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However, it can be shown the uncertainty of the position and momentum of a particle is physically related to the internal structure of the resonant system that defines a particle in Chapter two.
Chapter one postulated a volume of space is composed of four *spatial* dimensions and a continuous non-quantized form of mass.
In Chapter two, a particle was defined in terms of a resonant system or "structure" formed in space by oscillations in a continuous non-quantized form of mass.
Chapter three showed the energy or momentum of a particle is related to oscillations in a continuous non-quantized form of mass generated by a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
(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.)
Therefore, both the momentum and position of a particle is related to a matter wave in a continuous non-quantized form of mass.
This is because, as was shown in Chapter Three momentum of a particle is related to the wavelength of a matter wave in a continuous non-quantized form of mass. While, as was shown in Chapter two the position of a particle is related to where in space resonant "structure" associated with the matter wave component of that particle can be found. However, the probability of finding a specific value for the momentum of a particle is dependent on the energy distribution of the matter wave that defines its energy while the probability of finding a specific value for the position of a particle will be dependent on the spatial distribution of the resonant system that defines it position.
The uncertainty involved in simultaneously measuring both the momentum and position of a particle is related to fact that both of their values are dependent on the same matter wave in a continuous non-quantized form of mass.
The accuracy of a measurement is determined by how much of the measurement parameter is accessed. For example, one must access more of the wavelength component of the matter wave responsible for the momentum of a particle as he or she increase the accuracy of the measurement of its momentum.
However, this means that there is less of the matter wave responsible for a particle's position accessible for measurement, thereby increasing its uncertainty.
This is because the same matter wave responsible for a particle's momentum is also responsible for generating the resonant system responsible for a particle's position. Therefore if a portion of it is used to measure its momentum there will be less available to measure its position thereby making that measurement less accurate
Similarly, one must access more of the resonant system responsible for the position of a particle as he or she increase the accuracy of the measurement of its position.
However. because the resonant system associated with a particle's position is generated by a matter wave, there will be less of the matter wave component accessible for the measurement of its momentum, thereby increasing its uncertainty.
This means the uncertainty involved in the simultaneous measurement of the position or momentum of a quantum particle or "The Heisenberg's uncertainty principle" is due to the internal structure of a particle and the existence of a matter wave in a continuous non-quantized form of mass.
Additionally defining particle such as an electron in terms of a resonant "structure" in a continuous non-quantized form of mass as was done in Chapter two, also explains why quantum particles appear to randomly "move" or "jump" to different positions in space without ever moving though the intervening space.
An electron can "jump" from one atomic orbital to the next without going thought the intervening space because the resonant "structure" associated with an electron does not move from one atomic orbital to the next.
Instead the resonant "structure" associated with an electron collapses in its initial atomic orbital and is then reformed in a new atomic orbital. Because no resonant system is generated in the intervening space between the atomic orbital no electrons will be found there.
Defining a quantum particle in terms of resonant system formed by matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension also provides a physical mechanism responsible for probability of finding an electron at a certain position or Schrödinger's probability wave function.
This is because the position of an electron in an atomic orbital would be dependent on how the energy associated the matter wave responsible for generating the resonant system is distributed around the nucleus of an atom.
This defines a physical mechanism responsible Schrödinger's wave function in terms of a matter wave and the existence four *spatial* dimensions.
Therefore, defining a particle in terms of resonant "structure" formed by a matter wave in a continuous non-quantized form of mass allows one to define a physical mechanism responsible for Heisenberg's uncertainty principle and Schrödinger's probability wave function.
“The
universe's most powerful enabling tool is
not knowledge or understanding
but
imagination"
Jeffrey O'Callaghan