy →  The Travelling-Energy with  , �̅� ,  velocity.     

       𝐜   x (©)  [ i ]  ≡  Gf    →  The Gravity Force .   

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            In all above issue Kepler - laws , denoting that Macrocosm and Microcosm  Obey  

            the Newton`s Laws of motion , in all Scales , as was Proofed .    

 

 Figure - 13 - Vector-Geometry follows the Geometry rules as the left figure. EuclideanVector                                                                                                                                                                                                                                                   

       Carry Point A to  Point  B as , AB , following the Geometry rules , while The Material – 

      Points ≡ Quaternions ,  Carry the Motion ≡ Energy , from Point A , to the Point , B ,  

      linearly .  In both cases the  Points are nothing Possessing Zero-magnitude and Infinite- 

      directions . The Two Points in  E-Geometry consist the Straight-line-Segment Possessing  

      |AB| - magnitude  and the |A→B| Directions while the Two-Points in Material-Geometry  

      denote Two-Elements as one  (+) and  one (-)  Performing  the Space ≡ |AB| of motion =  

     Energy ≡ [A ↔ B] in |AB| Space .The above  comparison can bee seen in Figure-1- also .   

      Conclusions – 3 -  :  

      From above Analysis  is Seen the Path which Energy as motion follows to Propagate .  

      This Path is the Resultant of the Vector-Sum , or the Quaternion as Material–Point .    

      The Vector-Sum-length as a Geometrical-Resultant-Vector is the Quaternion`s Edge  

      Points Energy-vibration which transfers the motion from the vibrating-Edge-Points . 

      Thus  Stress → σ = [
 2πr 

Φ ²
] . f n  ←  is the Way of Information and Storage  in Nature .    

 Extending  above to all Planetary Systems and to Universe is seen that BIG - BANG . has 

Never been existed , Inversely Energy ≡ Motion ≡ Matter followed the (+) Stress-Storage , 

± σ = [
 2πr 

Φ ²
] . f n , and Anti-Matter followed the (-) Stress-Storage and Material-Geometry.   

2.b. The Complex Numbers  &  Quaternion .              

1…  De  Moivre´s  formula for complex numbers states that  the multiplication  of  any two  

Complex numbers  say z1 , z2 ,  or [z1 = x1 + i. y1 , z2 = x2 + i. y2] where  x = Real [z]  

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the Real-Part and y = Imaginary[z] . the Imaginary Part of , z , is the multiplication of  their  

moduli   r1 , r2 ,  where the  moduli  , r ,  is the magnitude  [ r = | r | = √x² + y² ]  and the  

addition of  their angles , φ1 , φ2 , where  φ = arg.(z) = atan2.(y , x)  and so  ,  z1 *  z2    =  

( x1 + i. y1) . ( x2 + i. y2)  =  r1. r2 [cos(φ1+ φ2) + i .  sin(φ1+ φ2) and when   z1 =  z2 = z  ,  

and φ1 = φ2 =  φ  , then z = x + i y  and  z . z = z² =  r².[cos2φ+i.sin2φ)  and for , w , complex  

numbers becomes the Euler`s ,  zw = rw. [ cos(wφ) + i. sin(wφ)]  and so for r = 1  then  →  

zw = 1w. [ cos φ+i. sin φ ] w = [ cos.(wφ) + i sin.(wφ) ] . The  n.th root of any number z , is a 

number b [ √z
n

 = b]  such that bn = z  and when  z  is a Point on the Unit circle r =1 , the first 

vertex of the Polygon where φ = 0  is [ b = (cosφ + i sinφ)] ⁿ =  b ⁿ = z = cos(nφ) + i .sin(nφ)= 

[cos(360/n) + i. sin(360/n)] ⁿ = cos 360  + i.sin360  = 1+ 0.i = 1        i.e.  

The w-Spaces which are the repetition of any Unit complex number z (multiplication by 

itself )  is equivalent to the addition of their angle and the mapping of the Regular Polygons  

on circles with unit sides , while the n Spaces which are the different roots of unit 1 and are  

represented by the Unit circle and have  Points  z = 1  as one of their vertices , are mapped as  

these Regular Polygons inscribed  the unit circle  , Figure-1- (1) 

Since also  𝐳𝐰 = 𝐳− 𝐧  and  𝐳− 𝐧 =  𝐳−𝟏/ 𝐧 = 𝐳+ 𝐧  therefore complex numbers are even and  

odd  functions ,  i.e. are  Symmetrical  about  y , axis ( mirror ) and  also about the origin .  

Euler`s  rotation in 3D Space is represented  by an axis (vector)  and an angle of  Rotation 

which is a Property of complex number and defined as  �̅� =  [ s ± �̅�.i ]  where  

s , �̅�  are real numbers  and  i  the imaginary Part such that  i ² = - 1 . Extending imaginary Part   

to three dimensions , 𝐯𝟏 , i , 𝐯𝟐 , j ,  𝐯𝟑 , k →  �̅�. i   becomes Quaternion which  has  1 + 3 = 4   

degrees  of  freedom  i.e.  [ dx – dy – dz – df ] ≡ The Space - Energy- Mode .   

2… De Moivre´s  formula  for the  n-th  roots of quaternion ,where  q =  k.[ cos.φ+ [ i].sin.φ]   

       is for  w = 1/n  , 𝐪𝐰 = 𝐤𝐰. cos.wφ + ε . sin.wφ] where , q = z = ± ( x+y.i ) decomposed 

into its scalar (x) and vector Part [y.i] and this because all the inscribed regular Polygons  in 

the Unit circle have this first vertex at points , 1 , or at  ,- 1 , (for real part φ = 0 , φ = 2π ) and 

all others at imaginary Part where , k = 𝐓 𝐳 = Tensor (the length) of vector  , z , in Euclidean  

coordinates  which is k = 𝐓 𝐳=√𝐱 ² + 𝐲²𝟏 + 𝐲²𝟐 + 𝐲²𝐧   and for imaginary Unit vector  

�̅� (𝐚𝟏, 𝐚𝟐, 𝐚𝟑, 𝐚𝐧,w) the Unit vector ,ε, of imaginary Part is →  ε = (y.i / 𝐓𝐲) = [y.  i ] / [𝐓𝐲] = 

± ( 𝐲𝟏 . 𝐚𝟏+ 𝐲𝟐 . 𝐚𝟐) /  √ 𝐲²𝟏  +  𝐲²𝟐  + 𝐲²𝐧  ,  the rotation angle  0  < = φ < 2π , φ = ± sin - 1 

( 𝐓𝐲 / 𝐓𝐳 ) , cosφ = x / 𝐓 𝐳  , which follow Pythagoras theorem for them and for their reciprocal 

quaternions �̅�` [�̅� . �̅� `= 1] .  

Since also the directional derivative of the scalar field  relation  y.( 𝐲𝟏 , 𝐲𝟐 , …. 𝐲𝐧 ,,,)  in the  

direction , i ,  is → i ( 𝐲𝟏 , 𝐲𝟐 …. 𝐲𝐧 ) =  𝐢 𝟏. 𝐲𝟏 + 𝐢 𝟐. 𝐲𝟐 + i.n.𝐲𝐧  and is defined as →  i. grad y 

= 𝐢 𝟏.(  
𝝏𝒚

𝝏𝟏
 ) + 𝐢 𝟐.( 

𝝏𝒚

𝝏𝟐
) +…= [ i. ].y , which gives the change of field  y , in the direction → i ,  

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and [i. ]  is the single coherent Unit , Therefore coexistance between Spaces ,Antispaces  

and  Sub-Spaces  of Any monad →  𝐳   =  x + y .i  =  𝐀𝐁̅̅ ̅̅   , is happening through the general 

equation  which follows     

 

                  𝐦 [𝐬+𝐯 𝐢]  =  𝐪𝐰 = (𝐓𝐪) . [cos.wφ + ε .sin.wφ]      ,  where  ,        

                  m   =  𝐥𝐢𝐦(𝟏 + 𝟏/𝐰)𝐰   for   w = 1 → ∞  ,  q = z  =  ±  ( x+y.i )    

                 sinφ =   y / √𝐱² + 𝐲²  
𝟐

 ,  cos.φ  = x / √𝐱 ² + 𝐲 ²  
𝟐

 ,  |z|  = √𝐱² + 𝐲²  
𝟐

 

                 𝐓𝐪   =  √𝐱 ² +  𝐲²𝟏  +  𝐲²𝟐  + ⋯ . . 𝐲²𝐧   ,  Ty  =  √ 𝐲²𝟏  +  𝐲²𝟐 +. . … 𝐲²𝐧   ,   

                  ε    = (y.i / 𝐓𝐲) = [y.  i ] / [𝐓𝐲] =  ± ( 𝐲𝟏.𝐚𝟏+ 𝐲𝟐.𝐚𝟐) / √ 𝐲²𝟏  +  𝐲²𝟐  + ⋯ 𝐲²𝐧    i.e. 

    The Spaces , Antispaces and  Sub-Spaces of Any monad →  𝐳   = x + y.i  = 𝐀𝐁̅̅ ̅̅      

    follows the Euclidean Geometry (2a) and the Energy flow (2b) , as in Figure -1-3-21.  

    The Vectors-Sum of Vectors ,  Either on Points on  The Same - Linear-Direction of  

    Vectors , Or on Non-Linear-Directions , Results onto The-Resultant-Vector �⃗⃖�  , of all  

     System-vectors and becomes A Linear-Vibration between Quaternion-Edge-Points.   

    This Remark denotes that Quaternions which are composed of Real (+charge) and of  

Imaginary Part (- charge) act only on the Resultant-Direction End-Points carry Energy from 

One - Edge  to another- Edge as in Fig – 6 - The Above Property of Imaginary-Part ≡ Energy 

shows The How Elementary Particles are Originated from the three Charges (of The Spaces  

[⊕ -  - ⊝]) , Circularly-Placed on The-Three-Triangles of  STPL- Mechanism . [93]              

From Planck`s Energy E = h.fP  = [ 6,6262.10−34 J.s ] x [ [ 3,28393.1015 / s] =  

2 ,176.10−18 J , and in  eV becomes  → [ 2 ,176.10−18] / [1,6.10−19] = 13,6 eV  or ,  

Energy in  Gravity-Layer  g      13,6 eV =  h f  =  h / T  =  h /√𝐠. 𝐚³.  

  \Figure - 14 -  :  The Action  of  quaternion �̅� . �̅� = [s + �̅�. i] ² ≡ s² - |�̅�| ² + [2.�̅�].|s r|. i  ≡     

                       ≡  s² - s² + 2.𝐬² and follows Pythagoras theorem of the Euclidean Geometry.  

 3b…:  The Stability of   Space - Anti-Space , IN  the Neutral-Space     

 The number of Moulds of Stationary-States are as , 2n=1−4 Points ≡ 2 ,4 ,8 ,16 ≡ 4–Types 

  i.e. Monads are formed  from the first 4- Moulds as → The 1-Point which is  everywhere,  

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      the  2- Points which form Vectors , the 3- Points which form the Planes , the 4- Points 

which form the Volumes . For  n > 4 as this is the Atom Structure, follows the Sustainability 

of the Spaces and Anti-Spaces . Since Space-Energy Structures follow the M-Geometry  

Stability these follow the Mould of Spaces  2 n = 3 = 8  Elements which is The-Cube as    

was shown before for the Atoms structure  Fig-5-28 .   

The Atoms-Bonding follows → Space ≡ Electric-field  & Anti-Space ≡ Magnetic-field ←   

 

 4b… The Quantum Interference of the Duality-Photon  :                           

Quantum Interference is the Phenomenon when , a Photon Interferes with itself .[92E]. This 

Proposition is Right when Photon is considered having a twin-existance , [101]-3c.P-21. 

The Problem is to determine the expression of the Power developed by Gravitational Force. 

From Dual-Photon-equation , v̅.[ fn̅  + fn ] ≡ | 
𝐯 

𝛑².𝐫⁴𝐧  
|. B̅n  + | c ̅| fn ,when  c = 0 or c  = c⃖ , then  

Photon motion becomes →  | 
𝐯 

𝛑².𝐫⁴𝐧  
| . B̅n  ← ≡ Spin . i.e. The Stationary Photons exist as  

their Spin only. This Rest-Space is the Part  | 
𝐯 

𝛑².𝐫⁴𝐧  
|. B̅n  and its Communication Code to be  

the term | 
𝐯 

𝛑².𝐫⁴𝐧  
|=| 

𝐰 𝐫 

𝛑𝟐.𝐫⁴ 
| = | 

𝟐 𝐯 

𝟐𝛑 𝟑𝐫 ⁴ 
| ,The Rest Space is a Stationary Wave with fundamental 

frequency f 1= 
1

T 1
 = 

λ̅

c
 , with an Electric Wave , that is acting on vector c ̅ = ( i. cx + j. cy ) .  

       It was Proved [78] that the Newton`s Gravitational constant  G  does NOT effect on  

       Plane Surfaces , But on Volume Surfaces only .  

      This Property of , G , means that the only one Force which effects on the Rest-Space  

      in Torsional motion , and Onto the light velocity vector  c ̅, is the gravity force g only.  

 

Figure - 15-The Stability of {⊕- Space [Electric Wave},{⊝-Anti-Space [Magnetic Wave] 

of Sub-Space   { [⊕↔⊝] ≡ ds ≡ [⊕←ds→⊝] – or –The Neutral-Space  [A E , B E , C E]}  :  

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Since c is constant , it is analyzed to , ( cx , cy ) in any two directions x , y where  x ⏊ y and y 

to be the  gravity direction on where gravity is acting .          

The Produced Work is in  y - Range  , S y = cy t - 
1

2 
 g 𝑡2 = c sin 𝑎𝑡- 

1

2 
 g 𝑡2 , where maximum  

Range is   S max−y = cy 
2/ 2g = 

(c sin𝑎𝑡) ²

2 g
  = [

c ²

2g 
] sin² 𝑎 , happening at angle   a = 90° and  

where sin² 𝑎 = 1 . Since at Point (1)  the velocity   v y = 0 , the motion in 0 -1 , may be  

considered as falling in linear motion and so issues  v y = g t or time   t = 
 v y  

g 
 = 

(c sin𝑎𝑡) 

g
 , as  

halve Period with total Period → T = 
2 (c sin𝑎𝑡) 

g
 . In figure are seen the 4-Point Positions , at  

where change the Phase and the Work done in each Phase of Photon`s inner motion . The 4- 

Phases correspond to the Wavelength . λ , as   λ / 4 . distance with  90° = 
𝜋

2 
  to be the change  

of Phase . This means that the  Produced Work  in Prior Phase - Area as the  

Golden – Ratio Pattern is Stored in the Next and Perpendicular Phase-Area .  

The Total distance for doing Work is the Wavelength λ , in total Period T as  λ = cx T = 

c .cos 𝑎 .T   or    λ  = c . cos 𝑎 . 
2 (c sin𝑎𝑡) 

g
 =  [

2 c ²

g 
] sin 𝑎 , cos 𝑎 =  [ 

 𝐜 ²

𝐠 
 ] 𝐬𝐢𝐧 𝟐𝒂 ,   ……(1)  

                    since from trigonometry exists , sin 2𝑎 = 2 sin 𝑎 . cos 𝑎  .   

    The maximum  wavelength  λ  happens  when 𝐬𝐢𝐧𝟐𝒂 =1 or  2a = 90 ° and a = 45 °  , i.e.  

→The Total motion in the Wavelength , λ  , corresponds to the angle  a = 45 °, meaning  

that  the motion of  Space , The Electric-field  , and Anti-Space , The Magnetic-field , 

equilibrium  as  an Bellow .  The two Wings  in 90°  Type  simultaneously oscillate to its   

45 °  Bisector -axis , and the Produced Work from The Electric-field-area is Stored into  

the Magnetic-field - area . The  common axis  of the two Perpendicular fields , carry the   

 G-Ratio Surfaces  , Runs with the same velocity  c ̅ to the direction of  the inner motion  

or, From  90°→ 45° , the created Work  W = c y g , is Symmetrically Stored from  0°→ 45°.  

The created Work in [ 0-1 ] is in  →  λ / 4  of transverse surface  and is stored in the horizontal  

and perpendicular  surface [ 1`-2 ] = λ / 4  . Surface  [ 0 -1 -1` ] = ⏊  Surface  [ 1` -2` -2 ] . 

The created Work in [ 1-2 ] is in  →  λ / 4  of transverse surface  and is stored in the horizontal  

and perpendicular  surface [ 2-3 ` ] = λ / 4  . Surface  [ 1 -2 -1` ] = ⏊  Surface  [ 2` -3` -2 ] .  

The created Work in [ 2-3 ] is in  →  λ / 4  of transverse surface  and is stored in the horizontal  

and perpendicular  surface [ 3 `-4 ] = λ / 4  . Surface  [ 2 -3 -3` ] = ⏊  Surface  [ 3` -4` -4` ] .  

The created Work in [ 3-4 ] is in  →  λ / 4  of transverse surface  and is stored in the horizontal  

 and perpendicular  surface [ 3 `-4 ] = λ / 4 . Surface  [ 3 -4 -2 ] = ⏊  Surface  [ 4` -5` -4 ] .   

Since from Trigonometry issues  sin 2𝜋= sin(180 − 2𝑎) = sιn 2(90 − 𝑎) then (1) becomes   .   

λ  = c cos 𝑎
2 (c sin𝑎𝑡) 

g
 = [

2 c ²

g 
] sin 𝑎 , cos 𝑎 = [ 

 𝐜 ²

𝐠 
 ] 𝐬𝐢𝐧 𝟐𝒂 =  [

 𝐜 ²

𝐠 
].sin(𝜋 − 2𝑎) = 

[
 𝐜 ²

𝐠 
].sin(

𝜋

2
− 𝑎) …(2)  since  𝐬𝐢𝐧 𝟐𝒂 = sin(180 − 2𝑎) = sin(𝜋 − 2𝑎) , and  also  

                              𝐬𝐢𝐧 𝟐𝒂 = sin(180 − 2𝑎) = sin(
𝜋

2
− 𝑎)  ……(1a) 

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

From Dual-Photon-equation , v̅.[ fn̅  + fn ] ≡ | 
𝐯 

𝛑².𝐫⁴𝐧  
|. B̅n  + | c ̅| fn ,when  c = 0 or c  = c⃖ , then  

Photon motion becomes → | 
𝐯 

𝛑².𝐫⁴𝐧  
| . B̅n  ← ≡ Spin . i.e. The Stationary Photons exist as their  

Spin only . The Rest-Space is the Part  | 
𝐯 

𝛑².𝐫⁴𝐧  
|. B̅n   where  v = n.π.c ,  and Communication  

Code to be the term | 
𝐯 

𝛑².𝐫⁴𝐧  
|= | 

n.𝜋𝑐 

𝛑².𝐫⁴𝐧  
| = | 

𝑛.𝑐 

𝝅.𝒓⁴  
|=| 

𝐰 𝐫 

𝛑𝟐.𝐫⁴ 
| = | 

𝟐 𝛑.𝐟 

𝛑 𝟐𝐫³  
| = | 

𝟐 .𝐟 

(𝛑 𝐫 ³)  
| with Electromagnetic 

Radiation the in monads frequency-f , which is satisfied by the relation  |
2rw

2 v
|= π /2 , π , 3π /2  

.,,, n.[π/2] , and w = n.[
�̅� 

2r
]x[

π

2
] ,  where n = 1 → ∞ . When two Photons strike each other  

 c   =  c⃖ ,  or reflect on a wall , then  c = 0 , and from Spin  �̅�  = B̅  = π ². r ⁴. f1  its angular 

velocity w = n.[
�̅� 

2r
] x [

π

2
] = 2π.𝐟𝟏 , where then  its  fundamental frequency  𝐟𝟏 = n.[

�̅� 

𝟐𝐫
]x[

𝟏

𝟒
] = 

n.[
�̅� 

𝟖.𝐫
]   which for  n = [

16.𝑟²

v.c
] increases to  

λ

c
  . r3  and Photon-motion becomes → | 

𝐯 

𝛑².𝐫⁴𝐧  
| . 

B̅n  ← ≡   Spin , i.e. The Stationary Photons are Spin only and consist an Stationary- 

Harmonic - Vibration , (1) – (1a) , with the same Period  T of the two Waves  [92-E}.  

The effective-Range of the  Wavelength  λ , for the Dual-Photon is related to the consistence  

v x , v y , velocities  to any two Perpendicular directions of Electromagnetic fields E x , E y .   

The maximum  displacement in y , direction is the centrifugal  λ x =  
v² y 

2 E y 
 and sisin(φ)  λ y =  

= 
c2. sin ²(φ) 

2 E y 
  ,  where φ = The Phase difference between the two vibrations .  

Since time t , is the same between the two vibrations where then   t =  
v y  

E y  
 =  

c.sin(φ).

E x 
  and  

since  the Period = 2.t  then  T = 
2c.sin(φ).

E x 
    …... (2)   From the in x  →  direction velocity  

 v x =  c . cos(φ) , and  displacements  , λ x  , λ y ,  become ,     

λ x =  v x T  =  c. cos(φ){
2c.sin(φ).

E x 
} =  λ x = { 

2.𝑐²

𝐸 𝑥 
 }. sin(φ).cos(φ) =  { 

c ²

E x 
 }. sin(2. φ)  (3)    

Since in trigonometry issues , sin(2φ) = sin(𝜋 − 2φ) = sin(
𝜋

2
− φ) and in Physics E x = g ,  

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

then    →  𝛌 𝐱 = { 
𝐜 ²

𝐠 
 } .  𝐬𝐢𝐧(𝝅 − 𝟐𝛗) ,  𝛌 𝐲 = { 

𝐜 ²

𝐠 
 } . 𝐬𝐢𝐧(

𝝅

𝟐
− 𝛗)  ←     …….(4) 

Since Monads are Complex quantities as  AB ≡ �̅� ≡ x + i. y , then are Quaternions where 

Material-Points ≡ Quaternions , which  Carry the → Motion ≡ Energy ← from the two  

Edge-Poinds [ �̅�↔�̅� ] , as this is from Point A , to Point  B circularly .  

Since λ x ⏊ λ y , then issues λ y = [ i = √−1 ] * λ x , or equivalent to multiplying the  

quantities along the x – x  axis  , by  i = √−1 .  

i.e.  Photons occupy  1..  The Dual-Property of  Particles and  Waves  ,  

                                  2..  The Dual-Property of   Stationary and Spin  ,            

                                  3..  The Dual-Property of  Simultaneous existence  ,  

                                  4..   As  Electric and Magnetic Fields in  , 𝛌 𝐱 , 𝛌 𝐲 ,  

                                  5..  The  Bellow motion in transverse E-M- Waves as is the way to fly ,        

                                 6..  The  Transverse E-M - Waves are ⏊ to the Propagation-Direction , 

                                 7..  The Electric  Effective Range is thrusted through G only. [ Fig-5 ] .  

                                 8..  With the same initial velocity is succeeded the same Length-Range 

                                       with Two complementary angles .  since  v y = c. ,      

C.. : THE  ORIGINATION  OF THE  PHYSICAL  LOOPS ≡ CAVES     

        1c.. The Gravitation Force  G  ,  and the  Kick - Start  :  [78-79]  

 

 

Figure – 16.   The Newton`s Universal Laws in Primary-Material-Point ,  

      Above , is consisted of the Two-Primary-Opposite-Spaces , {+} {-} , Poles ,  

      with infinite Points and Parallel-lines such that G is a Uniform-Pointy–Force .   

      From where G , is Produced  ?   →   It was Prior referred that , 

Periodic excitation between Primary Space  (+)  and Anti-Space (-)  may exist only as  

collision of Opposite , so Energy  captured in Box-𝐁𝐏 , Planck`s Loop , contains these  

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63 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

three constitute elements [(+) ,[↔], (-)] without the inner acceleration but the Material– 

extreme case of Periodic acceleration [→ ←] = 0  and which is the Reciprocating motion  

So , above Property of Primary Space exists also and for all Primary Complex- Spaces.  

Complex Spaces either at , [(+)] or [(-)] , constitutes may be realized , exist , separately  

because of the → Primary-Opposites which Pull each other  ← therefore the Initial  

Property of Attraction , G , between Primary-Opposites continue issues and for All  

the other infinite Composite and Complex Structures as well as in all Groups of them .  

Since Force G is a Uniform-Pointy–Force , therefore needs a Conductor , a Layer , a 

kind of mass , to be spread and act on it as Surface-force , a Layer which is the Base or  

the Conductor Spin S , or the Stress g , as this is the Growing-Golden-ratio-Pattern Φ. 

Because of this Stress-Layer g , all the Energy-Structures Present → Reaction to any  

motion ← i.e. mass . The Gravity acceleration  g , produced from the in Material-Points   

acceleration is equal to the  Pressure σ , and  is the Conductor to all Waves as ,      

    Force G - Over-Layer - A → [A ≡ mass * g ] → Gσ ≡ G , and Stress = g = 
σ² r².Φ²

  8 
     

From Figure -15(3) is seen that Gravitational Force is Attractive following Newton 

inverse square law, and it is an Attractive-force [↔] , On any two Opposite-Elements  

[ (+) , (-)] realized through a Layer of Unit-Stresses  [σ = g ] , and becomes from an   

      HUGE Magnet in Planck`s - Loop containing the whole Universe [89] .   

      G - Kick-Start , is Planck`s frequency → fP  = 1 / TP = 
w

2π
 = √

1

 g.a ³
 

2
 and in this world   

      the How this frequency can → Enter , Format and cohesive , to the first or any other  

      Energy-Cave in Planck`s length , E-Unit Monad , 1 = g .𝐟 ²𝐧 . 𝐚
𝟑 =  [ 

𝟒𝛑² 

𝐆𝐌
 ] . 𝐟 ²𝐧 . 𝐚𝟑 ,   

      where  g = [ 
𝟒𝛑² 

𝐆𝐌
 ]   as this was shown in [79] for Unit-Monad-relation .   

An Energy-Rim = Cave is a Plane - Surface , an orbit , representing  an  Constant Energy  

becoming from the squared Frequency  𝐟𝐧²,  Representing the Imaginary Part , and  r P³ ,  

Representing the Real – Space - Part of monad as equation 1 = k.𝐟𝐧².𝐫𝐏³ . The Stationary 

Energy is spread in one Plane as this happens for the Stationary-waves in Caves , while in  

Propagating - Energy in Two , as are the Electromagnetic Transverse waves .  All these  

Energy-Rims consist the Quantized-Plane-curves as  Fig-15 . The two different motions of  

⊕ Space , ⊝ Anti-space , in any cave r and in a Finite Space , The Revolving and Periodic 

Excitation Create an Eternal frequency which influence all other Spaces , the caves .  

The minimum quantized-energy is stored in the Gravity-Layer , g , becoming from  the Unit  

Energy of the sinus orbit .  From equation ,  g = T ² / a³ ,  and minimum - a  then Period  is  

T = √g. a³ = √9,8076925. (2,1145016. 10−11)³ = 3,04513.10−16 s , Since the Unit-Work = 

Sine Integral =∫
sin t

t

𝑡

0
dt =1 , the semi-major axis , a , is  a = 2,1145016.10−16 m , where 

frequency T −1 = fP  = 3,28393..1015 /s , corresponds to a Sphere-loop in Planck`s scale as   

(4 / 3).π.r³ = 3,96 . 10−32 m³ ,  and then  the Energy in this Planck`s loop  is the minimum 

quantized . From Planck`s Energy E = h.fP  = [ 6,6262.10−34 J.s ] x [ [ 3,28393.1015 / s] =  

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64 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

2 ,176.10−18 J , and in  eV becomes   → [ 2 ,176.10−18] / [1,6.10−19] = 13,6 eV  or ,  

Energy in  Gravity-Layer  g      13,6 eV =  h f  =  h / T  =  h /√𝐠. 𝐚³.  

The above quantity of Energy consist the Hydrogen minimum Energy-Rim , which becomes 

from Loop-equation   a = √𝐓𝟐/𝐠
𝟑

 = √
[3,04513.10−16]²

9,80769251
 

3
 =  2,1145016.10−16 m , and it is the 

Energy-cave for the Unit  Energy quantity . From  Newtonian Constant of  Gravitation  

relation issues ,      G = E = h . fn = [ 
𝐜.𝐫³

𝐚³
].[ gL kL ] = g .k E = g . [ gL kL ]  ,  and since for  

The First Chemical-Neutral-material-cave , r , constants  gL ,kL  are equal to unity   i.e.   

𝐠𝐋 = 𝐤𝐋 = 1 , then above Energy of   E = 13,6 eV , in Hydrogen-Plane-orbit  corresponds  

to the minimum-Energy-Cave , or → The Phys-Quantized-Energy-Structure ←  

Since  G  Pushes →  g , on the Earth-Unit-coefficient , k E , and because is the Starting  

for the first time beginning  , of  this Mechanism then from    G =  g.[gL kL]  ≡  g.[1*1] ≡  

→ g ← or  G = g  , meaning that In  Earth System of Gravity , the Newton`s Gravitational  

constant  G , and Gravity g  are equal , while in all other relative Systems are equal  to the 

proportionality of their Local-constant 𝐤 𝐋 .  

              Gravity , g ,  is the minimum Energy becoming from the in-storages angular  

              Velocity acceleration   a = v²/ r  ≡  9, 8076941 . in the Material-Point .  [72] 

              Photon is a Material-Point , Box BR , with fix-ends  Inward-cave r , and which  

              is the Energy Storage 𝐁𝐑, Outward-cave-r is an Electromagnetic-Radiation on 

              wavelength  λ = c T = c / fP which EM-Radiation , carries the Box  BR .  

Universal Gravitational constant  G = g k  related to g , kR  , is a Force and through the  

Static g becomes the Principal stress  σ , or frequency f R which exists in nature as motion  

in the minimum Resonance Golden-ratio-frequencies  fR = fn = 1  , and this because of  

the Periodic motion , in Excitation , where issues the  Coulomb-Dipole law  and which  

Coulomb inverse law is as ,  

           F = kc [q1.q2 / r²] = kc [⊕→←⊝] /r² = 
8

πr(1+√5)
 [ 

B

r²
 ] , and Coulomb constant   

           kc = 9.109 Nm2/C²    ,  i.e.   

Because of the  Periodic excitation between the , Space (+)  and Anti-Space (-) ,  

[⊕→←⊝] exists only collision of opposite where the inner acceleration is equal  

to zero Gravity g  , and this because of the Material extreme-case of the Periodic  

acceleration {[→←]=0} which is zero , the Net force vanishes , issues the Coulomb  

Dipole-law where Static - Stress g , becomes from the Stationary constant Dipole  

moment  �̅� ≡ �̅� ≡ as momentum which is the analogous in the  Revolving motion  

where  then issues  →  G = g k = 𝐤𝐄 g = g.𝐤𝐑 𝐠𝐑 =  �̅� , 𝐠𝐜  =  σ  =  
𝐅𝐨𝐫𝐜𝐞

𝐀𝐫𝐞𝐚
 = 

 𝐠.𝐌𝐚𝐬𝐬

𝐀𝐫𝐞𝐚
    

For Earth-System  mass  ME = 5,9723.1024 Kg   and  Radius RE  = 6378,137 Km   

= 6,378.106 m , then Earth-constant  𝐤𝐄 = 
R²E 

ME 
 =  

[6,378.106]²

5,98.1024  = 6,811551810−12 and 

G = g 𝐤𝐄  = [ 9,8076941] . 6,8116.10−12 = 6 , 68056.𝟏𝟎−𝟏𝟏  m3/ N.s²  becoming  

       from  g , 𝐤𝐄  only ,  i.e.  G  as force Pushes → g  as Stress energy in → 𝐤𝐄  constant .  

       Now is Proved that , the Gravitational Constant  G  is the mechanism or the mould ,  

       for the  First-kick-Start  upon this  Unit-Granular-Energy-Stress-Layer , g , to  

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formulate in that orbit  a , into Planck`s cave  the lightest and the less-energy mass Particle  

of this Universe , which is the Hydrogen with the minimum  Quantized-energy of 13,6 eV.       

The Centripetal acceleration in Photon cave due to Pressure σ ,where issues only Rotational  

Energy  E R = B̅ . w̅  = 2L= J.w² , and  2E = B f  , or  → 2.(0,5.m.c²) = m.c² = 0,5.π.𝑟4.𝑐2/4 ,  

then  4. �̅� . f = 𝐜𝟐. 𝐫𝟒 , where the  Golden ratio frequencies →  fn = [
n.σ.Φ

2.π.r 
] ≡  

n.(1+√5 ) .σ

2.𝜋.𝑟
  =   

=  𝐜𝟐. 𝐫𝟒 /  4.�̅�  = 
E

h
  ←  i.e.  The box 𝐁 𝐏 , or the Planck`s Cave , carried with Light velocity c 

and Pressed into the Planck`s Loop ,  as  n 𝐜𝟐 = n. c c ,  becomes the Gravity g , which is a 

stress by which Gravitational-force G is communicating as , g G = [ 
π r v4

2
].𝑒3 = 9,808238 m/s .  

        Gravity is the minimum Unit-Stress-monad  in Planck`s scale becoming from a M-Point  

        and which is Under -Planck`s - length region . Since also acceleration in a Material-Point  

       ( Centrifugal-Centripetal ) becomes from the Principal Stresses  σ , therefore constant    

       g G  ≅ ± σ = 
Force

Area
 = 

g.Mass

Area
 = 

G

k
  , and for Unit-G  constant  k becomes ,       

        k = 
System Area

System Mass
  G where → 

1

𝐠
 = 

k

G
 = 

System Area  

System Mass
 and  G = k  g G  , and for the Earth  

G ≡ g.kE ≡ g .[gL kL ] ≡ [ 
T²P 

𝐚³
 ].[ gL kL ] ≡ 9,808238* 6,8116.10−12 ≡ 6,68056.10−11 𝐦³

𝐍𝐬²
 

So  G , is The Pulling and Cohesive Force  on all the Quantized-Energy-Structures  

which communicates with everything due to Periodic excitation on all Spaces .  

From equation g = G / [gL kL ] , is seen that g becomes from G under Local-laws ,   

And also , Gravity  g , is the Unit-Energy-Path , Quanta of Gravitation , due to M-Point  

Frequency  fg ≅ ± 𝜎  from the Revolving motion , and also the Unit-Energy-Stress per  

Surface and for the Force - G , is the Permitted Path ,  or the communication Conductor  

on all Energy Wave Structures , In and Out Planck`s length . 

Remarks :  Gravitational Force ,G, is the Pressure which every Object in the Universe 

Exerts on every other , whether Small or Big and is equal to Fgrav = 
G.M.m

d²
 =  

g.𝐑²𝐄 M.m

Md²
 = 

g.𝐑²𝐄 .m

d²
 = 

mg.𝐑²𝐄 

d²
  , and  G =  

g.𝐑²𝐄 M.m.d²

Md²
 =  

g.[ 𝐑²𝐄 ]

   M
 = g . kE  ,  where    kE = 

[ 𝐑²𝐄 ]

M
 , and  

        g  =  The minimum Quantized work as acceleration ≡ 9, 8076941  m/s²   

        kE  =  The Earth Local-coefficient between the two constants  g , G .      

        For Earth (E)   → k E = r ²E / m E  , For Bodies (B) → k B = r ²B / m B   ,  

        For any Body  → Local Gravity  g L = kE / kL    

From relation  G = g 𝐤𝐄  = 9,8076941.6,8116.10−12 = 6,68056.𝟏𝟎−𝟏𝟏  m3/ N.s²   

and from relation 1 = c. r³. 𝐟𝐏² → fP = √1/cr³ and from f = E/h then 
𝐄

𝐡 
 = √1/cr³  or →                        

 E = h . √1/c. r³ ,  
E²

h²
 = 

1

cr³
 → and ,  E ² = 

𝐡²

𝐜 𝐫³
 ,  is an Energy relation between c , r .   

Instances :  [77] 

1.. For Earth-System mass  ME = 5,9723.1024 Kg and for Area → Radius 6378,137 Km  

   = 6,378.106 m then the Earth-constant   𝐤𝐄 = 
[6,378.106]²

5,9723.1024 = 6,811551810−12 and  

   G ≡ σ.𝚽³ = g 𝐤𝐄  =  9,8076941* 6,8115518.10−12 = 6,6805616*𝟏𝟎−𝟏𝟏 m³/Kg .s² 

   i.e. Gravitational-constant  G  becomes from  g , 𝐤𝐄  , and issues     

   G = 6,6805616.10−11  m3 / N.s²  ……..….(7)    

   For Black-Holes-System mass M BH = 4,0.10 52 Kg  and for the Area   

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

   Radius  3,08.1025 m , then Black-Hole-constant kBH = 
[3,08.1025]²

4,0.1052  = 2,3716.10−2   

𝐠𝐁𝐇 = 
k E 

k BH  
 = 6,81155.10−12 / 2,3716.10−2 = 2, 872.10−10. gE →  i.e.  

For Earth-Unit-coefficient kE = 6,81155.10−12 → Black-Hole –Unit-coefficient  

kBH = 2,3716.10−2 m2/Kg , and Gravity acceleration of a Black-Hole is ,  

𝐠𝐁𝐇 = 2,872.10−10. gE , an expected explanation . 

For all Planes issues  G = 𝐤𝐄 g = 𝐠 . 𝐤𝐋 𝐠𝐋 , and for Black-holes also where , 

G = g . 𝐤𝐁𝐇 . 𝐠𝐁𝐇 = 9,8076941* 2,3716.10−2 * 2,872.10−10 = 6,6805616*𝟏𝟎−𝟏𝟏 

Meaning that Gravitational constant is the Same for all Systems .  

The Gravitational Force , G , is the Pressure which every Object in the Universe exerts 

on every other , whether Small or Big and from Newton are equal to  →  𝐅𝐠𝐫𝐚𝐯 =  
𝐆.𝐌.𝐦

𝐝²
  =   

𝐠.𝐑²𝐄 𝐌.𝐦

𝐌𝐝²
 =  

𝐠.𝐑²𝐄 .𝐦

𝐝²
 = 

𝐦𝐠.𝐑²𝐄 

𝐝²
 ,  G =  

𝐠.𝐑²𝐄 𝐌.𝐦.𝐝²

𝐌𝐝²
 = 

𝐠.[ 𝐑²𝐄 ]

   𝐌
 = g . 𝐤𝐄  where 𝐤𝐄 = 

𝐠.[ 𝐑²𝐄 ]

   𝐌
 =  

𝐠.𝐌

 𝐆
   

g  =The minimum Quantized Work as change of velocity → acceleration ≡ 9,807694 m/s²   

𝐤𝐄  =  The Earth Local-coefficient between the two Constants  , g , G , and  𝐤𝐄.G = g .M        

       For Earth (E)  → 𝐤 𝐄 = 𝐫 ²𝐄 / 𝐦 𝐄  , For Bodies (B) → 𝐤 𝐁 = 𝐫 ²𝐁 / 𝐦 𝐁   ,  

       For any Body  → Local Gravity  𝐠 𝐋 = 𝐤𝐄 / 𝐤𝐋       

2..  Coulomb Electrical Force , 𝐅𝐞𝐥𝐞𝐜𝐭𝐫𝐨𝐧 = 𝐤𝐜 
𝐐𝟏.𝐐𝟐 

𝐝²
 = 

[⊕→←⊝]

𝐝²
 = 

𝟖

𝛑𝐫(𝟏+√𝟓)
 [ 

𝐁

𝐫²
 ] , where  

      Coulomb constant  𝐤𝐂  = 9.𝟏𝟎𝟗 Nm²/C²    

3.. The Work done by the Electric field to Rotate the Dipole is W = 𝐅𝐞𝐥𝐞𝐜𝐭𝐫𝐨𝐧 . 𝐄 𝐅𝐢𝐞𝐥𝐝 .  

4.. The Work done in Material Point needs a Path to exit from the Box 𝐟𝐑 = [ 𝐁𝐏𝐇 ] ≡ 

     [ 𝐟𝟏=𝐍 , 𝐟𝟐 , 𝐟𝟑 , 𝐟 𝐑 =  𝐰²𝐍 ] ≡ [E² + H²]  , and from where is Propagated .  

     Resonance-Path happens as the Force , EM-Radiation in Two directions , which can  

     travel in any closed System , and for solids through Cauchy-Stress-Tensor where the  

     two Conveyers  E ⊥ B ⊥ r ≡ 𝛔𝟏 ⊥ 𝛔𝟐 ⊥ 𝛔𝟑 , can carry the Energy Storage r in System  

     [ + - 0 ] and Change the Inner-Structure of this System to another or Destroy it.    

In [70] , the Work Produced In Material-Point  𝐀𝐁⃖⃗⃗⃗  ⃗  is equal to → W = 2L = �̅� . �̅�  = J.w² ← 

consisting the First-Energy-Store which is a Stationary Wave with , n  lobes as , 𝐖𝐧(𝐧+𝟏) = 

[
𝟒𝝅𝐫²𝐟𝟏

𝟑
].n.(n+1)  and wavelength  𝛌𝐍 = 

𝛔.(𝟏+√𝟓)

𝟒𝛑𝐫
 = 

𝒏 .�̅�

𝟒𝛑𝐫² 
 = 

𝟐𝒏 .�̅�

𝐰 
  of  r = 

𝒎 .�̅�

𝐪.𝐁 
 related to M-Field B  

In [75-B] ,The Permeable-Resonance-Path for M-Point is → The Resonance-frequencies   

𝐟𝐑 [S≡ 𝐟𝟏=𝐧 ,𝐟𝟐, 𝐟𝐑 =𝐰²] with  𝐟𝐧= [n 
(𝟏+√𝟓)𝛔 

  𝟒𝛑𝐫 
 = 

𝐧𝛔.�̅�

𝟖 𝐫² 
 ] related to Spin �̅� , Stress 𝛔 and cave r . 

Since the frequency in Material-Point is  →   

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67 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

𝐟𝐧  = ( 
𝐧𝛔

𝟖 𝐫 ² 
 ) .�̅�  ≡ [

1+√5

2
] 

𝛔

𝟐𝛑𝐫
 ≡ [ 

nσ

8 r ² 
 ].B̅ ≡ [

1+√5

2
]

Stress

 Perimeter
 ≡  [

1+√5

2
]

Force [N]

Area∗L[m3]
  ≡ 

𝐄

𝐡
 ,  Then  

it occupies the Property of the Golden-ratio Pattern Φ , and equation defines  that the  

Material Point of frequency 𝐟𝐧  , when collide with another Material Point , or with any 

other Particle or Particles then Produces another monad as → 1 ≡ A New Quaternion 

and the first continuous to be of the same Identity , frequency 𝐟𝐧  , as before and from  

Euler`s , Rigid Body Dynamics work  →  W = 2L = B̅ . w̅  = J . w²  ≡  h. 𝐟𝐧  ←   i.e.  

The Frequency of  Photon , is embodied with the  → Growing-Golden-ratio-Pattern Φ and   

It Uses the Vibrating Physical Structures , or the same  the Granular Material-Instruments ,  

to Kick - Start all of them  and everything in this world . The How In [75-B]  Page 34 . 

Because of the  Periodic excitation between , Space (+) and Anti-Space (-) , [⊕→←⊝] 

exists only Collision of Opposite , where the inner acceleration is equal to zero Gravity g  

and this because of Material extreme-case of the Periodic acceleration {[→←] = 0} , and  

which is zero and the Net force vanishes , and in where issues The Coulomb Dipole-law  

and where acceleration g becomes from the Stationary  constant Dipole moment  �̅� ≡ �̅� ≡ 

momentum and which is the analogous in the Revolving motion in where  then issues →  

Gravitational force    G = g k = 𝐤𝐄 g = g . 𝐤𝐑 𝐠𝐑 =  �̅� . 𝐠𝐜  = σ = 
𝐅𝐨𝐫𝐜𝐞

𝐀𝐫𝐞𝐚
 = 

 𝐌𝐚𝐬𝐬

𝐀𝐫𝐞𝐚
 g    

In Page-33 [77] , the Earth-constant  𝐤𝐄 =  
R²E 

ME 
  =   

[6,378.106]²

5,98.1024  = 6,811551810−12 and the 

Gravitational Force  G = g 𝐤𝐄 = [ 9,8076941] . 6,8116.10−12 = 6,68056.𝟏𝟎−𝟏𝟏  m3/N.s²  

becoming from  g , 𝐤𝐄  only,   i.e.  G  is a force which Pushes  →  g  as energy in → 𝐤𝐄   

From Gravity relation  G = g 𝐤𝐄  =9,8076941.6,8116.10−12= 6,68056.𝟏𝟎−𝟏𝟏 m3/ N.s² and  

from Energy-loop relation 1= c. r³. 𝐟𝐏² → fP=√1/cr³ , from f = E / h  then f =  
𝐄

𝐡 
 = √1/cr³    

or → E = h.√1/c. r³ ,  and    
E²

h²
 = 

1

cr³
 →  E ² = 

h²

c r³
  , an Energy relation between  the , c , r  .  

         This relation is used for Black- Holes Energy where  r , result to zero , [71]      

     The Permissible - Permeable - Resonance - Paths  for the means , is as below . 

1)  Solids        →  The Normal-mode-Vibration - System { - w² [M] + [K] (X) } = 0     

2)  Liquids      → The Cauchy Stress-Tensor as Momentum equation { ∇.σ = -∇p +∇.τ }  

3)  Gazes        →  The combined Avogadro`s Pressure - law { PV = n RT = n.mv²/3 }  

4)  Crystals     →  The Cauchy Ellipsoid-Stress-tensor where { E⊥B⊥r ≡ σ1⊥ σ2⊥σ3 }  

5)  Molecules →  The Lattice-Crystal-Arrangement with their Chemical Bonds relation 

6)  Atoms       →  The Energy-Rims with Chemical Bonds , Ionic , Covalent , relation         

7)  Particles   →  The Resultance of the  One-Dimensional-Collision v̅ij= v̅j - v̅i = w̅ij. r̅ij                 

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68 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

8)  M-Points  → The Resonance-frequencies  𝐟𝐑 [S ≡ f1= n ,f2, f3,fR=w² ] = 𝐟𝐧 = [⊕ ↔ ⊝] 

       = n 
(1+√5)σ 

  4πr 
 = 

n.σ.B̅

8 r² 
   →  i.e. the Golden-ratio-Pattern , which is related to Spin.   

9)    Cave-Orbit→ The Relation  c.L s =  Lv , Light-velocity  3.108 m/s*1.10−42 m 

       cave =3.10−34 m²/s are the Cave-Energy-Plane-Rims in Atom`s , Planet orbits.   

In Vibrations of Systems , for Orbits issues  → W = 4π² . 
𝐫³

𝐓²
 . �̅� = 4π².r ³. 𝐟²𝐩 . �̅� ←   

which is the Energy in the Conic-Sections of Kepler`s  Unit - Orbits .     

The Energy-Storages  r = n.[
λ

2 
] ≡ Wn(n+1)= [ 

4𝜋r²f1

3
 ].n.(n+1) , are travelling through Bodies 

and follow, Lame Stress Ellipsoid  n1² + n2² + n3² = 
T1² 

σ1² 
 + 

T2² 

σ2² 
 +

T3² 

σ3² 
 =1 on Principal Stresses 

σ1, σ2, σ3 , which  is the Passage through which Forces  (The EM-Radiation)  travel in 

any Solid either it is in Motion or is at Rest .  Laplace`s Orbital Angular-momentum  ei.2πn = 

1 and for  n = 0 ,1,2 ,3,. n , consist the Eigenvalues Operator Lz which agree with prior  

Resonance-frequencies 𝐟𝐑 [S≡ f1=N , f2, f3,f R = w² ] as wavelengths λ ≡ [f1 , f2…fn= w²] ≡  

the n lobes , or → fN = n 
(1+√5)σ 

  4πr 
 = 

nσ.B̅

8 r² 
  , as the Principal-Stresses  σ , and Resonance- 

frequencies 𝐟𝐑  relation , which is  Energy stored in the  MP-lobes. [70]        

Type - Particles at sites - Type of Bounding-Force  -  Properties - EM-Radiation  

Ionic :   ⊕ , ⊝  Ions - Electrostatic ⊕ ↔⊝ -  non-conductors  -  Infrared  

Molecular : Atoms or Molecules - Dipole Attraction - Repulsion - non-conductors - 

                                                     Chemical-Bonds . 

Covalent : Atoms - Network- Bonds between Atoms -non-conductors - EM-Spectrum 

Metallic  : Atoms - Ions and Electrons Attraction - Conductors - E-conduction . 

The Kinetic-Energy E K of a moving Material-Point , as this is the Photon ,  is stored as  

motion in its Storage ,  r = [ n. λ/2] , with the  n frequencies  f n = n.f 1 , with the  n  lobes ,   

and with an fundamental frequency f 1 . From above is seen the Passage and The-How EM-

Radiation can travel in Crystals and which are the Cauchy-stress-Tensor , where  exists  

E ⊥ B ⊥ r ≡ σ1 ⊥ σ2 ⊥ σ3 , in-where Energy Propagates along Directions without any 

Birefringence , and carries the Energy-Storage r , which radiation is The Conveyer. 

Above procedure can be used in Cells , where cells are cases of an Birefringence material and 

the Resonance-Passage happens as the Force , an EM-Radiation in Two directions , can travel  

in Cell through Cauchy-stress-tensor where the two Conveyers  E ⊥ B ⊥ r  ≡ σ1 ⊥ σ2 ⊥ σ3 ,  

and can carry the Energy-Storage , r , in Cell , and alter the Inner-Structure of Cell to another  

desirable Property.  From Inner-velocity equation  v = w r = (2π/T).r =2π.f1 r , wavelength λ =  

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cT=c /f 1, cave  r = n.[λ/2], then r = n.(c/2f1)  and v =2π.f 1[n.c/2f1] = n.π.c  or  v= n.π.c  ....(4)    

showing that velocities in lobes are , n.π ,times that of light and for n = 1 then v = π.c  , more  

than three times faster of light velocity.  

Because of the above velocity v , an E field is produced , which produces the 𝛛𝐃/𝛛𝐭  field ,  

which in turn produces the H field which produces the 𝛛𝐁/𝛛𝐭 field and which again produces 

the E field , i.e. the Total  EM-field regenerates itself as it Rotates , and is a Phenomenon 

happening in a Propagating Plane-Wave . Its Permeable - Resonance - Path is impossible  

in an Three-times Stronger EM-field  because issues … (4)      

2c.. The  United-Coulomb-Newton Law for Interactions :  

For a Stationary interaction the Coulomb-Law-Force is  𝐅𝐂 = 
𝐤[𝐪𝟏𝐪𝟐]

𝐫²
 , and for Charges  

𝐪𝟏, 𝐪𝟐  where Constant  k = 9,0.109 N.m²/C² , and r , is the distance between the Charges. 

For a Stationary interaction Newton Law for masses m1, m2 is 𝐅𝐍 = 
𝐆[𝐦𝟏𝐦𝟐]

𝐫²
 , and for v̅=r̅ 

Conjugating Interaction , Energy E = 
𝐯²

𝟐
[m1 + m2] = 

𝐫²

𝟐
 [

F1

g 
 + 

F2

g
] = 

𝐅.𝐫²

𝟐
 [

1

g
 + 

1

 g
] = 

𝐅.𝐫²

 𝟐 
 =  

= 
𝐅.𝐫²

𝟐
[
2.g

  g ²
 ] = 

𝐅𝐍 .𝐫²

𝐠
 , where 𝐅𝐍 is Newton Force, and E is the Energy of the Field-System.[

g+g

g∗g
}  

Equating the two forces then  
k [q1q2]

r²
 = 

gE

r ²
  ,  or    k [𝐪𝟏, 𝐪𝟐] = g . E  ……..(1)  

Equation (1) relates any two Charges q1, q2, with Field-Energy E , under vector �̅� = �̅� = �̅� 

3c.. The  Origination of  Light velocity  c  :              

       Gravity  g  ≡  
𝐓²

𝐚³
  ≡ 

𝟏

f ²n.𝐚³
  ≡  9, 8076941 → The minimum Granular Quantized Energy ,  

       The  Forces Beyond-Planck-Length are  →  F = Φ³. [⊕ 𝛔 ⊝]  = σ x 𝚽 ³  ← (1)-[87]  

  Force  G  acts → on Spinning  M-Points on �̅� through g̅  →  on Planck`s - B̅ →  on  𝐠𝐆  ,  

through the Resonance frequency 𝐟 𝐑. It was Proved that G = σ Φ³, and σ = 
𝐆 

Φ³
 = 

𝐆.𝛔³ 

c ³
 , or →  

σ ² G = c ³…(2) , where σ is a Stress between the frequencies . From Force-relation  F = σ A  

= (2πf r) 
A

Φ
 = w r 

A

Φ
 = �̅�  

A

Φ
 , is seen that force G becomes a velocity �̅� . In the case of Planck`s  

length this velocity is  �̅� = w r = 
𝛔.𝚽 

  𝐫  
 𝐫𝐩 = σ x Φ = |

𝐆 𝐋𝐏 .

  r Φ³
|Φ = [ 

𝐆.𝐋𝐏   

𝐫.𝚽² 
] and from Gravity relation  

G ≡ σ x 𝚽³ ,  then issues → [ �̅� = 
𝐆 𝐋 𝐏 

  𝐫.𝚽² 
 ] = [ �̅� = 

𝟐.𝐆 𝐋 𝐏 

  𝝀.𝚽² 
 ] which is the Light-velocity vector .      

Since r , becomes from the Beyond-Planck`s-Region then    �̅� = 
F.Φ

A
 = [ 

G Φ

A
 ]  …...(f)   

 Equation (f) may be written as Force  G = �̅�  
𝐀

𝚽
 , which is a Viscus- Damping- Force  

 where  
A

Φ
  is a constant of Proportionality and the equation of motion is  𝐅𝐆 = [ 

𝐀

𝚽
 ] . �̇�  

Force G is applied in all Quantized-Universe A as Velocity �̅� and as Stress σ on Spaces  

Anti-spaces as Spaces-relation 𝐋𝐩 = ei.(
π

2
+2kπ).b ,where from Material-Geometry [24-58] ,  

Space ≡ 1 and Anti-Space ≡ √1 = + 1 , - 1 , and  √−1 = i = The Imaginary Part into the  

→ Anti-Space + Space  ≡ motion ≡  i  ≡ √−1
2    ≡ √−1

4   ≡ e−i.(
π

4
).b =  0,707106781 . b .   

The Base b , which for Natural logarithms issues << The Natural logarithm ln(x) of   a  

Magnitude x , is the Power to which , e , would have to be raised to equal x >>  and is 

Defining that → ln(x) is the Period-needed to Grow x , as this is in Integration ∫ x , so ex  

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

is the Amount of  Growth after Period x , and the Possible-Repetitive-Permutations for  

moulds and elements in which issues  𝐌𝐨𝐮𝐥𝐝 𝐄𝐥𝐞𝐦𝐞𝐧𝐭𝐬  =  The - Growth-Periods   i.e.  

when Mould = Elements then is succeeded maximum and for  e is ee, and any logx x .  
For logx x  and Base x = 10  then log10 10 =1010 and for the two elements [⊕ , ⊝] is  

10[10]² = 1020 Positions ≡ Distances ≡ r  and since 10−x = 
1

10x  then b = 10−20 ,  and  

The Anti-Space + Space-Positions are , 0,707106781.10−20 = 1, 0707106781.10−19. 

    In this Way The Non-Dimensional-number [ 0,707106781*10−1 = 0, 0707106781] ,  

    Is Quantized in cave , r , as distance and Becomes The-Dimensional-Space in the  

    Decimal - System b =10  as cave r , and which cave is monad r = 1, 0707106781  or , 

    r = 1, 0707106781 m , having Unit-Area π.r² =3.601588 m2 , and the QUA-Universe is     

A = 3.601588 . 𝟏𝟎−𝟏𝟗 m2/s ,which are The Space +Anti-Space Positions in Universe ...(i)         

From (h) , light-velocity  �̅� = [
𝐆 𝚽

𝐀
] = 

𝟔,𝟔𝟕𝟑𝟔𝟗𝟐.𝟏𝟎−𝟏𝟏𝟏,𝟔𝟏𝟖𝟎𝟑𝟑𝟗𝟖𝟖𝟕

𝟑,𝟔𝟎𝟏𝟓𝟖𝟖 .𝟏𝟎−𝟏𝟗 .
 = 2.99819938 .𝟏𝟎𝟖 m/s    

i.e.  Gravity Force G  ≡ motion , exists without mass and is Quantized  →  Spread in  

       {Space and Anti-Space} or ≡ QUA ≡ {is The Quantized-Units In-Area of Space  

        and Anti-Space },  and as a Mould  𝚽  Golden-Ratio , exists in the  Impedance b .  

        Impedance in Mechanics is the Friction Coefficient , where for Force G  to be  

        Proportional to the Light-velocity c = �̅� , then the Harmonic – Oscillation is an  

        Dumped-Oscillator , and  Can - Oscillate due to the excitation as ,     

  a..  with a frequency lower than in the Undamped case and an Amplitude Decreasing  

       with time , the Under-Damped-Oscillator which Originates the Quantum of motion  

       which is a limiting case between the oscillatory and Non-Oscillatory motion the   

       Critical Damping , and which Originates the Light-velocity �̅� ,  [49] 

  b..  with Undamped case frequency and Decay to the Equilibrium-Position without  

        oscillation and The Over-Damped-Oscillator Originating the n-times velocity c .  

        What is Quantization of motion and Impedance is analytically referred in [83]   

       A Parallel solution becomes also from the attendant Geometry logic ,   

 

The Three Elements ≡ Digits of Material-Geometry are →{⊕ , [⊕↔⊝] , ⊝} ≡ [+ ,0, -]← 

The Permutation , arrangement of the Two-Elements P1
2 = 2 , i.e. are→ [⊕,⊝] - [⊝,⊕]← 

The Three-Elements in Space need   P 1
3 = 3.(3-1).(3-2)  =  6 Positions and the same for  

Three-Elements in Anti-Space need  P 1
3 = 3.(3-1).(3-2)  =  6 Positions , and Total Places → 

P1
3 . P1

3 = 6 x 6 = 36 Positions = A , for Spaces and Anti-Spaces as Impedance and as before     

for logx x and Base x = 10 then log10 10 =1010 and for the two elements [⊕ , ⊝] the 

Growth is 10 [10] ² = 1020 Positions ≡ Distances ≡  r , and since issues  10−x = 
1

10x
  then   

b = 36.10−20 , and  �̅� = 
F Φ

A
 = [

G Φ

A
] = [

6,673692 .10−11.1,6180339887

36 .10 −20 .
] = 2.9795163. 108 m/s  

        i.e. The  Ubiquity of Material - Geometry in Electromagnetism is Everywhere .      

The  Gravity constant g , is the Permeable Path for inner stress σ , to pass the Material`s 

Point a surface  4πr³/3 and to expenditure its Energy .The same exists also  to the 

Electromagnetic force which is associated with a fundamental Property of matter  

which is the Electric - Charge  and which is a clue to the Ubiquity of Electromagnetism . 

From equation of Gravitation G = kE g = g. [ kR gR] seems that the two constants are related  

i.e. act each other through Local-coefficients or through Field-lines , called the Medium  

 or Permissible Path which are as σ = 
𝐅

𝐀
 = 

2πrf

Φ
 = 

w r

Φ
 = 

𝐯

𝚽
 , velocity vector in a Unit-Space 𝚽.  

 

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71 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

 It was shown that the first Path is  Gravity , g , and Original Field-lines of Force , G , are  

distorted by these Charges , Local-coefficients , the Layers following Newton`s laws .  

The Original Field-lines terminate at the surface on one side of the Medium , and new field  

lines originate from the other side of it . It was shown that the Momentum vector ,�̅� , is  

equal to spin  S , because it is following the Stationary - Wave - Nodes - Principle in the 

Material-Points  creating  the minimum quantized Energy which is conserved in lobes .  

This Property is extended also to the Number of lobes as well as to , π , number as velocity  

{ v = n.π.c } which is the minimum Number relating Lines and Surfaces .   

      Analogous happens in equation when v = c , and  →  r = c .      

      From Inner-velocity equation  v = w.r = (2π / T).r = 2π.f1. r , of fundamental  

      frequency  f1 , of wavelength  λ = c.T = c /  f1 , and cave   r = n.[λ/2] , then  

      r = n.(c /2f1)  and  v = 2π.f1 . [n. c / 2f1] = n.π.c  or  v =  n . π . c  ……..(π)   

Equation (π) shows that velocities in lobes are , n.π  times that of light , following , π ,  

number in circle , i.e.  In Material-Points exist velocities multi-times that of light and the  

minimum Surface-constant, Unit π , or the Growth of the velocity-vectors occurs in lobes  

by following the logarithm laws of Energy-constant  c which  acts on Space constant π.  

From velocity , v = n.π.c, is seen that light-velocity is the Quantum of Unit-velocity  

in Planck`s length . The Why velocity c and π , is such in [42-51-63]  

Kepler`s Laws → Explain How the Planets move around the Sun But NOT the WHY. 

Newton`s Laws → Explain the WHY by filling this Gap by a Force F = G.m 1.m 2/ r².  

acting instantly between the bodies that are moving around each other  But NOT their  

Nature and NOT the HOW Force is Acting .         

Markos-Spaces → Explain the WHY by filling the Gap with a Double - Ocean of the  

Pointy-Spinning- Material-Points , becoming from the Stationary- Material-Points ,  

Photons or Electrons , and from the moving-Energy- Storages , the Photons , which  

Orientate and Re-orientate the Stationary-Spins , and explain the HOW and the WHY  

all motions follow the ubiquity of the Electromagnetism , starting from the Primary-  

Material-Points, Photons ,which through the Golden-Ratio-frequency-Growth effect  

and conserve the Whole Natural-World from microcosm to macrocosm .  

    a)  In Vacuum ≡ [10−62-10−35m] , The {Energy-Space-Monad |�̅�| ≡ |AB|},Vanishes.  

    b)  In  Vacuum exists only Pointy vibrating ( The circular motion only ) between the  

         Opposite Dipole [⊕↻↺⊝] generating the , w , B , momentum. 

    c)  As Unit-Energy Vectors �̅� = σ / B̅ → exists ON {Unit-Space-Monad |AB| ≡ |R̅|←  

         And Then  → {The Energy–Space - Monad  |�̅�| ≡ |AB| ≡ The Existing Universe} 

    d)  STPL-Line-Machine  is the Physical - Rotor for the Cosmic-Particles origination .  

The Gravitational-Force G , Acting in the Beyond-Planck- Cave , and on the light Velocity  

Vector �̅�  , creates Electron-Charge �̅� Electron = 
G

c √2 
 = 1,574.10−19 C . which agrees with that  

of Coulomb`s charge  q̅ , and the Material-Points  �̅� Photon=  
G

√2.f
  , while by effecting on the 

Whole-Planck-Cave  𝐋 𝐏 ≡ e i . (- 5π/2) .10 , creates the Pointy-Gravity  Force as this is the Ocean 

of Spins  g̅ , and which Oriented-Spins , Originate Gravity �̅� = [↓= ↻]  , and Antigravity - g = 

[↑= ↺]  as Electron e̅ [72] . The Light-Velocity c̅  of Photons becoming from the Action of 

G on Planck`s Length , when act on a-cave , r = 
𝐡

𝐜.𝐙𝐜 
 ≠ 𝐋 𝐏  then originates the Hydrogen-cave  

E = h fm , because Angular-Momentum �̅� = 
2L

 w̅ 
 = 

 2L

 2πf 
 = [

2L

2π
].[

1

f
] = 

Constant

 2π
 [

1

  fm
] = SPIN [70].  

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72 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

               The  Four  Energy-Space Constants in Nature are , [99]           

    

𝐋 𝐏  ≡ 𝐞−i.(
π

2
+2kπ).b ≡ ei .(- 5π/2) .10  ≡  ei .(-5π/2) .10 ≡ { √3.π. 1,616199.10−35 m } →  

                                and is The Planck`s length cave , 

g   ≡    
𝐓²

𝐚³
  ≡ 

𝟏

f ²n.𝐚³
  ≡  9, 8076941  → The minimum Granular Quantized Energy ,  

       from the gravity frequency fg  , representing the Bedding-Quantum-Raw-material  

       of force G , on all Energy structures .  

G  ≡  σ.𝚽³ ≡  g. kE   ≡  g .[gL kL ] ≡ [
T²P 

𝐚³
].[gL kL ] ≡  9,8076941* 6,8116.10−12 ≡   

         6,68056.𝟏𝟎−𝟏𝟏  m3/ N.s²   The Pulling and Cohesive Bond , of all the  

         Quantized-Energy-Structures in all Spaces .   

𝐟𝐧  ≡  { [S ≡ BP ≡ EM-R  ≡  f1=N , f2 , f3, fD ,,f n] ≡ n 
(1+√5)σ 

  4πr 
 = 

nσ.B̅

2 r² 
   and from cave  

𝛌𝐍 =  
4𝜋.r c 

nσ.(1+√5)
  = 

𝜋2.𝑟 4 c

n.B̅ 
 ] } , The Amount of Energy , the unit meter of motion ,  

         in the Torsional and Resonance-Augmented-Golden-Ratio-Pattern Φ , and    

        �̅� = �̅� = σ . Φ = 
F

A
 Φ = [

G Φ

A
] = [

6,673692 .10−11.1,6180339887

36 .10 −20 .
] = 2.9985163. 108 m . 

4c.. The Origination  of  Electron-charge  �̅� ≡ �̅�  :         

From relation  G ≡ g.kE ≡ g .[gL kL ] ≡ [
T²P 

𝐚³
].[gL kL ] = g k  , is seen that Gravitational-Force  

G , is  The Spring-like central-force from a fix Point , the Source, on an attached , Probe,  

mass as     →  F = - k r = - k r.r̅ , as the 1-DOF equation , r̈ + w ² r = 0 ,  

where k = The Unit-Spring-Force ≡ [meter of area].[meter of force ≡ stress] ≡ π g ≡ with a 

general solution   r = A sinwnt  +  B coswnt , where A , B are constants and evaluated from  

the initial velocity-conditions which become r = [x́(0) / wn] . sinwnt + x(0).coswnt . 

Above equation represents the Natural-frequency of the Celestial-Structures , and  

for Planck`s length the only one Primary-Particle occupying the less frequency  

and  Negative-charge , which is the electron equation and with the solution as ,  

 
𝐰𝐧

𝟐𝛑
 = 𝐟𝐞 =  

1

2𝜋
 √

k

m
  ,  or   4 π² f ²e . me = k = π g   and or  →  𝐦𝐞 = 

𝐠

𝟒 𝛑 𝐟 ²𝐞 
  

From Planck`s min-equation f e = E / h = [-13,6 x 1,6.10−19 = 2,176.10−16 Joule]  /   

[ 6,6262.10−34 J.s ] = 3, 283998.𝟏𝟎𝟏𝟔 /s ,where in Hydrogen atom energy E = h f = -13,6 eV  

Substituting all the minimum-meters of Planck`s scale then , Electron mass is ,  

 𝐦𝐞 = 
g

4 π f ²e 
 =  

9,808238 

4.π.[3,28399.1016 ]²
     =  - 7 , 2373149. 𝟏𝟎−𝟑𝟎 kg  ……… (4b)     

 𝐟 𝐞 =  3, 283998.𝟏𝟎𝟏𝟔 /s , and Loop  𝐋 𝐞  =  2 , 3762992.𝟏𝟎−𝟏𝟔 m   …..(4c)  

Relation  4π²f²e .me = k = π g , denotes that Electric-field generated by an electron has  

both , a component oscillating at the Electron`s - Compton - frequency 𝐟 𝐞 ,   which is  

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73 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

The Energy-Part , and the Non-oscillating component , the Electric-field-lines as the  

Energy-Conductor , The Space-Part , which is connecting Gravity with Electric-field. 

So , Electron , is the minimum-Energy massive Particle in Hydrogen-cave {-13,6 eV} ,  

becoming from Material-Point In Planck`s-length , minimum-cave, occupying the less  

Unit frequency in Planck`s – Length ,with Negative-charge { 𝐟𝐞= 3,283998.1016 /s }.  

Because of the Negative-Energy in Hydrogen-cave , and the less-Negative Energy of 

Rims which consist the Plane-traces-Conductors or the Paths in-where electrons roll so   

Energy Rims consist the Energy-minimum-Paths in Hydrogen-cave-Potentials , as  

En - En−1 = [me.v²] .[2n-1] , where the electrons , the Electric–Charges , roll .  

Electron Charge   �̅� Becomes from Magnetic Field M which creates the Electric-Field  

E , which is acting on Charge q , and the acting Force per second creates Work which is  

conserved and coincide with the Planck`s constant h . This is because h → J s = N m s =  

Power ,where from, Energy = Power x Time , issues the Beyond Planck`s length 𝐋𝐏 , and   

The Voltage V is → q̅ ≡ 
KE 

VP =1
 = 

me  𝑐 ²

2
 = 

g c ²

8πf ².1  
 , and  V̅ ≡ VP ≡ 

 c .Charge

Total−Energy= h
 = 

c .q̅ 

h
 ...(1) 

Using the two Energy-equations for Linear-motion → fn = 
1

2π
√

k

m

2
 and Orbital-motion  

a =√
1

k .f ²

3
 , for Unit-Energy-Space-frequency k = g , a = π , then → g .f ². π ³ = 1  ...(2)  

Frequency fn =√
1

g.π ³

2
 =√

1

9,808238.π ³

2
 =1,8133418.10−3 , i.e. The Unit-Charge-Cave , q̅  

into Hydrogen cave [a =1,82043047.10−12m].[1,813342.10−3/s] = 3,3010625.𝟏𝟎−𝟏𝟓 C              

       From equations Charge and Voltage is the Self-Growing Property of frequency 𝐟𝐧    

       in Material-Point , therefore and for Hydrogen-cave is equal to → q̅.Φ  ,     

Because Gravitational Force is equal to → the Geometric-Resultant of light-velocity  

c , acting on Electron-Unit-Charge �̅�  ← or ,  G = c √𝟐  �̅� , then Electron-Charge is ,  

q̅ = 
G

c √2 
 = 

6,680561 .10−11 

1,41429.[2,9979346.10 8] 
 = 1,58.10−19 Coulomb , the known Coulomb`s  charge  

quantity, From  gL ,kL Universal constants  the  Newton`s Gravitational constant Force  

is ,  G ≡ g.kE ≡ g .[gL kL ] ≡ [
T²P 

𝐚³
].[gL kL ] ≡ 9,808238* 6,8116.10−12 ≡ 6,68056.10−11 𝐦³

𝐍𝐬²
 

The in depth Position of electrons allows to the Work Produced in Prior  Phase-Areas  as  

Golden Ratio Pattern , to be Stored in the Next . Energy = motion / T  ≡ (
v

2πr
) . [σ + σ Φ] = 

�̅�  . [ 
𝛔

𝟐𝛑𝐫
 + 

𝛔𝚽

 𝟐𝛑𝐫  
 ] ≡  �̅� . [. fn̅   + 𝐟𝐧 ] ≡ Moving - Storage →[ �̅� . fn̅   ] ← + Moving-Frequency  

→ [ �̅�.𝐟𝐧 ] ←  ≡ Material-Point   i.e.          

The Energy produced in Photon-Cave is consisted of  Two-moving-Storages , that travel as  

Wave  [�̅�.𝐟𝐧] →[ �̅� . fn̅   ] → [ �̅� = �̅� = λ
f

Φ
 ] → [ S ≡ EM-R ≡ f1=N , f2 , f3, fD ,,f n= w² ] , and as  

Particle  →[ f1= (E²+H²) = n 
(1+√5)σ 

  2πr 
 = 

 nB̅

π² r⁴ 
] →{W≡EM-R≡ [εE² + μB²] = 2.λc.sin.2φ} and is  

The Duality  of an Energy-Storage  S ≡ { [⊕← 𝐫 →⊝]  + Motion M  . [87-89]  

5c.. The Origination  of  Hydrogen Cave H  :   [99]    

From Kepler third law , the Energy-Closed-Space equation and Newton`s Laws of motion 

        Constant k = v². r = ( w r ) ².r = [ 
𝟐𝛑

𝐓
𝐫 ] ². r = 

𝟒𝛑² 𝐫²

𝐓²
. r = 

𝟒𝛑² 𝐫 ³

𝐓²
 = 4π².

𝐫³

𝐓²
 = 4π².r³.𝐟²𝐩 ……..(k)  

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

Because (k) is constant , r ³.f ²p , is also a Constant multiplication of cave  ,  r , and the  

frequency f , and the  Work ≡ motion are conserved in cave , r , as the , n , frequencies 

fN = n 
(1+√5)σ 

  2πr  
 = 

nB

𝜋2r4 
 , and for a Damping-cave → r(t) = r(t + w) ← as Planck`s scale is 

with min-Damping = 1  and Unit-Energy-Quantity 𝐖𝐮 , ( the critical-energy-unit in  

       min , r ) ,  is this Unit-Stress-Gravity  g , as    k = E = 
T²

a³
 = g = 

1

f ².a³
  , i.e. →  

       Stress  �̅�  , when is entering into the minimum cave , a , of a minimum Surface , then  

       from the Period of Rotation  T on the Perimeter , is created in Surface  the minimum  

       Quantity of Energy-cave and is the Hydrogen-Atom , where  gf ² ≡ the Energy-Part  

       embodied with stress �̅�  ,  and the cave  a³ , is  the Space-Part , in 3-DOF Space as →   

T ² = g a³ = 9,808238.[ 2 ,1145016.10−11 ] ³ = 9 , 2728158.10−32  s , and Period  

T = 3,04513.10−16 s , or frequency  f = 3,2839982.1015 / s . From equation E = h f  =  

6.62607.10−34 . 3,2839982.1015 = 2,175999. 10−18 J / (1,6022. 10−19 ) = 13,59999 eV 

Above Quantized Energy of  13,6  eV ,  corresponds to the Hydrogen-Atom-Cave .  

It was shown that in Conservative Systems of a Central-Force , the Total energy  

E is conserved and at Periapsis , energy  E =  
𝐆.𝐌𝐦

𝟐 𝐚
  and e = √1 + 2EL2/G²M²m³    

and for e = 0  then →  E = -  
G²M² m³

2 L²
  ,  i.e. Energy is always Negative .  

Hydrogen cave constant is   k = E = 
T²

a³
 = g = [

4π² 

GM
]  therefore  GM = 

4π²a 

g
  and  from  

Newton Total-energy  E = -  
GM m

2 a
 , Rotational-Momentum L = √(1 − e2). GMm². a  

Eccentricity  e = 0 , G Mm = - 2a.E , and then →  L² = GMm².a = - 2aE[a] = - 2a²E .  

 

i.e.    Equation  L² = - 2a².E , denotes that Angular -Momentum L ,  

         in Orbit - Rims is always Negative and equal to , L = - a √𝟐. 𝐚𝐄 .  

 

So , Hydrogen-Atom , is the minimum-Energy-cave In Planck`s-Length , occupying the 

minimum Negative-Energy in Rims ≡ Caves  , the Space , where Quantum-Energy-Rims  

are the Plane Traces-Conductors in where can roll the ⊝ charged Electrons .    

In Hydrogen-cave , the Resonance Frequency of an Electron ⊝ , and a Proton ⊕ ,  

happens from the Stationary Unit-Cave of a System of Kepler second Planetary-law as  

equation  , 4 π² m f ²o =  k , and from constant law of Areas 1 = k .𝐟 ²𝐨  𝐚
𝟑 .Their common  

Constant-Energy k , is  → k = 4 π² m f ²p =  
1

𝐟 ²𝐩  𝐚𝟑 
  or , f ⁴p = 

1 

4π²ma3  and  fp = √
1 

 4π²m.a3

4
 .  

A loop in Planck`s length  2a = L P = π.1,616199.10−35 m  with  frequency  f =  
c

𝜆
  , where  

then issues   f ⁴p = 
1 

4π²ma3 = [ 
c

𝜆
 ] ⁴ = [

1

𝜆
] ⁴.{𝑐4 = 

1 

[4πa3]mπa
 } , and  for the Unit Intensity  I = 

Energy

Area
 = 

E = hf

A = 4πa3
 = 

1KW

A
 =

1 

[4πa3]
 = 

1

𝜆⁴
 {mc4. πa}= 

1

𝜆⁴
{1}.80,760865.1032. (3,14).0,8081.10−35  

=0,5865.{ 
1

𝜆⁴
 }, and E-Intension is → I = 0,5865 . {

𝟏

𝝀⁴
} ← or , is the Rayleigh Scattering , i.e.  

    

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75 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

              The Quanta of Energy , Passing through a Unit-Surface or Volume ,  

              which becomes from the Kepler`s Second  and third  law Mechanism ,   

              is  Inversely Proportional  to the fourth Power of the wavelength 𝝀 .   

In Outer Electromagnetic fields , frequency , w , is that of inner motion → w = 
2π

T
 = 2π.fN  

≡ [
1+√5

2
] 

σ

2πr
 = 

𝛔.𝚽

𝐫 
 , which continuous to follow the Growth-Golden-Ratio-Pattern . Photon  

occupies such the Property of Material Point as the Growth-Pattern .With this way Photon`s  

frequency →  fP  = 1 / TP , Kicks-Start everything found on its-way . From the Resonance 

constant  k = 
1

 f ²n.a ³
 →  or  1 = k .f ²n. a3 ← and from   

Kepler`s laws and Newton`s Lagrange laws for  Orbits , the cave-Semi-major-axis is as ,  

        a  =  √T2/ k
3  = √

1

 g.f ²
 

3
=√

4.π².r²

g.σ².Φ²
 

3
  = √

[4π2].x   r²

[g.Φ2].x σ²
 

3
 ,   and      

       𝐟 𝐑 =  
wR

2π
  =  √

k=1

 g.a ³
 

2
     = √

𝛔

g .Φ2.a³
 

2
   ≡ √

k

md
   eV   …(a)   

i.e.  It is the  Resonance-frequency fR , in Photons loop , and which is the Energy-Space   

       Quanta , following the  Growth-Golden Ratio-Pattern , which travels in all Cosmos.    

a)... It was shown that when two Photons strike each other , c  = c⃖ , or reflect on a wall , then  

       c = 0  and so their fundamental frequency  f1 = n.[ 
�̅� 

2r
 ]x[

1

4
] = n.[

�̅� 

8.r
]  which for  n = [

8.𝜋𝑟𝑐

v.λ
]  

      increases to  
λ

c
  , therefore for n = N.[

8.𝜋𝑟𝑐

v.λ
] = N.|

c

𝜆
| and for N → ∞ then  f1 = E / h =∞ ...(b) 

     In Dual Photon v̅ [
σΦ

 2πr  
 + 

σ

2πr
 ] ≡ v̅ . [ fn̅  + fn ] , Colours are the Still-Sub-Units of Storage   

     [ v̅ . fn̅   ] , and  exist as  Frequencies , Violet , Blue , Green , which Stabilize with their  

     Complementary colors  Yellow , Orange , Red , of wavelength  d = λ → 𝝀 𝐦𝐢𝐧   𝝀 𝐦𝐚𝐱  =  

     3.10−7m   3.√3.10−7m .  

b).. The Quanta of Energy , Passing through a Unit-Surface or Volume is Inversely    

       Proportional  to the fourth Power of the wavelength  𝜆 as  I = 0,5865 . { 
1

𝜆⁴
 } .  

       When   fBE = E / h = ∞  then the Energy-Intension Increases and the  wavelength   

       𝝀  Decreases and  for fBE = ∞  then 𝝀 = 0  .  

      This is what happens in Black-Holes where d = 𝜆 = 0  , and  in where E = fBE = ∞ .    

Hydrogen-Energy  E = h.fP  = [ 6,6262.10−34 J.s ] . [ 3,28393.1015 / s] = 2,176.10−18 J  

and in   eV → [2 ,176.10−18] / [1,6.10−19] = 13,6 eV ,  

Above Quantity of Energy consist the Hydrogen minimum Energy-Rim , becoming from  

equation  a = √𝐓𝟐/𝐠
𝟑

  = √
[3,04513.10−16]²

9,80769411
 

3
 = 2,1145016.10−11 m , for Unit energy cave .  

From Angular-Momentum B = r.mv = r [
πrv

2
] v = 

𝛑 𝐫²

𝟐
 v² = 

𝛑 𝐫²

𝟐
v²  = 

πr³

2
 [n.π.c]² = 

𝛑³ 𝐫³

𝟐
 c² , or 

Black-Hole-Energy → 𝐁𝐄 = 2.π⁵.r³.f ² = (𝛑𝐫)³.w² ← i.e. Velocity in Black-Holes is Related  

to Cave , r ³, and Energy w² times of light velocity.  

 

c)..  Since the Primary motion ≡ [PM] exist from the three Breakages only , and STPL is the  

n =3 Mechanism creating Elementary Particles   [n-Knots=3] in  𝐕 GRA = 7,593.1035 V.   

Explanations :  

 

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

The Action-Spaces  ≡ The Infinite Quaternion - monads →  �̅� ≡ ( s + v̅.i ) ≡  𝐀𝐁̅̅ ̅̅   ≡  

      ≡  √s2 + [ v̅. i ]² ]  ,  or   �̅� ≡ x + i . y ≡  𝐀𝐁̅̅ ̅̅   ≡  moduli  , r ,  is their magnitude    

      [ r = | r | = √ x2 + y2 ] , on Unit-Diameter AB̅̅ ̅̅  . The [QMAS] . For Quaternion |v̅| = s      

Breakages  𝐳  * 𝐳  = (s + v̅.i )² = s² +[v̅]² +2.sv̅.i = s² – v̅ ² ± 2.s v̅ = |s|² - |�̅�|² ± 2.|s|.|s̅| , i.e. 

     In Figure -3-  the Vector of Amplitude is Quaternion  �̅� ≡ x + i . y , with vector �̅� , to  

     be from Definition of the Complex Vector Space , the Set of Vectors of length (the n  

    Vertices which form the n - Polygon Sides , or the Norm of  the Complex - Vectors ) 

a...The 4-Geometrical Spaces , [ Space , Anti-Space , Neutral-Space , Sub-Space ]  

      consist    →  The Geometrical - Mould of 𝐀𝐁̅̅ ̅̅  - Monad  ≡ [PM-2R-M] ←     

b...The  Vectors of Amplitude z = 2R , ON 𝐀𝐁̅̅ ̅̅   Monad , consist The Energy-Mould .     

      of  2R-Form .The Physical -Mechanisms → [ Physical Mould of 2R- Monad ] ≡   

      [GM-AB-M] ← are such and dependent on the n - Number of Accessories they use .   

A… The  Gravity Force  G  ≡ motion  ≡  σ.𝚽³ , exists without mass and  is Quantized  

        Spread in{Space and Anti-Space Or ≡ QUA ≡ {is The Quantized-Units In-Area of  

        Space and Anti-Space }, and as a Mould 𝚽  Golden-Ratio , exists as  Impedance b.  

Placing [ Physical Mould of 2R- Monad ] ON [ Geometrical - Mould of 𝐀𝐁̅̅ ̅̅  - Monad ]  

                                      [ PM-2R-M ]    →    ⇅   ←    [ GM-AB-M ] 

THEN → Gravitational-Force G ≡ [ Σ = n . h ] , and n-NA = 1  Creates & Constructs,  

        For n =1 ABM = [Σ = n h]   G / c = Charge  �̅� = 
𝐆

𝐜 √𝟐 
 =  1,58.10−19 Coulomb .    

1)..→ g  ← G  ≡ σ.𝚽³ ≡  g. kE  ≡ g .[gL kL ] ≡ [
T²P 

𝐚³
].[gL kL ] , and g = 

𝐆

    kE  
 = [

6,673692 .10−11

6,8116 .10 −12 .
] 

       ≡  9,8076941 . Gravity-Acceleration in Black-holes g G = [ 
π r v4

2
].𝑒3 = 9,808238 m/s . 

For  b = 36.10−20 ,  �̅� = 
F Φ

A
 = [

G Φ

A
] = [

6,673692 .10−11.1,6180339887

36 .10 −20 .
] = 2.9895163.108 m/s 

2).. → c̅ ←  �̅� = �̅� = σ . Φ = 
F

A
 Φ = [

G Φ

A
] = [

6,673692 .10−11.1,6180339887

36 .10 −20 .
] = 2.9985163.108 m . 

3).. → q̅ ←  from  G = c √𝟐  �̅� , Electron-Charge is ,  q̅ = 
G

c √2 
 = 1,58.𝟏𝟎−𝟏𝟗 Coulomb , 

B… The{TVPM} Mechanisms , from Charges on Two-Perpendicular-Vectors-Edges ≡      

        Markos Two-Vectors Three-Poles Mechanism is case {QUA} ≡ [ Σ = n . h ]  ∞ x 𝚽  

        which is the Physical Mechanism , and gives the ∞ - Impedance b , determining the    

        Objective Reality which is the existing Universe .  The two ⏊ Vectors Produce the  ∞  

        Squares ∞ , 𝐀𝐁̅̅ ̅̅   Monad  ≡ ∞ - [ GM-AB-M ] with  ∞ , 2R-Form [ PM-2R-M ]  and   

        n ≡ ∞  Number of Accessories , as from monad R = 
σ

J.w²
 = 

𝛔

�̅� 
  and velocity �̅� ≡  σ Φ . 

C…Primary motion ≡ [PM] exist from the three Breakages only [s² = ⊕ ,2s² = , - s² = ⊝] ,  

       on Triangle 3-Knots with n ≡ 3 Number of Accessories , therefore [STPL] Mechanism  

       is the  n = 3 Accessories-Mechanism creating the Elementary Particles , [n-Knots=3] in   

        the Gravity Voltage    𝐕 GRA = 7,593.1035 V.  This Physical Mechanism creates the  

        Elementary Particles  their  n = 1 - ∞ , masses of  Atom`s  & Compounds determining  

        their Atoms Complex-Vector-Response .These sparse Particles  exist in all of the  

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77 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

        universe in the sense that they are uniformly distributed . 

D…The { TCIC } Mechanisms ≡ [ Σ = n . h ]  8 x ①  is the Physical Mechanism , from  

       Charges In Three-Vectors-Conductors-Edges ≡ Markos  Tetrahedron Cube Inscribed – 

       Circumscribed Circles .The Tetrahedron Conductors -Vectors  DA̅̅ ̅̅  ⏊ DB̅̅ ̅̅  ⏊ DC̅̅ ̅̅   Curry   

       Energy as Electromagnetic-Fields  (Forces-Frequencies-Stresses-any motion) TO  the  

       Inscribed Sphere (Nucleus of Atoms), TO  Cube Vertices (Electrons-Position) ,TO the   

       Circumscribed Sphere  (The Electrons Orbits) for Equilibrium and for transferring  

       Information  and Signals . a..  The Protons and  the Nucleus Structure  :  

        From above [GM-AB-M] ≡ 8 x [(+)[↔](-)] ≡ Neutral = n , then     

a...   For 1 Proton [(+)[↔](-)]↔(+)  ≡ Neutral                                →      n = 1 p = 1   

b...  For  2 Proton (+)↔[(-)↔(+)][(+)↔(-)]↔(+)  ≡ Neutral      →      
p n
n p 

c...  For 3 Proton (+)↔[(-)(+)](+)[(-)(+)](+)[(-)(+)] ≡ Neutral            →     
n p n
p n p   

d...  For 4 Proton (+)↔[(-)(+)](+)[(-)(+)](+)[(-)(+)](+)[(-)(+)]           →     

p n p
n 0 n
p n p

  

h...  For k Proton (k1)↔[(-)(+)](k2)[(-)(+)](+)[(-)(+)](+)[(-)(𝐡𝐤)]   →    
kp kn kp
kn 0 kn
kp kn kp

 

where  n-NA ≡ k ≡  The Number of Accessories of {TCIC} Mechanisms ≡ [ Σ = n . h ] 

On →    
kp kn kp
kn 0 kn
kp kn kp

   k - Space  [ GM-AB-M ] .  

From above is seen the Way of Atoms Construction. (Geometrical-Mould of 𝐀𝐁̅̅ ̅̅ -Monad). 

E…From Energy = motion / T ≡ (
v

2πr
).[σ+σ Φ] = �̅�.[ 

𝛔

𝟐𝛑𝐫
 + 

𝛔𝚽

 𝟐𝛑𝐫  
 ] ≡  �̅� . [. fn̅  + 𝐟𝐧 ] ≡ Moving  

Storage →[ �̅� . fn̅   ] ≡ [GM-AB-M] ← + Moving-Frequency → [�̅�.𝐟𝐧] ≡  [PM-2R-M] ← ≡   

[ Σ = n . h ] , and n-NA = 1   Material-Point   i.e.  The Energy produced in Photon-Cave is 

consisted of Two-moving-Storages that travel as Wave  [�̅�.𝐟𝐧] →[ �̅� . fn̅   ] → [ �̅� = �̅� = λ
f

Φ
 ] → 

[S≡ EM-R ≡ f1=N] & as Particle→[ f1= (E²+H²) = n 
(1+√5)σ 

  2πr 
 = 

 nB̅

π² r⁴
]→{W≡EM-R≡ [εE²+μB²] 

= 2.λc.sin.2φ} and The Duality  of an Energy-Storage ≡{[GM-AB-M] ≡ S = [⊕← 𝐫 →⊝]  

+ Motion ≡ [PM-2R-M] ≡M≡ �̅�  −  𝐕𝐞𝐜𝐭𝐨𝐫  } , issuing [PM-2R-M] = √−1 .[GM-AB-M] ,  

Therefore → Photon-Mechanism  is for Both travelling  as Particle  and  as Wave , 

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

    6c.. THE  EPILOGUES  OF PRIOR  .                

 

Figure – 17 :  The Periodic motion in Caves follows Material - Geometry rules .       

In (1). Is shown the Geometrical Expose of , Dynamic-Space-Energy relation  g .r ³.𝐟²𝐩= 1 

In (2). Is shown the Mechanical Impress of the , Orbit-Space-Energy relation   g .r ³.𝐟²𝐩= 1  

In (3). Is shown the Extreme Design of the , Dynamic-Space-Energy relation  g .r ³.𝐟²𝐩= 1 

In (4). Is shown the Geometrical Creation of The Energy-monads-motion & The Physical  

          Monads - motion from their Unit - relation  g .r ³.𝐟²𝐩= 1  

       THE  ORIGINATION  OF  ANTI – GRAVITY - STRESS  -  g  :        

       6c1..  The Origination  & The Nature of  Gravity  g .  

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79 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

Figure -17a-:The Stability of ±SPIN as an Electromagnetic Wave of  Two frequencies ,0, c   

            From relation Angular Velocity  c = w r = 2πfn.r = 2πr .fn = σ Φ . Since light-velocity  

            is created from G beyond the Planck`s length r P =1,61626.10−35 m , therefore issues  

            c = w r = w r P = 2π rP .fn = σ Φ , and from the light-velocity Properties becomes , 

a).. The light velocity c is constant . Since c is constant then is analyzed to , ( cx , cy ) in any  

       two directions x , y  where  x ⏊ y and  y to be the gravity direction on where gravity is  

       acting . In figure (8) are seen the 4-Point Positions , at where Velocity Phase changes and  

       the Work done in each Phase of Photon`s inner motion .    

       The 4-Phases correspond to the Wavelength . λ ,  as  λ / 4 . in distance  with  90° = 
𝜋

2 
  to  

       be the change of Phase .  

This means that the  Produced Work in the Prior Phase-Area is as the  Golden-Ratio Pattern  

which is Stored in the Next and Perpendicular Phase-Area . The Light velocity  �̅� ,  changes  

       Phase every 90° and the created Work  { W = c y x [Quarter circle 1-O-4] }     is  

       Symmetrically Stored from  0° → 90° alternately + , - , - , + , in [Quarter circle 1-O-4]  

      in the [Quarter circle 4-O-2]  into  [Quarter circle 2-O-3]  into  [Quarter circle 3-O-1] 

      The Momentum ≡ Spin ≡�̅�≡ r m v = [ 
𝛑.𝐫𝟐 

𝟒
].�̅� x �̅�  where  ± [ 

𝛑.𝐫𝟐 

𝟒
] = The Quarter circle.  

      The Quarter circle , + + , consist the  + Spin ≡ �̅�  which is the Gravity Force , and the  

      Quarter circle , - - , consist the -Spin ≡ �̅� which is the Gravity Force from Total ,+, -,-,+,  

      When  r → 0  Or when  �̅�  doesn`t act on the Quarter circle  then happens  Black-Hole.  

      In [108] is determined the when Newton’s Gravitational Force  𝐆 , Stops Acting  

                    thrusting , on The Light velocity Vector �̅� , and happen the Black-Holes . 

b).. The Dual Property of the Simultaneously existing Spin as Electric and  as Magnetic  

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80 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

      Field   in  wavelengths , λ x , λ y ,  as Effective Range , is  thrusted through  the Light  

      velocity �̅� , and finally is from the Newton’s Gravitational Force  𝐆 . In Planck`s length   

      r P =1,616255.10−35 m the created Work from  �̅�, on 1-4 Position is stored in the [1-O-4]  

     Quarter-circle surface and at Phase-4 where  c = 0  is then stored  in  the [4-O-2 ] Quarter 

     circle surface . At Phase-2 where  �̅� = - �̅�  motion is stored in the  [2-O-3 ] Quarter circle  

     surface , and At Phase-3 where  �̅� = 0 motion is stored in the  [3-O-1] Quarter circle  

     surface , i.e.  is alternately repeated  the  + [ 
𝛑.𝐫𝟐 

𝟒
] =The +Quarter circle [1-O-4] , and the  

            - [ 
𝛑.𝐫𝟐 

𝟒
] =The - Quarter circle [4-O-2] both in the same Plane-surface [1-4-2-3] of   

              motion . The Surface  [ 1 – 4 – 2 – 3  ] is  ⏊  on the  SPIN Axis →  U – D . From  

              fn =
σ

2πr 
 Φ  and  c̅ = w̅.r = 2πfn.r = 2πr .fn = σ Φ , are frequencies , 0 , c , relation.   

            At  c = 0  exist  minima or maxima where is the change of two Energy-Semicircles.  

c)..  The  origination of Spin  in cave  H .  

 From Orbit vibration fn = 
(1+√5)σ 

  4πr 
 = 

σ

2πr 
 Φ  and from relation g.a³.f ²n = 1 ,  f ²n = 

σ²

4π²r² 
 Φ² = 

= 
1

g .a³  
   then   g.a³.Φ² = 

4𝜋²𝑎²

𝜎²
 , or 1).  a = 

1

g 
 [

2𝜋

σ Φ
] ² , and from Work W = 2E = B w = J.w² , or  

2E = 2π.f   and  �̅�f = 
E

 π  
  then  2). The Energy in Planck-scale-cave  2E = B̅fn = [

(1+√5)σ 

  4πr 
].B̅ =  

[
σ 

  2πr 
].B̅ Φ , or   E = [𝚽

𝛔 

𝟒𝛑𝐫 
].�̅�   i.e. The Energy in Planck-cave-Particles is Dependent on  

their Spin only , and for Electron  r = a e → E = [Φ
σ 

4π.r 
].B̅ =1,6180339[

1

4𝜋.1,6840307.10−17 
]x  

x 2,845976. 10−17= 
21,76.10−19

1,6.10 19 .
 = 13,6 eV ,  which is the min-Voltage in Hydrogen cave .  

d)..  The  Angular Momentum  in  cave  c̅ - r ,  

In cave , r ,  The Energy-Vector  �̅�  is Positive for   O3⃗⃗⃗⃗  ⃗  ,  O1⃗⃗⃗⃗  ⃗  , O4⃗⃗⃗⃗  ⃗  , Directions while ,   

                    The Energy-Vector  �̅�  is Negative for  O3⃐⃗⃗⃗⃗⃗   , O2⃐⃗⃗⃗⃗⃗   ,  O4⃐⃗⃗⃗⃗⃗  ,  Directions . 

Since Total-Energy  L = B w = 
J.w

2
 w = 

J.w²

2
 then 2L = J.w² , then Angular Momentum relation   

                                   B̅ = r.mv = r [
π.r⁴

2
]. 2πf r =  π ².𝐫𝟔.f .  and  B =  J w         i.e.  

Angular Momentum  �̅� = r m v =  
J.w

2
 =  [

π.𝐫𝟒 

4
] 

c

r
 = [

𝛑.𝐫𝟑

𝟒
].�̅� = [ 

𝛑.𝐫 𝟐

𝟒
 ].�̅� x �̅�   ......(a)   

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

For  �̅� = ± �̅�  ,  then  + �̅� = + Gravity – Spin = + [ 
𝛑.𝐫𝟐 

𝟒
].�̅� x �̅�   , The + Gravity Force  

                                 - �̅� = -  Gravity – Spin =  -  [ 
𝛑.𝐫𝟐 

𝟒
].�̅� x �̅�  , The  -Antigravity Force  

From Momentum relation  B̅ = m r v = m r² w = m r² (2πf) = 
J.w

2
 = [

πr⁴

2
].[2πf] then Spin S ≡   

Angular-Momentum   �̅� ≡ �̅� =  
J.w

2
 = 

πr⁴

4
 [2πf]= π².r⁴.[f] = 

𝛑.𝐫³𝚽.𝛔

𝟐
 ≡  

[𝟏+√𝟓 ].𝛔.𝛑.𝐫³

 𝟒
= 

𝛑𝐫𝟑𝛔.𝚽

𝟐
 ..(b)   

For  �̅� = ± �̅�  ,  then  + �̅� = + Gravity – Spin = +   
𝛑.𝐫𝟑𝛔.𝚽

𝟐
   ,  The Gravity Spin  

                                 -  �̅� = -  Gravity – Spin =  -   
𝛑𝐫𝟑𝛔.𝚽

𝟐
   ,  The Antigravity Spin  

From Spin-Momentum relation  S = �̅�  = 
𝐄

𝐰
 = 

𝐄

𝟐𝛑𝐟
 = 

𝐄𝐫

𝛔𝚽
 = 

𝐫𝐆

𝛔𝚽
 , and  �̅�² = 

𝐉²𝛔²

𝐫²
Φ², so → [�̅�]² = 

[
𝚽𝐉𝛔

𝐫
]²← while from  Gravity-force  𝐅𝐆 ≡ 𝐦𝐆g= g. [σ c].r = 𝐦𝐆

𝐜²

𝐫
 = Jw².𝐠𝐆 = 

𝐯²

𝐫
 . [

𝛑𝐫𝟒

𝟐
] 

𝐯²

𝐫²
 =  

 
𝛑𝐫𝐯𝟒

𝟐
, and Gravity-Acceleration ± 𝐠𝐆 = [

𝛑𝐫𝐯𝟒

𝟐
]. 𝒆𝟑  , Geometry Growth         

                [
 𝛑𝐫𝐯𝟒

𝟐
]=[

𝟑,𝟏𝟒𝟏𝟓𝟗𝟐𝟔([√𝟓+𝟏]. √𝟐
𝟒

.𝟏𝟎−𝟑𝟓).(𝟐,𝟗𝟗𝟕𝟗𝟑𝟒𝟓𝟖.𝟏𝟎𝟖 )𝟒

𝟐
 ].𝒆𝟑 =  

                = 6,044981.𝟏𝟎−𝟑𝟓. 80,773378.𝟏𝟎𝟑𝟐. 20,085536 = 𝐠𝐆  =  ± 9,8076925 .  

i.e. Gravity + 𝐠𝐆 = + 9,8076925 = 
𝛝𝐫c̅

𝛝𝐭
 = + �̅� , and Antigravity= - 𝐠𝐆 = - 9,8076925 = 

𝛝𝐫c̅

𝛝𝐭
 = - �̅�  

     are the Two Opposite Forces as Spin and for the Stability of the Spin - �̅� , Equilibrium.  

     For  c = 0  exist  minima or maxima and thus SPIN is equal to the Negative Gradient  

     of the Potential Energy in  the two Interchange Energy Semi circles . Centripetal force   

    Originates the Two-Momentum ± �̅� , �̅� = r m v = [
𝛑𝐫𝟑𝛔.𝚽

𝟐
] ≡ Gravity – Antigravity – Spin.  

      6c2.. The Stability of Equilibrium :  

In the Conservative System , of cave  �̅� - r , the Total Energy 𝐄 𝐓  remains constant and the  

Total-Energy is  𝐄 𝐓 = 𝐄 𝐊 + 𝐄 𝐔 = 
𝟏

𝟐
 [�̇�] ² + U(x) = constant …..(1) where  𝐄 𝐊= The Kinetic 

Energy and  𝐄 𝐔 = The Potential Energy . For  y = �̇�  then , y = �̇�  =± √𝟐. [𝐄 − 𝐔(𝐱)] …(2) 

The differential equation of motion in cave  �̅� - r , for  Conservative Systems is  ẍ = f(x) and 

Because  ẍ = ẋ (d�̇� /dẋ  )  then  ẋ. dẋ = f(x)dx =0 ..(3)  By Integrating then  
  ẋ²

2
 - ∫ 𝑓(𝑥)𝑑𝑥

𝑥

0
 =  

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

E ,  and by comparison to Priors  then →  U(x) = - ∫ 𝑓(𝑥)𝑑𝑥
𝑥

0
   or  f(x) =  -  

  𝐝𝐔

𝐝𝐱
  =  �̈�   …(4)   

i.e. For the Conservative System , of cave  �̅� - r ,  the force = �̅� = r m �̅� = 
J.w²

2
 = [ 

𝛑.𝐫𝟐 

𝟐
].�̅� ² is    

Equal  to the Negative Gradient of the Potential Energy Into 2-Energy Semi-circles.   

For y = �̇�  then (3) becomes  
dy

dx
 = 

f (x)

y
 = Φ (x , y ) , and the Singular Points correspond to  

f (x) = 0 , and y = ẋ = 0 and hence are the Equilibrium Points . For every Point x , y in the  

Phase-Plane for which  Φ (x y) is not indeterminate exists a unique slope of the trajectory.  

When the velocity vector is at Points 1,2  then y = 0 and f(x , y) = C ≠ 0 then the Slope of  

the trajectory is infinite and angle φ = 90ᶱ .  Since motion in cave  �̅� - r ,  is a  single-DOF 

oscillator , then motion equation is  ẍ + w² x = 0 .Equation indicates that at the Equilibrium  

Singular Points , 3 , 4 , the Slope of the Potential Energy curve U(x) must be zero, meaning 

minima or maxima , and which is  the  ± change of direction for the Four Energy- Quarter  

circles  [1-O-4] , [4-O-2] , [2-O-3] , [3-O-1] in  ( cx , cy ) where  𝐜𝐲 ̅̅̅̅  =  �̅�  = Spin Direction ,  

Conclusions :      

1… From A-Momentum �̅� = r m �̅� = 
J.w²

2
 = 

𝟏

𝟐
 [�̇�]² +U(x) = 

𝟏

𝟐
 [ y]² + 

𝟏

𝟐
 k x² = constant , then  

Spin S ≡ �̅� = 
1

2
 [y]² + 

1

2
 k x² = [y] ² + w ² x² = C = Constant , or  →  y² + w² x² = C ←….(a) 

Equation (a) is a series of Ellipses determined by C , and for w = 1   y/w = y  then reduce  

       to circles   y² +  x² = C , in  �̅� - r   Plane and Perpendicular to  S  since , [ �̅� - r ] ⊥ �̅� .  

2… In the Conservative System of cave  �̅� - r , where  �̅�  = Light-Velocity = 2.9985163. 108  

m/s , r = Planck`s -Length = √2
4

. 10−35 m  , motion in cave is an  single-DOF oscillator as  

equation  ẍ + w² x = 0 . Equation of motion is a circle on where exist  the 2-Singular Points   

3 , 4 , meaning  minima or maxima , where issues  
dy

dx
 = 

f (x)

y
  = Φ (x , y ) ,  and are in the 

Mode-Shapes at the Points of Equilibrium . At  Singular Points  3 , 4 , Velocity 𝐜𝐲 ̅̅̅̅  =  �̅� = 0   

and Spin  �̅� = Gravity = 0  ,  and since   
dy

dx
  < 0  , then Spin  �̅�  changes Direction becoming  

     - �̅�  = Antigravity = 0 , meaning that at  Singular Points  Gravity & Antigravity are Zero .  

3…At Point 1 , Velocity  𝐜𝐲 ̅̅̅̅  = + �̅�  because of  𝐜𝐲 ̅̅̅̅  , +↓ direction and corresponds the Spin �̅�  

     = Gravity = �̅� = r m �̅�  which is Constant and equal to Work = 𝐜𝐲 ̅̅̅̅  x [Quarter circle 1-O-4]    

      At Point 2 , Velocity  𝐜𝐲 ̅̅̅̅  =  - �̅�  because of  𝐜𝐲 ̅̅̅̅  , -↑ direction and corresponds the Spin �̅� =  

      Gravity = �̅� = r m �̅�  which is Constant and equal to  Work  = 𝐜𝐲 ̅̅̅̅  x [Quarter circle 2-O-3]       

      where  the [Semicircle 4-1-3] = + �̅� ≡The Gravity , and [Semicircle 4-2-3] ≡ - �̅� = The  

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

      Antigravity .The produced Work from the eternal Rotation is store in  the Semicircles as ,   

      (+) Total Work = [Semicircle 4-1-3] = + �̅�  and (-) Total Work =[Semicircle 4-2-3] = - �̅�      

4…From Newton`s law of Universal Gravitation  m r. �̅� ² = G 
𝐦.𝐌

𝐫 ²
  , and when m = 1 , issues   

 �̅� ² = 
𝐆.𝐌

𝐫 ³
  ,  and  B =  J w , therefore angular velocity  �̅� = ±  √

GM

r³
 

2
 = √

Gπ.r4

2.r³
 

2
 = √

π.Gr

2
 

2
.                              

This Angular-momentum is identical with Spin which is trapped in caves`s loops which are  

in   Phase with each other. The amplitude of Oscillation varies from Zero at Nodes to maxima  

at Antinodes .Since Frequency ≡ 𝐟𝐧 = (
nσ

8 r ² 
).�̅� , so Energy-caves are Stationary Wave-Fringes 

5… The Total-Energy , E T , in Caves , [70]   

a… → In any Moving System   E T = E R + E K = 
πc²

8
 r³ +

1

2
 m.v² = 3,535.1016. r ³ + 

1

2
 m.v² ,  

b… → Light-Velocity c̅  of Photons becomes from the Action of  G on Plancks Length LP  

       = r P =1,6162.10−35 m  cave r, and when cave r = 
𝐡

𝐜.𝐙𝐜 
 ≠ 𝐋 𝐏  originates Hydrogen-cave.  

       It is shown later that when the G action Area - Resistance ≡ Gravitational-Impedance  

       Z G−I = 6,344907.10−35 Kg  differs for any reason then Black-Holes happen.  

c… → Euler`s Rotating Rigid Body .The D-Work is  W = 2L = B̅ . w̅ = J .w²  ≡  h. 𝐟𝐧 , and  

      for m mass W = h fm ,Angular-Momentum �̅� = 
2L

 w̅ 
 = 

 2L

 2πf 
 = [

2L

2π
].[

1

f
] = 

Constant

 2π
 [

1

  fm
]= SPIN  

d… → In Central-motion ,Kepler constant  k = 4π². r³. fP², or 1 = [
4𝜋²

𝑘
] r³. fP², 1 = c . r³. 𝐟𝐏²   

      where  for →  r → 0  then 𝐟 𝐏 → ∞ ← , a case of a Black-Hole in any Central motion .  

e… →The Vibrations in Orbit-Systems  are as  → W = 4π² .[
𝐫³

𝐓²
] . �̅� = 4π². r ³. 𝐟²𝐩 . �̅� ←      

f… → In [PNS] Neutral Space , Dumping  force is   Fd = C . ṙ = ±  Co .w. [√A2 − r ²]  

      and  Fd ² / [ Co .w. A ] ² + r ² / A² = 1 ,  i.e.  Energy ≡ motion is mapped as an  Ellipse   

      with axis  , 𝐅𝐝 , x , and Energy Dissipated  Per - Cycle , the Area enclosed by ellipse.   

g… → The Energy in [PNS] , is either as momentum (mv)  or as Rotational Momentum   

       (Λ = r.mv) . Velocity �̇� , in form  ẋ = w A cos.(wt - θ) = ± wA.[ √1 − sin²(wt − θ) ]   

       =  w . [ √A² − x² ] where momentum relation  �̅� = m r v = m r² w = m r² (2πf) = 
J.w

2
  

       = [
πr⁴

4
].[2πf] = 

π2r4f 

2
 ,and Mass of Elementary-Particles is m =

π2r4f 

2w.r²
 = 

π2r3

2v
 f = 

π1r2

4
 , or  

       The repeated Quarter circle [ 
𝛑.𝐫𝟐 

𝟒
] Surface of the ± Spin Dual Property In Planck`s  

       length and area ,  𝐀 𝐐𝐂  = [
𝛑.𝐫²

𝟒
] = 

𝟑,𝟏𝟒𝟏𝟓𝟗𝟐𝟔.( √𝟐
𝟒

.𝟏𝟎−𝟑𝟓)²

𝟒
 = 1,1107206.10−70 m² . Since  

       issues the monad of mass to be [ 
eV

c²
 ] = 1,782662.10−36 Kg , then Energy Dissipated   

       Per - 𝐴 𝑄𝐶 =  𝐄 𝐐𝐂 = ( 1,1107206.10−70 m²/ 1,782662. 10−36 = 6,230715. 10−35 Kg ,  

       Or from the  G action Area - Resistance ≡ Gravitational-Impedance Z IQC , exists  

       ZIQC =√2𝑐3A QC / G , and 𝐦 𝐏𝐍𝐒 ≡ ZIQC = √2.𝑐3A QC / G = 
1,4143.(27.10"24)1,1107206.10−70

𝟔,680056.10−11
  

       = 6,344907.10−35 Kg  . The result agree with Prior because in [PNS] Dipole of Space  

       exists the Impedance  ZIQC , which Doesn`t exist in [MFMF] Space . [22-26] 

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

h… → In [MFMF] Space , Work = motion = Energy is zero as  W = ∫ P. ds
A

B
= 0 , and this  

      because ds = v⃗  = 0 and Time is not existing and v⃗  = 0  as relation  , s = �⃗� .T . Each  Unit      

      AB⃗⃗⃗⃗  ⃗  = ds > 0   exists by  this Inner Impulse ( P )  and so  P A+P B = 0 .  i.e.  The Position  

      and  Dimension  of all Points  which are connected  across Universe and  that of  Spaces   

      exists because  of  this Static Inner Impulse , on the contrary  should  be one Point only    

 

Or , Primary  Point  A  =  Black  Hole →  ds = 0  and  P  = ∞ . Since Impulse  is   ∞  then   

      may  be → Vacuum  , Momentum  or  Potential  or  Induced  Potential and it is  a Type   

      of  Effect , to  Push the nature → (Impulse ≡ Motion ≡ Energy) ←       

      6c3.. The Nature of  Antigravity  (- g ) .  

       From Mechanics in case that , in an Axisymmetric Rotating Body , with constant  

      Angular-Velocity , w ,  the moment of Inertia  , 𝐉𝐱 =  𝐉𝐲  , is equal about the two of  

      the three Principal axis , and then ,  

1.. The Angular – velocity - vector , �̅�  , describes the Ellipsoid of Angular Velocity  

      and its nib describes a Cone of which Plane-Base is Fixed  Simultaneously ,  

2.. The Angular-Momentum , �̅� , describes the Ellipsoid of Angular-Momentum and  

     its nib describes a Cone also of which Plane-Base is also Fixed .   

3.. The Nib of Angular - velocity - vector , �̅�  , describes on the Tangential-Plane  

     of the Angular-Momentum-Ellipsoid , the Herpolhode , while ,  

4.. The Nib of Angular-Momentum  , �̅� , describes on the Tangential-Plane ,  

     of the Angular-Velocity-Ellipsoid , the Polhode . 

5.. The Fixed-Tangential-Planes on , �̅�  , and , �̅� , nib are alternately Perpendicular  

     to , B̅ , and , w̅  , common Central Axes of Rotation .   

6.. The Kinetic Rotational – Energy of monad , which is the Work in monad , is the  

     Scalar quantity , L , The Vector Angular Momentum quantity is , �̅� , and the Vector of 

    Angular-Velocity quantity is , �̅�  , which Three monads are related as  �̅�.�̅�  = 2L = J.w² 

    where  J = The moment of inertia around the axis of rotation = ⇅  

7..All above happen in , Material-Point , where the Positive ⊕ constituent  The  + �̅� ,  is  

    Eternally self - rolling on the  Negative ⊝ constituent ,The - �̅� , with Angular-Velocity  

    w , in Infinite  Spherical traces , either at Great-circles [+ or - ] , or Small-circles , [+]  

    where is the  Clockwise Left direction and [-] where is Anti-Clockwise Right direction or 

    any other close Spherical-curve , and Applying all laws of Mechanics into this Energy 

    Chaos , is thus created the → First–Discrete-Energy–monad �̅� , the Material Point ←  

    i.e.  The Angular Momentum  �̅� , is the Quantum of Physics and is , for all the Energy – 

           Space-Universe .The Energy = E dissipated per cycle is equal to the Work Wd = E =  

           h f = 
h(1+ √5 ] )

4π
.[ 

𝜎

𝑟
 ] = 8.kζ(πr²) and is Stored in monad , which is a Stationary Wave  

          with and - in   , n ,  loops as   𝐖𝐧 = [ 
𝟒𝝅𝒓²

𝟑
].𝐟𝐧  =  [

𝟒𝝅𝒓²

𝟑
].𝐧𝐟𝟏 = n 

(𝟏+√𝟓)𝛔𝐫

𝟑
 = n 

[𝛔𝚽.𝐫]

𝟏,𝟓
 .              

   8.. Geometry has as Monad ,The discrete continuity 𝐀𝐁⃖⃗⃗⃗  ⃗ -length becoming from the Zero 

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

    Point ≡ 0 , and  Mechanics-Physics  the Recent-Acquisition of the Material - Geometry,  

    where  Zero-Point ,  0  =  = {⊕+⊝} = The Material-Point = The Quantum of Space ,  

    as , The Positive Space and The Negative Anti-Space . [58]             

          In Fig-8 , The Light velocity vector   �̅�  = 2,9979. 10 8 m/s   Rotates In the Planck`s  

          length  Perimeter  𝐫 𝐏 = 1,616255.10−35 m  , and is  thrusted through The Newton’s – 

          Gravitational Force  𝐆 , During Rotation is created Work which is stored in the circle   

Surface as Angular - Momentum  �̅� = r m v =  
J.w

2
 =  [

π.𝐫𝟒 

4
] 

c

r
  = [

𝛑.𝐫𝟑

𝟒
].�̅�  = [

𝛑.𝐫 𝟐

𝟒
].�̅� x �̅� , in 

Semi circle {+[ 4 -1-3]} , and Semi circle { - [ 4-2-3] }, for  the Stability of  Equilibrium .   

i.e.  Gravity + g ≡ The Vector of Angular-Momentum  �̅� ≡ + Spin ≡  ↓↻ ≡ The Work  

                        stored in the [4-1-3]  Semi circle of the , �̅� - �̅�  Vectors  circle - Surface 

                        Produced  from the Gravitational-Force  , G , as ACTING  into the – 

                        Planck- Cave , AND  on the light Velocity Vector in  , + ↓ �̅�  Direction .  

Antigravity - g ≡ The Vector of  Angular -Momentum  �̅�  ≡ - Spin ≡ ↑↺ ≡ The Work   

                       stored in the complementary  [4-2-3]  Semi circle of the , �̅� - �̅�  Vectors  

                       circle-Surface which is Produced from the Gravitational-Force , G , as  

                       ACTING  into the - Planck- Cave , AND  on the light Velocity Vector in  

                       The  , - ↑ �̅�  Direction .     

 

Figure – 17b -  The Material , LRC Circuit on Orbit , on Focus-Planet-Sector |F↔P| 

In (1). Force  g , as Wave , is directed to the center of rotation F , and is proportional to the 

        distance  PF ≡ Focus - Planet .The Gravitational Potential-Energy 𝐠𝐆 = 9, 8076925 is  

        stored in → Focus-Planet-Sector ≡ FP ← which is the Material Capacitor Stores charge  

        as that of Material-LRC-circuit , and Inductors .  

        Because of the  chains of Spins and of their Periodic excitation [↔] , is thus created a 

        Magnetic field due to the LRC-circuit and which is tuning to the critical Quantum and 

        critical-State  𝐠𝐆  . The chains of Spins are Pointy - vibrating  with their characteristic  

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

frequencies f = 
(1+ √5 ] ) .σ

4πr
 B̅ , and filling up the entire universe .   Since Inner-stresses  

𝛔𝟏,𝟐 = σ1/2 ± (½)√σ1² + 4. σ1²  = σ1/2 [1±√5] follow the Golden ratio on stresses then  

this Quantum-energy gG  Produced , is the State causing them to Magnetically- Resonate . 

In Material-Point-chain of caves  r = λ/2 , and since ẋ = w.r → w = ẋ/r  then  Golden ratio  

Damping-Force  is the Work produced with Unit Damping-ratio ζ=1 .Since also  ẋ = v then  

exists , Fd = c. ẋ = 1m.wn .ẋ = 1.[ (π r²/2) v2].
ẋ ²

𝑟
 = [

𝛑𝐫𝐯𝟒

𝟐
] = g = 

𝟐

𝒓
 [ σ (1+√5) ] ² = 

𝟒𝝈²

𝒓
[ 3+√5 ] .     

     This dissipation of Energy is determined under conditions of cyclic oscillations , and is 

     dependent on Glue-bond  σ , and  r , cave . Since r  is in denominator then for the very  

     small caves , the under Planck`s caves, Damping-Force becomes infinite independently  

     of Glue-bond . This may be considered as a Type which happens in Black holes as this  

     happens in algebra inverse fractions also .     

In (2)  is Presented the Back-Up Electromagnetic current flowing in Opposite direction  

      FP , by changing the Spin Direction of the Sector-Material-Points such that work W = g .  

       From Kepler`s 2nd  law the  , Area  S , swept by any Focus-Planet-Sector ≡ FP  is the 

       constant  k , and equal to,      

      S² = 
L² T²

4m² 
 = π²a².[ b = πa (

L²

2mE
) ] , or  

T ²

 a ²
 = 

4π²m

2E
 = 

4π²

2E/m
 = 

4π² a

GM
  and → 

𝐓 ²

 𝐚 ³
 = 

𝟒𝛑² 

𝐆𝐌
 = k    

     and  k  = 
𝟏

 𝐟 ²𝐧 .𝐚 ³
  , from which issues   →  1 = k . 𝐟²𝐧 . 𝐚

𝟑   and ,   k =  
4π² 

GM
   where 

Is seen that , Resonance between Focus-Planet exists through Space a and Energy f .   

From the Second-order differential equation excited by a Harmonic external force ,  

Ft .sin wt  , and is as ,   m 
d²x

dt²
 + c 

dx

dt
 + k . x = Ft . sin w t , corresponds Physically to  

the free damped vibration , where  x = the displacement , dx / dt =  the velocity and ,  

d²x / dt² = the acceleration of monad , m ,c ,k constants , with the general solution  

given by the equation   x = A . 𝑒𝑠1.𝑡+ B.𝑒𝑠2.𝑡 + X sin(wt-φ) ……(1) 

The Equation →   L 
d²q

dt²
  +  R 

dq

dt
  +  

1

𝐶
 q  = E t . sinwt .Corresponds Physically to the free 

damped vibration , where Charge q = is the Physical Property of matter that causes it to  

experience a force which can be Positive or Negative , dq / dt = the least quantized amount  

of charge , and d²q / dt² = the Space distribution of charge , and  L , R , C Inductance , 

Resistance , Elasticity constants with general solution given by the equation   

                  q  =  A . 𝑒𝑠1.𝑡+ B. 𝑒𝑠2.𝑡 + X sin(wt-φ)  …...(2)  

Equations (1) , (2) give the analogic relation of the Classical mechanics [Space Position x] 

and the Electromagnetism [Quanta of Energy , q ] of Storing and Removing of energy in  

Energy-Space cosmos .Distributed forces  L1- L2 = L (di/dt) , R1- R2 = R . i , C1- C2 = q / C   

respectively , showing the Identification of the  Mechanical and  Physical laws .  

 

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

The way that Potential-Energy is stored , is that of Material - LRC- Circuit , which is for  

the Gravitational-Potential-Energy the Material-Capacitor or the → Focus-Planet–Sector –

Stores-Change ← which develop a Voltage in response to that charge .The coil of wire is the  

infinite Stationary-Dipole-Spinning Material-Points of this → Focus – Planet - Sector ←  

which develops the Back-Electromagnetic-force ,when current through them changes .  

In-Cave-Box exist two motions ,Revolving and Periodic, the acceleration of Gravity g ≡  σ  

exists for the First Box-𝐁𝐑  , while Local-Extreme-case for the Second Box-𝐁𝐏  . In this  

Gravity g ≡  σ , is Locally altering S , by changing the Principal-stress σ with  Local uniform 

Pressure  𝐠𝐋 ≡ g kE = g * [Force/Area] = G ,  i.e. is Proved that the minimum Local-Energy  

acceleration is the known Universal Gravitational-constant  G = g k = 𝐤𝐄 g = 𝐤𝐋 σ = g gL kL  

such for Macrocosm as for Microcosm , and both cases Obeying Newton`s Laws of motion .  

4.. Since Electron is rotating in Orbits so Electromagnetic Wave is also rotating , therefore is  

     needed a Proper-Stationary-Magnet on which Rotation becomes Oscillation in order to  

     succeed a clear 3-dimensioned , Φ ³, Magnetic-Resonance-Imaging [The MRI ] and the  

     other Systems use this  Property of  Bottom-Information . This Property of Spin in all  

     depths of Energy - caves allows  the Granularity of  Energy in Energy- loops , and after to  

     be Bonded  .This Property of Electron may be used  for  Cancer Chromosomes .       

     6c4.. The Conservation of Energy in → velocity �̅�  and in gravity �̅�  Caves ←     

Since Gravity- �̅�  is the Energy ≡The Angular-Momentum {�̅� =r m v}in Planck`s length r P ,  

and it is a Stationary-Wave or an Electromagnetic Wave-Signal which transmits Informations   

Then follows the Waves-Frequency-Signal-Spectrum .The Gravitational Constant G is the  

Active force on light velocity  �̅� and consequently on  g̅  also .  

 From Waves theory → Position  x = A.sinwt  and Acceleration  �̈�  = A w ² ← where the  

 Signal-Spectrum is consisted of the Amplitude 𝐀 𝐂 and of the Angular frequency �̅� , from   

 where all other Properties follow. Since �̈�  ts the acceleration Force of Position x , then for  

 Planck`s length issues ẍ = G = A²G.w ², or   �̅̅̅� = √G/A² = √6,68. 10−11/[2,6262. 10−35]² so  

 Gravity-frequency→ �̅̅̅� = 0,5057.1030 H and Gravity-Wave-frequency 𝐟 𝑮𝑾=8,05.1028 H ←  

THE GRAVITATIONAL FORCE ACTION  :  [[G]] → {[�̅� ] ± 𝐄𝒏}≡ �̅� ≡ 𝐄𝒏+{[G] ± [�̅� ]} 

              and    →  𝐄 𝐑 = 𝐄 𝐆 + 𝐄 �̅�    ←         where , 

[[G]] =  [Gravitational Constant G]  ≡ The Signalling.(W c) → The Carrier - Wave      

[[�̅�]]  =  Any Action of [G - ON- �̅�]  ≡  Any Signalling.(�̅�) Modulating Velocity-Wave   

[[�̅�]] =  The New Modulated [G ↔ �̅�] Signal  ≡  f 
 �̅� m+wc

2
   +  f 

 �̅� m−wc

2
  ≡  [MAS]           

COMPOUND  = The Demodulated [MAS] ≡ f 
w+2wc

2
  +  f 

w−2wc

2
 ≡  [DMAS] . �̅� , since   

[ G = The CARRIER ] →[  �̅� = The MODULATOR ]→[ G+ �̅� = The MODULATED ]  

and        [ G+ �̅� ] + �̅�  ↔ [ DM = ANTIDOTES ] = The DEMODULATION ]  

i.e.        The Communications–Frequencies In Planck`s Cave , are the Wave 

             Resonances which consist  the Master-Keys  of these wave - caves . 

                   

The Conservation of Energy in Caves and  in Atoms Compounds .  [106]  

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THE ATOMS – ACTIONS  : [[A]] → {[B]±𝐄𝒏} ≡ C ≡ 𝐄𝒏+ {[A] ± [B]},→ 𝐄𝒏= 𝐄𝐂 + 𝐄𝐀 ←     

             and  where  

[[A]] = [Atom OR Compound]  ≡ The Signalling.(Wc)  → The Carrier - Wave      

[[B]] = Any[A-OR-C]  ≡ Any Signalling.(w)  Wave  = The  Modulating - Wave   

[[C]] = The New Modulated Wave [A] Signal  ≡  f 
w+wc

2
   +  f 

w−wc

2
  ≡  [MAS]           

ANTIDOTE = The Demodulated [MAS] ≡ f 
w+2wc

2
  +  f 

w−2wc

2
 ≡  [DMAS] , �̅� , as  

The Atoms Action (1) ...  [A] → {[B]±𝐄𝐍} ≡  [C]  ≡ ± 𝐄𝐍 + {[B] + [A]} , , [A] ≡ [C] +{ 𝐗 𝐍}  

[A] = The Initial ,  [C] = The Final  ,  [ X N ]  =  {[B] ± [EN]}   ≡  The Antidote .         

The Atoms Action (2) ….  [A]  →  [ ± E N ]  ≡  [C] ≡≡≡  ± 𝐄𝒏 + [A] , , , ,  [A] ≡ [C ] +  [ E N ]     

[A] = The Initial ,  [C} = The Final ,  [ E N ] ≡ The Antidote , The Circular-Signal-Action is     

            as  ,  I → F = [ I + F ]  and  [ I + F ]  ↔ [ DM ] ≡ Antidote , or  Still-Actions  

            [ I = CARRIER ] →[ F = MODULATOR ]→[ I+F = MODULATED ] →  

            → [ I+F ] + M  ↔ [ DM = ANTIDOTES] = THE DEMODULATION ] 

            The Communications –Frequencies In Atoms - Caves , are their Wave 

             Resonances  which  consist  the Master-Keys  of all the wave - caves . 

6c5.. The Energy - Superflow in MFMF-PNS Space-Levels for Black-Holes Origination.  

      1)..It was Prior Proved that Angular-Momentum of the Primary-motion in PNS Space  

           is a  Quaternion of dimension Power ( s + �̅� i) ¹/ d = √( s + �̅� i) d , which follows  

           that of Spaces Origination .  

     2)- It was Prior Proved [70] that in PNS - Space the inner Forces of a System , are the two  

           equilibrium Centripetal and Centrifugal Forces due to the Eternal  , ± σ ,  Stresses  

           of  Opposites [⊕↔⊝]  Originate motion  u , as    𝐉𝟏. 𝐮² 𝐜𝐨𝐬𝛝 -  𝐉𝟑 𝐰𝟑 .u + s . Q = 0 .    

     This Quadratic equation has 4 - Solutions where the Angular velocity Complex number   

                u = |�̅�| = 
s Q

B
 = 

s Q

  J3w
  = |�̅�| =  

dφ

dt
  =  [

   J3. w3

2 J1.cos ϑ
] ± [

 k PNS

2 J1.cos ϑ
].i  =  s ± v i  , or  

          → Angular-velocity |�̅�| = 
   𝐉𝟑. 𝐰𝟑

𝟐 𝐉𝟏.𝐜𝐨𝐬𝛝
  ± √−

𝐬𝐐

 𝐉𝟏.𝐜𝐨𝐬𝛝
+ (

   𝐉𝟑. 𝐰𝟑

𝟐 𝐉𝟏.𝐜𝐨𝐬𝛝
) ²

𝟐
 = s ± {√�̅� }.i ←     

              where  s = [
   J3. w3

2 J1.cos ϑ
] , �̅� = [

 k PNS

2 J1.cosϑ
] , 𝐤 𝐏𝐍𝐒 = √ [ J3. w3]² − 4. sQ. J1 cos ϑ

2
   

The constant Work exists on the common Central Axes of  Rotation which is Fixed to  

the Tangential-Planes of  �̅� & �̅�   nib , being alternately Perpendicular  to , B̅ , and , w̅  ,  

and found to be as   �̅� . �̅�  = 2L =  J.w² . The frequency monad of rotation in the PNS  

Space  is  as  →  𝐟 𝐏𝐍𝐒 = 
𝐬 𝐐

 𝟐𝛑.𝐉𝟐.𝐰 
  ←  with the following  4 - Solutions for  |�̅�| ,   

Solution-1  | 𝑤 1 | =  [ s ] + [ √�̅�  ]    →  Real Root  ≡ Huge  Minerals at Edge of Universe.   

Solution-2  | 𝑤 2 | =  [ s ] - [ √�̅�  ]     →  Real Root  ≡ Atoms & Compounds into Structures.   

Solution-3  | 𝑤 3 | =  [ s ] + [ √�̅�  ].i  →  Imaginary Root ≡ Huge BH at centres of Galaxies.   

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89 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

Solution-4  | 𝑤 4 | =  [ s ] -  [ √�̅� ].i  →  Imaginary Root ≡ Micro BH at centre of Molecules.  

where  BH = Black Hole .     From  4-above issues  ,      

A-Velocity |𝑤1 ̅̅ ̅̅ | = 
   𝐉𝟑. 𝐰𝟑

𝟐 𝐉𝟏.𝐜𝐨𝐬𝛝
 ±√−

𝐬𝐐

 𝐉𝟏.𝐜𝐨𝐬𝛝 
+ (

   𝐉𝟑. 𝐰𝟑

𝟐 𝐉𝟏.𝐜𝐨𝐬𝛝
 )²

𝟐
  ≡  

   𝐉𝟑. 𝐰𝟑

𝟐 𝐉𝟏.𝐜𝐨𝐬𝛝
 +√−

𝐬𝐐

 𝐉𝟏.𝐜𝐨𝐬𝛝 
+ (

   𝐉𝟑. 𝐰𝟑

𝟐 𝐉𝟏.𝐜𝐨𝐬𝛝
 )²

𝟐
    

A-Velocity |𝑤2 ̅̅ ̅̅ | = 
   𝐉𝟑. 𝐰𝟑

𝟐 𝐉𝟏.𝐜𝐨𝐬𝛝
 ±√−

𝐬𝐐

 𝐉𝟏.𝐜𝐨𝐬𝛝 
+ (

   𝐉𝟑. 𝐰𝟑

𝟐 𝐉𝟏.𝐜𝐨𝐬𝛝
 )²

𝟐
 ≡  

   𝐉𝟑. 𝐰𝟑

𝟐 𝐉𝟏.𝐜𝐨𝐬𝛝
 -√−

𝐬𝐐

 𝐉𝟏.𝐜𝐨𝐬𝛝 
+ (

   𝐉𝟑. 𝐰𝟑

𝟐 𝐉𝟏.𝐜𝐨𝐬𝛝
 )²

𝟐
    

A-Velocity |𝑤3 ̅̅ ̅̅ | = 
   𝐉𝟑. 𝐰𝟑

𝟐 𝐉𝟏.𝐜𝐨𝐬𝛝
 ±√−

𝐬𝐐

 𝐉𝟏.𝐜𝐨𝐬𝛝 
+ (

   𝐉𝟑. 𝐰𝟑

𝟐 𝐉𝟏.𝐜𝐨𝐬𝛝
 )²

𝟐
 ≡ 

   𝐉𝟑. 𝐰𝟑

𝟐 𝐉𝟏.𝐜𝐨𝐬𝛝
 +√−

𝐬𝐐

 𝐉𝟏.𝐜𝐨𝐬 𝛝 
+ (

   𝐉𝟑. 𝐰𝟑

𝟐 𝐉𝟏.𝐜𝐨𝐬𝛝
 )²

𝟐
. i 

A-Velocity |𝑤4 ̅̅ ̅̅ | = 
   𝐉𝟑. 𝐰𝟑

𝟐 𝐉𝟏.𝐜𝐨𝐬𝛝
 ±√−

𝐬𝐐

 𝐉𝟏.𝐜𝐨𝐬𝛝 
+ (

   𝐉𝟑. 𝐰𝟑

𝟐 𝐉𝟏.𝐜𝐨𝐬𝛝
 )²

𝟐
 ≡  

   𝐉𝟑. 𝐰𝟑

𝟐 𝐉𝟏.𝐜𝐨𝐬𝛝
 -√−

𝐬𝐐

 𝐉𝟏.𝐜𝐨𝐬𝛝 
+ (

   𝐉𝟑. 𝐰𝟑

𝟐 𝐉𝟏.𝐜𝐨𝐬𝛝
 )²

𝟐
. i 

Angular-velocity �̅�  is a vector , and  Rotates in one  axis k  with respect to variable �̅�  

Momentum and , the Ellipsoid of |�̅�| ≡ Quaternion of dimension Power (s ± �̅� i)¹/d 

The Inertia  J-Ellipsoid of |�̅�|  gives two Anti-Symmetrical Inertial Ellipsoids , a Real  

                              and an Imaginary in their Polhode and Herpolhode Cones as below,  

 

The-Real �̅�  ≡ { Polhode ≡ Cone OPS , Herpolhode ≡ Cone OPT , [ ↻ Rolling ] on the  

                              the Ellipsoid axis , ↓ Normal ON the Unmovable & Attitude-Plane of   

                              the [ PSPT ] Truncated-Polar-Cone }.      

The-Imaginary  �̅�  ≡ {Polhode = Cone OPS , Herpolhode = Cone OPT [↺ Rolling ] on  

                              the Anti-Symmetrically-Ellipsoid-axis, ↑ Normal  ON the Unmovable  

                              &  Attitude-Plane of  the [ PSPT ]  Truncated-Polar-Cone } .    

It has been Proved that  �̅� , �̅�  Vectors  exist as , E = Energy =motion , S = Space =Length    

----------------------------------------------------------------------------------------------------------------  

   Both magnitudes define the Unit-Energy Vectors  → { Unit-E Vector R = 
σ

J.w²
 = 

𝛔

�̅� 
 } ←  

   When the Unit-E.Vector R is Placed ON [AB≡2R S.Diameter of Spaces-Neutral-circle]  

   Then Energy-Monad |�̅�| , exists on , Space-Monad |AB| ≡ |�̅�| and is {E+S -Monad |�̅�|}   

                     Or is The { Energy – Space - Monad  |�̅�| ≡ |AB|  } ,     where the magnitudes,  

   Spaces Sides  𝛌𝐧 = 2,√R2 − a²n ,  &  the  Quantum Critical-Side  𝐚𝐧 = 
1

2
 √4R2 − λ²n ,   

   Every=Monad occupies AB = 2|R| Diameter = Space & Unit-E-Vector R=
σ

J.w²
 = 

σ

B̅ 
= motion 

   

The Quantization of Energy in Spaces happens by following the Archimedes formula for 

   Duplication of Sides as 𝛌𝟐𝐧=√2R2 − R√4R2 − λ²n  & Critical-Sides 𝐚𝟐𝐧= 
1

2
 √4R2 − λ²2n    

        The Energy-Monad |�̅�| = 
σ

J.w²
 = 

𝛔

�̅� 
  remains the same in PNS - Space while  

        The Spaces Sides change as 𝛌𝟐𝐧 , 𝐚𝟐𝐧 , when the Monad |�̅�| enters the 2n .    
--------------------------------------------------------------------------------------------------------------------------  

        The  4 - Solution for Real and Imaginary Root is as below ,  

The |w1 ̅̅ ̅̅ |  Solution is the Real -Root giving the Strongest in Amplitude Energy-Structions.   

The |w2 ̅̅ ̅̅ |  Solution is the Real -Root giving the Weakest in Amplitude Energy-Structions.      

The |𝑤3 ̅̅ ̅̅ |  Solution is the Imaginary-Root giving the Mega Tapered-Amplitude E-Structions.   

The |𝑤4 ̅̅ ̅̅ |  Solution is the Imaginary-Root giving the Micro Black-Holes Structions .      

From Gravity relation  G = g 𝐤𝐄  =9,8076941.6,8116.10−12= 6,68056.𝟏𝟎−𝟏𝟏 m3/ N.s² from 

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90 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

Energy-loop relation 1 = c. r³. 𝐟𝐏² → fP=√1/cr³ , and from  f = E / h  then f =  
𝐄

𝐡 
 = √1/cr³    

or → E = h .√1/c. r³ ,  and  
E²

h²
 = 

1

c r³
  or  ,  E ² = 

h²

c r³
  , an Energy relation between  the , c , r  .  

         This relation is used for Black- Holes Energy where  r , result to zero ,    

         The Permissible-Permeable-Resonance-Paths for their means are for ,   

7)  Particles   →  The Resultance of the  One-Dimensional-Collision v̅ij= v̅j - v̅i = w̅ij. r̅ij          

8)  Particles   →  The Cauchy Ellipsoid-Stress-tensor where { w̅ ⊥ B̅ ⊥ r̅ ≡ σ1⊥ σ2⊥σ3 }  

9)  M-Points  → The Resonance-frequencies  𝐟𝐑 [S ≡ f1= n ,f2, f3,fR=w²]= 𝐟𝐧 = [⊕↔⊝] 

       =  n 
(1+√5)σ 

  4πr 
 = 

n.σ.B̅

8 r² 
   →  i.e. The Golden-ratio-Pattern , which is related to Spin.  

--------------------------------------------------------------------------------------------------------------  

From Solution-3 the magnitude D becomes maximum when  
𝐬𝐐

 𝐉𝟏.𝐜𝐨𝐬𝛝
 ≡ maximum or ,when 

|θr̅|  axis is ⊥ B̅  and Cone-angle  𝛉  90 . From Energy relation E = W = 2L = B̅ .w̅  = J.w²   

Angular-Momentum �̅� = [3 ,3770539.10−96J].[5,613308.1045Hz] = 1,895644.𝟏𝟎−𝟓𝟎 J/s,  

i.e. The Planck`s cave ,10−35 m , is The Safety-Valve ≡ The Critical State for the Stress  

       Ellipsoids ,B̅ w̅, Vectors in order that this Total-Energy to Superflow and be Still into  

       Vacuum ≡ [10−62-10−35m]. This Vacuum between the |Gravity cave - Planck`s cave|   

       CONSISTS  The  BLACK - HOLES - CHAOS , as the Recycling–Energy into which  

            → The { Energy – Space - Monad  |�̅�| ≡ |AB| } , Vanishes ≡ Decomposes ← 

--------------------------------------------------------------------------------------------------------------  

     In Physics exist ,Two different Potential-Energies between Planck Spaces and Gravity 

     Spaces as UPLANC and  UGRAVITY .The difference ∆U = UGRA- UPLA is the Flow-Energy  

     between the Two Energy Levels  L PLA = 6,6262.10−34 m , and  L GRA= 1,777.10−62 m , 

    From cave L PLA = 6,6262.10−34m  and fP = √
g

a³

2
 = √

9,8078 

(6,6262.10−34)³  
 

2
= 1,83585.10 50 H  

    then → E PLA = h.fP = 6.62607.10−34 . 1,83585.10 50 = 1,216447. 1017 J            

    The minimum Charge in Planck`s cave →  q PLA =  1Cb = 1,6 .10−19 eV , 

    From Voltage relation  ∆U = 
Energy

Charge 
  issues , 1Volt = 

1Joule

1Culomb 
 or  1V = 

𝟏𝐉

  𝟏𝐂 
 ….(v)     

    In order that 1Cb may overflow and Flow from  Planck`s cave To the Gravity cave , 

    then must exist  a Voltage  ∆U > = 7,593.10 35  eV , and be as  ....(v)        

                      𝐕 𝐆𝐑𝐀 = 
    𝐡.𝐟𝐏  .

  𝟏𝐂𝐛 
  =  

  1 ,216447.1017 J 

1,6022.10−19eV
  =  7,593.𝟏𝟎 𝟑𝟓 V   ,   i.e.  

→ When the Energy in Planck`s cave  LPLA , Increases  to an  Voltage >= 7,593.10 35 V    

     then the motion≡ Energy between the Two Opposite elements of MP-Dipole [⊕↔⊝] 

     Becomes a  Stationary Flow [⊕,⊝] ≡ Charges [⊕--⊝ ] in Gravity Cave  L GRA. 

     So Energy ≡ motion , exists in L GRA as an → Pointy Rotational Centripetal Force ←  

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91 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

→ When the Energy in Planck`s cave  LPLA , Decreases  to an Voltage =< 7,593.10 35 V     

     then motion ≡ Energy between the Two  Opposite elements of M-P-Dipole  [⊕↻↺⊝]  

     Creates the A-velocity-vector �̅� which Rotates in the axis k with respect to variable �̅�. 

    So when Unit-Energy Vectors �̅� = σ / �̅�  exists on the  Unit-Space-Monad |AB| ≡ |�̅�| ,   

        Then is → {The Energy –Space - Monad  |�̅�| ≡ |AB| ≡ The Existing Universe} ←         

        For  The Chaos - Motion → Angular – Momentum ≡ The Rotational Energy �̅�  ←  

        For  The  PNS – Spaces   → Angular – Momentum ≡ The Rotational Energy �̅�  ←  

From Fig-13 and Solution-3 , magnitude D  becomes maximum  when  
𝐬𝐐

 𝐉𝟏.𝐜𝐨𝐬𝛝
 ≡ maximum 

or , when |θr̅|  axis is ⊥ B̅  and Cone-angle  θ  90 , where Energy E =W= 2L= B̅ .w̅ = J.w²   

Angular-Momentum  �̅� = [3 ,3770539.10−96J].[1,15346.1051Hz] = 3,895312.𝟏𝟎−𝟒𝟓 J/s,  

i.e. The Planck`s cave , 10−35 m , is The Safety-Valve ≡ The Critical State for the Stress  

       Ellipsoids ,B̅ w̅, Vectors in order that this Total-Energy to Superflow and be Still into  

       Vacuum ≡ [10−62-10−35m] . This Vacuum between the |Gravity cave - Planck`s cave|  

       CONSISTS  The  BLACK - HOLES - CHAOS , as the Recycling–Energy into which  

                  → The { Energy – Space - Monad  |�̅�| ≡ |AB| } , Decomposes ← {Fig-13} 

IN FIGURE , THE  HERPOLHODE- CONE PLANE IS A CIRCLE WHERE VECTOR B̅  

ROTATES , AND  WHEN 𝛉  90 . THEN  CONE  BECOMES  A  CIRCLE ,   where  

Energy follows [ ⊕    ⊝ ] mode as → + when 𝛉 = 0 = < 90 , and - when 𝛉 = 90 – 180 ←  

It was shown that , the Energy from Chaos [⊕ -  - ⊝ becomes  Momentum  �̅� , �̅� ,  

and is Composed ≡ Quantized through the Physical-[STPL]-line-Mechanism , In-circle  

 Triangles   Ex-circle  Ex-Triangles consisted with the three Spaces . On this PM  

exist the Three Breakages [s² = ⊕  , 2s ² =   , - s ² = ⊝] which Circularly-Charge ON    

the Three – Extreme - Triangles {A B C} , {KA KB KC}, {AE  BE  CE} and thus launch     

The Energy-Quantity  ±  𝐐𝐩−𝐩= [
𝒄.𝑺

𝒓
] ≡ Centripetal-Force from Chaos to PNS  Space ,  

On the Pascal`s -Desargues Points-Line through the STPL Circuit caves  r , and from  

the Ptolemy`s  & Ceba`s  Still-mechanism . {Fig-24}     

      Remark .                        

     1.. Electron , e ,  me = 0 , 511MeV = 0, 511.10−6 eV . [1,80. 10−27] = 9,198.10−34 Kg      

     𝐚𝐞 = 5,0.10−18 m ,Charge 𝐂 𝐞 =1,602.10−19 C , Spin 𝐒𝒆 = 
𝐒

2
 =2,845976.10−34{Kg/m/s},    

    Using  𝐄 𝐞𝐊 = 
𝐤

𝐫
+

𝒄𝐒 𝟐

𝟐𝐦.𝐫𝟐 = 
36.10−20 

7,10−18 
 + 

3.108(5,691952.10−34)² 

2.9,198.10−34[5.10−18]² 
 = 51,428 eV + 2,111843.1010J  

    = 51,43 eV+ 1,32 .1029 eV  ,   i.e. The Energy Increases inverse analogous to the cave .    

    2…Since Primary motion ≡ [PM] exist from the Three Breakages only STPL is the n =3 

          Mechanism creating Elementary Particles as [n-Knots=3] in  𝐕 GRA = 7,593.1035 V .    

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

   The  Unit-Space -Vectors , �̅�.�̅� , &  The Unit-Energy-Vectors , �̅�.�̅� , Ellipsoids .   

   

Figure.17c .. Shown the Geometrical-meaning of  ao̅̅ ̅ ri̅ , √ri² − (ao̅̅ ̅ ri̅)² terms of radius OA i   

          In (1)  is shown the  Inertial - Ellipsoid ( O, a̅) of Radii , a̅, and the Interchangable  

                 Momentum–Ellipsoid (O , ρ̅) of Radii , ρ̅. (O , ρ̅) . The same for {B̅ , (O, B̅)} 

          In (2)  is shown the  Momentum - Energy - Ellipsoid ( O, B̅) of Radii , B̅, and  

                 the Interchangable Angular Velocity – Ellipsoid (O , w̅) of Radii , w̅ .   S = Space  

          In (3)  is shown  in Mohr-method , the Geometrical construction from the two  

     Interchangable Ellipsoids→The Energy-Rotational Momentum–Ellipsoid ( O , ρ̅) , where  

    { Work } = The Angular-Velocity-vector -Unit-sphere , S =The Inertial- Ellipsoid (O , a̅) ,  

    { Force }= The reaction to the velocity-change-motion , S = The Mass - Ellipsoid  

     { Mass } = ( GD = Ja ≡ M̅ ) , and Between the Types of Ellipsoids issues  ρ̅ . a̅  = J a ..(12)   

The above Property of the two Interchangable-Ellipsoids defines the deep relation between ,    

The Angular-velocity-Ellipsoid  →  J1w1² + J2w2² + J3w3² = 2L = C = Ja w̅ ²  ….(13)  and   

       The Momentum-Energy-Ellipsoid  →  
1

J1
 B1² + 

1

J2
 B2² + 

1

J3
 B3² = 2L = C = Ja w̅ ²   .....(13a)          

Conclusions  :  

1..From the generated Radius �̅� =The INERTIAL-Ellipsoid of a Solid Fig-17-1 corresponds 

another Radius B̅ , Fig-17-2  Momentum –ENERGY– Ellipsoid , to the Common-Point O of 

Rotation .The Radius �̅�  is Perpendicular to the Tangential-Plane at the Nib  of the �̅� Angular 

Velocity-Ellipsoid . Similarly  the Radius  �̅�  is Perpendicular to the Tangential-Plane at the 

Nib of the �̅� of the Angular-Momentum-Ellipsoid . Relation  ρ̅ . a̅  = J a= a constant , means  

ρ̅  ⊥  a̅  ≡  Space + Anti-Space ≡ motion    �̅�  ≡  [ i ≡ √−1
2  

 ] * ρ̅ ≡ The Argand-Diagram.        

From relation (12) , the vertical-Projection of the radius , ρ̅ , at the corresponding conjugate  

radius a̅ , of the Unit Sphere , denotes  the meter to the Solid last Angular momentum .      

Because  the Unit-Energy-Vectors , �̅�.�̅� , are related as  �̅� = AB = σ / B̅ = σ / J.w² ,  i.e. the  

common velocity vector  c = w r = 2.B / π r ³ , therefore issues and for all the 5-Spaces .   

2..Inversely The Unit-Energy-Vectors , �̅�.�̅� , Decompose when  Bcrit=J w = 
𝜋r3

2
[c/r] = [

𝜋r2

2
]c  

Or when �̅� becomes maximum , i.e. for  Gravity and Antigravity happens when |θr̅| axis is   

Perpendicular (⊥)  to B̅ and the Cone-angle  θ  90 , and  Energy  E =W= 2L= B̅ .w̅ = J.w².     

From the �̅�  Physical -Magnet , �̅�  is  Quantized to the 2-Constitutes  ⊕ ⇉ ⊝  as the Prior . 

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6c6.. The De-Quantization of Energy from  , PNS   MFMF , ≡ Empty Space .  

 

Figure.17d.. The Angular-velocity |�̅�| = 
   𝐉𝟑. 𝐰𝟑

𝟐 𝐉𝟏.𝐜𝐨𝐬𝛝
 ±√−

𝐬𝐐

 𝐉𝟏.𝐜𝐨𝐬𝛝
+ (

   𝐉𝟑. 𝐰𝟑

𝟐 𝐉𝟏.𝐜𝐨𝐬𝛝
) ²

𝟐
 = s ± {√�̅� }.i    

 |𝑤3 |= [s]+[√�̅� ].i  , s = [
   J3. w3

2 J1.cos ϑ
] , �̅� = [

 k PNS

2 J1.cosϑ
] , 𝐤 𝐏𝐍𝐒 = √ [ J3. w3]² − 4. sQ. J1 cos ϑ

2
   

      From 10.c, the Unit-Energy-Vectors , �̅�.�̅� , fP = 1,836.1045Hz in  PNS–Space become  

1).. From relation w̅ =2π.f PNS , then 𝐰 PNS = 56,13308 .1044Hz = 5,613308 .1045Hz ,   

2).. From Centripetal Force in MFMF Space  FC = σ = 
m.v³

r
 =J w² r =B̅ w r , then B̅ =J w ,or  

      B̅ = J w =  [
π.r4

2
].w = 

π[1,6162.10−35]4  (5,613308 .1045)

2
 = 3 ,3770539.10−96 J and  for  eV , 

      B̅ = 3 ,3770539.10−96 J / 1,6022 .10−19 C = 3,754935.10−76 eV.     

3).. From Sol -3 the magnitude D becomes maximum when  
𝐬𝐐

 𝐉𝟏.𝐜𝐨𝐬𝛝
 ≡ maximum or , when 

|θr̅|  axis ⊥ B̅  and Cone-angle  𝛉  90 . From Energy relation   E = W = 2L = B̅ .w̅  = J.w²   

Angular-Momentum �̅� = [3 ,3770539.10−96J].[5,613308.1045Hz] =1,895644.𝟏𝟎−𝟓𝟎 J/s,  

i.e. The Planck`s cave ,10−35 m , is The Safety-Valve ≡ The Critical State for the Stress  

       Ellipsoids ,B̅ w̅, Vectors in order that this Total-Energy to Superflow and be Still into  

       Vacuum ≡ [10−62-10−35m]. This Vacuum between the |Gravity cave - Planck`s cave|  

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

       CONSISTS  the  BLACK - HOLES - CHAOS , as the Recycling–Energy , into which  

             → The { Energy – Space - Monad  |�̅�| ≡ |AB| } , Vanishes ≡ Decomposes ← 

→   In Physics exist , Two different Potential-Energies between Planck Spaces and Gravity 

       Spaces as UPLANC and  UGRAVITY .The difference ∆U = UGRA- UPLA is the Flow-Energy  

       between the Two Energy Levels  L PLA = 6,6262.10−34 m , and  L GRA= 1,777.10−62 m , 

       The Total Energy in Planck`s cave is     →  E PLA = 1,216447. 1017 J             , and    

       The minimum Charge in Planck`s cave →  q PLA =  1Cb = 1,6 .10−19 eV ,  

       From Voltage relation  ∆U = 
Energy

Charge 
  issues , 1Volt = 

1−Joule

1−Culomb 
 or  1V = 

𝟏𝐉

  𝟏𝐂 
 ….(v)     

In order that  1Cb may Overflow and Flow from  Planck`s cave To the Gravity cave , then    

must exist  a Voltage  ∆U > =  7,592354 .10 35 eV ,  and be as ..….(v)        

                    𝐕 𝐆𝐑𝐀 = 
    𝐡.𝐟𝐏  .

  𝟏𝐂𝐛 
  =  

  1 ,216447.1017 J 

1,6022.10−19eV
  =  7,593.𝟏𝟎 𝟑𝟓 V   ,   i.e.       

  When the Energy in Planck`s cave = LPLA , Increases  to an Voltage =  7,593.10 35 V     

     then the motion≡ Energy between the Two Opposite elements of MP-Dipole [⊕↔⊝] 

     Becomes a  Stationary Flow [⊕,⊝] ≡ Charges [⊕ -  - ⊝] in Gravity Cave L GRA . 

     So Energy ≡ motion , exists in L GRA as an → Pointy Rotational Centripetal Force ←  

 When the Energy in Planck`s cave  LPLA , Increases  to an Voltage  𝐕𝐂𝐑 > 7,593.10 35 V       

     then motion ≡ ⇄ ≡ Energy between the Two Opposite elements of M-P-Dipole [⊕↻↺⊝]  

     Creates the  Negative-Angular -velocity-vector �̅� ↓ , which Rotates  in the  Symmetrical 

     to Neutral circle axis  k = ↓  with respect to the Interchangable variable �̅� ↓ .  
               This is the Case of  The Black-Holes - Origination .  

 When the Energy in Planck`s cave  LPLA , Decreases  to an Voltage = < 3,695.10 30 V  

     then motion ≡ ⇄ ≡ Energy between the Two Opposite elements of M-P-Dipole [⊕↻↺⊝]  

     Creates the  Positive-Angular -velocity-vector �̅� ↑ , which Rotates  in the  Symmetrical 

     to Neutral circle axis  k = ↑  with respect to the Interchangable variable �̅� ↑ .  
               This is the Case of  The Universe - Origination .  

               So thus , are  defined the  Unit-Energy - Vectors , �̅� = σ / �̅� = σ / J.w² ,  

               which Exist  ON the  Unit – Space – Monad  |AB| ≡ |�̅�|  , and which is   

              { The Energy – Space – Monad  |�̅�| ≡ |AB| ≡ The Existing Universe }.        

In  Fig-14 are shown the 5-States for angle  →  θ  0ᶱ , 45ᶱ , 90ᶱ , 135ᶱ , 180ᶱ .  

1.. For angle  →  θ   00ᶱ  , �̅� ≡ �̅� , Voltage   = 7,593.10 35 V ,  ↑ On Neutral – Circle  

2.. For angle  →  θ   45ᶱ ,  �̅� /  �̅� , Voltage   < 7,593.10 35 V ,  < ≠  Neutral – Circle  

3.. For angle  →  θ   90ᶱ ,  �̅� ⏊ �̅� , Voltage  ≡ 7,593.10 35 V ,  ⇉ In Neutral - Circle  

4.. For angle  →  θ  135ᶱ , �̅�  \  �̅� , Voltage  > 7,593.10 35 V  ,  ≠ > Neutral – Circle  

5.. For angle  →  θ  180ᶱ , �̅� ⏊ �̅� , Voltage >=7,593.10 35 V , ⇅ Off Neutral-Circle  

4).. From Solution-4 , The {Energy-Space-Monad |R̅| ≡ |AB|} Vanishes in BH-Chaos ,       

      where Energy Increases to an Voltage >> 7,593.10 35 V and then motion ≡ Energy  

       between the Two Opposite elements collides them to the MP-Dipole [⊕↔⊝]. 

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

5).. From Solution-5 , The {Energy-Space-Monad |R̅| ≡ |AB|} Vanishes in BH-Chaos , 

      & Energy is Quantized to the 2-Constitutes from the �̅� , Physical-Magnet ⊕ ⇉ ⊝.  

  Figure.17e..The Stability of  Photon as Electromagnetic Wave with the Two frequencies .  

       The Dual Property of The Simultaneous existence  as Electric and  as Magnetic Fields  

       in  wavelengths , λ x , λ y , as Effective Range .which is thrusted through the Newton’s  

       Gravitational Force  G only , becoming from the Trigonometry relations [The Space ] ,     

                 sin(2φ) = sin(𝜋 − 2φ) = sin( 
𝜋

2
− φ ) , and from Physics  [Energy] E x = g ,  

Maxwel  Electric Displacement current  𝝑D / 𝝑t  is created from the ( 𝐜𝐱 , 𝐜𝐲 ) Vectors  

motion happening from gravity continuous action , and Producing the Work W = 𝐜 𝐲 g  

For Photon { Markos Rotating Method of{ 2-Vectors 3-Poles Mechanism }which Circles  

and Squares as Areas Pass from the Point M determined by the Position 𝐀 𝐞 , and where is 

such that issues  π r ² = CMNH Square then .The Squaring of the circle becomes at the 

equilibrium - Positions which are from relation →  π [
𝐂𝐀

√𝟐
]² = CM² = |CM`|² ← namely   

     The square | CMNH | = square | CM`N`H`| . Because of the Bellow motion then ,     

     The Total motion in the Wavelength , λ  , corresponds to the angle  a = 45 °, meaning   

     that the motion of  Space ≡ The Electric-field , and Anti-Space ≡ The Magnetic-field    

     equilibrium  as  an Bellow .  The two Wings  in 90°  Type  simultaneously oscillate to  

     its  45 ° Bisector -axis , and the Produced Work from The Electric-field-area is Stored  

     into  the Conjugate Magnetic-field-area . The  common axis of the two Perpendicular  

     fields , carry the  Golden-Ratio Energy-Surfaces , and  Runs with the same velocity  c ̅  

     to the direction of  the inner motion .  

     The EPILOGUS  in  [89 - 96]   

     IT  WAS PROVED  and  ELUCIDATED  THAT ,   

a.. Monad is Quaternion [x + i y] = λ̅  type , and its Energy is Vector as  Q⃗⃗  = {λ}.X  , where  

     X = The Displacement . Since 1 = c. r³. fP² = constant , so →  r³. fP² = constant . Since also 

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     λ = 2r  then  r³. fP² = λ ³. fP² = c  , and  Energy becomes →Vector Q⃗⃗  = {λ}.√c/ fP² 
3 ← [𝐄 𝟏]                                                                                                                                                                                                                                                                                                                                                                                                                   

b.. In Mechanics an Energy-Vector is an Conductor  AKA
⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗   = |Q⃗⃗ |  , and is The Quaternion in 

     Material-Geometry where Zero-Point  0  ≡  ≡ {⊕+⊝}on where motion |Q⃗⃗ | ≡ �̅� 𝐱 as  

     an Electric field on AKA axis and as Q⃗⃗ |  ≡ �̅� 𝐲 ≡ Magnetic field ⊥ AKA , is Transferred   

     from One Edge Point A , to the  Other Edge Point K A as  → �̅� , �̅�  𝐱 , �̅�  𝐲 ← [𝐄 𝟐]     

c.. Energy is the Work , The motion , Produced in Energy-monads and for Photon is Equal to   

     W = 2L = B̅ . w̅ = r m v = [r. p] = J w² ≡ [ �̅� 𝐱 ⊥ �̅�  𝐲 ] where �̅�  𝐱 = �̅�  𝐲 , in the Conductor   

     AKA
⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗   = 2.r ≡ λ where , λ  Is -The -Wavelength  and  p = m c = The Momentum . [𝐄 𝟑]    

d.. It was Prooved That → Any Diameter D of a circle in the STPL – Circuit , the Three – 

     Poles –Squares-Rotational - System is an Conductor where D = AKA
⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  = |Q⃗⃗ |  = |

𝐜.�̅� 

  𝐫 ²
| = 𝐈𝐄   

     The - Electric-Wave-Intensity , And   A ↑ KA
⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗ ≡ 𝐈𝐌 is The - Magnetic–Wave Intensity.  

     Their  Square -Vectors – Area = [ AKA 
⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ]x[A ↑ KA

⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗ ] = [�̅�  𝐱�̅�  𝐲] = The Energy - Square  

    ≡ CM x CM = CMNH  square = on circle ( E , EA ) , and from relation  �̅� = σ . Φ = 
F

A
 Φ 

    area A = F /  σ = |CM|² / σ  , i.e.  Plane-force F = σ . |CM|² , and in Space Volume-Force                      

      F = σ . |CM| ³ ≡ [𝐄 𝟒] or  [ AKA 
⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ]x[A ↑ KA

⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗ ]x[D] = CMNH x 𝐐 ⤱ ⇉⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗ = CMNH x �̅� ⤱ ⇉ ,    

     where |𝐐 ⤱⇉⃗⃗⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  | ≡ �⃗⃗�  , which is the Energy-Quantum In The Propagating Electromagnetic    

     Wave where  | 𝐈𝐄 ⊥ 𝐈𝐌 | . Since motions B̅xw̅ , are Constants from (b) and from Poinsot`s  

     solution w1² + J2 w2² = a² , then Angular velocity-Ellipsoid Polar-Paths are the  Parallel  

     circles and Perpendicular to  the Angular-Momentum Ellipsoid Nibs.. [𝐄 𝟓] , [70]       

e.. When is found  an Obstacle at Point 𝐊𝐀 , Then The Particles of  Conductor medium  

    Oscillate Perpendicular . This  Obstacle at  KA Point , is The Presentation of the , ⊕  

    constituent and the Absent of ⊝ constituent and  so   , Transverse- Propagating-Wave , Or 

moving Energy-Vector |⊕ 𝐐 ⇈ AKA⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗ |=|↕| at Node KA Is Equal  to E-Vector| ⊕ 𝐐 ⇉ AKA⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗ |≡ |↔| 

at Node A , and Energy Volume is Doubled as ,  2L = B̅ .w̅ , in  KAA⃐⃗⃗⃗ ⃗⃗ ⃗⃗⃗  Conductor meaning that 

the meter of Volume is the Duplication of Total Energy L .The Reaction to the motion of  

     Squares {|QX =CO ⇉| x|Qy= CB ⇈|} ≡ |𝐐 ⤱⇉⃗⃗⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  | ≡ [
𝐜𝐒

𝐫²
].|𝐐 ⇉⃗⃗⃗⃗⃗⃗ ⃗⃗   | is equal to Quantum �⃗⃗�  . [𝐄 𝟔]    

f..  Any Two Perpendicular Energy-Vectors , |𝐐 ⇉ AKA⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗  = ↔ | , |𝐐 ⇈ AKA⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗  = ↕ |  of this  

      Propagating Energy , FORM The Energy-Square , |↔|.|↕|≡|𝐐 ⇉ |.| 𝐐 ⇈| ≡ q0 , on  

     Conductor AKA and Then Energy-Circular-Prism = |AKA| .{𝐐 ⇉ AKA⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗  }.{ 𝐐 ⇈ AKA⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗  } ≡ 

     ≡ [�̅�  𝐱�̅�  𝐲].|AKA| = | ↔ |.|↕|.|AKA| ,  i.e. An Energy-Circular-Cone which is a Moving  

     Energy -Volume and Because from Cauchy equations of Stresses in three Dimensions ,  

    The Energy Stress remains Flat ONLY- WHEN the Plane-Section is a circle [𝐄𝟐 ] and The  

     Square becomes circle ,Anti-Quadrature. Because from Mechanics , The Sphere occupies  

    The Least-Resistance to motion where the Geometrical Square–Cone [CM x CH x[CO⃗⃗⃗⃗  ⃗ ↑]  

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

    is altered to Equivalent Energy- Circular - Cone [π.[
𝐂𝐌

𝟐
 ]² (x) [CO⃗⃗⃗⃗  ⃗ ↑] and  

    To the Energy Unit -Volume CO³.[𝐐 ⇉⃗⃗⃗⃗⃗⃗ ⃗⃗  ] ≡ 2 .Sphere 
𝟒𝛑

 𝟑
 r ³  And To Energy-Sphere  

     Cone  ⸿ = k π r³ , where The Geometry- Cube [|↔|.|↕|.|𝐀𝐊𝐀|] = x ³  so becomes The  

     Energy -Sphere – Cone as → k π r³ = x ³ ←  [𝐄 𝟕]      

g.. Since Frequencies fn are The Quantum of Energy , and Electromagnetic Vectors are    

     always Perpendicular between them as | 𝐅 𝐄 ⊥ 𝐅 𝐌 | , so are everywhere in nature from  

     microcosm to macrocosm . Because Gravitational Force exists Beyond Planck`s length  

     therefore  the Propagating-Plane-force  𝐅𝐏 = σ . |CM|² , is continually Perpendicular to  

     the two Perpendicular constituents of Electromagnetic Vectors as |𝐅𝐏 ⊥ 𝐅 𝐄 ⊥ 𝐅 𝐌 |.  

    Distance is the Quantum of E-Geometry , while Material-Point is the Quantum in  

    Physics and in Material – Geometry which is the composition of Opposites and are  

    The Elements in Chemistry and Physics .  

    As in Algebra Zero ,0, is the Master-key number for all Positive and Negative numbers  

    because their Sum and multiplication is Zero , and the same on  coordinate - System , ± ,  

    axes pass from zero . [𝐄 𝟖]    

    The Rolling of Positive ⊕ , constituent on the Negative ⊝ , constituent , creates the     

    Neutral Material Point which Equilibrium . Spin �̅� , is Its Angular momentum and also  

    the First -Discrete-Energy-monad which occupies Discrete-Value and Direction , in   

    contradiction to the Point which is nothing , Dimensionless and without any Direction .  

    Point-caves Are the  Energy-Magnets from which the Quantum of Energy are Generated . 

h.. The Space is Quantized as Energy-Caves under the effect of Gravitational-force G , as  

     well in Conductors and this Energy or motion is Quantized as Frequency in Energy- 

     Caves , Or in Conductors , following the Kepler`s  First-law of Equal Areas where in  

     equal intervals and in Conductors , is the Electricity or Electromagnetic - Waves . [𝐄 𝟗]    

Quaternion [(+)↻↺(-)] is a Quantum-Mould for Space [(+)(-)] and Energy ≡ motion ≡ 

Force x Displacement as [↻↺ or ↑↔↓] ≡ Standing Box 𝐁𝐐  ≡  An Material Point which 

carries the Principal Stress σ between Positions A (+) , B (-) , and σ , is the Centripetal -

acceleration of minimum Energy becoming from the in-Storage AB acceleration and which is   

equal to the Gravity g . From Quaternion Quantum Mould  [r + v̅ i ]𝟏/𝐰  = 𝐞− 𝐢.(𝛑/𝟐+𝟐𝐤𝛑).𝐰  

is created the min-Space ≡ cave r = 1, 07.𝟏𝟎−𝟕 m and the min-Energy ≡ v̅ = w r = 2πr f , as  

frequency  𝐟𝐦= 2,839844 . 𝟏𝟎𝟏𝟎  H . G  Pushes the → min-Quantum-Energy ≡ motion 𝛔𝐄 ,  

into the Inscribed-Cave π.[
𝐂𝐌

𝟐
 ] ² ≡ π.EA² . Gravitational-force G effecting on light velocity 

�̅�  creates the Electron-charge �̅� and Electron 𝐞 ̅, while acting on Planck`s-cave on the Gravity 

g ≡  σ , as  G = g k = 𝐤𝐄 g = 𝐤𝐋 σ = g.gL kL , and �̅�  effecting on the min-Planck-cave in LP 

formulates Hydrogen-cave  H  with its electron as  He . [𝐄 𝟏𝟎]  , [109]    

i.. The Physical-Notion of The Duplication of the Cube , in The Quadrature Physical Energy   

     Mould Shows that Nature follows the Geometry-Rules in Order to Exist as Space and as  

     Energy , which is motion of  The ,+,  Constituent to The , -  , Constituent . This motion is  

     conserved by Propagating in caves either for Standing ≡ | 
𝐯 

𝛑².𝐫⁴𝐧  
|. B̅n   or for moving caves   

     as this is the Duality-Photon → v̅ . [ fn̅  + fn ] ≡ | 
𝐯 

𝛑².𝐫⁴𝐧  
|. B̅n  + | c̅ | fn .Material-Geometry 

meters for Quantum-length is the Quaternion ≡ Dipole ≡ The Two-Points joint with motion 

between them ,while for The Quantum-Surface is The Unit circle π.r ² = π , and is r =Unit 1. 

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For the Quantum-Volumes , is the. Unit Volume Sphere  
4

3
 π.r ³ = [ 

4.r

3
 ] (π.r ²) = 

4 π

3
  , for  r = 

Unit 1 . The Unit-Volume is formulated from The Inscribed-Square of Unit Circle-Side CO = 

CB = 1 /√2 , and when Placed The-Unit-Energy-magnitude OC on Square CO x CO then is 

Unit-Volume [CO x CO x CO⃗⃗⃗⃗  ⃗ ↑] . This Unit-Volume when Placed in , The Three -Poles -

Squares-Rotating-System ,Then at Point KN , Unit Volume  [CO x CO x [CO⃗⃗⃗⃗  ⃗ ↑] becomes 

[CM x CH ] x CH⃗⃗⃗⃗  ⃗ ↑] = Circular-Cone [π.( 
𝐂𝐁

√𝟐
)²] . [CO⃗⃗⃗⃗  ⃗ ↑] = Unit - Sphere 

4π

 3
 r ³ , Equal to 

Quantum of Energy . Because Physical-Magnet ⊕ ⇉ ⊝ compels Force �̅�  ⇉ AKA⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗  , Between  

A and KA Points and Then Unit-Sphere 
4π

 3
 r ³ becomes The Double - Unit-Sphere  2.{

4π

 3
 r³} 

and because the Energy Square [CAKAP] is Double that the Unit Square |CB x CO| , then 

Force �̅�  ⇉ AKA⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗  ⃗  is The Pivot of Spinning indicating ± �̅�  ≡ �̅� , in all Energy monads .[𝐄 𝟏𝟏]        

j.. Gravity and Antigravity are the two Halve - Spins from the  Angular Momentum  �̅� ≡ ±    

    Work created from the velocity vector �̅�  by Rotating  ↻ on Planck`s Cave Diameter.[𝐄𝟏𝟐]   

This Property , ± �̅�  ≡ �̅� , is in all Energy monads and when Applied on Initial , ⊕ ⇉ ⊝ ,  

Answers  to the 3D-Stability of All  Elementary-Particles and Cosmology Equilibrium .  

Gravity + g ≡ The Vector of Angular-Momentum �̅� ≡ + Spin ≡ ↓↻ ≡ The Work stored  

                        in the [4-1-3] Semi circle of the , �̅� - �̅�  Vectors circle-Surface ,Produced  

                        from the Gravitational-Force , G , as ACTING  into the -Planck- Cave ,  

                        AND  on the light Velocity Vector of  , + ↓ �̅�  Direction . [107] 

Antigravity - g ≡ The Vector of  Angular -Momentum  �̅�  ≡ - Spin ≡ ↑↺ ≡ The Work   

             stored in the complementary  [4-2-3]  Semi circle of the , �̅� - �̅�  Vectors circle  

             Surface which is Produced from the Gravitational-Force G , as ACTING into  

             the-Planck-Cave , AND  on the light Velocity Vector of  The  , - ↑ �̅�  Direction . 

k.. The Black-Holes exist as  Parallel origination either as    Planar Black-Holes  or   

    Atoms - Black – Holes , when  G - Force is ACTING On the -Planck – Cave . [𝐄 𝟏𝟑]   

Momentum B̅ & w̅ , as Real ≡ The EXISTING - UNIVERSE as is the Real Objective 

                     Reality |�̅�| ≡ The Numeric Vector-value of  The Material-Point [⊕, r ,⊝]  

                     in [PNS] ≡ The Work stored in POLHODE - CONE of the |𝐎𝐒̅̅ ̅̅ | Rolling  

                     Nib -Vector Produced from the Eternal CENTRIPETAL - FORCE , 𝐅 𝐂  

                     AS THE Newton`s ACTION  in the Planck`s - Cave, AND  from the  �̅�  

                     Angular Momentum in  the , + ↓ B̅ , Direction . The Real Type is applied  

                    on all different Monads and their Compounds Monads .  [109]  

Momentum B̅ & w̅ ,  as Imaginary ≡ The  BLACK - HOLES  as is their Real Objective 

                     Reality ± �̅�.i ≡ s  The Numeric Amplitude-Vector-value of Material-Point  

                     [⊕,r,⊝] in [PNS] and The Imaginary - �̅�.i ≡ CENTRIPETAL - FORCE 𝐅 𝐂  

                     ≡  The Wave Amplitude -value ≡ The Work stored in the HERPOLHODE   

                     CONE of the |𝐎𝐁̅̅ ̅̅ | Rotating �̅� -Vector and also Produced from the Eternal 

                     CENTRIPETAL - FORCE  𝐅 𝐂 , AS THE Newton`s  REACTION  into the      

                     Planck`s - Cave AND  from the �̅� Angular Momentum in , - ↑ �̅�  Direction.   

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l.. In case of  Points  A , B , C  being on a Sphere then  [STPL] becomes a Cylinder as this   

    is the  Angular-Momentum �̅� = 
2L

 w̅ 
 = 

 2L

 2πf 
 = [

2L

2π
].[

1

f
] = 

Constant

 2π
 [

1

  fm
] = SPIN    [89]   

    D... THE ORIGINATION OF THE  FUNDAMENTAL PARTICLES            

       1d…  The  Balancing of  the Space and Anti-Space  . [64]  

                      ↺ ↻                                      ↻↺                  →           ↻↺  + ↺ + ↻                          

  Figure -18- : The work W, of Two-Quaternion-monads  𝐳  = (s + v̅. i) ≡ 𝐀𝐁̅̅ ̅̅  ≡ �⃗⃗�   is the  

      Action  Of any two Tangential & Opposite Equilibrium-Dipole [⊕↔⊝] with v = w⃗⃗⃗ .r.  

      For  Quaternion Actions exists the square law for both Real and Imaginary Part , as   

 𝐳  * 𝐳  = (s + v̅. i )² = s² +[v̅. ]² +2.sv̅. i = s² – v̅ ² ± 2.s v̅ = |s|² -|s̅|² ± 2.|s|.|s̅| , for |v̅| = s       

Vorticities ± Λ (Rotating Energy) , Becomes from the Collision on Common-circle and   

from the Thrust  on  the Velocity-Breakages .The work is , W = [ n . P ] = [ λ.Λ] , where    

λ  = Displacement of  A  to  B  and  it is a scalar magnitude called wavelength of dipole AB.  

Λ = the amount of Rotation on Dipole AB ( this is Angular Momentum and it is a vector ) .  

Momentum ± Λ̅ = r.m.v = r m wr = mr².w̅ , where w̅  is the angular velocity (Spin) which  

maps  velocity vector  v̅  on the Perpendicular to ± Λ̅   Plane with two components v̅ E ⊥ v̅ B .   

The Tangential velocity v̅ E = wr , is the quaternion  v̅ E = w r = z̅ = [ s + v̅. i ] where  s = v̅ E  

= |r.w̅|  and   v̅. i  =  |w̅ x r̅ |. In a Spherical cave the  Biaxial Ellipsoid  (σx = σy)  exists as  

momentum +Λ on caves of diameter 2r with parallel circles → 0 .The Biaxial Anti-Ellipsoid   

(- σx = - σy) exists as equal and Opposite momentum - Λ on the same diameter 2r with Anti  

Parallel circles → 0  . Equilibrium  of the Two  Ellipsoids  ± Λ ,  Presupposes   a Stabilizer-

System attached  to Ellipsoids such  that Opposite Momentum  is distributed to the Center of  

Mass  of the Total - System , recover equilibrium , which  is  the center of the Spherical cave. 

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The Biaxial - Ellipsoid and Anti-Ellipsoid  are inversely directed  and Rotated  in the same  

circle  , so the  two velocity vectors , v̅ ,− v̅ , collide .This collision of  the two Opposite 

Velocity-Vectors is the Physical-Action ( Thrust ) of  the Two-Quaternion and their Action is , 

( s + v̅. i )(©)( s + v̅. i ) = [s + v̅ . i] ² = s² + | v̅| ². i ² + 2|s|.|v̅ |. i = s² - |v̅| ² + 2|s|.| w̅ r|. i  

= s² - |v̅| ² + [2w̅].|s| |r|. i , where , s²  =  (r w) ² → Is  the  Real-Part of  the New-Quaternion,  

- |v̅|²  =  |w̅ x r̅|² = - (w.r) ² → The always  Negative-Anti-Space  ( a vector ⊥ to w r Plane ) , 

[2 �̅�].|s|.|�̅�. i  =  2w.(sr). i → The double Angular-velocity-Term , and for the PNS Space   

where    |s| = |v̅|²  then   s²     =                     (w.r) ²  ≡     ⊕           ≡   s ²  =  +  Charge  

                                   - |v̅|²   =    |w̅xr̅|² =  - (w.r) ²  ≡     ⊝           ≡ - s ²  =   -  Charge  

                      [2w̅].|v̅||.r̅. i  =    2 |v̅|² =  2 (w̅.r)     ≡  2[⊕↔⊝]  ≡  2s ² =   0  Charge  

i.e. For  the Equilibrium-Recovery (maybe a surface cylinder with 2r diameter) , Fig-16-17 

2d.. The Vibration of Particles  in all Levels  [54] . 

    Figure - 19-  :  The  Glue-Bond Electrons  of Nucleus Rotor , form  Rhodonea-like - Curves  

    Curves created by Rotor`s electron are such that they keep a continuous Pressure on Protons.   

   1.. The Continuous action of Negative ⊝ , on One Positive ⊕ , is equivalent to a Circular  

  motion of  the ⊝ , ⊕ , with velocity v = √F. r/m , and this because exists l = r = constant .  

   2.. The Continuous action of Negative ⊝ , on Two Positive ⊕⊕ of glued Bond , is equal to  

        a Circular - and  Other of  one-step longer motion of  ⊝ to  ⊕⊕ , or  Circular motion on  

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

       the Common–length , l ,  in Polar equations is ,  l = a . cos(c.θ)  or  l = a . sin(c.θ)  where   

a = the length of the base =2r+2r = 4r , c = Rim`s number which Produce a  c-Petaled rose ,  

If  c  is odd or 2c-Petaled Rose and if c is even number. The Period of both cos(cθ) , sin(cθ)  

     is 2π/c , and the number of petals for the period is [ 0 ,2π/c] will be c or 2c , according to  

     as  c  is odd or c  is even ,  so the degree of the Cartesian equation  of the curve is , c +1  

     for odd-c  ,  and 2(c+1)  for even-c .    

3.. The Continuous action of Negative ⊝ , on Three Positive ⊕⊕⊕ of glued Bond , is  

      equivalent  to a Circular-and  Other of two-step longer motion of  ⊝  to ⊕⊕⊕ , or   

      Circular motion on the Common–length . Length , l , in Polar equations is , 

      l = a . cos(c.θ)  or  l = a . sin(c.θ) , where  a is the length of the base = 2r + 2r + 2r = 6r ,  

      c = Rim`s number which produce a  c-petaled rose , where  c  is odd or 2c - petaled rose  

      number . This is seen and from equations issuing in Figure.21-2  →   r = rD.sin φ and   

      R = RD.sinφ where a , are the equal radius of Point A of Polar path .  Rhodonea  curves  

     follow the Odd or and Even number of Protons in Nucleus by changing their  Rolling- 

     length a = (2r) , and the Polar – length  l = a . cos(c.θ) depending on ,θ, as above .  

     The common bonding Point of the Negative circle and  the Positive line of the Rolling  

      circle obliges that Point to follow the Cycloid motion in  maximum  degree and thus  

      executing Hypocycloid motion . Particles Vibration in all Levels of Material-Geometry .   

4..  The n-Knots Figures exist in Figures where the Vector -Force - Polygons have the same  

      number n , as the in Figures . For The Circularly- Charged  Breakages the 3-elements     

      [Σ = n . h]  [s² = ⊕  , 2s²= , - s² = ⊝] formulate the Primary-Particles  3-K,Figures. 

      Since n =3 , the only Shape in Spaces is the Regular Triangle , and from this  n <  4→ n  

      there are vast regions of space that are very nearly empty of them , 

5..  The case of {TCIC}≡ [ Σ = n . h ]  8 x ①  which is the Physical Mechanism , gives  

       the n-masses of Atom`s &Compounds determining the Atoms Complex-Vector-Response.  

      These Particles  exist in all of the universe in the sense that they are uniformly distributed  

      throughout space and consist the Objective Reality which is the existing Universe  

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Figure – 20- : The Carbon , Nitrogen ,  Oxygen , Sulfur , Atoms-Conductors Sustains  

            Into  the First 4-Dimentional Spinning , Tetrahedron - Cube – Sphere - Mould .   

Figure– 20a- :The Hydrogen , Carbon , Oxygen , Atoms-Conductors Into the Sphere-Cube- 

               Mould . Deka hexahedron , Octahedron ≡ Cube , Tetrahedron ≡ 4-Points , Triangle ≡ 

3-Points , Vector ≡ 2-Points ≡ The Closed-Conductor , 1-Point ≡ The Opened -Conductor ≡  

The Bracket-Hook . Oxygen is the Element which fills 8 - 2 = 6 vertices of Cube as EL →  

{

1𝑒  0𝑒 1𝑒

  1 𝑒 2⃡  0 𝑒
1𝑒 1𝑒 1𝑒

 } ≡   (± 2
2 ) , where ⓪ is the first , Zero-Acting Cube  filled with 1e ,  

therefore is the only Steady element which occupies the first Energy-Level ① with 2 

Electron-Positions as ① = 2e = 2⃡  Positions at 1⃗  , 1⃗⃖    

The Electron being in the Hydrogen-cave Precesses because of the different axis of Rotation  

And Nutation`s , from the continuous and immense-communication to the effect of gravity g .  

Since Electron is continually oscillating , with the Nutation-frequency 𝐟 𝐍 , so  Produces a  

continuous and oscillating Magnetic-field –M- which in turn is the source of an oscillating  

Electric-field – E - which implies the Regeneration of each other , i.e. it is a Propagating  

Electromagnetic-Wave where E = B c , and with a quantum-Energy E = h fN or  E = 2μ.B ,    

This Energy E consists the Hydrogen Bracket  Hook HBH , or [BH⃗⃗⃗⃗  ⃗]  and it is the only  

free monad which can Bond to all Energy structures . 

5d.. The Natural Electromagnetic Energy-Tetrahedron and , The  3- Conductors  

          Into The  Energy - Cube  and Spheres  :  [102]       

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Figure – 20.a- The Dynamic Loading of → Tetrahedron – Cube - Sphere  ← Atom –Structure. 

Material Geometry uses the Only-Three Elements for the Origination of  Primary - Particles , 

as  Weak , W−Zo  and  Strong  W+Z+0,− Forces , Spin B̅ = S̅ , Hydrogen cave , r H , and Electron 

e−.  where [0]  ≡   ≡ The Rest-Energy ≡  [⊕ ↔ ⊝]  → [ ⊕
∷

2
+⊝

∷

2
  ]  , Split into Two . and  

, [0]  ≡  ZD̅̅̅̅   ≡ The Rest Space  ≡ Conductor  
− DM⃗⃗⃗⃖ ←  
+ Z E⃗⃗  ⃗  →  , from relation  [⊕←ds→⊝] , where 

their Properties and Corelations  are all motions into their Spaces , from Energy.  

In Fig-20b  The Electric - Magnetic Field of 3-Conductors which lie on the DABC  

    Tetrahedron .The Stability of the → { ⊕ 4-Space [D A B C]} Regular –  Tetrahedron ,  

    occurs  INTO the {⊝ 8-Anti-Space Cube , [DA1A D1 , B B1CC1]}, and The Positive →  

    { ⊕ 8 - Space – Cube , [DA1A D1 , B B1CC1]} , INTO  The {⊝ 16-Anti-Space [ 1 ,2 ,3 ,4  

     ,5 , 6, 7, 8 - 9 ,10 ,11, 12 , 13 ,14 , 15, 16] } Sphere Cube on Vertices.= Point [The Point 16  

     ≡ |⇉|Z|] consists the Navel-String  Gate  into the Triangle-Circle-System  {Z-(∆D,ABC) ,   

     ∆[T1T2 T3]} of the Stationary Bases which Results on the 2 -Anti-Parallel-Strands . 

     The Dual Photon v̅ [
σΦ

 2πr  
 + 

σ

2πr
 ] ≡  v̅.[ fn̅  + fn ] , occupies Stresses =  σ  and velocities v̅ , in  

     The Tiny-caves r . The Colours in light , are the Still-Sub-Units in Storage →[v̅ . fn̅  ]←  

     and exist as   Frequencies of → Violet , Blue , Green , with their Complementary  

     Yellow , Orange , Red ←  

Every 8-electrons are vibrations on Atoms-Cube-Structure {A Tetrahedron in Cube in a 

Sphere } whether it be Sound or Light . Above Structure is followed by all Compounds .  

Molecules are Systems consisted of The PERIFERAL ≡ Skeleton  𝐌 𝟏𝟔 and The CENTRAL 

≡ Fittings  𝐌 𝟖 , and  the ACCESSORIES ≡  𝐌 𝟒  or  𝐌 𝟐 , 𝐌 𝟏 . This Property of Atoms and 

of the Compounds is The Critical-Valve of  Switching the motion as this happens in the 

Electro-magnetic Solenoid Valves with High or low Pressure and flow  rates directly or Not . 

Figure – 20.b- :The Electric - Magnetic Field of 3, Conductors Results on 2 -Anti-Parallel- 

Strands .The Stability of →{ ⊕ 4-Space [D A B C]} Regular - Tetrahedron , IN {⊝ 8-Anti-

Space Cube , [ DA1B D1 , C C1AB1]}, and The →{ ⊕ 8- Space [ DA1BD1 , CC1AB1]} Cube, 

INTO    The {⊝ 16-Anti-Space [ 1 ,2 ,3 ,4 ,5 , 6, 7, 8 - 9 ,10 ,11, 12 , 13 ,14 , 15, 16]} Sphere 

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Cube Vertices . Point [16 ≡ |⇉|Z|] consists the Navel-String Gate in {Z-(∆D,ABC),∆[T1 T2 

T3]} Stationary Bases . Stability Analysis in [88]  

      DATA  :  

A.. The Atoms Cube Coordinate-System :         

      The relation of a Cube of Side a ,inscribed in a Sphere of Diameter d =2r , is in their Volumes  

      as V Sphere = 
4.𝜋 r ³.

  3
 = 

 𝜋 d ³.

  6
 ,  V Cube = a³ and since d² = 2a² + a² = 3,a² , then  a = 

d.

  √3
 = 

d.,√3

  3
  

      =  
√3,d

  3
 =  

2√3,r

  3
 ,and  the Coordinates of the 8-Cube-Vertices are for Center O  

→  𝐗 𝐎 = 0 , 𝐘 𝟎 = 0 , 𝐙 𝟎 = 0 ←   𝐗 𝟏 = 
− a.

  2
 , 𝐘 𝟏 = 

− a.

  2
 ,  𝐙 𝟏 = 

− a.

  2
  , 𝐗 𝟐 = 

+ a.

  2
 ,  𝐘 𝟐 = 

− a.

  2
 ,  

       𝐙 𝟐 = 
− a.

  2
 ,   𝐗 𝟑 = 

+ a.

  2
 , 𝐘 𝟑 = 

+ a.

  2
 , 𝐙 𝟑 = 

− a.

  2
 ,  𝐗 𝟒 = 

− a.

  2
 , 𝐘 𝟒 = 

+ a.

  2
 ,  𝐙 𝟒 = 

− a.

  2
 ,  𝐗 𝟓 = 

− a.

  2
 ,   

      𝐘 𝟓 = 
+ a.

  2
  ,  𝐙 𝟓 = 

+ a.

  2
 ,  𝐗 𝟔 = 

− a.

  2
 ,  𝐘 𝟔 = 

− a.

  2
 , 𝐙 𝟔 = 

+ a.

  2
 ,      

      𝐗 𝟕 = 
+ a.

  2
  , 𝐘 𝟕 = 

− a.

  2
  , 𝐙 𝟕  = 

+ a.

  2
 ,  𝐗 𝟖 = 

+ a.

  2
 , 𝐘 𝟖 = 

+ a.

  2
 , 𝐙 𝟖 = 

+ a.

  2
 ,       

Since Tetrahedron in Cube is formed in three Equal-Diagonals 𝐝 𝟏−𝟑 = a.√2 , 𝐝 𝟏−𝟓 = a.√2 ,  

𝐝 𝟏−𝟕 = a.√2  of the Perpendicular 3-Planes , P X−Y = P Y−Z = P Z−X =  a² , and since issues  

𝐝 𝟏−𝟑   ⏊  𝐝 𝟏−𝟓   ⏊  𝐝 𝟏−𝟕  ,  these consist The-Scanning Vectors-Plotting for all Systems .     

Since the Cube’s Outer-Sphere diameter d , is equal to the Cube-Diagonals [1-8] , [2-5] ,[3-6] , 

[4-7] , therefore consist 4-Big circles on Sphere and Perpendicular between them , in 

Contradiction to the 3  circles in the 3-Planes which consist the Small circles .   

The Geometrical Matric of Tetrahedron-Cube-Sphere Mould = ( STCS ) where , 
𝐏𝟏 𝐏𝟐 𝐏𝟑
𝐏𝟓 𝐏𝐨 𝐏𝟒
𝐏𝟔 𝐏𝟕 𝐏𝟖

      P O = The Coordinates  X O , Y O , Z O  of the Common Center of 2-Spheres   .    

P 1 = The Coordinates  X 1 , Y 1 , Z 1  of the   Tetrahedron- Cube Point -1       

P 2 = The Coordinates  X 2 , Y 2 , Z 2  of the   Sphere - Cube Point - 2       

P 3 = The Coordinates  X 3 , Y 3 , Z 3  of the   Tetrahedron- Cube Point -3        

P 4 = The Coordinates  X 4 , Y 4 , Z 4  of the   Sphere - Cube Point - 4       

P 5 = The Coordinates  X 5 , Y 5 , Z 5  of the   Tetrahedron- Cube Point -5        

P 6 = The Coordinates  X 6 , Y 6 , Z 6  of the   Sphere - Cube Point - 6       

P 7 = The Coordinates  X 7 , Y 7 , Z 7  of the   Tetrahedron- Cube Point -7        

P 8 = The Coordinates  X 8 , Y 8 , Z 8  of the   Sphere - Cube Point - 8       

On  the above Geometrical Coordinates SYSTEM  are Placed the 4-Spaces  

from  the  OZ = OD  - EXTENDED  CONDUCTOR  and equal to Monads .   

For the Cave-Spin , �̅� = r m v which is  a Monad , exist the  4-Spaces as Fig-1  

      → (( The n - Spaces of Spin  �̅�  are the Polygons  𝐒𝐧 ,  

               The n Anti-Spaces of Spin - �̅�  are the Polygons - 𝐒𝐧  )) ← 

      The Sub-Spaces  ± √ �̅�  
𝒏=𝟏−∞

 are the Polygons with  n = 1 ≈ ∞ Knots  

      Since Knots are the Degrees of the Polynomials of each Monad then ,   

The  OZ Monad  Determines the Number of Knots beginning from Number 3 ,  

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3     is the Figure of  Regular Triangle  in Poly-3rd Degree . The  - 3 and ± √ OZ̅̅̅̅   
𝑛=3

 

4     is the Figure of  Regular Square  in Poly-4rd Degree .  The  - 4 and ± √ OZ̅̅̅̅   
𝑛=4

 

5     is the Figure of  Regular Pentagon in Poly-5rd Degree . The  - 5 and ± √ OZ̅̅̅̅   
𝑛=5

 

6     is the Figure of  Regular Hexagon in Poly-6rd Degree . The  - 6 and ± √ OZ̅̅̅̅   
𝑛=6

 

7     is the Figure of  Regular Heptagon in Poly-7rd Degree .  The  - 7 and ± √ OZ̅̅̅̅   
𝑛=7

 

8     is the Figure of  Regular Octagon in Poly-8rd Degree . The  - 8 and ± √ OZ̅̅̅̅   
𝑛=8

 

9     is the Figure of  Regular Eniagon in Poly-9rd Degree . The  - 9 and ± √ OZ̅̅̅̅   
𝑛=9

 

N     is the Figure of  Regular  N-gone in Poly-Nrd Degree . The  - N and ± √ OZ̅̅̅̅   
𝑛=𝑁

  

Remarks : 

1… Gravity Force G  ≡ motion , exists without mass and is Quantized  →  Spread in  

       {Space and Anti-Space} or ≡ QUA ≡ {is The Quantized-Units In-Area of Space  

        and Anti-Space },  and as a Mould  𝚽  Golden-Ratio , exists in the  Impedance b .  

2…The case of {QUA} ≡ [ Σ = n . h ]  ∞ x 𝚽 which is the Physical Mechanism , gives  

       the ∞ - Impedance b determining the Objective Reality which is the existing Universe. 

       For n =2 then [Σ = n h]  2 x G /Φ , IS the  light-velocity  �̅� = [
𝐆 𝚽

𝐀
] =2.9982.108 m/s.              

       For n =1 then [Σ = n h]   G / c = Charge  q̅ = 
𝐆

𝐜 √𝟐 
 = 1,58.10−19 Coulomb .    

3… For n = 3  is  STPL Mechanism which creates the  Elementary Particles , [n-Knots = 3]  

       in  Gravity-Voltage  𝐕 GRA = 7,593.1035 V.  This is because the Primary motion ≡ [PM]  

       exist from the three - 3  Breakages  elements [Σ = n . h]  [s² = ⊕  , 2s²= , - s² = ⊝] 

B.. The Atoms-Elements Mass , Stiffness - Flexibility  [101]   

6d..The Dimensioning of the  [STPL] – Mechanism   

Defining the lengths  , a = KB KC , b = KC KA , c = KA KB , d = [
a+b+c

2
] =The semi-perimeter  

then the Inscribe radius  r = 
√d(d−a)(d−b)(d−c)

d
 = |OA| , The Coordinates for the Point K=DA    

are  [
bc

b+c−a
] : [

ca

c+a−b
] : [

ab

a+b−c
]  , while for Point  O  are  [

b+c−a 

a
] : [

c+a−b 

b
] : [

a+b−c 

c
] . Fig-17   

The STPL Mechanism is the Mould consisted from any Common circle O,OA=[OA`≡ OAE], 

O,OB = [OB`≡ OBE] , O,OC = [OC`≡ OCE] , and the Common lines  DA-PA , DB-PB , DC-PC  

all on a line of  STPL . On the infinite Sectors  ADA-APA , BDB-BPB , CDC-CPC  vibrate , the  

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Breakages [± s² = ± (w r)²] and [ i = 2(w r)²] forming all families of curves and the Euler -

Savary Coupler - curves of  the  Cubic-Of-Stationary - Curvature Mechanism of  Spaces ,  

Anti-spaces  Vibrating the End-curves . The Dimensioning of the Mechanism is Possible by  

using  the analytical geometry.  [91]   The Dimensioning of Proton – Neutron In Fig-26 , and 

others with Compounds In Fig-27 .The Dimensioning of Hydrogen and Atoms   In Fig-28-30,         

The Linear-Vibrations [ ẍ + w ² x = 0 ] of Three-masses , Occur on Two-Line-Vectors  

    Perpendicular each other , vibrating on Straight-line , ÿ + w ² y = 0 , of x ⊥ y Plane  

    and follow the Lissajous Shapes , [83] , where for ,    

    a.. Difference of Phase   dφ = 90⁰  emission is → The Eight-Shapes  Ꝏ .  

    b.. Difference of Phase   dφ = 0⁰   emission is → The Ellipse-Shapes ∝  .  

    c.. Difference of Phase   dφ = 45⁰  emission is → The Double-Saddle-Shapes . Ց , Ѡ .  

For Planck length [73] P-49, was shown that the Rotated Energy case , when  s = 0 and  

   cosφ = 0 , exists for angle φ = π /2 and Quaternion ( s + v̅ i )𝟏/𝐰 = 𝐞− 𝐢.(𝛑/𝟐+𝟐𝐤𝛑).𝐰...(1)  

   the dimension power → w = b ←  and for  k = 1  then (1) becomes ,  [84] -P.74     

   𝐞− 𝐢.(𝛑/𝟐+𝟐𝐤𝛑).𝐰 =  𝐞− 𝐢.(𝛑/𝟐+𝟐𝐤𝛑).𝐛  =  𝐞− 𝐢.(𝟓𝛑/𝟐).𝐛  = 𝐞− 𝐢.(𝟓𝛑/𝟐).𝟏𝟎     [86]  …... (2) 

Equation (2) fits , as minimum cave , in the Planck length and is  𝐋 𝐩 = 𝐞− 𝐢.(𝟓𝛑/𝟐).𝟏𝟎  .....(3) 

Equation (3) is the smallest Energy-Unit of Space , and this because is for  s = 0  and  k = 1.  

It was shown [31] that Space and Energy is quantized and measured on the two Constant and 

Natural numbers  e , π , where for base the natural logarithm , e , and exponent  the decimal  

base , b = 10 . From → z¹/w = ( s + �̅� i  ) ¹/ w = |zo|−w.[cos.(φ + kπ)/w + i.sin.(φ + kπ)/w]   

=|zo|−w . e−i.(φ+kπ).w for cos.(φ+kπ)/w = 0  then exists only the Imaginary part of monad  

(�̅� i  ) ≠ 0 , where φ = π /2  and then , z¹/w  = |zo| ̄ w . e i.(φ+kπ)/w = e−i.(
π

2
+kπ).10

 which is the 

Diffraction Energy mechanism for all Space Levels of quantization which are the Energy 

Particles only i.e. The Energy particles in Stationary caves are z¹/w = |zo| ̄ w. Lv = E-Monad.    

Extending quantization of Energy according to exponential formula→ 𝐋 𝐯 = 𝐞− 𝐢.(𝟓𝛑/𝟐).𝟏𝟎 then                  

𝐋 𝐯  on the decimal base  b = 10  and for  k = ± 0 → ± ∞ , are the Energy caves as ,  

For base  e = 2,71828  and  base  b = 10  then e^ - (13,8155)  =  1 .10  ̄ 6    m       

For base  e = 2,71828  and k = 0  Lv = e^i.( ± π/2)b then e^ (-15,7079) = 1,78118 .10  ̄ 7 m    

For base  e = 2,71828  and  base  b = 10  then e^ - (16,1181) = 1 .10  ̄ 7 or r = 1,07.𝟏𝟎−𝟕 m.  

Placing r , in the Dynamic-Space-Energy relation when g =1 then  r ³.𝐟²𝐩= 1 and 𝐟²𝐩 = 
1

r ³
  

= 8,0647139.1020 m and occurs the , minimum frequency  𝐟𝐦𝐢𝐧 = 2,839844. 𝟏𝟎𝟏𝟎 H …(4) 

7d.. The Cosmic Particles in The Cycloid , Anti-cycloid Evolute : 

The moving  monads in Cycloid Equilibrium in the  Anti - Cycloid ( Evolute ).  

The equilibrium of the Resultant forces is obtained by the above  Cycloid , Anti-cycloid  

Evolute Forces  , or by the Rotor and Spin in one Rim , as was shown. 

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

In Rims is possible the forming velocities greater than that of light , and this because of 

different , r , and the Tangential velocities are kept with the same angular velocity ,  the 

Spinning ,  unless Spinning changes in such way to keep light-velocity constant .    

Figure 25  The Equilibrium of the Resultant Forces ,  in the Cycloid and for motion  

                    Wavelength , and  of any other Removal Monad . The Intrinsic Space is  

                    (Wavelength = [λ] ) , as  the Energy Quanta . 

The Equilibrium of the Three-Spaces , The Space Anti-Space , Neutral-Space : [60]   

The Stability of Elementary Particles , Conductors and the Atoms -Nucleus  Fig-24    

     The Equations of motion become everywhere from any Opposite Space ≡ ⊕ , Anti- 

     space ≡ ⊝ . During these motions as , ds . is Done a Constant-Work , k , or and from  

     their velocities �̅� and this Work may be Positive or Negative for Equilibrium . In F-23 

     Cycloid Anti-cycloid motion is as , D. The Origination of Gravity g , Antigravity [- g ]  

In Fig-20.b , Conductor D = d = AKA where ⊕ constituent attacks ⊝ by a Hook`s law force  

as Stress  σ = E u , and an Coulomb force F [+ ↔ −] = 
[⊕↔⊝ ]

r²
 = 

[2 σ]

r²
 , creating Work ≡ motion  

as was shown  It was shown that , The Stability of Nucleus Forces , is succeeded through 

The Pascal`s - Ceba`s  triangle launched caves r , while Leptons from their Anti - Leptons  

existence in the same launched Pascal`s - caves r .  [58] 

The Equilibrium of the Three-Spaces is Done on the three Cyclic-Quadrilaterals (ABEAECE) 

(BCEBEAE) , (CAECEBE) of the  6 Conductors each for ,  [a , b , c , d , p , q ] x [3-ABC] = 18  

Conductors .  Linearly is through the Products of the Diagonal - connectors as , → → →   

[AAE].[BECE] = [ACE].[AEBE]+[ABE].[AECE] , [BBE].[CEAE] = [BAE].[BECE]+[BCE].[BEAE] , 

[CCE].[AEBE] = [CAE].[BECE]+[CBE].[CEAE]   and , Rotationally through the Ratio of  the  

Diagonals ≡ The Conductors | 
AKB

AKC
|x| 

BKC

BKA
 |x| 

CKA

CKB
| = 1 or   Rotational-Equilibrium as ,  

[AKB].[CKA].[BKC] = [AKC].[BKA].[CKB] , of all Opposites  Tangential-Electromotive 

Forces . From Mechanics-Physics , all Systems Possessing Elasticity ≡ motion and Reaction 

to motion , the called mass , are capable of  free vibration  or vibration taking Place in the 

Absence of External Excitation [7] .This Principle issues for Both Closed or Open Systems.  

 

      i.e. either for the Nucleus where issues The Pascal`s - Ceba`s  triangle  Stability ,  

             or for the  Orbitals where issues  the  Tetrahedron - Cube – Sphere – Mould .  

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108 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

8d.. The Stability of the Cosmic Particles Conductors and Atoms – Nucleus .    

Figure -26- : The Stability of → { ⊕ - Space [A B C] },{⊝ - Anti-Space [KA  KB  KC]} ,  

    of The Sub-Space [A E , B E , C E]}, and Neutral-Space {[⊕↔⊝] ≡ ds ≡ [⊕←ds→⊝]}.  

         Since , Energy of the first Wheel-Rim or Orbital  is distributed to the couple of (2e)   

         Electrons  of  the Orbital , then this is a Cycloid - Anti-cycloid - Stability System .  

        This Still Systems of Space –Anti space DOES NOT mean Matter–Antimatter but  

        The State of Equilibrium in Caves ≡ The Ceba`s  Energy triangle .  

 

a…The Space Anti-Space  and , Neutral-Space Conductors  :  [60]      

      The Equations of motion become everywhere from any Opposite , Space ≡ ⊕ , and  

      Anti-space ≡ ⊝ . During these motions as , ds . is done a Constant-Work , k , or and  

      from their velocities �̅� . In Figure Conductor D = d = AKA where ⊕ constituent attacks  

     ⊝ by a Hook`s law force as Stress  σ = E u , and an Coulomb force F [+ ↔ −] = 
[⊕↔⊝ ]

r²
 =  

     
[2 σ]

r²
 ,  creating Work ≡ motion as was shown . [58]  

It was shown that , The Stability of Forces is succeeded in The Pascal`s - launched caves r  

while Leptons , from their Anti - Leptons existence in the same launched Pascal`s-caves r .  

The Equilibrium of the Three-Spaces is succeeded on the three Cyclic - Quadrilaterals → 

(ABEAECE) , (BCEBEAE) , (CAECEBE) of 6 Conductors each [a , b , c , d , p , q ] x [3-ABC] = 

18 Conductors .  

Linearly is through the Products of the Diagonal - connectors as , → → →  [AAE].[BECE] =  

[ACE].[AEBE]+[ABE].[AECE] , [BBE].[CEAE] = [BAE].[BECE]+[BCE].[BEAE] ,[CCE].[AEBE] =  

[CAE].[BECE]+[CBE].[CEAE]   and , Rotationally through the Ratio of Diagonals ≡ The 

Conductors |
AKB

AKC
|x| 

BKC

BKA
 |x| 

CKA

CKB
| = 1 or the   Rotational-Equilibrium [AKB].[BKC].[CKA] = 

[AKC].[BKA].[CKB] ,of all above Opposites → Tangential-Electromotive-Forces ← From 

Mechanics ,all Systems Possessing Elasticity ≡ motion and Reaction to motion , called 

mass , are capable of free vibration or vibration taking place in the Absence of External 

Excitation . [7] From Lorentz-Force , F = �̅� �̅� x �̅� 𝐅 , where , q̅ ≡ Charge , v̅ ≡ The velocity 

of Charge , B̅ F ≡  The Strength of Magnetic field and Centrifugal Force , 𝐅 𝐂𝐅 = m.𝐰²𝐑.r . 

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

From Cave-Spin , �̅� = r m v  then mass m = (
S

  r.v 
) .Equating equations then , F ≡ FC F ≡ 

 q̅ v̅ x B̅ F , and 𝐐  = m.w²R.r = (
S

  r.v 
).w².r = 

S.w²

  v 
 = 

S.v ²

 r².v 
 ≡ |

𝐯.�̅� 

  𝐫² 
| ….(EMF)  where exists 

rmin= √πb−n 
2  , [95] , [96BB] .  

Electromotive-Forces , F = �̅� �̅� x �̅� 𝐅 = 𝐐  = 
𝐯.�̅� 

  𝐫² 
 ≡ | 

𝐜.�̅� 

  𝐫 ² 
 |, are The Elementary-Particles  

{F, L ,Q }. From Electromotive-Force in min-cave  r = 1,7724538.10−3  m. exists Electron- 

Force-Charge q̅ e as  𝐐  = | 
𝐜.�̅� 

  𝐫 ² 
 | = 

[2,998.108].[1,0546.10−34]J

 (1,7724538.10−3) ²
 = 1,6022.10−19 eV , which is the 

Electron-Force-Charge and  also from the Gravitational-Stress-Charge  �̅� Electron =  
G

c √2 
   

= 
6,6736923 .10−11 

1,41429.2,9979346.108 
 = 1,574.10−19 C . Electromotive-Force in the min-cave 𝑒−15,572707=  

r = 1,7252787.10−7 m , and the  Gravitational-Force G becomes also as ,  

𝐐  = | 
𝐜.�̅� 

  𝐫 ² 
 | = 

[2,998.108].[6,62606957.10−34]

 (1,7252787.10−7) ²
 = 6,673692. 10−11 , which is  the G - Physical-Force-

Charge.  When the Heap of the Elementary Particles on  DA-PA line , is compressed and gets  

out the line then is a reason for Black Hole creation .    

b…The relation of the n , Degree of Polynomials and Electromotive-Forces Vibration . 

      The Transportation of Energy on Edge-Points  happens in Material Geometry , while  

the Transportation of  the Edge-Points as  , Positions ,  exists in Vector  Geometry only.  

Since in Vibrations the Deformation of the Spring  is an equilibrium Position in ∆ , and   

the Spring-Forse  k ∆ = w = m g = Gravitational force w acting on mass m , then exists  →   

m �̈� = ΣF = w = k [ ∆ + x] ….(1) , and because k ∆ = w  we obtain  w ²n = k/m.. (2) and (1)  

becomes →  �̈� + 𝐰 ²𝐧 = 0 ,… (3) ←  i.e.  The Transportation of  Energy is a Harmonic -

Vibration in cave  ∆ , meaning the Wave Pattern . From before the Cave-Spin , �̅� = r m v  

is  a Monad , and occupies the  4-Spaces as the Fig–1 .  i.e.  

             → (( The n - Spaces of Spin  �̅�  are the Polygons  𝐒𝐧 ,  

             The n Anti-Spaces of Spin - �̅�  are the Polygons - 𝐒𝐧  )) ← 

      The Sub-Spaces  ± √ �̅�  
𝒏=𝟏−∞

 are the Polygons with  n = 1 ≈ ∞ Knots  

Since the number of  Knots n , are the Degrees N of the Polynomials of each Monad  and 

Since the n - masses - Spring 𝐦 𝐧 is an equilibrium Position in  ∆ , of the equation of  motion  

→  �̈� + 𝐰 ²𝐧 = 0  ←  then the  4-Spaces of Monad are the Polygons of  n-Knots and equal  

to the N Degrees  Roots of the Polynomials .  

      THE PROCESS OF ACTIONS  IN THE 4=SPACES  

1…A Heap of   n-masses  Vibrates and Equilibrium .  

2…A Heap of   n-masses  Equilibrium at the n-Mode Shapes Waveform .  

3…A Heap of   n-masses  of n-Mode Shapes occupies the Resultant  E-Spectrum  

4…Each-One of the  n-masses  occupies  n-Mode Shapes , n-Element .Spectrum ,  

      4-P.Spaces , 4.n.. Regular-Polygons of  n-Degree , with  4.n..Knots and Roots .          

5…Each-One of the  n-masses is an E -Monad  occupying  4-Primary-Spaces , and  

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

      Forms  4.n.. Regular-Polygons of the n-Degree , and with  4.n..Knots as Roots ..           

6…Each-One of the  n-masses is an  E-MONAD occupying all above Properties (Signals).  

9d.. The Origination of Proton and Neutron Cosmic Particles .    

The Elements in the Proton & Neutral-caves → { Masses – Charges - Forces } [89]   

 

 Figure-27 : The Sphere-Structure of the Hydrogen-Nucleus , ⊕ Proton ,[⊕↔⊝]=Neutron  

                   Proton is consisted of Three-Primary-Opposite-Spaces ⊕ , ⊝ , [⊕↔⊝] , having  

masses m p , Charges q̅p , and caves a p = r .  

The Nucleus`s  Cave  r ,  exists in the Inscribed to the Tetrahedron  Sphere .                                     

The elements in Proton are the Two u-Quarks and One  d-Quark .  

The Hydrogen-Nucleus is in the Inscribed Sphere from the  

{ Inscribed Sphere -Tetrahedron – Cube - Circumscribed Sphere - System }.    

In order to shift the u-d-Quarks of an Anti-Proton into a Proton Spin-Pair require an  

extra input of  Energy-(MeV) , so would Proton  Paired with a Neutron be Stable .      

The Total mass MT in Proton follows , The Parallel Connections Resistors inverse  

law , where The Proton Total-Harmonic mass ≡ MT is → 
1

MT
 = 

1

mu
 + 

1

mu
 + 

1

md
  ,  

The System Total- Harmonic-Charge ≡ QT ≡ 2.qu + qd  = 2.(2/3).e – (1/3) e = + 
3

3
 e =   

+ 1,6022.10−19 C , and the System-Resonance-Charge  QT = + 1, 6022.10−19 C  ...(2) 

The Proton Total- Harmonic- Charge → QT ≡ 2.qu + qd  ,and for the Resonance Frequency 

of the Unit-Cave is the Stationary-System becoming from Kepler second Planetary-law as 

equation , 4 π² m f ²o = k , and constant law of Areas 1 = k .𝐟 ²𝐨  𝐚
𝟑 . Their common k , is the  

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Constant-Energy → k = 4 π² m f ²p = 
1

𝐟 ²𝐩  𝐚𝟑 
    or ,  f ⁴p  = 

1 

4π²ma3  and  f p  = √
1 

 4π²m.a3  
 

4
 . 

   The measured magnitudes are as follows ,    

a-Proton⊕→ mass 𝐦𝐩 = 1,672.10−27 Kg →Charge 𝐂 𝐩 =1,602.10−19 C → a = 8,4.10−16 m 

b-Electron⊝→mass 𝐦𝐞 = 9,11.10−31 Kg →Charge 𝐂 𝐞 =1,602.10−19 C → a = 5,0.10−17 m 

c-Neutron[⊕↔⊝]→mass 𝐦𝐧 = 1,672.10−27 Kg →Charge 𝐂 𝐧 = 0 ,0 C → a = 1,7.10−15 m 

d-u-Quark →from equal masses mp =2.mu + md =3.mu =1,672.10−27 Kg and Quark masses 

𝐦𝐮  = 𝐦𝐝  = mp / 3 = 5,573.10−28 Kg , and 
1

MT
 = 

1

mu
 + 

1

mu
 + 

1

md
 = 

3

mp
 +

2.3

mp
 = 

9

mp
  and Proton  

Resonance mass MT = 
m p

9
 = 1,857777.10−28 Kg ≈ 16,7267 m Ev/c²  …….(m) 

For Proton issues qp  =  2.qu + qd = 2. 
2

3
 e - 

1

3
 e = e , and the Stability of forces is axial .  

Electron-Charge 𝐂𝐞 =1,602. 10−19 C , while 𝐂𝐪𝐮 = 
2

3
 e = + 

𝟐

𝟑
 1,602.10−19 C 

                             𝐂𝐪𝐝 = - 
1

3
 e = - 

𝟏

𝟑
 1,602.10−19  C , and from  

QT ≡ 2.qu + qd  , then Proton Resonance charge QT = 
3.q p

3
 = 1,602.10−19 C   ………..(c)      

Proton-Resonance frequency f p =√
1 

 4π²m.a3  
 

4
= √

1 

4π²5,573.10−28(8,4.10−16)³  
 

4
= 5,26241.1017 H 

Using the United Newton-Coulomb Electro-Mechanical Equation, q B̅L=2π.m f , the Proton   

Magnetic-field B̅F = 
|2π.m T|

QT
 f = 

2𝜋.1,85777.10−285,262409.1017 

1,6022.10−19 
 (Kg/Cs) = 3,83389.109 Tesla     

which is the Strength of a Magnetar , i.e.  A type of Neutron-Star having an extremely  

Powerful Magnetic-field , and Electric-Forces to be over Ten-Thousands-Newton .  

The Electric Force between the u-Quarks and d-Quarks in Proton is from Coulomb law  

𝐅𝐮𝐝−𝐩 = C
q1.q 2

r ²
 = 8,9875.109(Nm2/c²).

2

9
[1,602.10−19 C]²

1

(10−16)²
 = 1,997222.10 6 N ...(F p) 

           and The Electric Force between the u-Quarks and d-Quarks in Neutron is  

𝐅𝐮𝐝−𝐧 = C
q1.q 2

r ²
 = 8,9875.109(Nm2/c²).

2

9
[1,602.10−19 C]²

1

(10−16)²
 = -1,997222.10 6 N ..(F n) 

i.e.  Forces between the Opposites Equilibrium-Linearly  ←[d-u-d]→  or  →[u-d-u]←   

For the Neutral-cave issues qn = 2.qd + qu = - 2. 
1

3
 e + 

2

3
 e = 0.e , and the Stability of forces   

     is axial as in Proton and this because the Dynamic-Strip-Polygon doesn`t close .  For ,      

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            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

1.. Neutrinos , v , mass m = (3,11 .10−6) MeV/c² x 1,8.10−28  =  5 , 598 .𝟏𝟎−𝟑𝟒 Kg  

     The Spin is , 𝐒𝒗 = 5,691952.10−34{Kg/m/s}, 𝐚𝐯 = 7,0.10−21 m ,  𝐟𝐯 = [𝐄 𝐯𝐊 = mc²] / h =  

     5,6.10−34 [1017].1,6022.10−19 = 8,96912.10−36 J/[6,626.10−34 Js = 13,536244. 𝟏𝟎𝟏/s 

     From cave r = 7.10−21 m then f = √
1

g.a³

2
 = √

 1

9,81(7.10−21)³  
 

2
= 5,347345.𝟏𝟎𝟑𝟎 H  and exists ,           

     𝐄 𝐯𝐊 = h 𝐟𝐯 = 6,62607.10−34J s.[ 5,347.1030] /(1,6022.10−19 eV) = 2,2114518.𝟏𝟎 𝟏𝟒eV       

     Using  𝐄 𝐯𝐊 =
𝐤

𝐫
+

𝒄𝐒 𝟐

𝟐𝐦.𝐫𝟐 =
36.10−20 

7,10−21 
+

3.108(5,691952.10−34)² 

2.3,922.10−36[7,0.10−21]² 
 =51,428 eV+ 2,528774.1017eV  

     = 252,8774, [1015] TeV → The Total Energy of the Sun striking Earth-face per second.   

2…Electron , e ,  me = 0 , 511MeV = 0, 511.10−5 eV . [1,80. 10−27] = 9,198.10−31 Kg      

      𝐚𝐞 = 5,0.10−18 m ,Charge 𝐂 𝐞 =1,602.10−19 C , Spin 𝐒𝒆 = 
𝐒

2
 =2,845976.10−34{Kg/m/s},    

      From cave r = 5.10−18 m then  f = √
g

a³

2
 = √

9,8078 

(5.10−18)³  
 

2
= 2,801114.10 26 H  , and by             

     Using  𝐄 𝐞𝐊 = 
𝐤

𝐫
+

𝒄𝐒 𝟐

𝟐𝐦.𝐫𝟐 = 
36.10−20 

7,10−18 
 + 

3.108(5,691952.10−34)² 

2.9,198.10−34[5.10−18]² 
 = 51,428 eV + 2,111843.1010J  

     = 51,43 eV+ 1,32 .1029 eV → The Energy of 133 gr to fall 1 meter against gravity.    

      Remarks : 

1.. Gravitational force → G ≡ σ A ≡ [
2πrf

Φ
 ] A ≡ v̅ [ 

𝐀

𝚽
 ] ≡ σ.Φ³ ≡ Φ ² . [{σ Φ}] ≡  

         G ≡ Φ². [{σ Φ}≡ 2πfP r ≡ w r ≡ v̅ ≡ m g = c̅ = 
2.B

πr³
 ]  →   i.e.    G  is related  To 

        → motion ≡ work W , Spaces r , Anti-Spaces 1/r , Stresses σ , Areas A , Caves a ,  

        → Periods  T , Frequencies  f , Angular-waves  w , Angular-Momentum B ,   

        → Spin B ≡ S , velocities  v , Light-velocity c , Impedances Zn, Masses m ,   

        → Gravity g̅ , Charges , q̅ , Electromagnetic – Fields  , E̅ , M̅ , Hydrogen H ,   

        → Atoms , Molecules , Golden-Ratio Φ , i.e. All-Universe . Markos 9/4/2020.       

By Sweeping the Φ Surface through Stresses σ ≡ [
2πrf

Φ
] , and scanning frequencies  f ,    

Explanation :  

The Action-Spaces  ≡ The Infinite Quaternion - monads →  �̅� ≡ ( s + v̅.i ) ≡  𝐀𝐁̅̅ ̅̅   ≡  

      ≡  √s2 + [ v̅. i ]² ]  ,  or   �̅� ≡ x + i . y ≡  𝐀𝐁̅̅ ̅̅   ≡  moduli  , r ,  is their magnitude    

      [ r = | r | = √ x2 + y2 ] , on Unit-Diameter AB̅̅ ̅̅  . The [QMAS] . For Quaternion |v̅| = s      

Breakages  𝐳  * 𝐳  = (s + v̅.i )² = s² +[v̅]² +2.sv̅.i = s² – v̅ ² ± 2.s v̅ = |s|² - |�̅�|² ± 2.|s|.|s̅| , i.e. 

     In Figure -3-  the Vector of Amplitude is Quaternion  �̅� ≡ x + i . y , with vector �̅� , to  

     be from Definition of the Complex Vector Space , the Set of Vectors of length (the n  

    Vertices which form the n - Polygon Sides , or the Norm of  the Complex - Vectors ) 

a...The 4-Geometrical Spaces , [ Space , Anti-Space , Neutral-Space , Sub-Space ]  

      consist    →  The Geometrical - Mould of 𝐀𝐁̅̅ ̅̅  - Monad  ≡ [PM-2R-M] ←     

b...The  Vectors of Amplitude z = 2R , ON 𝐀𝐁̅̅ ̅̅   Monad , consist The Energy-Mould .     

      of  2R-Form .The Physical -Mechanisms → [ Physical Mould of 2R- Monad ] ≡   

      [GM-AB-M] ← are such and dependent on the n - Number of Accessories they use .   

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113 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

A… The  Gravity Force  G  ≡ motion  ≡  σ.𝚽³ , exists without mass and  is Quantized  

        Spread in{Space and Anti-Space Or ≡ QUA ≡ {is The Quantized-Units In-Area of  

        Space and Anti-Space }, and as a Mould 𝚽  Golden-Ratio , exists as  Impedance b.  

Placing [ Physical Mould of 2R- Monad ] ON [ Geometrical - Mould of 𝐀𝐁̅̅ ̅̅  - Monad ]  

                                      [ PM-2R-M ]    →    ⇅   ←    [ GM-AB-M ] 

THEN → Gravitational-Force G ≡ [ Σ = n . h ] , and n-NA = 1  Creates & Constructs,  

 

Figure -28- :  On any Energy - Monad A ↔ B  , exist the 4-Primary Spaces which are  

         the Roots of the Nth Degree Polynomial , Becoming from the equation of  motion .  

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                    Markos Georgallides        

[97B]  [M]  The Duality Photon , DNA , and the Cruise-Missile Elementary-Particles ,  

                    Conductors , http://science MPG ≡ Markos Georgallides     

[98A]  [M]  The Nature of  Greek-Special-Problems  & their functioning in Electromagnetic  

                    Forces  In DNA - Conductors  , https://www.lap-publishing.com/.   

                     E-book. LAP  LAMBERT  Academic Publication .  

[98B]  [M]   The  Why , the  How and When , the Atoms – Bond .         

                     http://science MPG ≡ Markos Georgallides      

[99A]  [M]    The  How , Why  and When , the Atoms – Bond .   

                     https://mts.Intechopen.com.book.process/ ≡ Dragan Miljak       

[99AAA]     [M]  The  How , Why  and When , the Atoms – Bond .   

                     http://science MPG ≡ Markos Georgallides      

[99CCC]      [M]  The  4-Frequencies of Atoms – Bonding related to Octave Periodic-Table .   

                     http://science MPG ≡ Markos Georgallides      

       IJO - INTERNATIONAL JOURNAL OF MATHEMATICS          (ISSN: 2992-4421 )

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118 

            The Fundamental Particles Origination - Mechanism in MFMF - PNS Caves .  

 

[99]    [M]   The Bonding of Cosmic-Particles and Resonance Photoelasticity ,    

                     http://science MPG ≡ Markos Georgallides      

[100]   [M]   Programming  , The Atoms and  their Compounds Energy ,   

                      http://science MPG ≡ Markos  Georgallides      

[101]   [M]   The Why and How Atoms and Compounds Bond ,and Chemistry-Programming  

[102]   [M]   The Markos-Method of Conservation of Motion = Energy , by Division .     

[103]   [M]   The Markos-Method of Conservation of Motion in Nature and Medicine . 

[104]   [M]   Programming of Atoms and their Compounds and their Modulated-Energy,   

                      http://science MPG ≡ Markos Georgallides      

[105]   [M]   The ERP   Argument , Under the Critic of the Material—Geometry  

                    AND  ,  The  Space  Energy  Universe .       

[106]   [M]   Programming the Atoms and Compounds and the Unification of Physics  

                    AND Chemistry —- ["JMSEAT - 2024"]  atul@scientificadvances.co.in 

[106]   [M]   Programming the Atoms and Compounds and the Unification of Physics  

                    AND Chemistry —-  ASRP.hspublishing@gmail.con 

[107-A]  [M]  The  Planck`s  << Duality  Angular - Momentum >>  as  GRAVITY and  .   

                    ANTIGRAVITY <editor@granthaalayah.com> Research International Journal     

[107]    [M]  The  Planck`s   << Duality  Angular - Momentum >>  as  GRAVITY  

                    and   ANTIGRAVITY    http://science MPG ≡ Markos Georgallides      

[108]   [M]   The Planar and Atoms Black Holes , Under the Critic of Material-Geometry & 

            Planck–Dual Spin as Gravity-Antigravity http://science MPG ≡ Markos Georgallides           

[109]   [M]   The DUAL Quaternion  Momentum -B  as  { The Existing Universe } &  The  

                      Black -Holes ,  http://science MPG ≡ Markos Georgallides           

[110]   [M]   The Origination-Mechanism  of Fundamental Particles in the Energy-Planck`s 

                      Confinement and  their existence, http://science MPG ≡ Markos Georgallides           

[111]   [M]   The Polynomials , n-Knots Figures , Edge Points Vibration & M-Geometry .   

                     by  http://science MPG ≡ Markos Georgallides           

[112]   [M]   An Way  for Deceptioning  the Normal  OR the  Dangerous Cells   

                     by  http://science MPG ≡ Markos Georgallides           

[113]   [M]   The Origination of Universe from Energy ≡ Motion into the E-Geometry .   

 

                  Markos Georgallides  comes from Cyprus and  currently  

                     resides in the City  Larnaca , Cyprus after being expelled  

from his Home Town Famagusta-Varosha , by The Barbaric Turks in August 1974. He 

works as a consultant Civil and Architect Engineer having his own Business . He is also The 

author of numerous scholarly Articles focusing on Euclidean and Material Geometry , and 

mathematical To Physics and Mechanics related Subjects . He obtained his degree from the 

Athens , National Technical , Polytechnic University [NATUA] Athens- Greece , and  

subsequently studied in Germany , Math Theory of  Photoelasticity .   

       IJO - INTERNATIONAL JOURNAL OF MATHEMATICS          (ISSN: 2992-4421 )

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