History has shown the most successful theories are those based on what has come to be called Occam’s razor or that “the explanation of any phenomenon should make as few assumptions as possible, eliminating those that make no difference in the observable predictions of the explanatory hypothesis or theory”.
Newton applied it when he defined the properties of planetary motion in terms of a single concept called the law of gravity which assumes that every point mass attracts every other point mass by a force pointing along the line intersecting both points.
He could have complicated it by assuming the existence of other perimeters such as a repulsive force acting between each point mass and then make a proportional increase the magnitude of the attractive force so that their movements corresponded to observations but he chose not to. However, a law of gravity based on this assumption would be just as successful in predicting their motion as the one he proposed.
But as technologies advance and more accurate measurements of planetary motions were made scientists realized not all them can explained by Newton’s laws. This led to the acceptance of more universal explanation of planetary motion based on Einstein’s assumption that space and time can be merged into a single entity called space-time. However, Einstein also applied Occam’s the principal of the eliminating all assumptions “that make no difference in the observable predictions of the explanatory hypothesis or theory” because he based his redefinition of Newton’s laws only on the single assumption that space and time can be merged to form one entity called space-time.
Unfortunately the assumption that space-time is responsible for the motion of the planets cannot be used to explain the quantum properties of energy/mass. To do this Quantum theories have to assume they are defined by the mathematical properties of Schrödinger’s wave equation.
However, this presents a problem for scientists who believe, as Occam did that “the explanation of any phenomenon should make as few assumptions as possible because presently it takes two assumptions, a quantum and relativistic one to fully explain the properties of energy/mass.
But we may find the key to why we have not been able to do so by looking at them together instead of individually.
For example, Einstein conceptually defined the relativistic properties of motion by assuming it was caused by a physical interaction of time with space even though no one has ever observed time to have physical properties. Therefore one must make the added assumption that time has physical properties to allow it to interact with physical properties of space to the assumption that the geometry of space and time are responsible for the relativity properties of energy/mass.
However Einstein gave us the ability to eliminate that assumption when he use the equation E=mc^2 and the constant velocity of light to define the geometric properties of space-time because that provided a method of converting a unit of time to unit of space identical to those of the three spatial dimension it already contains. Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.
In other words if the only assumption needed to explain the relativistic properties of energy/mass is that the physical properties of a four *spatial* dimension is identical as was done above one can eliminate the assumption that time has physical properties thereby reducing the number of assumptions by one because we have already assumed that three-dimensional space has physical properties.
However this also allows one to eliminate the assumption that the quantum properties of energy/mass are a result of the mathematical properties of Schrödinger’s wave equation because they can be derived from the geometric properties of four *spatial* dimensions.
For example as the article “Why is energy/mass quantized?†Oct. 4, 2007 showed one can explain them by extrapolating the laws of classical wave mechanics 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 occur in one consisting of 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 to oscillate spatially 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 space.
Therefore, these oscillations in a “surface” of a three-dimensional space manifold would meet the requirements mentioned above for the formation of a resonant system or “structure” in four-dimensional space if one extrapolated them to that environment.
Classical mechanics tells us the energy of a resonant system can only take on the discrete or quantized values associated with its fundamental or a harmonic of its fundamental frequency.
Hence, these resonant systems in four *spatial* dimensions would be responsible for the discrete quantized energy associated with the quantum mechanical systems.
Yet it also allows one to define the boundary of a quantum system in terms of the geometric properties of four *spatial* dimensions.
For example 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 spatial boundaries associated with a particle in the article “Why is energy/mass quantized?†Oct. 4, 2007.
In other words by assuming space it composed of four *spatial* dimensions instead of four dimensions space-time allows one to not only eliminate the assumption that time has physical properties but also the assumption that the quantum properties of energy/mass are a result of mathematical properties of Schrödinger’s wave equation.
Physics as the name imply is devoted to understanding the laws that control our physical environment and those who practice it should realized the most successful theories are those based on what has come to be called Occam’s razor or that “the explanation of any phenomenon should make as few assumptions as possible, eliminating those that make no difference in the observable predictions of the explanatory hypothesis or theory”.
Later Jeff
Copyright Jeffrey O’Callaghan 2009