We have shown throughout the Imagineer’s Chronicle that one can derive all the forces of nature by extrapolating the classical laws governing a three-dimensional environment to one made up of four *spatial* dimensions.

If so one should be able to define the weak force in those terms.

The weak force is responsible for changing to one quark to another or a lepton to another lepton – the so-called "flavor changes" when particles undergo radioactive decay. In Physics speak the weak interaction involves the exchange of the intermediate vector bosons, the W and the Z.

Earlier in the article "Why is energy/mass quantized?" Oct. 4, 2007 it was shown that one can derive the quantum mechanical properties of energy/mass by extrapolating the laws of classical resonance in three-dimensional space to a matter wave on a surface of a three dimensional space manifold with respect to four *spatial* dimension.

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

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.

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 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 at 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 four *spatial* dimensions.

These resonant systems are responsible for the quantum mechanical properties energy/mass.

Later in the article "The geometry of quarks” Mar. 15, 2009 it was shown that one can understand why a particle is made up of three quarks of different "colors" again by extrapolating the geometric of three-dimensional space to a fourth while the article "Embedded dimensions" Oct. 22. 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.

Using the concepts developed in those articles one derive the mechanism responsible for why observe of particles are made up of distinct components called quarks of which there are six types, the UP/Down, Charm/Strange and Top/Bottom. The Up, Charm and Top have a fractional charge of 2/3. The Down, Strange and Bottom have a fractional charge of -1/3. Scientists have also determined that quarks can take on one of three different configurations they have designated by the colors red, blue, and green.

The explanation is based in part on the fact that 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" 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.

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 stable.

This suggests that the stability of the energy/mass components of particles are related to a resonant interaction between the components of three and fourth *spatial* dimensions.

As mentioned earlier the weak force manifests itself in the transmutation of a quark from one flavor or color to another when nuclear particles decays and manifest itself by changing one quark to another, or a lepton to another lepton, the so-called "flavor or color changes".

However this is what one would expect if their stability was related to, as mentioned above the geometric configuration of their central axis because the only thing that distinguishes their color or flavor is how their central axes in the fourth *spatial* dimension orientated with respect to three-dimensional space. If the individual quark components of a particle were not in the lowest energy configuration they would rotate around that axis until they were.

However, as mentioned earlier a particle’s stability is related to how the central axis of its component quarks are oriented with respect to a fourth *spatial* dimension. Therefore the weak force could be defined in terms of the energy associated with their most stable geometric configuration. In other words to form a stable particle the central axis of its quarks would have to rotate around their fourth dimensional axis until the particle they were a part of had obtained the lowest geometric energy configuration possible with respect to a fourth *spatial* dimension.

Hence one could derive the casualty of the transmutation or the flavor or color change of quarks from to another in terms of the reconfiguration of its central axis with respect to a fourth *spatial* dimension required to form a stable particle.

This is analogous to the central axis of a wind vane rotates in three-dimensional towards the direction of the wind to reduce the amount of force or energy on its two-dimensional surface by the wind.

Similarly the three-dimension axis of quarks will rotate in four *spatial* dimensions to reduce the energy content of a particle to its lowest level.

As mentioned earlier the binding energy holding quarks together is dependent on the resonant interaction their central axis. Therefore, magnitude of weak nuclear force binding them together would be associated with the flavor or color change that occurs when an atomic decay takes place.

The reasons the weak force manifests itself in the exchange the vector particles called the W and Z bosons is because as was shown in the article "Why is energy/mass quantized?" all energy is propagated in discrete resonant structures. Therefore, it will have particle properties that article associates with them.

This shows how one can derive mechanism responsible for the weak force by extrapolating the classical laws governing resonance in a three-dimensional environment to one made up of four *spatial* dimensions.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

## 1 Comment to “The weak force in four *spatial* dimensions”

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Great story over again. I am looking forward for more updates=)