Nuclear Gravitation Field Theory (NGFT) evaluates Strong Nuclear Force with respect to Newton's Law of Gravity, and General Relativity. NGFT demonstrates that when enough nucleons are present in the nucleus to classically form a near perfect spherical shape, the proton and neutron energy levels fill in the same way the electron energy levels fill indicating the potential function is proportional to 1/r^2. NGFT demonstrates the intensity of the Nuclear Gravitation Field is stronger than the Nuclear Electric Field in order to hold the protons and neutrons together in the Nucleus. The Nuclear Gravitation Field at the surface of the Nucleus rivals that of a Neutron Star or Black Hole, therefore, it drops like a rock just outside the Nuclear surface due to Space-Time Compression. The Nuclear Gravitation Field then propagates outward with the feeble intensity we see as gravity.
The update demonstrates the apparent "saturation" of the Strong Nuclear Force occurs because of Space-Time Compression occurring within the Nucleus. This effect can only occur if the Strong Nuclear Force is Gravity.
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Nuclear Gravitation Field Theory Demonstrates Strong Nuclear Force is Gravity
1. Nuclear Gravitation
Field Theory
▬ Update ▬
A Field Theory Demonstrating the
Strong Nuclear Force and
Gravity are One and the Same
By Kenneth F. Wright
December 21, 2016
2. Nuclear Gravitation Field Theory
• Theory Incorporates the Following:
• Newton’s Law of Gravity
× × ×
Quantum Mechanics – Schrodinger Wave Equations
• Electrons, Protons, and Neutrons have both a Particle and Wave Characteristic
• Total Energy = Kinetic Energy + Potential Energy
• General Relativity
• Strong Gravitational Fields result in significant Space-Time Compression
• Nuclear Gravitation Field and Strong Nuclear Force are
considered the same in this evaluation to determine if observed
characteristics of Nucleus is consistent with Theory
2
3. Nuclear Gravitation Field Theory
• If the given field acts upon a particle where the Force is proportional to 1/r2 then the
Potential Energy (PE) of that particle can be determined by integrating that Force over a
given distance. The PE is considered a negative value when bound by a system and
becomes zero at infinity (∞). The PE function will be proportional to 1/r, where r is the
variable in the PE Function incorporated in the Schrodinger Wave Equation:
Force x Distance = Work or Energy
= = =
• Electric Field Force and Potential Energy of electron to nucleus with Z number of Protons
=
( )( )
=
( )( )
=
( )( )
• The following equations represent the Nuclear Gravitation Field Force and Potential Energy
of either a Proton or Neutron an Electron to a Nucleus with Z number of Protons and N
number of Neutrons:
=
( )
=
( )
=
( )
3
4. Nuclear Gravitation Field Theory
• Quantum Mechanics – Generic Schrodinger Wave Equation for Nuclear
Electric Field and Nuclear Gravitation Field Using Spherical Coordinates
( , , , )
=
ћ
+ V (
= + = + = + = +
• Nuclear Electric Field Solutions to Schrodinger Wave Equation
( , , , )
=
ћ
+
( )( )
• The Electrons are far enough away from the Nucleus relative to Nuclear diameter and
Atomic diameter.
• The Nucleus appears as a point source for the Electric Field propagating outward
relative to the Electrons, therefore the Electric Field Potential Function is proportional
to 1/r for all conditions as indicated by Schrodinger Wave Equation, above
• Solutions are Known and Determine the Arrangement and Chemical Properties of the
Elements in the Periodic Table (See Slide 6)
4
5. Nuclear Gravitation Field Theory
• Quantum Mechanics – Schrodinger Wave Equation Incorporating Newton’s
Law of Gravity in the Potential Function for the Nuclear Gravitation Field
Using Spherical Coordinates
( , , , )
=
ћ
+
( )
Nuclear Gravitation Field Solutions to Schrodinger Wave Equation
• Nuclear Gravitation Field Schrodinger Wave Equation, above, is only valid if the
Nucleus forms a near perfect sphere from a classical aspect because a 1/r2 Gravity
Field assumes symmetric omnidirectional propagation outward of the Nuclear
Gravitation Field – Protons and Neutrons are evaluated when placed next to the
Nucleus
• A Nucleus not forming a perfect sphere will have distortion in the outward
propagation of the Nuclear Gravitation Field, therefore, the 1/r2 Gravity Field, hence
the 1/r Gravity Field Potential Energy Function will be invalid
• If the Nucleus is a near perfect sphere, then the Gravity Field is proportional to 1/r2
and the Potential Energy Function is proportional to 1/r. The number of Proton and
Neutron Energy Level Fills for the Applicable Energy Levels should be the same as
the number of Electron Energy Level fills for those same Electron Energy Levels
5
6. Nuclear Gravitation Field Theory
Energy Level Magic Numbers
Energy
Level
Electrons -
1e0
Energy
Level Δ
Protons
1p1
Energy
Level Δ
Neutrons
1n0
Energy
Level Δ
1 2 --- 2 --- 2 ---
2 10 8 8 6 8 6
3 18 8 20 12 20 12
4 36 18 28 8 28 8
5 54 18 50 22 50 22
6 86 32 82 32 82 32
7 118 32 114 32 126 44
8 168 50 164 50 184 58
Magic Numbers represent the number of Electrons, Protons, or Neutrons to completely fill
energy levels. Matching Energy Level Changes for Protons or Neutrons to Electrons are in Red.
6
7. Nuclear Gravitation Field Theory
The Elements with Electron Magic Numbers are in Group 18 at the right.
The Elements with Proton Magic Numbers are outlined in Red. 7
8. Nuclear Gravitation Field Theory
• Nuclear Gravitation Field Solutions to Schrodinger Wave Equation Differ
from Nuclear Gravitation Electric Field
• Newton’s Law of Gravity assumes Masses M1 and M2 are spherical. Stars, Planets,
and Moons are, typically, spherical, therefore the 1/r2 Gravity Field attracting mass
M2 to mass M1 of the equation is valid. The Gravity Field Potential Energy is
proportional to 1/r.
× ×
=
×
• The Nuclear Gravitation Field and the Gravity Field Potential Energy Function will be
dependent upon the shape of the Nucleus as “seen” by the Proton or Neutron of
interest next to Nucleus – classically Nuclei with number of Protons and/or Neutrons
< 50, the Nucleus is not near perfectly spherical
• The Heisenberg Uncertainty Principle indicates that all nuclei are spherical in shape
• The Solutions for the Schrodinger Wave Equation evaluating the Nuclear Gravitation
Field for the range of smaller nuclei result in Proton and Neutron Energy Level fills
different from the Electron Energy Levels fills inconsistent with a spherical nucleus
• Either Heisenberg Uncertainty Principle does not drive how Proton and Neutron
Energy Levels are filled or one cannot confirm the Strong Nuclear Force = Gravity8
9. Nuclear Gravitation Field Theory
• Nuclear Gravitation Field Solutions to Schrodinger Wave
Equation Differ from Nuclear Gravitation Electric Field
• The Solutions for the Schrodinger Wave Equation evaluating the
Nuclear Gravitation Field indicate a 1/r2 Gravity Field and a 1/r Gravity
Field Potential Energy Function for the larger Nuclei with the number
of Protons and Neutrons > 50 each – Nuclei closely approach a
spherical shape with Nuclear Gravitation Field Propagating outward
omnidirectional from the Nucleus – the 1/r2 Gravity Field indicates
Strong Nuclear Force = Gravity:
• The fill for Protons in the Sixth Energy Level and in the Seventh Energy Level
are identical for the fill for Electrons in the Sixth Energy Level and Seventh
Energy Level at a change of 32 for each
• The fill for Protons in the Eighth Energy Level is Identical for the fill of Electrons
in the Eighth Energy Level at a change of 50 9
10. Nuclear Gravitation Field Theory
• Nuclear Gravitation Field Solutions to Schrodinger Wave
Equation Differ from Nuclear Gravitation Electric Field
• The fill for Neutrons in the Sixth Energy Level is Identical for the fill of Protons
and Electrons in the Sixth Energy Level at a change of 32
• The fill of Neutrons for the Seventh Energy Level at a change of 44 and the
Eighth Energy Level at a change of 58 deviate from the Electrons and Protons
for the Seventh Energy Level at a change of 32 and for the Eighth Energy Level
at a change of 50
• Suspect that Proton like charge Coulombic Repulsion Force is contributing to
Potential Function and a need for more Neutrons to establish Stability of the Nucleus
is required
• All known Elements beyond Element 83, Bismuth-209, are considered radioactive
(not stable)
10
11. Nuclear Gravitation Field Theory
• Relativity – Pythagorean Theorem and Trigonometry Provide
Simple Explanation:
• Hypotenuse of Right Triangle
Represents Speed of Light as Unity =
c/c = 1.000
• Opposite Side of Right Triangle
represents measured velocity relative
to light = v/c = sinθ
• Adjacent Side of Right Triangle
represents length contraction in
direction of motion =
= cosθ
11
12. Nuclear Gravitation Field Theory
• Relativity – Pythagorean Theorem and Trigonometry Provide
Simple Explanation:
• Effective velocity, veff = c × tanθ
• We cannot reach a measured velocity of c if
we have mass
• As v → c, cosθ → 0 = measured distance to
be traveled
• If v/c = sinθ = 0.7071, then veff/c = tanθ = 1.000
v = measured velocity = 0.7071c veff = 1.000c
• Compressed Space-Time Distance = cos θ =
−
• Compressed Space-Time Distance =
0.7071 x Uncompressed Space-Time Distance
12
13. Nuclear Gravitation Field Theory
• Relativity – Pythagorean Theorem and Trigonometry:
30°-60°-90° Triangle
13
14. Nuclear Gravitation Field Theory
• Relativity – Pythagorean Theorem and Trigonometry:
45°-45°-90° Triangle
14
15. Nuclear Gravitation Field Theory
• Relativity –
Pythagorean
Theorem and
Trigonometry:
60°-30°-90° Triangle
15
16. Nuclear Gravitation Field Theory
• General Relativity – Gravity and Accelerated Reference Frames:
• Gravity fields propagate based upon Uncompressed Space-Time
• Gravity fields generate Compressed Space-Time due to the acceleration of
light, electric fields, and magnetic fields – Since speed of light is a
constant at 2.9975 x 108 meters/sec, the distance traveled is reduced
• Light, Electric Fields, and Magnetic Fields propagate based upon
Compressed Space-Time
• We observe events in Compressed Space-Time in our reference frame
• Let’s assume the gravitational field next to the nucleus of the atom was
equal to 2.9975 x 108 meters/sec2
• If light was subjected to this acceleration field, in one second the speed of
light would be doubled to 5.9950 x 108 meters/sec = the speed of light in
Uncompressed Space-Time
• Since the speed of light remains constant at 2.9975 x 108 meters/sec, the
distance traveled by light in Compressed Space-Time must be reduced to
half the Uncompressed Space-Time distance
16
21. Nuclear Gravitation Field Theory
21
• Nuclear Fusion: Takes Place at the Center of Sun
• Temperature at Sun Center = 10,000,000°F Proton Kinetic Energy sufficient
to allow Protons to overcome like charge Coulombic repulsion and come in
contact with one another to facilitate Nuclear Fusion
22. Nuclear Gravitation Field Theory
• General Relativity – Gravity and Accelerated Reference Frames:
• Calculate the acceleration field of a proton from a nucleus
• We will assume the first step in Solar Fusion – the Proto-Proton interaction
• The Strong Nuclear Force must overcome like charge Coulombic repulsion of Protons
• Radius of Proton is 1.20 x 10-15 meter: Distance r, between the center of two Protons
is twice the radius of a Protons = 2.40 x 10-15 meters
= =
= =
( . × )( . × )
( )( . × )( . × ) ( . × )
= ( . × ) = ( . × )
The value of acceleration, , represents the repulsive electric field established by the
first Proton on the second Proton. In order to overcome this repulsive field, is the
minimum required attractive field required by the Strong Nuclear Force to overcome the
Electric Field repulsion of the two Protons
22
23. Nuclear Gravitation Field Theory
• General Relativity – Gravity and Accelerated Reference Frames:
• The minimum calculated gravitational acceleration field required to overcome
the Coulombic Repulsion of two protons in a nucleus is 2.441 x 1027g
• From the Table “Accelerated Reference Frame Space-Time Compression Due
to Gravity Field,” the Space-Time Compressed distance that light travels is
essentially a zero distance for gravity acceleration fields > 1.00 x 1013g
• The Strong Nuclear Force is observed to vanish immediately outside the
surface of nucleus of the atom – this observed characteristic of the Strong
Nuclear Force could only occur if the Strong Nuclear Force is gravity because
the Strong Nuclear Force is accelerating light
• Evaluate the Strong Nuclear Force = Gravity propagating outward from a
single Proton – in Table “Proton Gravity Field Propagation in Uncompressed
Space-Time and Compressed Space Time”
23
26. Nuclear Gravitation Field Theory
• General Relativity – Gravity and Accelerated Reference Frames:
• Proton gravitational field in Compressed Space-Time drops over 19 decades in
intensity, from 2.395 x 1028 meters/sec2 to 1.379 x 109 meters/sec2 before
Compressed Space-Time quantized gravitational field propagates outward from the
Proton surface by > 20% of Proton radius or 1.478 x 10-15 meter
• Highlighted in the first red entry of Table “Proton Gravity Field Propagation in
Uncompressed Space-Time and Compressed Space-Time.”
• At Uncompressed Space-Time distance from the Proton of 0.5 meter the Proton
gravitational field intensity is 1.379 x 10-1 meters/sec2 equal to 1.406 x 10-2g, the
Compressed Space-Time distance is 6.12 x 10-11 meter just outside Hydrogen Atom
Electron Cloud
• Highlighted in the second red entry of Table “Proton Gravity Field Propagation in
Ucompressed Space-Time and Compressed Space-Time”
• Proton gravitational field of 1.379 x 10-1 meters/sec2 equal to 1.406 x 10-2g relatively
feeble, but still much larger than average gravitational field outside Atom.
26
27. Nuclear Gravitation Field Theory
• Quantized Gravity Versus Average Gravity – Analogous to Quantized
Light Energy and Average Light Energy:
• Light Energy is Quantized - Discrete “Chunks” of Energy
• Electrons have discrete energy levels about Nucleus of the Atom
• Photoelectric Effect – Liberate Electron from Sodium Atom – Quantized Light Energy
has 1.201 x 109 intensity factor over Average Light Energy distribution
• Electron energy levels are on order of Electron Volts (eV)
• Proton and Neutron energy levels are on order of Million of Electron Volts (MeV)
• Higher energy narrows the energy level bandwidth, lower energy broadens the
energy level bandwidth
• Nuclear Energy Levels expected to have on order 1 million times the intensity factor
of Electron Energy Levels – intensity factor on order of 1.00 x 1015 to 1.00 x 1016
27
28. Nuclear Gravitation Field Theory
• Quantized Gravity Versus Average Gravity – Analogous to Quantized
Light Energy and Average Light Energy:
• Determine the classical physics value of the gravity field for the Proton at the surface
of the Proton
= =
×
=
. × × ( . × )
( . × )
= . × = . ×
• Determine the classical physics value of the gravity field for the Proton outside the
electron cloud of the Hydrogen atom – about a radial distance of 5.00 x 10-11 meter
from the center of the Proton
=
×
=
. × × ( . × )
( . × )
= . × = . ×
28
29. Nuclear Gravitation Field Theory
• Quantized Gravity Versus Average Gravity – Analogous
to Quantized Light Energy and Average Light Energy:
• Quantized Proton Gravity just outside Hydrogen Atom Electron
Cloud: 1.379 x 10-1 meters/sec2 = to 1.406 x 10-2g
• Classical Physics (Average) Proton Gravity just outside Hydrogen
Atom Electron Cloud: 4.464 x 10-17 meters/sec2 = to 4.550 x 10-18g
• Determine the Quantized Gravity intensity factor = ratio of Quantized
Proton Gravity to Classical Physics (Average) Gravity =
1.406 x 10-2g / 4.550 x 10-18g = 3.090 x 1015
An expected ballpark value based upon bandwidth analysis
29
30. Nuclear Gravitation Field Theory
• General Relativity – Gravity and
Accelerated Reference Frames:
• Nuclear Gravitation Field and Electric
Field Propagating Outward from Nucleus
in Compressed Space-Time
• Nuclear Gravitation Field is stronger than the
Nuclear Electric Field at Nuclear Surface
• Nuclear Gravitation Field = 1 x 10-12 intensity
of Nuclear Electric Field within and outside
Electron Cloud
• Space-Time Compression is directly
proportional to the intensity of the Nuclear
Gravitation Field
30
31. Nuclear Gravitation Field Theory
31
• Strong Nuclear Force Properties Indicate Equal to Gravity:
• Determine Nuclear Gravitational Field and Nuclear Electric Field as a
function of position inside the Nucleus
32. Nuclear Gravitation Field Theory
32
• Strong Nuclear Force Properties Indicate Equal to Gravity:
• Determine Nuclear Gravitation Field intensity as a function of radial
position inside Nucleus from Center of Nucleus to Nuclear Surface
• Assume that Strong Nuclear Force is Gravity to develop equations:
• Mass, MIN, is equal to constant mass density times Volume, ρMass X
VIN, as a function of r, radial distance from Center of Nucleus
= × = × × × =
×
=
× × × ×
= × × × ×
• Therefore, the gravitational acceleration inside the Nucleus, gIN, is
proportional to r.
• The mass contributing to gIN is only the mass from Center of Nucleus
to position r inside the Nucleus.
33. Nuclear Gravitation Field Theory
33
• Strong Nuclear Force Properties Indicate Equal to Gravity:
• The gIN calculated previously with linear rise relative to radial distance from
Center of Nucleus, r, is not correct because it assumes classical physics
• General Relativity must be considered and gIN must be evaluated with Space-
Time Compression
• The Nucleus is observed in Compressed Space-Time, therefore the Mass, MIN is
calculated based upon Compressed Space-Time radial distance from the Center
of the Nucleus rCST
• Gravity propagates based upon Uncompressed Space-Time, therefore, the value
of gIN is calculated based upon Uncompressed Space-Time radial distance from
Center of Nucleus, rUST
= × = × × × =
×
=
× × × ×
34. Nuclear Gravitation Field Theory
34
• Strong Nuclear Force Properties Indicate Equal to Gravity:
• rUST rises faster than rCST and the rate of rise of rUST goes up because Gravity
field intensity rises as a function of rUST resulting in rising Compressed
Space-Time
• gIN will no longer rise linearly, it will tend to level off as rUST and rCST rise
• gIN-NCST = Nuclear Internal Gravity
Field, No Compressed Space-Time
Present
• gIN-CST = Nuclear Internal Gravity
Field With Compressed Space-Time
Present
35. Nuclear Gravitation Field Theory
35
• Strong Nuclear Force Properties Indicate Equal to Gravity:
• Determine Nuclear Electric Field intensity as a function of radial
position inside Nucleus from Center of Nucleus to Nuclear Surface
• Use acceleration field equation for repulsion of charges inside
Nucleus:
= × = × × × =
×
× × × ×
× × × ×
× × × ×
× ×
× ×
• Therefore, the Nuclear Electric Field acceleration field inside the
Nucleus, aEF-IN, is proportional to r.
• The charge distribution inside the Nucleus contributing to aEF-IN is
only the charge distribution from Center of Nucleus to position r
inside the Nucleus.
36. Nuclear Gravitation Field Theory
36
• Strong Nuclear Force
Properties Indicate Equal to
Gravity:
• SNF-NSTC = Strong Nuclear
Force – No Space-Time
Compression present
• SNF-WSTC = Strong Nuclear
Force With Space-Time
Compression
• NEF-CRP = Nuclear Electric
Field – Coulombic Repulsion of
Proton
• Net Nuc Accel Field is the
difference between fields SNF-
WSTC and NEF-CRP
• Dropoff of SNF-WSTC results
in the apparent “saturation” of
the Strong Nuclear Force
Acceleration Fields Inside Nucleus
38. Nuclear Gravitation Field Theory
38
• Strong Nuclear Force
Properties Indicate Equal to
Gravity:
• SNF-NSTC = Strong Nuclear
Force – No Space-Time
Compression present
• SNF-WSTC = (If Gravity) Strong
Nuclear Force With Space-
Time Compression
• NEF-CRP = Nuclear Electric
Field – Coulombic Repulsion
of Proton
• Net Nuc Accel Field is the
difference between fields SNF-
WSTC and NEF-CRP
Acceleration Fields vs Atomic Mass
• Drop-off of SNF-WSTC results in the apparent “saturation” of the Strong
Nuclear Force and has a profile appearance similar to Binding Energy per
Nucleon curve.
39. Nuclear Gravitation Field Theory
• Nuclear Configuration of Lead-208 and Bismuth-209:
Nucleon Energy Levels for Lead (Pb-208) and Bismuth (Bi-209)
Energy
Level
1
(He)
2
(O)
3
(Ca)
4
(Ni)
5
(Sn)
6
(Pb)
7
(Fl)
Total
Protons
and
Neutrons
Protons
Lead
(82Pb208)
Neutrons
2p
2n
6p
6n
12p
12n
8p
8n
22p
22n
32p
32n 44n
82p
126n
Protons
Bismuth
(83Bi209)
Neutrons
2p
2n
6p
6n
12p
12n
8p
8n
22p
22n
32p
32n
1p
44n
83p
126n
39
The importance of the items in red are explained in the following slide.
40. Nuclear Gravitation Field Theory
• Nuclear Configuration of Lead-208 and Bismuth-209:
• Lead-208 is “double magic” with 82 Protons and 126 Neutrons
• 82 Protons fill Six Energy Levels
• 126 Neutrons fill Seven Energy Levels
• Nuclear Gravitation Field for Lead-208 is relatively strong – Space-Time
Compression next to the Nuclear Surface is relatively strong compared to
average stable nuclei
• Bismuth-209 has 83 Protons and 126 Neutrons
• 82 Protons fill Six Energy Levels
• 83rd Proton is lone Proton in Seventh Energy Level
• 126 Neutrons fill Seven Energy Level
• Nuclear Gravitation Field for Bismuth-209 is significantly weaker next to the
nucleus in comparison to Lead-208 – gravity outside the Bismuth electron
cloud will be measurably stronger than for Lead-208
40
42. Nuclear Gravitation Field Theory Proof Tests
• Cavendish Experiments can Prove
Bismuth-209 Has Stronger
Gravitational Field than Lead-208
and Prove Strong Nuclear Force =
Gravity:
• Cavendish Experiment was used to
determine G in Newton’s Law of
Gravity equation:
× ×
• Perform Cavendish Experiment with
Lead-208 to measure its G.
• Perform Cavendish Experiment with
Bismuth-209 to measure its G.
• If Strong Nuclear Force = Gravity,
then GBi > GPb
• G is not Universal but specific to
each isotope of each element 42
43. Nuclear Gravitation Field Theory
• Nuclear Gravitation Field
Propagating Outward from Nucleus
and the Effect of Space-Time
Compression:
• Nuclear Gravitation Field 1 is more
intense than Nuclear Gravitation
Field 2
• Nuclear Gravitation Field 2 is more
intense than Nuclear Gravitation
Field 1 inside and beyond the
electron cloud of the atom
• As previously noted, the Nuclear
Gravitation Field for Bismuth-209
should be greater than Nuclear
Gravitation Field for Lead-208
because it is weaker at Nuclear
surface
43
Higher Intensity Nuclear Gravitation Field results in a greater
amount of Space-Time Compression occurring resulting in a
weaker gravity field outside electron cloud.
Lower Intensity Nuclear Gravitation Field
results in a lesser amount of Space-Time
Compression occurring resulting in a
stronger gravity field outside electron cloud.
The electron cloud does not
change its relative position to
the nucleus because the electric
field propagates based upon
Compressed Space-Time.
44. Nuclear Gravitation Field Theory
• Conclusion
• When classical Nuclear shape is a near perfect sphere, the Proton and Neutron
energy level fill methodology for the Strong Nuclear Force is consistent with a
1/r2 Potential Energy function
• The observed Strong Nuclear Force virtually vanishes outside the Nuclear
Surface consistent with the extreme Space-Time Compression present in the
vicinity of the Nucleus if Strong Nuclear Force is Gravity.
• In order to provide a field stronger than Coulombic Repulsion of Protons, the Strong
Nuclear Force must have an acceleration field of greater than 2 x 1028g which rivals a
Neutron Star or Black Hole if Gravity
• Neutrons must be added to Nucleus to boost Strong Nuclear Force because of
the apparent “saturation” of the Strong Nuclear Force which is an expected
observation due to Nucleus Internal Space-Time Compression if Strong Nuclear
Force is Gravity
• The “saturation” of the Strong Nuclear Force results in elements beyond
Bismuth (83Bi209) to be radioactive. If Strong Nuclear Force was not Gravity,
Space-Time Compression would not exist and a Nucleus could contain only
Protons from one to infinity and be stable. 44