One is that it would allow one to understand why a proton and an election have different masses even though the absolute magnitude of their charge is the same in terms of the laws of classical three-dimensional space.
In the article “Why is energy/mass quantized?” Oct. 4, 2007 it was showed one can derive its quantum mechanical properties by extrapolating the laws of classical resonance in a three-dimensional environment to a matter wave in a continuous non-quantized field of energy/mass moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

(Louis de Broglie was the first to predict the existence of a continuous field of energy/mass when he theorized that all particles had a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.)

Briefly it showed the four conditions required for resonance to occur in a classical three-dimensional 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 would occur in one consisting of four *spatial* dimensions.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimension 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.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established in a continuous field of energy/mass. 

Classical mechanics tells us the energy of a resonant system can only take on the discrete quantized values associated with its resonant or a harmonic of its resonant frequency.

The article “Why is energy/mass quantized?” showed why these resonant systems in four *spatial* dimensions are responsible for the discrete quantized energies associated with protons and electrons.

However, one can also use the above concept of four *spatial* dimensions to understand the physical boundaries of a proton and electron.  

In classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space. 

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate “up” or “down” with respect to a fourth *spatial* dimension.

The confinement of the “upward” and “downward” oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries associated with a particle in the article “Why is energy/mass quantized?“

(The internal structure of quarks, a fundament component of particles was derived in the article “The geometry of quarks” Mar. 15, 2009 in terms of an interaction between a continuous energy/mass component of space and the geometry of four *spatial* dimensions.)

Meanwhile in the article “The reality of the fourth *spatial* dimension” Dec. 1, 2010 it was shown that one can derive all forms of energy including gravity in terms of a displacement or curvature 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 “The General Theory of Relativity” hypothesized is responsible for gravitational energy.

One advantage, as will be shown below to defining the universe in terms of four *spatial* dimensions is that allows for a bidirectional spatial movement of a “surface” of a three-dimensional space manifold whereas defining it in terms of four dimensional space-time does not.  This is because one can move in two directions up or down, forwards or backwards in a spatial dimension but in only one direction, forward in a time dimension.

For example in the article “Electromagnetism in four *spatial* dimensions” Sept. 27, 2007 showed one can derive the polarity and absolute magnitude of the charge on a proton and electron in terms of a bidirectional displacement of a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

It derived the positive charge of a proton in terms of a “downward” displacement  in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  While the negative the charge of an electron will be derived in terms of oppositely directed “upward” displacement in that surface.

One can understand how these displacements would define their electrical properties by extrapolating the laws of classical mechanics of displacements in water to it.

Classical mechanics tell us that if one lifts a bucket full of water or pushes down on an empty one a force will be developed that will cause the bucket raised above or the one that was pushed down below its surface to move or become “attracted” to its surface.

Similarly if one lifts or pushed down on a “surface” of three-dimensional space manifold a force will be developed that will cause the raised or depressed regions to become attracted to its surface.

Therefore, one could derive why the unlike charges attract each other in terms of a classical mechanism if one assumes that they are a result oppositely directed of a displacement  in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

Additional classical mechanics also tells us there is a direct relationship between the magnitudes of a displacement in the surface of water to the magnitude of the energy resisting that displacement.

For example the force resisting the further displacement of an empty bucket in water is directly related to the depth of that displacement.

This defines why like charges repel each other because the displacement in a “surface” of a three-dimensional space manifold 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 energy resisting the displacement will be greater for two identical charges than it would be for a single charge.

The mechanism responsible for generating this movement was defined in the article “The reality of the fourth *spatial* dimension” were it was shown when mass is converted to energy or energy to mass, the “surface” of a three-dimensional space manifold either “expands” or “contracts” with respect to a fourth *spatial* dimension.  This would result in the movement of that “surface” respect to it.

The effects these movements have on the density of continuous energy/mass component of the resonant systems that defined the quantum mechanical properties of a proton and electron in the article “Why is energy/mass quantized?” are analogous to the effects high and low pressure areas in the earth’s atmosphere have on density of air molecules.

In a high-pressure area, the energy of air molecules is directed downwards towards the surface of the earth.  This results in the density of the air molecules at the apex of a high-pressure area to be greater than their density in the volume of air adjacent to it.

Conversely, in a low-pressure area the energy of the air molecules is directed upward away from the surface of the earth which results in their density at the apex of a low-pressure area to be less than the density of the air molecules in the volume of air adjacent to it.

A similar effect would occur in space with respect to the density of their continuous energy/mass component

In a dimensional “high-energy volume” associated with the positive charge of a proton, the energy of the continuous energy/mass component of space would be directed “downward” with respect to a fourth *spatial* dimension, towards the “surface” of a three-dimension space manifold.  This results in its density in the resonant system of a proton to be greater relative to its density in the volume adjacent to it.

This is analogous to how the air molecules at the apex of a high-pressure area in the earth’s atmosphere would be denser than the air molecules in the volume of air adjacent to the apex of a high-pressure area.

Conversely in a dimensional “low-energy volume” associated with the negative charge of an electron, the energy of the continuous energy/mass component of space would be directed “upward” with respect to a fourth *spatial* dimension, away from the “surface” of a three-dimension space manifold.  This results in its density in the resonant system of an electron to be less relative to its density in the volume adjacent to it.

Therefore, the density of the continuous energy/mass component of the resonant system of a proton will be greater than that of an electron even though the absolute magnitude electrical energy or charge is the same.

This is analogous to why the density of air molecules in a high-pressure area is greater that in a low-pressure area even though the magnitude of their energy is same but oppositely directed.

In the article “Gravity and electromagnetism linked in four *spatial* dimensions” Dec 14, 2007 it was shown that the mass of a particle or object is directly related to the density or concentration of the continuous field of energy/mass contained in the volume of a particle or object.

Therefore because the density, as mentioned earlier of the continuous non-quantized field of energy/mass is greater in a proton than that of an electron its mass will also be greater than that of an electron.

This shows that one of the theoretical advantages to define the space in terms of a continuous field of energy/mass and four *spatial* dimensions instead of four dimensional space time is that it would allow one to understand why the relative mass of a proton is greater than that of an electron even though the absolute magnitude of their charge is the same by extrapolating the laws of a classical environment to four *spatial* dimensions.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

The post The relative masses of a proton and electron appeared first on Unifying Quantum and Relativistic Theories.