Einstein was often quoted as saying "If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless."

For example in his General Theory of Relativity he derived gravity in terms of a curvature in the geometry of space and time.

Additionally he showed us one can understand why in terms of the physical image of a marble on a curved surface of a rubber diaphragm.  The marble follows a circular pattern around the deformity in the surface of the diaphragm. Similarly planets revolve around the sun because they follow a curved path in the deformed "surface" of space-time.

In other words he was able to integrate the physicality of gravity into our consciousness in terms of a physical image based on the reality of a marble moving on a curved surface.

However he was unable to do the same for electrical forces even though he felt, as documented by the American Institute of Physics  "that electromagnetism and gravity could both be explained as aspects of some broader mathematical structure".  

Electromagnetic Theory II

“From before 1920 until his death in 1955, Einstein struggled to find laws of physics far more general than any known before. In his theory of relativity, the force of gravity had become an expression of the geometry of space and time. The other forces in nature, above all the force of electromagnetism, had not been described in such terms. But it seemed likely to Einstein that electromagnetism and gravity could both be explained as aspects of some broader mathematical structure. The quest for such an explanation — for a “unified field” theory that would unite electromagnetism and gravity, space and time, all together — occupied more of Einstein’s years than any other activity.

One reason may be because electrical force appears to be more closely related to the spatial not the time properties of our universe because they can be both attractive and repulsive whereas gravity is unidirectional attractive force. 

In other words because time is only observed to move in one direction forward, it is difficult to incorporate the bidirectional component of electrical forces in terms of a physical image based on the geometry of space-time.  However it is much easer if one defines them in terms of the geometry four *spatial* dimensions because one can more two directions, backwards of forwards in a spatial dimension. 

Einstein gave us the ability to do this when he used the velocity of light and the equation E=mc^2 to define geometric properties of space-time because it allows one to convert a unit of time in his four dimensional space-time universe to a unit of space in a one consisting of only four *spatial* dimensions.   Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by mathematically defining the geometric properties of time in his space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions thereby giving one the ability to define the bidirectional components of electrical forces in terms of the multi directional properties of the spatial dimensions.

The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with gravity in terms of four *spatial* dimensions is one bases for assuming, as was done in the article “Defining energy?” Nov 27, 2007 that all forms of energy including gravitational and electromagnetism can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This would have allowed him to form a physical image of electrical force as was done in the article "What is electromagnetism?" Sept, 27 2007 in terms of the differential force caused by the "peaks" and "toughs" of a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly it showed it is possible to derive the electrical properties of electromagnetism by extrapolating the laws of Classical Wave Mechanics in a three-dimensional environment to a matter wave moving on a "surface" of 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 will be 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 the apex of that displacement.

This shows how one can define a physician image for the causality electrical forces in terms by extrapolating the laws of classical mechanics in a three-dimensional environment to consisting of four dimensional space time or four *spatial* dimensions.

However viewing electromagnetism in terms of its spatial instead of its time properties allows one to understand its quantum mechanic properties in of a physical image based on the observable properties of waves in three dimensional space.

However it also allows one to integrate the quantum mechanical properties of  electromagnetism into the continuous field properties General Relativity

For example the article “Why is energy/mass quantized?” Oct. 4, 2007 showed one can physical derive the quantized wave properties of electromagnetism  by extrapolating the field properties 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 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 it 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 properties of a photon or electromagnetic field.

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?

In other words one can form a physical image of why electromagnetic energy is quantized in terms of the same wave properties that was earlier was associated with its attractive and repulsive properties.

As mentioned earlier Einstein felt "that electromagnetism and gravity could both be explained as aspects of some broader mathematical structure". 

The above discussion vindicates that belief because it shows that one can not only incorporate gravity and the continuous wave properties of electromagnetism but also its  quantum properties into a broader mathematical structure by rewriting the space-time field concepts of General Theory of Relativity in terms of four *spatial* dimensions

It should be remember that Einstein’s genius allows us to choose whether to create physical images of an unseen "reality" 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.

Later Jeff

Copyright Jeffrey O’Callaghan 2015

 

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In 1933 Fritz Zwicky a Swiss astronomer, was trying to measure the mass of a galactic cluster using two different methods. First he tried to infer it from the rational speed of the galaxies around the center of the clusters.  Just like kids on a merry-go-round have to hold on to avoid being ejected, galaxies are held together in a spinning galactic cluster by the gravitational force provided by the matter it contains because if there were not enough matter to create this force, the galaxies would simply scatter.

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.

 3D Dark Matter Density Field Simulation

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 Einstein’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

 

Anthology of
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Vol. 1 thru 5

2007 thru 2014


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The Reality
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Ebook

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Chronicles
Vol. 5 — 2014

 
Paperback
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The Imagineer’s
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Vol. 4 — 2013


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The Imagineer’s
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The Imagineer’s
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The Imagineer’s
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