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It has been experimentally verified that energy in itself is not quantized because a photon can have any frequency and therefore any energy greater that zero or less than infinity. Additionally, the equation defining the relationship between mass and energy, E=m*c^2, also indicates that mass is completely convertible to one or more photons with energies greater than zero or less than infinity.
This is the basis for postulating in Chapter one that space is composed of four *spatial* dimensions and a continuous non-quantized form of mass and energy.
However, it can and will be shown that resonant systems or "structures" in a continuous non-quantized form of mass are responsible for the quantum properties of mass and energy.
First, we will define the mechanism responsible for generating the resonant "structures" of a quantum particle and then mathematically derive the density of a continuous non-quantized form of mass in a vacuum in terms of Planck's Length.
In Chapter one an analogy involving the formation of water particles in the earth's atmosphere was used to define the formation of a quantum particle.
Water vapor in the atmosphere condenses to create particles of fog.
This was shown to be analogous to a continuous non-quantized form of mass "condensing" to form quantum particles in space.
However, space also posses another physical property associated with water.
A particle or molecule of water is made up of a discrete resonant structure formed by the electrical properties of atoms of hydrogen and oxygen.
Similarly, a quantum particle is made up of a discrete resonant "structure" formed by the oscillatory properties of a continuous non-quantized form of mass.
In Chapter three it will be shown that the propagation of a photon is the result of a matter wave moving on a surface of a three dimensional space manifold with respect to a fourth *spatial* dimension. The oscillations caused by this matter wave on the "surface" of a three-dimensional space manifold with respect to a four *spatial* dimension is responsible for generating the resonant structure of all quantum particles.
(Louis de Broglie was the first to theorize that all particles had a wave component. His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer. However, this means there must be a continuous non-quantized medium for it to be propagated on because even the smallest possible particle must have a wave component. Therefore, there must exist a continuous non-quantized medium to propagate the wave of the smallest possible particle. However, macroscopic observations of wave energy indicate that it can only be propagated on a medium made up of mass. Therefore, the success of Louis de Broglie theory indicates that a continuous non-quantized form of mass exists.)
The mechanism responsible for the formation of the resonant "structure" of a quantum particle is similar to the mechanism responsible for the formation of all classically resonating systems.
In a closed classically resonating system a vibrational pattern is created in space when the inertial properties of a mass vibrate in a manner that allows the reflected waves from one end of the medium to interfere with incident waves from the source in such a manner that those specific points along the medium appear to be standing still.
Similarly, in a closed resonating "system" defining a quantum particle, a vibrational pattern is created in space by the inertial properties of a continuous non-quantized form of mass that allows the reflected matter wave to interfere in such a manner that specific points along the medium appear to be standing still.
How "vibrations" in a continuous non-quantized form of mass can generate the energy associated with a quantum particle can be understood by comparing it to the vibrations of a wave on the surface of water.
The trough of a standing wave on water displaces the vertical volume of water with air and the peak of the wave displaces the air above the surface of the water with water.
If space was composed of four *spatial* dimensions as was postulated earlier in Chapter one a matter wave in a continuous non-quantized form of mass could establish a resonate or "standing" wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
The trough of a "standing" matter wave on a "surface" of a three-dimensional space manifold would "displace" a continuous non-quantized mass component of space "below" a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension with a component of a fourth *spatial* dimension.
The peak of a resonant or "standing" matter wave on "surface" of a three-dimensional space manifold would "displace" a component of a fourth *spatial* dimension "above" a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension with a continuous non-quantized mass component of three-dimensional space.
Chapter Ten will derive all forms of energy in terms of a "displacement" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
Therefore, the displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension generated by a "standing" matter wave on a "surface" of a three-dimensional space manifold would be responsible for the internal energy associated with all quantum particles.
We will now derive the relative density of a continuous non-quantized form of mass in a vacuum in terms of the quantum fluctuations describe on page 169 of John A Wheeler's book, "At Home in the Universe" were he defines the fundamental length of a quantum particle to be universally constant and unchanging.
"There is only one truly fundamental length in nature a length free of all reference to the dimensions and rate of revolution of the planet on which we happen to live, free of any appeal to the complex properties of any solid or gas: free of every reference to the mysterious properties of any elementary particle: what we call today the Planck length,
L= (hG/C^3)1/2= 1.6X10^-33 cm
And what we identify with the characteristic scale of quantum fluctuations in the geometry of space".
Since the quantum fluctuations mentioned in John A Wheeler's book define the fundamental quantum component of a vacuum it can be used to define density of the continuous non-quantized mass in a vacuum.
In Chapter three the energy associated with the resonant vibrations in the continuous non-quantized form of mass responsible for the internal energy of a photon and all quantum particles will be derived in terms of the equation E=hf. Where “E” equals the energy of the photon “h” is Planck’s constant (6.547 X 10^-27 erg sec) and “f” is the frequency of the vibrations in the continuous non-quantized form of mass.
In classical physics the internal energy of resonant system is, in part, related to the kinetic energy associated with the velocity of the mass component of that system or 1/2mv^2.
This indicates the equation E=hf defining a photon's energy could be redefined in terms of the kinetic energy of a continuous non-quantized of mass component of a photon to be equal to 1/2mc^2=hf, where "m" equals the magnitude of the continuous non-quantized mass component of the photon.
However, a photon's energy is moving at the velocity of "c" with respect to an observer who is measuring the length of the "standing" matter wave that was shown earlier to be responsible for the quantum fluctuations mentioned in John A Wheeler's book.
Therefore, an observer must divide the observed length of a standing matter wave of a photon by the velocity of light "c" to define the physical length of a fundamental quantum fluctuation associated with a photon in terms of Planck's length.
This indicates the equation 1/2mc^2=(h/c)*f would define the length of the quantum fluctuations in a continuous non-quantized form of mass and energy responsible for the energy of a photon with respect to an observer who is stationary with respect to movement of a photon through space.
However, the value of Planck's length 1.6X10^-33 cm is the spatial length associated with Planck's constant.
Therefore the above equation can be rewritten, using the value for Planck's length and solving for "m", as m= 2*(1.6X10^-33 cm/c^3)f.
The minimum possible quantum fluctuation in space would have a frequency of one.
This means the density of a continuous non-quantized form of mass in a vacuum would be m=3.2X10^-33 grams/c^3sec or 3.2X10^-33 grams per cubic light second or a cube that has the dimensions of the distance light travels in one second.
“The
universe's most powerful enabling tool is
not knowledge or understanding
but
imagination"
Jeffrey O'Callaghan