The search for this missing mass has focus on three different types of particles or objects that would be invisible or would not interact with electromagnetic energy while at the same-time influence the gravity forces of the visible mass component our universe.

The first or Axions are very light particles with a specific type of self-interaction that makes them a suitable CDM candidate.  Axions have the theoretical advantage that their existence solves the Strong CP problem in QCD, but have not yet been detected.

The second or MACHOs or Massive Compact Halo Objects are large, condensed objects such as black holes, neutron stars, white dwarfs, very faint stars, or non-luminous objects like planets. The search for these consists of using gravitational lensing to see the effect of these objects on background galaxies. Most experts believe that the constraints from those searches rule out MACHOs as a viable dark matter candidate.

Finally, WIMPs or Dark matter which is composed of Weakly Interacting Massive Particles. There are no currently known particles that have its properties, but many extensions of the standard model of particle physics predict such particles. The search for WIMPs involves attempts at direct detection by highly sensitive detectors, as well as attempts at production by particle accelerators. WIMPs are generally regarded as the most promising dark matter candidates. The DAMA/NaI experiment and its successor DAMA/LIBRA have claimed to directly detect dark matter particles passing through the Earth, but many scientists remain skeptical, as null results from similar experiments seem incompatible with the DAMA results.

However, Einstein suggested another possibility in the speech “Aether and the theory of Relativity” he made on May 5th 1920 at the University of Leyden Germany where he indicated The General Theory of Relativity predicts that “space is endowed with physical qualities”

“Recapitulating, we may say that according to the General Theory of Relativity space is endowed with physical qualities; in this sense, therefore, there exists Aether. According to the General Theory of Relativity space without Aether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time, nor therefore any space-time intervals in the physical sense. But this Aether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts, which may be tracked through time. The idea of motion may not be applied to it.”

However, Einstein only endowed space with the field properties of a space-time dimension and not the physical qualities of mass.  Therefore, if one accepts the validity of his theory the physical properties he was referring to must be a result of those field properties not those of mass in its particle form.  This suggests a portion of the missing mass found by Fritz Zwicky may be related to those field properties is not what most associate with the mass of objects or particles.

Yet it is difficult to form a clear picture of how a field consisting of space-time can have the physical properties of Dark Matter because as was shown in the article “Defining what time is” Sept. 20, 2007 time is not perceived by most as matter but as an irreversible physical, chemical, and biological change in physical space.  Therefore, it is hard to understand how the physical properties Einstein associated with space can interact with the non-physical properties of a time or a space-time dimension to create mass.

But Einstein gave us the ability to solve this and develop more direct understand how and why the field properties of space-time can be responsible for Dark Matter when he used the equation E=mc^2 and the constant velocity of light to define the geometric properties of mass in a space-time universe.  This is because that provided a method of converting a unit of time he associated with energy in a space-time dimension to unit of space associated with mass in four *spatial* dimensions.  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.

The fact that one can use Einsteinâ€s equations to qualitatively and quantitatively redefine the field properties of a space-time environment in terms of four *spatial* dimensions means as was done in the article “Defining energy?” Nov 27, 2007 that one can also define the gravitational properties mass in terms of a spatial displacement in field properties of four *spatial* dimension.

Therefore, according to Einstein if the continuous field properties of a three-dimensional space manifold were displacement with respect to a fourth *spatial* dimension a gravitational field would be created which because it is not made up of particles would not interact with light and therefore be Dark.

In other words, a portion of the gravitational forces associated with Dark Matter may not be the mass associated with particles but with the physical qualities Einstein in his speech “Aether and the theory of Relativity” tells us that a displacement of space must have

However, this contradicts the current worldview shared by most physicists and cosmologists that gravitational forces can only be created by mass in its particle or quantized form.  This is true even though observations tell a different story.

For example Louis de Broglie was the first to predict mass is made up of the continuous field properties of space when he theorized that all particles have a wave component because according to modern theories that is the only thing that can support continuous properties of a wave.

Additionally the electron diffraction by crystals in 1927 by Davisson and Germer provides experimental confirmation of this because that one can observe the transfer of momentum from a particles wave component to the electron caused by that interaction.

In other words, the mass we associate with particles must be composed of the oscillation in the field properties of space because that is the only thing that could be responsible for their wave components.  Therefore, those fields must also have the properties associated with mass.

If this is true why then do we only observe its particle properties?

One can understand why by extrapolating the laws of governing resonance in a three-dimensional environment, as was done in the article “Why is energy/mass quantized?” Oct. 4, 2007 to the field properties of the wave Davisson and Germer observed particle to be composed of 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 continuous field properties of space or as was shown above mass the ability to oscillate 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 the field properties of space would be responsible the mass and therefore the gravitational potential of particles.

However, there are at least two reasons why we are unable to directly observe the field properties of the mass component of space. The first is because all observations require an exchange of energy between what is being observed and the observer. Yet the most effective way for nature to transfer information to our instruments is, as was shown in the article “Why is energy/mass quantized?“ in a resonate system made up of the field properties of mass.  Therefore, in all measurements the particle properties associated with its resonant system will always be predominant over its field ones.

This is why as mentioned earlier its field properties are only observable in terms of the interference of the wave properties particles as was demonstrated by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.

The second and probably the most significant is that to measure a quantity there must be a physical difference between what is being measured and what is doing the measuring.

For example, one cannot measure the force on the walls of ship lock created by the changing level of water from a ship in it by measuring how high it is above its surface because it is changing at the same rate.

As was mentioned earlier Einstein tells us a displacement in the continuous “surface” or field properties of a three-dimensional space manifold which are displaced with respect to a fourth *spatial* dimension would result in the creation of a gravitation field.

However, as it was with a ship one cannot measure the gravitational force on the “walls” of our universe generated by the mass associated with a displacement in a “surface” of three-dimensional space manifold because we and all our instruments are floating on that “surface”.

Yet as mentioned earlier we can determine the mass component of space by measuring how the inertial properties of its field components interact with crystals in experiments such as those conducted by Davisson and Germer

It should be remember Einsteinâ€s genius allows us to choose to define all environments in either space-time or one consisting of four *spatial* dimension when he defined their geometry in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the quantum and field properties of space thereby giving us a new perspective on physical make up of dark matter

Later Jeff

Copy right Jeffrey O’Callaghan 2016

The post Finding Dark Matter appeared first on Unifying Quantum and Relativistic Theories.

He then compared his result with the mass evaluated from the light the galaxies shed. He realized that there was way more matter in the cluster than what was visible or baryonic matter. This matter of an unknown type generated a gravitational field without emitting light; hence its name, dark matter.

Further observations suggest the baryonic or visible forms of matter in the universe only comprise approximately 5 to 10% of the mass required to account for the total gravitational energy in the universe.

The search for this missing mass has focus on three different types of particles or objects that would be invisible or would not interact with electromagnetic energy while at the same-time influenced by the gravity forces of the visible mass component our universe.
The first or Axions are very light particles with a specific type of self-interaction that makes them a suitable CDM candidate.  Axions have the theoretical advantage that their existence solves the Strong CP problem in QCD, but have not been detected.

The second or MACHOs or Massive Compact Halo Objects are large, condensed objects such as black holes, neutron stars, white dwarfs, very faint stars, or non-luminous objects like planets. The search for these consists of using gravitational lensing to see the effect of these objects on background galaxies. Most experts believe that the constraints from those searches rule out MACHOs as a viable dark matter candidate.

Finally WIMPs or Dark matter which is composed of Weakly Interacting Massive Particles. There is no currently known particle with the required properties, but many extensions of the standard model of particle physics predict such particles. The search for WIMPs involves attempts at direct detection by highly sensitive detectors, as well as attempts at production by particle accelerators. WIMPs are generally regarded as the most promising dark matter candidates. The DAMA/NaI experiment and its successor DAMA/LIBRA have claimed to directly detect dark matter particles passing through the Earth, but many scientists remain skeptical, as null results from similar experiments seem incompatible with the DAMA results.

However Einstein suggested another possibility in the speech “Aether and the theory of Relativity” he made on May 5th 1920 at the University of Leyden Germany where he indicated that The General Theory of Relativity predicts, that “space is endowed with physical qualities”

“Recapitulating, we may say that according to the General Theory of Relativity space is endowed with physical qualities; in this sense, therefore, there exists Aether. According to the General Theory of Relativity space without Aether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time, nor therefore any space-time intervals in the physical sense. But this Aether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts, which may be tracked through time. The idea of motion may not be applied to it.”

However Einstein only endowed space with the field properties of a space-time dimension and not the physical qualities of mass.  Therefore if one accepts the validity of his theory the physical properties he was referring to must be a result of those field properties not those of mass in its particle form.  This suggests the missing mass found by Fritz Zwicky may be related to those field properties not those most associate with the mass of objects or particles.

Yet it is difficult to form a clear picture of how a field consisting of space-time can have the physical properties of Dark Matter because as was shown in the article “Defining what time is” Sept. 20, 2007 time is not perceived by most as matter or space but as an irreversible physical, chemical, and biological change in physical space.  Therefore it is difficult to understand how the physical properties Einstein associated with space or Dark Matter can interact with the non physical properties of a time or a space-time dimension to create a gravitational field.

But Einstein gave us the ability to solve this and develop more direct understand how and why the field properties of space-time can be responsible for Dark Matter when he used the equation E=mc^2 and the constant velocity of light to define the geometric properties of mass in a space-time universe.  This is because that provided a method of converting a unit of time associated with energy in a space-time dimension to unit of space associated with mass in four *spatial* dimensions.  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.

This tells us that one can use Einstein’s theory to define gravitational potential in terms of the continuous field properties of four *spatial* dimensions which means if one is to accept his theory one must also assume that space contains a continuous field of mass.

However this contradicts the current world view shared by most physicists and cosmologists that mass only exists in its particle or quantized form.  This is true even though observations tell a different story.

For example Louis de Broglie was the first to predict space is made up of the field properties of mass when he theorized that all particles have a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.

In other words the mass we associate with the particles must be composed of the oscillation in the field properties of space because that is the only thing that could be responsible for their wave components.  Therefore those fields must also have the properties associated with mass.

If this is true why then do we only observe its particle properties?

One can understand why by extrapolating the laws of governing resonance in a three-dimensional environment, as was done in the article “Why is energy/mass quantized?” Oct. 4, 2007 to the field properties of the wave Davisson and Germer observed particle to be composed of 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 continuous field properties of mass 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 the field properties of space would be responsible for it particles properties.

Yet one can also define its boundary conditions in terms of the classical laws space and time.

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 the field properties of mass 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?“

However there are at least two reasons why we are unable to directly observe the field properties of the mass component of space. The first is because all observations require an exchange of energy between what is being observed and the observer.  However the most effective and efficient way for nature to transfer information to our instruments is, as was shown in the article “Why is energy/mass quantized?“ in a resonate system made up of the field properties of mass.  Therefore in all measurements the particle properties associated with its resonant system will always be predominant over its field ones.

This is why as mentioned earlier its field properties are only observable in terms of the interference of the wave properties particles as was demonstrated by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.

The second is that to measure a quantity there must be a physical difference between what is being measured and what is doing the measuring.

For example one cannot measure the changing level of water in a ship lock from a ship in it by measure how high it is above the surface of the water ship is floating on because it is changing at the same rate.

Similarly one cannot measure the field properties of the mass component of space because the field properties in the measuring instrument would be changing at the same rate.

However as mentioned earlier we can indirectly measure how the field properties of mass interact with particles as was shown by in 1927 by Davisson and Germer observation of electron diffraction by crystals

The above discussion not only defines why we cannot directly observer Dark Matter but also how it creates gravitational potential in terms of the field properties of four dimensional space-time or four *spatial* dimensions.

Unfortunately for those who disagree the above conclusion is based purely on observations and the validly of Einstein theories.  Therefore to deny the existence of a continuous field of Dark Matter and it gravitational influence one would have to deny the validity of Einstein theories.

It should be remember Einsteinâ€s genius allows us to choose to define all environments in either space-time or one consisting of four *spatial* dimension when he defined their geometry in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the quantum and field properties of space thereby giving us a new perspective on their interactions.

Later Jeff

Copy right Jeffrey O’Callaghan 2015

The post Dark Matter as a field property of space-time appeared first on Unifying Quantum and Relativistic Theories.

The evidence for the existence of Dark matter comes from the detained analysis of the orbital motions of galaxies in galactic clusters.

In 1933 a Swiss astrophysicist Fritz Zwicky, of the California Institute of Technology applied Newtonâ€s law of gravity to the Coma cluster of galaxies and obtained evidence of unseen mass.  He estimated the clusterâ€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 or dark form of matter which would provide enough of the mass and gravity to hold the cluster together.”

The fact that 70% of the universes energy is “dark” is determined by analyzing its spatial geometry.

(For those who are interested the video on the right gives a detail description of how its geometry determines the quantity of dark energy and matter it contains.)

At the present time we have some very good theories about the normal matter in the universe.  The standard model of particle physical tells us what the particles are and how they interact in a manner that is consistent with all experimental observations.   However the same cannot be said for dark matter because as of yet no one has observe any particles that could explain its properties.

However science has developed some theoretical models explaining its properties in terms of the existence of a non-baryonic form of particles such as neutrinos, and entities such as axions, supersymmetric particles, or WIMPs.

Yet, as Lee Smolin points out in his book “The Trouble with Physics” none of them are 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.

Yet it may be possible to understand what Dark Matter is if one assumes it is made up of a continuous field of mass because it will allow one to derive both its gravitational and quantum properties by extrapolating the laws of classical mechanics to the wave properties associated with particles.

Louis de Broglie was the first to theorize that all particles have the properties of waves.  His theory was confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer. .

However this observation allows one to explain as was done in the article Why is energy/mass quantized?” Oct. 4, 2007 how the continuous field properties of mass or dark matter become quantized and why we cannot directly observe it by extrapolating the laws of classical wave mechanics in to the properties of a continuous field.

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 in a a space-time environment

The existence of four dimensional space-time would give a wave in a continuous field of mass the ability to oscillate spatially on a “surface” of three dimensional space 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.

However if dark matter and the gravitational forces it posses in made up of a continuous field of mass why is it that we cannot directly observe it.

There are at least two reasons for this. The first is because all observations require an exchange of energy between what is being observed and the observer.  However as was shown above the most effective and efficient way for nature to transfer information to our instruments is, as was shown in the article “Why is energy/mass quantized?“ in a resonate system made up of the field properties of mass.  Therefore in all measurements the particle properties associated with its resonant system will always be predominant over its field ones.

The second is that to directly measure a quantity there must be a physical difference between what is being measured and what is doing the measuring.  For example one cannot measure the changing level of water in a ship lock from a ship in it by measure how high it is above the surface of the water ship is floating in because it is changing at the same rate.

Similarly one cannot measure the field properties of the mass component of space because the field properties in the measuring instrument are changing at the same rate.

However we can indirectly measure how the field properties of mass interact with particles as was shown by in 1927 by Davisson and Germer observation of electron diffraction by crystals.

In other words assuming Dark Matter is made up of a continuous field of mass not only explains why we cannot observe 25%.percent of the universe mass but also the Davisson and Germer discovery of  electron diffraction by crystals in 1927 while at the same time deriving the quantum mechanical properties of particles in terms of the classical filed properties of space and time.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

The post Why we cannot see 25% percent of the universe mass appeared first on Unifying Quantum and Relativistic Theories.

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.  

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

The post The Geometry of Dark Matter appeared first on Unifying Quantum and Relativistic Theories.