The geometry of the fundamental particles

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As Brian Greene pointed out in his book “The Elegant Universe“, one of the unsolved mysteries of modern particle physics is why every fundamental particle encountered to date can be group into three families.

“Physicists have recognized a pattern among these particles displayed in the following table.  The matter particles neatly fall into three groups, which are often called families.  Each family contains two of the quarks an electron or one of its cousins and one of their neutrino species.  The corresponding particle types across the three families have identical properties except for their mass, which grows larger in each successive family.”

The answer to Brian Greene’s question regarding why the particles in the above table can be group into three families is related to the resonant “structures” that defined their quantum mechanical properties in the article “Why is energy/mass quantized?” Oct. 4, 2007.
We have shown throughout the this blog that observations of our environment suggest space is composed of a continuous non-quantized field of energy/mass and four *spatial* dimensions while the article “Why is energy/mass quantized?” showed that one can derived its quantum mechanical properties by extrapolating the laws governing classical resonance in a three-dimensional environment to one of  four *spatial* dimension.  

(Louis de Broglie was the first to predict the existence of a continuous non-quantized form of energy/mass 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 showed that 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 in one consisting of four.

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 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 four *spatial* dimensions.

Classical mechanics tells us that resonant systems can only take on the discrete or quantized energies associated with a fundamental or a harmonic of their fundamental frequency

Therefore, these resonant systems in a continuous non-quantized field of energy/mass would define the quantum mechanical properties of energy/mass.

Yet if true, one should be able to derive the relative masses of each family member by extrapolating the laws governing classical resonance in three-dimensional environment to one made up of four because as was shown in the article “Defining energy” Nov 27, 2007 one can also derive all forms of energy, including gravitational, electrical and thermal, in terms of a displacement in the “surfaces” of a three-dimensional space with respect to a fourth *spatial* dimension.

Therefore one would define the temperature or energy content of the environment a particle occupies in terms of a displacement in a “surface” of a three-dimensional space manifold.

As mentioned earlier the article “Why is energy/mass quantized?” showed the mass of a particle is related to the energy contained within a resonant system generated by a matter wave on that “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore using the concepts developed in those article one could derive the total mass of a particle in terms of the sum of the energies associated with that resonant structure and the displacement in the “surface” of three-dimensional space associated with the energy of the environment it is occupying.

Yet Classical Mechanics tells us there will be specific points in space where the matter wave that Louis de Broglie associated with a particle the can interact with the energy content or temperature of its environment to form a resonant system.

Therefore, the mass of each family member would not only be dependent on the energy associated with the resonant system that defined their quantum mechanical properties in the article “Why is energy/mass quantized?” but also on temperature of the environment they are occupying.

Thus suggest the reason “The corresponding particle types across the three families have identical properties except for their mass, which grows larger in each successive family.” is because of an interaction between the resonant properties defined in the article “Why is energy/mass quantized?” and the energy content of the environment they are occupying.

This means the particles in the first family would be found in relativity low energy environments, are relatively stable, and for the most part can be observed in nature.  However, the particles in the second and third families would be for the most part unstable and can be observed only in high-energy environments of particle accelerators.  The exception is the Muon in the second family, which is only observed in the high-energy environment of cosmic radiation.

The relative masses of the fundamental particles increases in each successive family because the higher-energy environments where they occupy would result in the corresponding particles in each successive family to be formed with a greater relative “separation” in the “surfaces” of a three-dimensional space manifold with respect to a fourth *spatial* dimension..

Therefore, the corresponding particles in the second family will have a greater mass than the particles in the first family because the “separation”, with respect to a fourth *spatial* dimension of the three-dimensional space manifold associated with them is greater than the “separation” associated with the first family.

Similarly, the corresponding particles in the third family will have a greater mass than those in the second family because the “separation”, with respect to a fourth *spatial* dimension, of the three-dimensional space manifold associated with them is greater than the spatial “separation” associated with the second family.

Additionally the corresponding particle types across the three families have “identical properties” because as shown in the article “The geometry of quarks” Mar. 15, 2009 they are related to the orientation of the “W” axis of the fourth *spatial* dimension with the axis of three-dimensional space.  Therefore, each corresponding particle across the three families will have similar properties because the orientation of the “W” axis of the fourth *spatial* dimension with respect to the axis of three-dimensional space is the same for the corresponding particles in all of the families.

This explains why “The corresponding particle types across the three families having identical properties except for their mass, which grows larger in each successive family” in terms of the properties of classical resonance and the existence of four *spatial* dimensions.

Jeff

Copyright Jeffrey O’Callaghan 2010

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