Chapter X:

Quantum Mechanics, General Relativity,
and the Nuclear Gravitation Field Theory

In order to better understand the Nuclear Gravitation Field in the vicinity of the nucleus of the atom the Nuclear Gravitation Field must be evaluated using the Schrodinger Wave Equation to determine the quantized energy states of the protons and the neutrons in the nucleus using the potential function for Newton’s Law of Gravity in the equation.  This evaluation assumes that Gravity and the “Strong Nuclear Force” are one and the same because one must assume the “1/r²” gravitational potential function of the Schrodinger Wave Equation to properly evaluate the results.  On the atomic and nuclear scale, it is reasonable to assume that Gravity would have a dual particle and wave characteristic in a like manner to electromagnetic radiation (light), electric fields and magnetic fields (light is made up of a propagating electric field and a propagating magnetic field), protons, neutrons, and electrons.  The Schrodinger Wave Equation demonstrates the electron’s dual particle and wave characteristic when applied to the electrons that “orbit” the nucleus of an atom.  The Schrodinger Wave Equation demonstrates the Nuclear Electric Field established by the positive charge in the nucleus is a quantized field, rather than a continuous field, leading to the quantized energy levels of the electrons.  The discrete “orbits” or energy levels of the electrons about a nucleus must either contain a complete single wavelength or contain whole multiples of a wavelength for an electron to exist in the particular energy state bound by the nucleus.  Although Physicists have not agreed on the equation representing the form of the “Strong Nuclear Force,” which holds the protons and neutrons together in the nucleus, they do agree that each of the protons and neutrons of the nucleus fills a specific quantized energy level within the attractive potential well of the nucleus.  The Schrodinger Wave Equation will demonstrate gravity is quantized and will establish the discrete energy levels of the protons and neutrons in the nucleus.  The Schrodinger Wave Equation assumes the wave function for either a proton or a neutron is a function of its distance from the center of the nucleus (0 to infinity), azimuthal angle (0 to 2π Radians), altitude angle (-π/2 to +π/2 Radians), and time.  The assumed wave function is designated as ψ(r,θ,φ,t).

Total Energy  =  Kinetic Energy  +  Potential Energy

Schrodinger Wave Equation for the Nuclear Electric Field:

Schrodinger Wave Equation for the Nuclear Gravitation Field:

If the “Potential Energy” function for both the Nuclear Electric Field and the Nuclear Gravitation Field are a function of the inverse of the square of the distance from the nucleus (1/r²), then why do the “Nuclear Gravitation Field” (or “Strong Nuclear Force”) solutions for the Schrodinger Wave Equation for the Nuclear Gravitation Field differ from the solutions for the Schrodinger Wave Equation for the Nuclear Electric Field?  In other words, why are the “magic numbers” for the protons and neutrons in the nucleus, different than the “magic numbers” for the electrons orbiting the nucleus as introduced in Chapter VII and discussed in Chapter VIII?  Why does the field intensity of the “Strong Nuclear Force” drop off much faster than the expected 1/r² function based upon Newton’s Law of Gravity as discussed in Chapter IX?  The Gravitational Potential Function must be more complicated than indicated by the Schrodinger Wave Equation for the Nuclear Gravitation Field, above.  Quantized gravitational fields may be intense enough to result in the General Relativistic effect of “Space-Time Compression.”  The purpose of this chapter is to determine whether or not the “quantized” Nuclear Gravitation Field is sufficiently intense to result in “Space-Time Compression” taking place.  “Space-Time Compression” will affect both the time dependent and spatial dependent portions of the Schrodinger Wave Equation and must be accounted for if the Nuclear Gravitation Field is intense enough.  Otherwise the solutions for the Schrodinger Wave Equation for the Gravitational Potential would be expected to be identical to the solutions for the Electrostatic Potential for the electrons.  The Nuclear Gravitation Field potential represents the field established by the nucleus as it interacts with either an external proton or an external neutron.  Both protons and the neutrons in the nucleus contribute to the Nuclear Gravitation Field potential.  The Nuclear Electric Field potential represents the field established by the nucleus as it interacts with an external electron.  Only protons in the nucleus contribute to the Nuclear Electric Field potential.  Protons and neutrons each have unique quantum numbers.  Protons can only fill energy levels for protons and neutrons can only fill energy levels for neutrons.  Figure 6-1, “Structure Within the Atom,” in Chapter VI, indicates that a proton contains two up quarks and one down quark and a neutron contains one up quark and two down quarks.  The quarks within the protons and neutrons may have to be accounted for in different manners by the Potential Function in the Schrodinger Wave Equation.  Solving the Schrodinger Wave Equation in three-dimensional spherical coordinates, with allowances for particle differences between the protons and the neutrons and for Space-Time Compression, is not an easy task.  However, it is reasonable to assume that the order of magnitude of the Quantum Mechanical effects versus the Classical Physics predictions for the photoelectric effect would be analogous to quantized Nuclear Gravitation Fields relative to Classical Newtonian Gravity.  Rather than attempting to solve the Schrodinger Wave Equation to determine the intensity of the Nuclear Gravitational Field, a ballpark value for the quantized Nuclear Gravitational Field will be determined by multiplying the classical Nuclear Gravitation Field intensity calculated in Chapter IX by the magnitude difference between an assumed Classical Physics continuous distribution of light energy and its calculated energy imparted to an electron versus the light energy imparted to an electron by a photon (quantized light particles) as observed when the “Photoelectric Effect” takes place.

In order to explain the frequency distribution of radiation from a hot cavity (blackbody radiation) German physicist Max Planck, in 1900, proposed that radiant energy could only exist in discrete quanta, versus a continuous distribution of energy.  These quanta of light contained energy proportional to the frequency of the light emitted.

The quantum idea was soon seized to explain the “Photoelectric Effect,” became part of Niels Bohr's theory of discrete atomic spectra, and quickly became part of the foundation of modern quantum theory.  In 1916, American physicist Robert Millikan experimentally verified the photoelectric effect and measured Planck's constant.

The photoelectric effect is the absorption of light energy by an electron that allows the electron to break free from the atom it is associated with.  Electrons ejected from a sodium metal surface, as indicated by Figure 10-1, “Photoelectric Effect on Sodium Plate,” were measured as an electric current.  Finding the opposing voltage it took to stop all the electrons gave a measure of the maximum Kinetic Energy of the electrons in electron volts (eV).  This experimental data led Millikan to believe that light was quantized rather than being a continuous distribution of energy.  Millikan determined that electron ejection was a function of frequency of light rather than intensity.  From Figure 10-2, “Early Photoelectric Effect Data,” the threshold light frequency where the Sodium metal liberated electrons is 4.39×10¹⁴ Hz.

Figure 10-1:  Photoelectric Effect on Sodium Plate

Figure 10-2:  Early Photoelectric Effect Data

Figure 10-3:  The Electromagnetic Radiation Spectrum

Figure 10-4:  Early Photoelectric Effect Data

Reference:  http://hyperphysics.phy-astr.gsu.edu/hbase/mod2.html

The wavelength of this light capable of liberating an electron from the Sodium metal is 683×10^-9 meter equal to 6830 Angstroms.  The color of visible light is determined by its wavelength.  Energy at the short-wavelength end of the visible light spectrum with wavelengths from 3800 Angstroms to 4500 Angstroms produces the sensation of violet light.  Energy at the long-wavelength end of the visible light spectrum with wavelengths from approximately 6300 Angstroms to 7800 Angstroms produces the sensation of red light.  Between these energy levels lie the wavelengths which the eye sees as blue, 4500 Angstroms to 4900 Angstroms; green, 4900 Angstroms to 5600 Angstroms; yellow, 5600 Angstroms to 5900 Angstroms; and orange, 5900 Angstroms to 6300 Angstroms.  The region of the spectrum adjoining the long-wavelength end of the visible band is known as the infrared or “below the red.”  The region of the spectrum adjoining the short-wavelength end of the visible is the ultraviolet or “beyond the violet.”  Neither the infrared nor the ultraviolet is visible to the human eye, but both have applications in which lighting engineers or designers are sometimes interested.  The location of the visible light spectrum relative to the overall electromagnetic spectrum is provided in Figure 10-3, “The Electromagnetic Radiation Spectrum.”  The minimum energy level of light required to liberate electrons from a plate of Sodium is in the visible light range appears as red-orange in color based upon the wavelengths of the visible light spectrum.

In order to compare Classical Physics to Quantum Mechanics, the energy of light shining on a surface must be assumed to be a continuous distribution.  In other words, light energy is assumed neither to be discrete nor quantized.  Based upon that assumption, the amount of energy available to be absorbed by an electron can be determined.  That calculated value will then be compared to the results of Millikan’s “Photoelectric Effect” experiments.  For this calculation, a 100 watt (Joules/second) orange light source with a wavelength of 6000 Angstroms is directed onto a square plate of Sodium 0.1 meter by 0.1 meter.  The surface area of the square Sodium plate is 0.01 meter².  It is assumed that all the light emitting from the orange light source is directed onto the Sodium plate.  The atomic radius of the neutral Sodium atom is 2.23 Angstroms which is equal to 2.23×10^-10 meter.

Reference:  http://chemlab.pc.maricopa.edu/periodic/periodic.html

The diameter of the Sodium atom is twice the radius or 4.46 Angstroms equal to 4.46×10^-10 meter.  It now must be determined how many Sodium atoms can fill the square surface of the Sodium plate assuming only the top layer of Sodium atoms (one Sodium atom deep).  Although the Sodium atoms are spheres, this calculation will assume that they are square.  The side of the “square Sodium atom” has the same length as the diameter of the spherical atom.  A spherical atom of Sodium will fit into each of the theoretical “square Sodium atoms” that make up the top layer of Sodium atoms on the square plate.  Therefore, each Sodium atom will take up the following surface area on the plate:

Area of Sodium Atom = (4.46×10^-10 meter)×(4.46×10^-10 meter) = 1.989×10^-19 meter²

Number of Sodium Atoms on Surface of Plate  =  Area of Plate divided by Area of Sodium Atom

Number of Sodium Atoms on Surface of Plate = (0.01 meter²)/(1.989×10^-19 meter²)

Number of Sodium Atoms on Surface of Plate  =  5.027×10¹⁶ Sodium Atoms

In one second, the Sodium plate surface absorbs 100 Joules of energy.  1 electron volt (eV) is equal to 1.6022×10^-19 Joules.  The next step is to calculate the amount of energy imparted to one Sodium atom in eV assuming a continuous even distribution of light energy across the Sodium plate.  The intent here is to perform a comparison of the values of the classical electron absorption energy to the Quantum Mechanical electron absorbed energy as provided in Figure 10-4, “Early Photoelectric Effect Data.”

Energy Imparted to 1 Sodium Atom (ENa)  =
	Total Energy Imparted to Plate divided by Number of Sodium Atoms

Each Sodium atom is receiving 1.242×10⁴ eV of energy each second.  The light is only illuminating one side of the Sodium atom because it is coming from one direction, therefore, as the spherical Sodium atom is considered, half the surface area of the Sodium atom is illuminated by the light.  The total surface area of a spherical Sodium Atom is calculated as follows:

The illuminated portion of the sphere of the Sodium atom is equal to half the value calculated, above, or 3.124×10^-19 meter².  In actuality, from a classical point of view, the size of the Sodium Atom is not important or required to determine how much light energy the electron will receive from the from the light source based on classical physics.  The size and exposed surface area of the electron is all that is required to complete this calculation.  In this calculation it is assumed that the density of an electron is the same as the density of a proton or neutron.  The mass of a proton, neutron, or electron is proportional to the cube of its radius or its diameter.  The surface area of either the proton, the neutron, or the electron is proportional to the cube root of its volume squared.  The surface area of the electron, then, should be proportional to the surface area of a proton or neutron by the ratio of its mass to the mass of a proton or neutron to the 2/3 power.  The diameter of a proton or neutron is about 1.0×10^-15 meter.  The radius of a proton or neutron is equal to half the diameter or about 0.5×10^-15 meter.  The total surface area of either a proton or neutron is calculated below:

Since the light is shining from one direction, the light only illuminates half of the surface area of either a proton or neutron.  Therefore, the illuminated surface area of a proton or neutron is equal to 1.571×10^-30 meter².

The electron mass is only 1/1840 that of the proton or neutron.  Therefore, the surface area of an electron will be equal to the surface area of a proton or neutron multiplied by the cube root of 1/1840 squared.  The surface area of an electron can be calculated based upon the surface area of a proton or neutron (nucleon) as follows:

A_{surface-electron}  =  2.092×10^-32 meter²

Since the light is shining from one direction, the light only illuminates half of the surface area of the electron.  Therefore, the illuminated surface area of the electron is equal to 1.046×10^-32 meter².

The calculated amount of energy by the classical physics illumination from the light source received by the Sodium’s electron is as follows:

The Classical Physics analysis predicts the electron only receives 4.163×10^-10 eV of light energy per second.  The amount of energy required to liberate an electron from the Sodium atom is on the order of 0.5 eV.  The Classical Physics analysis result indicates that it is impossible for the photoelectric effect to ever take place.  Quantum Mechanics predicts that the electron can absorb energies on the order of 0.5 eV or greater and can be liberated from the Sodium atom because the incoming light energy propagates in discrete packets or quanta of energy rather than as a continuous distribution of energy.  The vast difference in magnitude of the energy that the electron would absorb based upon Classical Physics to the amount of the energy the electron will absorb by Quantum Mechanics is extremely important.  It is quite reasonable to assume that this significant relative difference in magnitude of field intensity can also apply to the intensity of the Nuclear Gravitation Field.  The Nuclear Gravitation Field would be much more intense if it was a discrete function rather than a continuous function.  Figure 10-4, “Early Photoelectric Effect Data,” states the electron Kinetic Energy is about 0.5 eV when it absorbs light at a wavelength of 6000 Angstroms.  The electron must absorb a minimum amount of “Ionization Energy” to remove it from the Sodium atom before it obtains any Kinetic Energy.  To be conservative, this calculation assumes the Ionization Energy of the electron in the 3s orbital of the Sodium atom to be equal to zero.  The ratio of the quantized energy absorbed by the electron versus the classical calculated energy absorbed by the electron is as follows:

The ratio of the amount of energy absorbed by the electron, assuming Quantum Mechanics, versus the amount of energy absorbed by the electron, assuming Classical Physics, is on the order of 1.2×10⁹ times greater or over a billion times greater.

Let’s assume that the ratio, above, can be applied to the Nuclear Gravitation Field of the ₉₂U²³⁸ nucleus.  In Chapter IX, the Nuclear Gravitation Field was calculated using Classical Physics and Newton’s Law of Gravity and the value of 1.607×10^-7g was obtained.  If the Nuclear Gravitation Field is a quantized, or discrete, field, then the ratio of the “Photoelectric Effect” Quantum Mechanics electron energy versus Classical Physics electron energy, equal to 1.201×10⁹, for the absorption of light energy by the electron can be used as a multiplier to the Classical Physics calculation for the Nuclear Gravitation Field in order to obtain a “ball park” value for the intensity of the quantized Nuclear Gravitation Field of the ₉₂U²³⁸ nucleus.

Quantized Nuclear Gravitation Field of U-238   =    (1.607×10-7 g)×(1.201×109)
	=    1.930×102 g
	=    193.0 g

Recall that the Sun’s gravitational field calculated previously at the Sun’s surface was 27.8 g.  The gravitational field calculated previously for the Neutron Star was 2.10×10¹⁰ g.  Assuming Quantum Mechanics, the Nuclear Gravitation Field of the ₉₂U²³⁸ nucleus is on the order of 7 times greater than that of the Sun.  General Relativistic effects must be applied to the Sun’s gravitational field, therefore, General Relativistic effects must be applied to the nucleus.  Significant “Space-Time Compression” is expected to take place in the vicinity of the nucleus.  The best way to physically describe the effects of “Space-Time Compression” would be to perform the following exercise.  Take a thick rubber band, stretch it out, and maintain it in the stretched condition.  While the rubber band is stretched, draw an X-Y Cartesian coordinate system onto the rubber band with the origin at the center of the rubber band.  Draw the function “y = 1/x²” where the origin of the graph represents the nucleus, “y” represents the intensity of the Nuclear Gravitation Field and “x” represents the distance from the nucleus.  After drawing the graph to scale on the stretched rubber band, release the tension on the rubber band.  Note the compressed shape that the function “y = 1/x²” takes on after rubber band compression.  One will note that the Nuclear Gravitation Field seems to drop off to near zero much faster than when the rubber band was stretched.  This exercise provides a visual representation and analogy of the “Space-Time Compression” (“warping of Space-Time”) that occurs in an intense gravity field.  The stretched rubber band analogy is not exactly the correct representation of “Space-Time Compression.”  The rubber band analogy assumes the Nuclear Gravitation Field is a constant field as it propagates outward from the nucleus because the rubber band has a constant compression rate throughout its length.  In reality, the amount of “Space-Time Compression” taking place is directly related to both the intensity of the Nuclear Gravitation Field as a function of distance from the nucleus and the amount of time a photon, traveling at the speed of light, will spend in the vicinity of the nucleus.  The Nuclear Gravitation Field intensity would drop off as a 1/r² function if “Space-Time Compression” was not an issue.  Therefore, the actual amount of “Space-Time Compression” that takes place in the vicinity of the nucleus will continue to drop off consistent with the drop off of the Nuclear Gravitation Field intensity until the General Relativistic effects are too insignificant to be considered.

The results of the comparison of the Quantum Mechanics analysis to the Classical Physics analysis demonstrates why the Nuclear Gravitation Field is intense enough to expect significant “Space-Time Compression” taking place in the vicinity of the nucleus.  The significant “Space-Time Compression” due to the intense gravity field in the vicinity of the nucleus provides the justification for the intensity of the “Strong Nuclear Force” dropping off much faster than the expected 1/r² function as predicted by Newton’s Law of Gravity for a field propagating omni-directionally from the nucleus.  Therefore, the “Strong Nuclear Force” and Gravity are one and the same force.  The Schrodinger Wave Equation must incorporate the effects of Einstein’s General Relativity Theory in order to properly solve the Quantum Mechanical energy levels for the protons and the neutrons in the nucleus.  The “Strong Nuclear Force” follows Newton’s Law of Gravity dropping off 1/r² as a function of distance from the nucleus at distances from the nucleus where its intensity is low enough that General Relativistic effects need not be considered.  In the vicinity of the nucleus where General Relativistic effects must be considered, one will find that the “Strong Nuclear Force” will follow Newton’s Law of Gravity once the General Relativistic correction factors have been incorporated into the Schrodinger Wave Equation to convert “Compressed Space-Time” to the equivalent “Normal (Non-Compressed) Space-Time.”

Index and Direct Links to Other Chapters of Nuclear Gravitation Field Theory
and Nuclear Gravitation Field Theory Home Page/Table of Contents:

Nuclear Gravitation Field Theory

1. Purpose for Evaluation of the Strong Nuclear Force and the Force of Gravity



2. Executive Summary



3. The Classical Physics Evaluation of Electrostatics and Gravity
1. The Electrostatic Repulsion Force
2. Newton’s Law of Gravity - The Attractive Force of Masses
3. Comparison of Electrostatic Repulsion and Gravitational Attraction



4. Nuclear Gravitation Field Theory:  Major Stumbling Blocks to Overcome



5. New Theory Results Must Equal Old Theory Results When and Where Applicable
1. Newton’s Law of Gravity as It Applies to Large Masses and Nuclear Gravitation Field Theory
2. Kepler’s Laws, Gravity, and Nuclear Gravitation Field Theory



6. Structure of the Nucleus of the Atom



7. The Schrodinger Wave Equation and Quantum Mechanics - The Particle and Wave Characteristics of Matter



8. Nuclear Gravitation Field Theory Versus Accepted Strong Nuclear Force Overcoming Electrostatic Repulsion



9. Comparison of the Nuclear Gravitation Field to the Gravitational Field of the Sun and the Gravitational Field of a Neutron Star



10. Quantum Mechanics, General Relativity, and the Nuclear Gravitation Field Theory



11. Properties of the Strong Nuclear Force, Nuclear Properties of Bismuth, and the Nuclear Gravitation Field Theory



12. Conclusion



13. Appendix A:  References



14. Appendix B:  Background of the Author

Index and Direct Hyperlinks to the Other Web Pages on this Website:

1. Gravity Warp Drive Home Page



2. Nuclear Gravitation Field Theory  (Specific Chapter Links are Provided on this Web Page)



3. Purchase e-Books



4. History of My Research and Development of the Nuclear Gravitation Field Theory



5. “The Zeta Reticuli Incident” by Terence Dickinson



6. Supporting Information for the Nuclear Gravitation Field Theory



7. Government Scientist Goes Public



8. “Sport Model” Flying Disc Operational Specifications



9. Design and Operation of the “Sport Model” Flying Disc Anti-Matter Reactor



10. Element 115



11. Bob Lazar’s Gravity Generator



12. United States Patent Number 3,626,605:  “Method and Apparatus for Generating a Secondary Gravitational Force Field”



13. United States Patent Number 3,626,606:  “Method and Apparatus for Generating a Dynamic Force Field”



14. V. V. Roschin and S. M. Godin:  “Verification of the Searl Effect”



15. The Physics of Star Trek and Subspace Communication:  Science Fiction or Science Fact?



16. Constellation:  Reticulum



17. Reticulan Extraterrestrial Biological Entity



18. Zeta 2 Reticuli:  Home System of the Greys?



19. UFO Encounter and Time Backs Up



20. UFO Testimonies by Astronauts and Cosmonauts and UFO Comments by Presidents and Top U.S. Government Officials



21. Pushing the Limits of the Periodic Table



22. General Relativity



23. Rethinking Relativity



24. The Speed of Gravity - What the Experiments Say



25. Negative Gravity



26. The Bermuda Triangle:  Space-Time Warps



27. The Wright Brothers



28. Website Endorsements and Favorite Quotes



29. Sponsors of This Website



30. Romans Road to Eternal Life In Jesus Christ

© Copyright Kenneth F. Wright, April 10, 2000.
All rights reserved.  No portion of this document may be
reproduced in any form without written permission of the author.