We have shown throughout the Imagineer’s Chronicles there would be many theoretical advantages to defining the universe in terms four *spatial* dimensions instead of four dimensions space-time. 

One is that it would allow one to derive a common mechanism responsible for all the forces found in nature by extrapolating observations made in a three-dimensional environment to a fourth *spatial* dimension.

Presently the Standard Model of Particle Physics links the strong and weak forces with electromagnetism through the abstract mathematical formulation called gauge symmetry.

However, for the past 50 years brightest minds in the scientist community have been unable to verify the integration of gravity through observations into its theoretical structure. 

There can be only two reasons for this.

The first is that nature has made the graviton or the gauge symmetric particle the proponents of standard model say is responsible of gravity so elusive as to make it undetectable with modern instrumentation. The second is that gauge symmetry is not responsible for gravity.

However as time goes by the first scenario becomes less and less creditable because with the increasing sensitivity of our measurement technologies and the ability modern computers to create accurate theoretical models that tell us exactly where to look for the graviton it is difficult to understand why it has not yet been observed.

Some say that the reason is because it interacts so weakly with matter that modern instruments are not sensitive enough to detect it even with, as mentioned earlier the recent exponential increase in their sensitivity.  However the proponents of the standard model will eventually have to face the reality that if it is not observed soon it may not exist and therefore the gauge symmetric foundation of the Standard Model is invalid with respect to gravitational forces.

Yet what is even more damaging to the creditability of the Standard Model is that there is an alternative explanation for the origins of the four forces that is based on the observable and therefore verifiable properties of a three-dimensional environment instead of on the unobservable abstract mathematical properties of gauge symmetry. 

As mentioned earlier one of the theoretical advantages to assuming space is composed of four *spatial* dimensions instead of four dimension space-time is that it would allow one to define a common mechanism responsible for the all of the forces of nature by extrapolating observations of a three-dimensional environment to a fourth *spatial* dimension.

For example in the article “The “Relativity” of four spatial dimensions” Dec. 1, 2007 it was shown that one 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 in a manner that makes prediction identical to those of General Relativity without having to assume existence of the graviton.

Later the article “What is electromagnetic energy” Sep 27, 2009 showed one can derive electromagnetic forces in terms of the displacement created by a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension by extrapolating the classical laws of three-dimensional wave mechanics to a fourth *spatial* dimension.

This would enable one to define a theoretical connection between electromagnetic and gravitational forces in terms of a displacement in a “surface” of a three dimensional space manifold with respect to a four *spatial* dimension.

For example 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 the force 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 will result in its elevated and depressed portions moving towards or become “attracted” to each other. 

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 electromagnetic radiation in terms of the energy associated with its “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 and why a theoretical model based on the existence of four *spatial* dimension instead of four dimensional space-time would allow one to derive a physical link between electromagnetic and gravitational forces because, as the articles “The “Relativity” of four spatial dimensions” and “What is electromagnetic energy” showed on can derive both in terms of a displacement in the “surface” of three-dimensional space by extrapolating the laws of classical mechanics in a three dimensional environment to a fourth *spatial* dimension. 

This cannot be done in terms of four-dimensional space time because a time or a space-time dimension is only observed to move in one direction forward and therefore could not support the bidirectional movement required to create a differential displacement.

However it also provides a method of linking electromagnetic and gravitational forces to their quantum mechanical properties because as the article “Why is energy/mass quantized?” Oct. 4, 2007 showed one can derive them by extrapolating the laws of classical 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. 

Briefly it showed 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 (the substance) to oscillate with respect to a fourth *spatial* dimension at 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.

Observations of a three-dimensional environment tell us that the energy of a resonant system can only take on the discrete or quantized values associated with the fundamental or a harmonic of its fundamental resonant

Similarly the energy of a resonant system in an environment consisting of four *spatial* dimensional environment could only take on the discrete or quantized values associated with the fundamental or a harmonic of a resonant system in that environment. 

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

Yet one can also derive theStrong and Weak forces by extrapolating the properties of resonance in three-dimensional environment to a fourth *spatial* dimension

The weak force manifests itself in the transmutation of a quark from one flavor or color to another when nuclear particles decays and is responsible for changing one quark to another quark, or a lepton to another lepton,

The mechanism responsible was for this was derived in the article the “The geometry of quarks” Mar 15, 2009.

Observations of particles indicate they 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 mechanism responsible for the fractional charge of quarks can be found in article “Embedded dimensions” which 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 is 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 be stable. 

As mentioned earlier the weak force manifests itself in the transmutation of a quark or lepton from one flavor or color to another when particles decay.

However this is what one would expect if their stability was related to, as shown 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. 

Therefore the weak force could be derived in terms of the force required to produce the lowest energy configuration possible by the transmutation or the change of a quark or lepton 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 between the components of three and fourth *spatial* dimensions. 

However, the fact the resonant interaction between the components of three and fourth *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 individual 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 of the positive charge of a proton. 

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. 

Yet this indicates that the magnitude of the strong nuclear force would be related to the size of the nucleus. 

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 neutron to uniformly share the energy require 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 unstable and 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 drop rapidly off as the distance from the nucleus increases.

This shows how one can derive mechanism responsible for the strong nuclear and weak forces by extrapolating the classical laws governing resonance in a three-dimensional environment to an environment consisting of four *spatial* dimensions.

However it also provide a physical link between them, gravitational and electromagnetic forces because it defines them in terms of a common mechanism associated with displacements in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension created by either the rest mass of an object or a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

Briefly the article “The “Relativity” of four spatial dimensions” extrapolated the laws of classical dynamics to derive gravitational forces in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension while the article “What is electromagnetic energy” Sep 27, 2009 derived electromagnetic forces in terms of the differential displacements created by a matter wave moving on a “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension.  Additionally the article “Why is energy/mass quantized?” showed one can also derive their quantum mechanical properties and those of  energy/mass and by extrapolating the laws governing resonance in a classical three-dimensional environment to a matter wave in four *spatial* dimensions while as was just shown the strong and weak forces can also be derived in terms of a resonant properties associated with a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension

This demonstrates that if one assumes as was done here that space is composed of four *spatial* dimension instead of four dimension space-time one can theoretical unify the four forces of nature by extrapolating the classical laws of a our three-dimensional environment to displacements in  a “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

 

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