We have shown throughout the this blog and its companion book “The Reality of the Fourth *Spatial* Dimension” there would many theoretical 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 derive a physical link between gravity and the strong and weak forces by extrapolating the classical laws governing resonance in a three-dimensional environment to a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
(Louis de Broglie was the first to theorize that all particle and forces have a matter wave component. His theory was confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer;)Â
In the article “The “Relativity†of four spatial dimensions” Dec. 1, 2007 it was shown that one can derive gravity in terms of a continuous curvature or displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension in a manner that makes prediction identical to those of General Relativity.
One of the advantages to using this theoretical approach is that it would allow one to derive a physical link between it and the quantum mechanical properties of energy/mass because as was shown in the article “Why is energy/mass quantized?” Oct. 4, 2007 one can derive its quantum mechanical properties in terms of a resonant system generated by the displacements associated with a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Â
Briefly it was shown the four conditions required for resonance to occur in a classical 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 be meet by a matter wave in an environment consisting of four *spatial* dimensions.Â
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* dimensions thereby fulfilling one of the requirements for classical resonance to occur.
These displacements or oscillations with respect to a fourth *spatial* dimension 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.
The oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established in four *spatial* dimensions.
Classical mechanics tells us the energy of a resonant system can only take on the discrete quantized values associated with their fundamental or a harmonic of their fundamental frequency.
Similarly these resonant systems in four *spatial* dimensions would be responsible for the quantum mechanical properties energy/mass because they could only take on the values associated with fundamental or a harmonic of its fundamental frequency.
Earlier it was mentioned that one can define gravitational energy in terms of a continuous curvature in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.Â
However the article “Embedded dimensions” Oct. 22, 2007 also 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.
This would allow on to define a physical link between gravity, the quantum mechanical properties of energy/mass, and the weak force can be understood by integrating their geometric properties to the one responsible for the fractional charges of quarks as was done in the article “The geometry of quarks” Mar. 15, 2009.
Briefly it was showed one can derive the 2/3 fractional charge of the Up, Charm and Top and the 1/3 charge of UP/Down, Charm/Strange and Top/Bottom and 1/3 charge of The Down, Strange and Bottom in terms of the geometry of four spatial dimensions.Â
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.Â
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” Oct. 4, 2007 there are three ways the individual axis of three-dimensional space can be oriented with respect to a fourth *spatial* dimension. Therefore, the configuration or “colors” of each quark may be related to how its energy is distributed in three-dimensional space with respect to a fourth *spatial* dimension.Â
However, it also explains why it takes three quarks of different “colors” to form a 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 be stable.Â
The weak force manifests itself in the transmutation of a quark from one flavor or color to another when they decay with emission or absorption of W and Z bosons.
However this is what one would expect if their stability was related to, as shown above to the geometric configuration of their central axis because the only thing that distinguishes their color or flavor is how their central axes is oriented with respect to four *spatial* dimensions. If the individual quark components of a particle were not in the lowest energy configuration they would rotate around that axis until they were.Â
However, as mentioned earlier a quark’s color is related to how its central axis is oriented with respect to a fourth *spatial* dimension. Therefore the weak force could be defined as the energy required to produce the transmutation or the change of a quark from one flavor or color to another by the rotation of its central axis with respect to a fourth *spatial* dimension.
This suggests that the stability of the energy/mass components of particles such as a proton and neutrons are related to a resonant interaction of the displacements in components of three and fourth *spatial* dimensions.Â
One can also understand why a “W” or “Z” boson is either emitted or absorbed during the transmutation quarks in terms of the particle properties of the resonant system defined earlier in the article “Why is energy/mass quantized?” Oct. 4, 2007
In other words the same mechanism responsible for the quantum mechanical properties of energy/mass is also responsible for the particle properties of the forces associated with the “W” and “Z” boson.
However, the fact the resonant interaction between the components of three and four *spatial* dimensions is strong enough overcome the repulsive electrical energy of the two up Quarks in a proton also defines the causality of the strong force and the stability of a nucleus.
The strong force is a result of the spatial separation between the protons in a nucleus becoming small enough so the excess resonant binding energy associated with their dimensional properties can interact. The sharing of this excess binding energy allows the up quark of one of the adjacent protons to be replaced with a down quark resulting in the formation of a neutron consisting of one up quark and two down quarks
However, the addition of a neutron to a nucleus adds the excess binding energy associated with its resonant system without the repulsive effects associated with the positive charge of a proton.Â
Therefore, the existence of neutrons in a nucleus allows for creation of larger ones consisting of multiple positively charged protons because they add the binding energy associated with their resonant system without adding any repulsive electrical charge.Â
Yet this indicates that the magnitude of the strong nuclear force would be related to the size of the nucleus.Â
The size or diameter of a nucleus increases as is the atomic weight increases.
However, after a certain atomic weight is reached a nucleus will become physically too large for the individual resonant “structures” associated with the protons and neutrons to uniformly share the energy required to maintain its structure. This will result in that nucleus expelling the energy/mass required to reduce its physical size to a point where a stable nucleonic structure can be maintained. Therefore, any nucleus that is physically larger than this critical value will be radioactive.
Additionally, the nucleus of atoms that have an atomic weight less than the critical value would increase its weight and size by “absorbing” energy/mass from an external source. This will result in increasing the size and atomic number of that nucleus.
This indicates that the effectiveness of the strong nuclear force in absorbing or emitting energy/mass would only be effective on length-scales of the atomic nucleus and would drop rapidly off as the distance from the nucleus increases.
This shows how one can derive the mechanism responsible for the quantum mechanical properties of energy/mass, the strong and weak forces by extrapolating the classical laws governing resonance in a three-dimensional environment to the oscillatory displacements associated with a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
However as mentioned earlier the article “The “Relativity†of four spatial dimensions” Dec. 1, 2007 it was shown that one can also derive gravitational energy in terms of a displacement in a continuous “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension in a manner that makes prediction identical to those of general relativity.
Therefore One can establish a link between it, and the strong and weak forces in terms of the continuous properties of four *spatial* dimensions because of the fact that the matter wave defining the resonant system responsible for the strong and weak forces is by definition continuous which means the geometry supporting it must also be continuous. Therefore this define a link between them in terms of the continuous geometry of four *spatial* dimensions.
This demonstrates how one can derive a theoretical connection between the strong and weak forces and gravity in terms of the continuous geometric properties of a “surface” of a three-dimensional space with a fourth *spatial* dimension.Â
Later Jeff
Copyright Jeffrey O’Callaghan 2011