Richard Feynman on pages 24 and 25 of his book “The Character of Physical Laws†describes how both gravitational and electrical forces are linked in terms of a 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/(4.17 X 10^42) Now therein lies a very deep mystery. Where could such a tremendous number come from? 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.”
However, one may be able to show that gravity and electricity are different aspect of the same thing and derive “this fantastic ratio” if one extrapolates the laws of classical physics in a three-dimensional environment to a fourth *spatial* dimension as done in this blog.
Because as the article “Why is energy/mass quantized?” Oct. 4, 2007 showed one can derive the quantum mechanical properties of electrical forces by extrapolating the laws governing resonance in a three-dimensional environment to a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
There are four conditions required for resonance to occur in a classical Newtonian environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial.
The existence of four *spatial* dimensions would give the “surface” of three-dimensional space (the substance) the ability to oscillate spatially between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.
These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.
Therefore, these bi-directional oscillations in a “surface” of a three dimensional space would meet the requirements mentioned above for the formation of a resonant system or “structure” in space.
Observations of a three-dimensional environment show us the energy associated with resonant system can only take on the incremental or discreet values associated with a fundamental or a harmonic of the fundamental frequency of its environment.
Similarly the energy associated with resonant systems in four *spatial* dimensions could only take on the incremental or discreet values associated a fundamental or a harmonic of the fundamental frequency of its environment.
This shows that one can understand the origins of the quantum mechanical properties of an electromagnetic wave in terms of classical mechanics if one assumes that it is a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth “spatial” dimension.
However as the article “The Photon: a matter wave?” Oct. 1, 2007 one can also understand the origins electrical forces and their quantum mechanical properties by extrapolating the laws of classical wave mechanics in a three-dimensional environment to a matter wave moving on a “surface” of a three-dimensional space manifold with respect to fourth *spatial* dimension.
Briefly a wave on the two-dimensional surface of water causes a point on that surface to be become displaced or rise above or below the equilibrium point that existed before the wave was present. A force will be developed by the differential displacement of the surfaces, which will result in the elevated and depressed portions of the water moving towards or become “attracted” to each other and the surface of the water.
Similarly a matter wave on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension would cause a point on that “surface” to become displaced or rise above and below the equilibrium point that existed before the wave was present.
Therefore, classical wave mechanics, if extrapolated to four *spatial* dimensions tells us a force would be developed by the differential displacements caused by a matter wave moving on a “surface” of three-dimensional space with respect to a fourth *spatial* dimension which will result in its elevated and depressed portions moving towards or become “attracted” to each other.
This would define the causality of the attractive forces of unlike charges associated with the electromagnetic wave component of a photon because it tells us a force would be developed by a differential displacement of a point on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
However, it also provides a classical mechanism for understanding why similar charges repel each other because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement.
Similarly the magnitude of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by two similar charges will be greater than that caused by a single one. Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two similar charges than it would be for a single charge.
One can define the causality of electrical component of an electromagnetic wave in terms of the energy associated with the “peaks” and “troughs” that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement.
However, Classical Mechanics tells us a horizontal force will be developed by that perpendicular or vertical displacement which will always be 90 degrees out of phase with it. This force is called magnetism.
This is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls matter horizontally towards from the apex of that displacement.
This shows how one can understand electric and magnetic forces by extrapolating laws of classical mechanics in a three-dimensional environment to a displacement in a “surface” of a three-dimensional space with respect to a fourth *spatial* dimension.
The reason why electromagnetic forces are quantized is because as mentioned earlier its energy is propagated through space in quantized resonant systems defined in the article “Why is energy/mass quantized?”
However as the article “Gravity in four *spatial* dimensions” Dec. 15, 2007 showed one also can derive gravitational forces in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension by extrapolating the laws of classical physics in a three-dimensional environment to a fourth “spatial” dimension
One can understand how by comparing the forces on objects would experience in four *spatial* dimensions to those experienced by a marble on a rubber diaphragm with a rod pushing down it.
The surface of the diaphragm will represent the “surface” of three-dimensional space the marble, the energy/mass of an object and the rod will represent the “W†axis of a fourth *spatial* dimension.
(The “W” axis of the fourth *spatial* dimension was defined in the article “Embedded dimensions Oct. 27, 2007″)
If the end of the rod is orientated perpendicular to the “surface” of the diaphragm and is allowed to touch it without putting any pressure on it, the surface of the diaphragm will remain flat. The marble on the flat diaphragm would not move.
However, if pressure is applied to the rod, the “surface” of the diaphragm will become displaced and will no longer be perpendicular to the rod.
Gravitational forces will then have a tangential component along the displacement in the “surface” of the rubber diaphragm. The tangential component of the gravitational force directed along the “surface” of the diaphragm will cause the marble to move towards the apex of the depression
Similarly objects interacting with a displacement in “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension will experience a differential force directed towards the apex of that curvature. This force is called gravity.
(This curvature is analogous to the space-time curvature or displacement Einstein postulated is responsible for gravity.)
This would make gravitational and electrical forces different aspects of the same thing because it defines both in terms of the physical properties of a displacement in a “surface” of a three-dimensional space manifold with respect to a four *spatial* dimensions.
However, they also share a common property defined by the E=mc^2 because it defines the ratio of all forms of energy including electrical to the gravitational energy contained in mass.
If true one should be able to define a mechanism responsible for why “The ratio of the gravitational attraction to electrical repulsions is given by a number with 42 digits tailing off” in terms of the equation E=mc^2 and the fact that they are both have a common origin in a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
Solving the equation E=m*c^2 for “m” gives m=E/c^2. This would define the ratio of electrical to its gravitational energy/mass equivalent because as mentioned earlier it defines the ratio of electrical to the gravitational energy associated with mass.
The law of gravitation states that the forces between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them or m x m/d^2
If one then substitutes E/c^2 for “m†in that equation one gets F=(E/c^2)^2/r^2. This would define the ratio of the attractive properties of gravity to the repulsive properties of electrical energy in terms of the geometry of four *spatial* dimensions.
Using 3.0 x 10^10 cm/sec for the speed of light (c) and substituting we obtain for the ratio of electrical to gravitation forces to be F=E/(3.010^10 cm/sec)^4/r^2 or F=E/(8.1X 10^41 cm/sec).
This value represents 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 to electrical forces.
The theoretical result of 1/8.1 X 10^41 differs from the experimental value of 1/(4.17 X 10^42) because the equation of E=mc^2 that defines the ratio between gravitational and electrical energy tells us that some of the electrical energy in a system is derived from its mass or gravitational component. Therefore, one must subtract the quantity of the gravitational equivalent of the electrical forces associated with that mass from the above derived value to obtain the experimental value.
Therefore it appears one can 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 the same thing†if one assume as we have done they are both caused by a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension and answers Mr. Feynman’s question as to “how could they (gravitational and electrical forces) come in such disproportion”.
Later Jeff
Copyright Jeffrey O’Callaghan 2012