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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 than 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.
The continuous properties of the electromagnetic spectrum and mass is the basis for hypnotizing, in Chapter one that space is composed a continuous non-quantized form of mass and four *spatial* dimensions instead of four dimensional space-time.
However, it can and will be shown the laws of classical mechanics suggest that resonant systems or "structures" would be generated in a continuous non-quantized form of mass and that they may be responsible for the quantum properties of mass and energy.
(The internal structure of quarks will be derived in Chapter nineteen in terms of an interaction between a continuous non-quantized mass component of space and the geometry of four *spatial* dimensions.)
There are 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.
In Chapter three it will be shown the wave characteristics of a photon could be explained and predicted in terms of a matterwave in a continuous non-quantized form of mass moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
However, the existence of four *spatial* dimensions would give a matterwave made up of continuous non-quantized form of mass 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, these oscillations in a continuous non-quantized form of mass caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in a continuous non-quantized form of mass. These resonant systems are known as particles.
The only way to dampen the frequency of a classically resonating system is to add or remove energy from that system which results in changing the characteristics of that system. If no energy is added or removed from a classically resonating system the characteristics of that system does not change.
(Louis de Broglie was the first to theorize 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. 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. 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.)
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 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
because it extends the reality of
one's environment.""
Copyright 1995 Jeffrey O'Callaghan
