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The Imagineer's Chronicles: A theoretical blog
Chapter Fourteen
A link between gravitational and electrical forces can be established by analyzing a physical relationship between a continuous non-quantized form of mass responsible for gravitational forces and a slope of a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimensions responsible for electrical forces
Chapter one postulated space is composed of four *spatial* dimensions and a continuous non-quantized form of mass.
Chapter twelve derived gravitational forces in terms of the quantity of a continuous non-quantized form of mass contained a curvature or "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth "spatial" dimension.
(This curvature is analogous to the space-time curvature Einstein postulated is responsible for the force of gravity.)
Chapter nine derived electrical forces in terms of the energy associated with a slope of a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension
Chapter two defined the physical relationship between a continuous non-quantized form of mass and the energy associated with a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension in terms of the equation E=mc^2.
This indicates that gravitational and electrical forces share a common physical link in terms of a curvature in "surface" of a three-dimensional space manifold and the relationship defined by the equation E=mc^2.
However, as Richard Feynman points out on pages 24 and 25 of in his book “The Character of Physical Laws” both gravitational and electrical forces also share another common relationship with respect to the inverse square law.
"The inverse square law appears again in the electrical laws, for instance, Electricity also exerts forces inversely as the square of the distance, this time between charges, and one thinks perhaps that the inverse square of distance has some deep significance. No one has ever succeeded in making electricity and gravity different aspects of the same thing."
Later he talks about the ratio of gravitational attraction to electrical repulsions:
"The ratio of the gravitational attraction to electrical repulsions is given by a number with 42 digits tailing off. (The exact number was given in a diagram as Gravitation attraction / Electrical repulsion = 1/(417 X 10^42) Now therein lies a very deep mystery. Where could such a tremendous number come form? If you ever had a theory from which both of these things are to come how could they come in such disproportion? What equation has a solution which has for two kinds of forces an attraction and repulsion with that fantastic ratio."
The solution of the equation defining why the ratio of gravitational attraction to electrical repulsions have such a "fantastic ratio" can be found by analyzing the relationship between mass and electrical forces defined in Chapter two in terms of the equation E=mc^2. Were "E" equals the magnitude of the "slope" in four-dimensional space "m" equals the magnitude of the continuous non-quantized form of mass associated with a slope in four-dimensional space and "c" equals the speed of light.
Therefore, one should be able derive an equation that will define “The ratio of the gravitational attraction to electrical repulsions” in terms of the equation E=mc^2.
Solving the equation E=m*c^2 for "m" or the continuous non-quantized form of mass responsible for gravitation forces gives m=E/c^2.
The law of gravitation states that F=g*m*m/r^2.
Substituting the equation that defines the magnitude of a continuous non-quantized form of mass in terms of the electrical energy of associated with that mass or E/c^2 into the equation that defines the law of gravitation F=g*m*m/r^2 gives F=(E/c^2)^2/r^2.
Since, as mentioned earlier the quantity of a continuous non-quantized form of mass in a "depression" in a "surface" of a three-dimensional space manifold is responsible for gravitational forces and the slope in the "surface" of a three-dimensional space manifold is responsible for electrical energy, the equation F=(E/c^2)^2/r^2 would define the ratio of the magnitude of gravitation force to the magnitude of the electrical energy associated with that continuous non-quantized form of mass.
Using 9.0 x 20 cm/sec for the speed of light (c) squared and substituting we obtain F=E/(9.0 X 20)^2/r^2 or F=E/(8.1 X 10^41).
The value of 1/(8.1 X 10^41) represents the value of the ratio of “Gravitation attraction / Electrical repulsion” Richard Feynman was referring to in the earlier quote from his book “The Character of Physical Laws” because it numerically defines the ratio of gravitational energy to electrical energy.
However it appears to have solved the “very deep mystery” as to why the inverse square law can be applied to both gravitational and electric forces by “making electricity and gravity different aspects” of a common interaction between a continuous non-quantized form of mass responsible for gravitation force and the slope of a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension responsible for electric force and answered Mr. Feynman's question as to "how could they (gravitational and electrical forces) come in such disproportion".
“The
universe's most powerful enabling tool is
not knowledge or understanding
but
imagination"
Jeffrey O'Callaghan