"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 have “identical properties" except for their mass, which grows larger in each successive family” is related to the resonant "structures" that defined a fundamental quantum particle in Chapter two, and a mechanism defining mass in Chapters eight and twelve.

In Chapter one "Shadows" postulated a volume of space is composed of four *spatial* dimensions and a continuous non-quantized form of mass.

Later, in Chapter two, the quantum properties of mass and energy were derived in terms of the integral energies associated with resonant "structures" formed in space by "oscillations" in a continuous non-quantized form of mass.

In Chapter twelve, the relative mass of a macroscopic object, such as a star or planet was derived in terms of a quantity of a continuous non-quantized form of mass contained in a "depression" in "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  It was shown the magnitude of a mass was related to the magnitude of a spatial *separation* or "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

(This curvature caused by a "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension this paper postulates is responsible for the mass of an object is analogous to the space-time curvature the Einstein postulated is responsible for the mass of an object mass.)

In Chapter eight the relative masses of a proton and electron were derived in terms of the relative "separation" between two "surfaces" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Chapter ten derived all forms of energy, including gravitational, electrical and thermal, in terms of the relative magnitude of a spatial "separation" with respect to a fourth *spatial* dimension of two different "surfaces" of three-dimensional space manifolds.

Together Chapters eight, twelve and ten define the relative masses and the energy of all objects, such as stars and planets and quantum particles including the fundamental ones in terms of a common mechanism related to a "separation" between two "surfaces" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This means the relative masses of the families of the fundamental quantum particles in the above table would be dependent on energy content of the environment where they are created because as Chapter ten indicated, the energy content of an environment is one of the factors that determines the spatial "separation" between two "surfaces" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, Chapter two and ten showed the masses of fundamental quantum particles cannot take on any random value because the mass associated with the particles in each family would be the result of a resonant relationship between a continuous non-quantized form of mass and energy and the energy of the environment in which they were generated.

Therefore, because there are only specific points in space where a continuous non-quantized form of mass and energy and the energy content of their environment can resonant, each of the corresponding particle type across the three families must have a specific mass related to the energy of the environment in which they were created.

The particles in the first family are 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 are 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 of fundamental particles, 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 as shown in Chapter ten the higher-energy environments were they are generated in 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 than the particle in the preceding families.

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 the second family is greater then the "separation", with respect to a fourth *spatial* dimension, of the three-dimensional space manifold 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 the third family is greater then the spatial "separation", with respect to a fourth *spatial* dimension, of the three-dimensional space manifold associated with the second family.

This defines the mechanism responsible for the increase in mass of the fundamental quantum particles across the three families in terms of a "separation" in surface of a three-dimensional space manifold with respect to a fourth *spatial* dimensions and the resonant properties associated with a continuous non-quantized form of mass.

The corresponding particle types across the three families have similar electrical properties because as shown in Chapter nineteen the electrical properties of a fundamental quantum particle 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 electrical 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 defines the physical mechanism for “The corresponding particle types across the three families having identical properties except for their mass, which grows larger in each successive family”.

“The universe's most powerful enabling tool is
not knowledge or understanding
but imagination"
Jeffrey O'Callaghan

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