We have shown throughout this blog and its companion book “The Reality of the Fourth *Spatial* Dimension” there would be many theoretical advantages to defining space in terms four *spatial* dimensions instead of four-dimensional space-time.
One of them is that it would allow one to understand the classical origins of Heisenberg’s Uncertainty Principle by extrapolating observations of a three-dimensional environment to a fourth *spatial* dimension.Â
For example In the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown it is possible to understand its quantum mechanical properties by extrapolating the laws of classical resonance in a three-dimensional environment to a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
Briefly it showed 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 by a matter wave in four *spatial* dimensions.
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.
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 the energy of a resonant system can only take on the discrete or quantized values associated with its resonant or a harmonic of its resonant frequency
Therefore the discrete or quantized energy of resonant systems in a continuous form of energy/mass would be responsible for the discrete quantized quantum mechanical properties of particles.
However, it did not explain how the boundaries of a particle’s resonant structure are defined.
In classical physics, a point on the two-dimensional surface of paper is confined to that surface. However, that surface can oscillate up or down with respect to three-dimensional space.
Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate “up” or “down” with respect to a fourth *spatial* dimension.
The confinement of the “upward” and “downward” oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the geometric boundaries of the “box” containing the resonant system the article “Why is energy/mass quantized?” associated with a particle.
However if this is true that one should be able to explain why the other properties of quantum systems are what they are in the same terms
For example in quantum mechanics, the uncertainty principle asserts that there a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position x and momentum p, can be simultaneously known.
However, Quantum Mechanics mathematically defines the position and momentum of a particle in terms of non-dimensional point.
Therefore according to the above concepts there would be an uncertainty in determining its position because that point could be found anywhere within the volume of the “box” mentioned above.
Similarly there would be an uncertainty in measuring its momentum, again because quantum mechanics defines movement in terms of a non dimensional point. Therefore before one could determine a particle’s momentum one would have to know the exact position of the “end” points one use to measure its velocity. However, as mentioned above that non dimension point representing a particle could be found anywhere in the box containing the resonant structure that define a particle in the article “Why is energy/mass quantized?“ Therefore one could not determine its exact velocity and momentum because there will always be an uncertainty as to where the non dimensional point representing a particle is in the box when the measurement was taken
The reason why one cannot simultaneously measure both with complete accuracy is because the act of measure its momentum or position requires one to access different segments the “box” containing the one dimensional point particle.
For example if one wants to make the most accurate measurement possible of its momentum internal to the box one would have to measure the time it took for it to transverse a given segment of it. However this means that one could not determine its position because it would be changing through the entire time that it took it to transverse that portion of the box.
However if one wanted to make the most accurate measurement possible of its position internal to the box it would have to be stationary with respect to the box’s geometry meaning that one could not determine its monument because it would not be moving. Since these two measurements required one to access different segments of a particles geometry they are mutually exclusive.Â
Therefore one cannot simultaneously measure a particle position x and momentum p with complete accuracy.
This defines in terms of classical mechanics why there is a limit to the precision with which certain pairs of physical properties of a particle, such as position x and momentum p, can be simultaneously known.
Later Jeff
Copyright Jeffrey O’Callaghan 2012