We have shown throughout "The Imagineer’s Chronicles" that there would be many advantages to defining the universe in terms of four *spatial* dimensions instead of four-dimensional space-time.
One is that it would allow one to understand in terms of classical mechanics the origin of the fractional electrical and color properties Quantum Chromodynamics associates with quarks.
Quantum Chromodynamics, which is an integral part of the Standard Model of Particle Physics, defines how quarks interact with themselves and each other to form particles such as protons and neutrons. The word quantum stands for the fact that interactions (forces between particles) on this level can be represented as things that occur only in chunks called quarks. The word Chromodynamics stands for the color properties it associates with them.
To this point physicists have identified six types of quarks, called the UP/Down, Charm/Strange and Top/Bottom. The Up, Charm and Top have a fractional charge of 2/3 while the Down, Strange and Bottom have a fractional charge of -1/3.
They assume each quark carries a charge called "color" which like electric charge is always conserved. However, unlike electric charge, the color charge (the chromo in Chromodynamics) comes in three varieties or red, green, and blue and that each quark comprising a particle must have a different color, red, green, or blue.
The reason is because Pauli’s exclusion principle says no particle can be made up of components with identical quantum states. They incorporate this principal into Quantum Chromodynamics theoretical structure by assigning a color to individual quarks and adopting a rule that says for a stable particle to exist the colors of their components must combine to make a colorless particle. This requires particles to conform to Pauli’s exclusion principle because colorless or white light only exist if it is made up of one part red, blue, and green light. Therefore a stable particle can only exist it is made up of three different types of quarks with colors of red blue and green.
However as of yet no one has been able to define a physical mechanism responsible for fractional charge or the color component of quarks.
Yet as was show in the article "The geometry of quarks" Mar. 15, 2009 one can derive a physical reason for their fractional charge and color properties if one assumes as was done in the article “Why is energy/mass quantized?” Oct 4, 2007 that the quantum mechanical properties of energy/mass can be derived in terms of a resonant structure formed by a matter wave on "surface" a three-dimensional space manifold with respect to a fourth *spatial* dimension.
Briefly that article showed the 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 would occur in four spatial dimensions.
The existence of four *spatial* dimensions would give space (the substance) the ability to oscillate spatially on a "surface" 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 oscillations in 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 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.
These resonant systems in four *spatial* dimensions are responsible for the incremental or discreet energy associated with quantum mechanical systems.
The only way to dampen the frequency of a classically resonating system is to add or remove energy from it, which results in changing the characteristics of that system.
Additionally the energy in a classically resonating system is, as mentioned earlier is discontinuous and can only take on the discrete values associated with its fundamental or harmonic of its fundamental frequency.
However, these properties of a classically resonating system are the same as those found in a particle in that they are made up of discreet or discontinuous packets of energy/mass and when energy is either added or removed from it, its characteristics changed.
But if space was made up of four *spatial* dimensions one should also be able to explain why quarks have a fractional charge and how their color properties interact to form stable particles in terms of the geometry four *spatial* dimension.
The article Defining energy Nov. 26, 2007 showed it is possible to define all forms of energy including electrical in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
However, we as three-dimensional beings can only observe three of the four *spatial* dimensions. Therefore, the energy associated with a displacement in its "surface" with respect to a fourth *spatial* dimension will be observed by us as being directed along that "surface". However, because two of the three-dimensions we can observe are parallel to that surface we will observe it to have 2/3 of the total energy associated with that displacement and we will observe the other 1/3 as being directed along the signal dimension that is perpendicular to that surface.
This means the 2/3 fractional charge of the Up, Charm and Top may be related to the energy directed along a "surface" of a displaced three-dimensional space manifold with respect to a four *spatial* dimension while the -1/3 charge of The Down, Strange and Bottom may be associated with the energy that is directed perpendicular to that "surface".
The reason why quarks come in three configurations or colors with a fractional charge of 1/3 or 2/3 may be because, as was shown in the article Embedded Dimensions Nov. 22, 2007 there are three ways the individual axis of three-dimensional space can be oriented with respect to a fourth *spatial* dimension. Therefore, the geometric configuration or "colors" of individual quarks may be related to how its energy is distributed in three-dimensional space with respect to a fourth *spatial* dimension.
However, it may also explain why it takes three quarks of different "colors" to form a stable particle because, as mentioned earlier one can define a particle in terms of a resonant system on a "surface" a three-dimensional space manifold with respect to a fourth *spatial* dimension. If the colors of each quark represent the central axis associated with its charge then to form a stable resonate system would require three quarks that have different central axis to balance its energy with respect to the axes of three-dimensional space. A particle could not exist if two quarks have the same central axis or color because it would cause an energy imbalance along that axis. Therefore, a particle consisting of anything but quarks of three different colors would not stable.
This shows how one can put the color and therefore the Chromo in Quantum Chromodynamics by assuming that space is composed of four *spatial* dimensions instead of four dimensional space-time.
Copyright 2012 Jeffrey O’Callaghan
2007 thru 2010 Paperback