We have shown throughout this blog and its companion book “The Reality of the Fourth Spatial Dimension” there would be many theoretical advantages to assuming the existence of four *spatial* dimensions instead of four-dimensional space-time.
One of them is that it would provide explanation for both the gravitational properties of particles and those of Dark Matter based on the geometry of four *spatial* dimensions
Wikipedia tells us “The first person to provide evidence and infer the presence of dark matter was Swiss astrophysicist Fritz Zwicky, of the California Institute of Technology in 1933. He applied Newton’s law of gravity to the Coma cluster of galaxies and obtained evidence of unseen mass. Zwicky estimated the cluster’s total mass based on the motions of galaxies near its edge and compared that estimate to one based on the number of galaxies and total brightness of the cluster. He found that there was about 400 times more estimated mass than was visually observable. The gravity of the visible galaxies in the cluster would be far too small for such fast orbits, so something extra was required. This is known as the “missing mass problem”. Based on these conclusions, Zwicky inferred that there must be some non-visible form of matter which would provide enough of the mass and gravity to hold the cluster together.”
Many physicists believe the vast majority of the dark matter is in a non-baryonic form such as neutrinos, and entities such as axions, supersymmetric particles, or WIMPs.
However, as Lee Smolin points out in his book “The Trouble with Physics” none of these scenarios is supported by observations.
Neutrinos because of their mass would be characterized by high random speeds in the early universe. However, observations of the early universe indicate the matter that condensed to form galaxies was not hot enough to support the energy that would be associated with those high speeds.
The other particles, which could provide the missing mass fall into two classes: those which have been proposed for other reasons but happen to solve the dark matter problem, and those which have been proposed specifically to provide the missing dark matter.
Examples of objects in the first class are axions and the supersymmetric particles. Their properties are defined by the theory, which predicts them, and by virtue of their mass; they can solve the dark matter problem only if they exist in the correct abundance.
The second class of particles contains entities such as the WIMP or “Weakly Interacting Mass Particle” whose properties are not specified. However, they are assumed to have properties that would allow them to explain the missing mass associated with dark matter along with other “ad hoc” ones that would explain why they have not yet been observed experimentally.
However, the existence of them along with axions and the supersymmetric particles is not based on observations so therefore there is no way to either confirm their existence or that they are responsible for the gravitational force associated with dark matter.
However, there is another theoretical possibility based on extrapolating observations of our three-dimensional environment to a fourth *spatial* dimensions which has been overlooked by many in the scientific community.
In the article “The reality of the fourth *spatial* dimension” Dec. 1 2010 it was shown that one can derive all forms of energy including gravitational in terms of a displacement or “curvature” in a continuous “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
Additionally it was shown this curvature or displacement would be analogous to the space-time curvature the General Theory of Relativity associates with gravity.
While the article “Why is energy/mass quantized?” Oct 4, 2007 showed one can derive the quantum mechanical properties of particles and energy/mass by extrapolating the resonant properties of a classical three-dimensional environment to a matter wave on a continuous “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 the “surface” of a three-dimensional space manifold the ability to oscillate spatially with respect to it 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, the oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established in space.
These resonant structures are responsible for dividing the continuous properties of four *spatial* dimensions and energy/mass into their quantum mechanical components.
This cannot be done in terms of four-dimensional space-time because time is only observed to move in one direction forward. Therefore, it could not support the bidirectional movement required to generate a resonant structure.
As mentioned earlier the article “The reality of the fourth *spatial* dimension” derived all forms of energy including gravitational in terms of a displacement or curvature in a continuous *surface* of a three-dimensional space manifold with respect to a fourth *spatial* dimension while the article “Why is energy/mass quantized?” derived the energy/mass of a particle in terms of a resonant system formed by the continuous properties of matter wave on that same “surface”.
However Classical Mechanics when extrapolated to a fourth *spatial* dimension tells us that because of the continuous properties the of curvature the article “The reality of the fourth *spatial* dimension” associates with gravitational energy and the continuous properties of the matter wave the article “Why is energy/mass quantized?” associates with the energy/mass of a particle both will be distributed throughout the entire “surface” a three-dimensional space manifold with respect to a fourth *spatial* dimension.
This would be analogous how the curvature generated when one pushes a rod downward on a rubber diaphragm would be distrusted throughout its entire surface and diminishes as one moves away from the point of contact. Â
Additionally it also tells us that the magnitude of the curvature in its surface would be directly related to the number of rods contacting it.
However, this means if one extrapolates the mechanics of the rubber diaphragm to a “surface” of a three-dimensional space manifold one must assume the curvature and gravitational energy associated with each individual particle must also be distributed throughout the entire volume of three-dimensional space and diminishes as one moves away from its location.
One can understand the gravitational component of Dark Matter or “empty space” by assuming that the rubber diaphragm in the previous example was resting on another much larger rubber platform.
The curvature in the first diaphragm would represent the gravitational energy the article “The reality of the fourth *spatial* dimension” associated with particles while the curvature in the second would represent the gravitational energy associated with Dark Matter or empty space.
Classical mechanics tells us the magnitude of the curvature in the second diaphragm would be directly dependent on the total combined number of rods or groups of them that were in contact with the first one and the mass of the first rubber diaphragm. While the magnitude or degree of that curvature would be less than that associated with the individual rods because the force on it would be distributed over a larger area.
For the same reason the magnitude or degree of curvature associated with the gravitational forces with Dark Matter of the energy/mass of empty space between particles, stars or galaxies would be less than that associated with their individual gravitational components because as with the diaphragm, it would be distributed over a larger volume.
Yet this means that the total gravitational energy associated with particles, stars or galaxies would consist of two components. The first would be the displacement caused by the energy/mass associated with the resonant structures defined in the article “Why is energy/mass quantized?“ while the second would be the displacement associated with the energy/mass of the volume of space containing them. (The energy/mass associated with that volume would be analogous to the mass of the first rubber diaphragm in the earlier example.) The curvature associated with the displacements that defined the particle component of stars and galaxies in that article would be associated with their gravitational mass while the curvature associated with the energy/mass of the displaced volume of the three-dimensional space containing them would define the gravitational forces of Dark Matter or the empty space between gravitational objects.
However, because as mentioned earlier the magnitude of the gravitational curvature in empty space is considerable less than the curvature associated with the individual stars of planets the effects of the gravitation component of Dark Matter should only be observable when they are grouped together in large formations such as galaxies or galactic clusters.
This completes the derivation of one of the gravitational component of dark matter in terms of the geometry of four *spatial* dimensions.
Later Jeff
Copyright Jeffrey O’Callaghan 2011