We have shown throughout “The Imagineer’s Chronicles” there are many theoretical advantages to assuming the existence of four *spatial* dimensions a continuous non-quantized form of mass.

One of them is that it would provide a more logical explanation of the observed properties of Dark Matter than can be found based solely on the quantum mechanical assumption that mass exists only in particle form.

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, 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, 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 contain 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 that is based on observations that has been overlooked by the scientific community.

In the article “What is Dark Matter?” Sept 10, 2007 it was shown that one could theoretically explain and predict the gravitational forces associated with Dark Matter in terms of a continuous non-quantized form of mass.  This non-baryonic and non-particle form of mass would have all the observed properties dark matter in that it would not interact with ordinary matter via electromagnetic forces and since it is made up of mass it would add to the gravitational force of the particle matter in the universe.

However, unlike WIMPS its existence is supported by observations.

For example, the observation that energy in itself is not quantized because a photon can have any frequency greater than zero or less than infinity and the equation defining the relationship between mass and energy, E=m*c^2 indicates that mass is completely convertible to one or more photons with energies greater than zero or less than infinity.

This means a continuous non-quantized medium must be available to support the continuous properties associated with mass energy and the electromagnetic spectrum.

Additionally the existence of a continuous non-quantized form of mass is supported by the observation of Davisson and Germer, when, in 1927 they observed that electrons along with other particles are diffracted by crystals.  This is because the only way to explain the observed wave properties of individual particles is to assume they must have the continuous non-quantized geometric substructure associated with a wave.

However, the most significant theoretical advantage to assuming its existence is that it would allow one understand, in terms laws of classical wave mechanics the quantum mechanical aspects of mass and energy.

In the article "Why is mass and energy quantized?" Oct. 4, 2007 it was shown that one could explain and predict the quantum properties of mass and energy in terms of a classically resonating system or "structure" form by a matter wave moving through a continuous non-quantized form of mass. 

Classical wave mechanics tells us a resonant phenomenon will occur with all types of vibrations or waves: there is mechanical resonance, acoustic resonance, electromagnetic resonance, nuclear magnetic resonance (NMR), electron spin resonance (ESR), and resonance of quantum wave functions.  Resonant systems can be used to generate vibrations of a specific frequency (e.g. musical instruments), or pick out specific frequencies from a complex vibration containing many frequencies.

However, as mentioned earlier the observation that particles mass has the continuous non-quantized geometric substructure associated of a wave means that according to classical wave mechanics a resonant system will be established is space.  This provides observational evidence supporting the derivation of the quantum mechanical or particle aspects of mass and energy, as was done in the article "Why is mass and energy quantized?" in terms of discrete resonant systems formed by vibrations in a continuous non-quantized form of mass.

The are some who feel that the existence of substance like a continuous non-quantized form of mass permeating space validates the Newtonian concept of absolute space.  However, as was shown in the article “Reference frames” July 1, 2008 this is not true.

Briefly, in  the article "Defining energy" Nov. 26, 2007 it was shown the momentum or energy of an inertial reference frame can be derived in terms the displacement of its three dimensional volume with respect to a fourth *spatial* dimension.

Isaac Newton defined an inertial reference frame as one in which an object at rest will remain at rest, and an object in motion will remain in motion in a straight line at a constant speed.

However, as was shown in the article "Defining energy" the momentum or velocity of an inertial reference frame is defined by a constant displacement with respect to a fourth *spatial* dimension of the continuous non-quantized form of mass defining its volume. 

Therefore, the existence of a continuous non-quantized form of mass does not validate the existence of absolute space because its motion can only be measured relative to other reference frames.

This shows there is viable alternative based solely on experimentally verifiable observations to the assumption that dark matter is made up of exclusively of matter in a particular form.

Later Jeff

The "Shadows" of four spatial dimensions

Copyright 2010 Jeffrey O’Callaghan

(In a PDF format)

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