It has been shown throughout this blog and its companion book “The Reality of the Fourth *Spatial* Dimension” observations of our environment suggest that space is made up of a continuous non-quantized field of energy/mass and four *spatial* dimensions instead of four dimensional space-time.Additionally redefining Einstein space-time universe in terms of four *spatial* dimension would allow one to understand several of the more puzzling aspects of quantum mechanics: such as why an electron does not fall into the nucleus of an atom.
Einstein gave us the ability to do this when he qualitatively and quantitatively defined the geometric properties of a space-time universe in terms of the constant velocity of light. This is because it allows one to redefine a unit of time he associated with energy in his space-time universe to unit of space in a one consisting of only four *spatial* dimensions.Â
In other words by defining the geometric properties of a space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.
This would give one the ability to understand the why an electron does not fall into the nucleus of an atom by extrapolating the laws of classical resonance in three-dimensional space as was done in the article “Why is energy/mass quantized?” Oct. 4, 2007 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 Newtonian 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 continuous non-quantized field of energy/mass (the substance) 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.
Therefore, these oscillations in a continuous non-quantized form of energy/mass, would meet the requirements mentioned above for the formation of a resonant system or “structure” in four-dimensional space.Â
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.
Therefore these resonant systems would be responsible for the discrete quantized energy associated with the quantum mechanical properties of energy/mass.
This defines a common mechanism responsible for both the wave and particle properties of energy/mass because it derives one in terms of the other.
However it also tells us in terms of the physical properties four dimensional space-time or four *spatial* dimensions why an electron cannot fall into the nucleus is because, as was shown in that article all energy is contained in four dimensional resonant systems. In other words the energy released by an electron “falling” into it would have to manifest itself in terms of a resonate system. Since the fundamental or lowest frequency available for a stable resonate system in either four dimensional space-time or four spatial dimension corresponds to the energy of an electron it becomes one of the fundamental energy units of the universe.
Another puzzling aspect of quantum mechanics is how the wave properties of electromagnetic energy can be generated by the particle called a photon.
Yet this can be easily understood if one extrapolates the properties to a wave on the two-dimensional surface of water to a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of one in a space-time environment.
For example in the article “The Photon: a matter wave?” Oct. 1, 2007 it was shown that one can derive its electromagnetic properties in terms of resonant system generated by a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth “spatial* dimension.
A wave on the two-dimensional surface of water causes a point on that surface to be become displaced or rise above or below the equilibrium point that existed before the wave was present. A force will be developed by the differential displacement of the surfaces, which will result in the elevated and depressed portions of the water moving towards or become “attracted” to each other and the surface of the water.
Similarly a matter wave on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension would cause a point on that “surface” to become displaced or rise above and below the equilibrium point that existed before the wave was present.
Therefore, classical wave mechanics, if extrapolated to four *spatial* dimensions tells us a force developed by the differential displacements caused by a matter wave moving on a “surface” of three-dimensional space with respect to a fourth *spatial* dimension that will result in its elevated and depressed portions moving towards or become “attracted” to each other.
This defines the causality of the attractive forces of unlike charges associated with the electromagnetic wave component of a photon in terms of a force developed by a differential displacement of a point on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
However, it also provides a classical mechanism for understanding why similar charges repel each other because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement.
Similarly the magnitude of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by two similar charges will be greater than that caused by a single one. Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two charges than it would be for a single charge.
One can define the causality of electrical component of electromagnetic radiation in terms of the energy associated with its “peaks” and “troughs” that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement.
However, Classical Mechanics tells us a horizontal force will be developed by that perpendicular or vertical displacement which will always be 90 degrees out of phase with it. This force is called magnetism.
This is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls matter horizontally towards from the apex of that displacement.
This also solves the puzzle as to why the continuous wave properties of an electromagnetic field are always propagated in the particle called a photon because as mentioned earlier the article “Why is energy/mass quantized?” showed energy is propagated through space in quantized resonant system generated by the matter wave responsible for its electromagnetic properties. .
Therefore, one could argue that this defines a classical explanation for the wave properties of the electrical and magnetic components of a quantum mechanical system such as a photon because it is derived by extrapolating the laws of a classical three-dimension environment one of four.
Defining a particle in terms of a resonant system in four *spatial* dimensions can also explain another one of most puzzling aspects of quantum theory: how and why a particle can generate the interference pattern associated with a wave.
Thomas Young demonstrated the wave characteristics of a particle in an experiment using a light source in front of a screen containing two slits. Each of the slits could be covered individually. On the other side of screen was a wall against which the light coming through the slits could shine on.
When a very dim light was shined on the screen with one slit covered, it impacts the wall in a line between the source and hole in the screen. However, when both holes are open the photons impacting the wall generate an interference pattern that is characteristic of a wave. This interference pattern is generated even when a very dim light consisting of series of single photons are allowed to pass thought a screen with two slits.
When a device is used to determine or measure which silt the individual photons passed thought the interference disappeared.Â
However, this is what one would expect if the particle properties of a photon were the result of a resonant system formed by a matter wave on a “surface” of a three-dimensional space manifold. This is because it would occupy the volume of space associated with the wavelength of its resonant structure therefore; the energy of single photon could pass through both slits if their separation was small compared to its wavelength, forming an interference pattern on the screen whereas the act of measuring which slit it passes through would alter the frequency of the wave passing though it because that act requires a transfer of energy. Therefore, no interference pattern will form because the properties of the wave passing through one will be different from the one passing through the other slit.
Additionally if one allows a series of single particle to pass through a relatively narrow slit one also observers that they form an interference pattern screen.
This appears to contradict the particle characteristics of mass/energy because a series of individual particle generate an interference pattern associated with a wave when passing thought a screen with a relatively narrow slit.
However, this is what one would expect if the particle were, as defined in “Why is mass and energy quantized?” are the result of resonant system made up of a matter wave on a “surface” of a three-dimensional space manifold because as Classical wave mechanics tells us there will be minimal interference if a wave passes through an opening that is relatively wide with respect to its wavelength and that it will increase as it is narrowed.
The reason why the interference pattern is observed to be made up of discreet or quantized units called photons is because, as mentioned earlier the article “Why is mass and energy quantized?” showed that all energy must be propagated in quantized resonant systems. Therefore one can only observe the interference pattern in terms of the quantized system called photons.
This defines a mechanism in terms of classical wave mechanics for the “wave-particle duality” or how a single quantum system can have both the properties of a wave and a particle because it defines its particle properties in terms of a resonant system formed by matter waves in four *spatial* dimensions
Finally defining particles in terms of a resonant system in four *spatial* dimensions can also explain why particles appear to randomly “move” or “jump” to different positions in space without ever moving though the intervening space.
For example an electron can “jump” from one atomic orbital to the next without going thought the intervening space because the resonant “system” associated with an electron does not move from one atomic orbital to the next.
Instead, the resonant system associated with an electron collapses in its initial atomic orbital and is then reformed in a new atomic orbital. Because no resonant or “standing” matter wave is generated in the intervening space between the atomic orbital no electrons will be found there.
This shows how many of the puzzling aspects of quantum mechanics such the particle / wave duality can be solve extrapolating the laws of a three-dimensional environment to a fourth *spatial* dimension.
It should be remember Einstein’s genius allows us to choose to define a quantum system in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories thereby giving us a new perspective on the probabilistic properties of a quantum environment and how they physically connected to our observable universe.
Later Jeff
Copyright 2007 Jeffrey O’Callaghan