Title: The "Shadows" of four spatial dimensions.

A proposal for unifying the relativistic properties of the macroscopic universe with the quantum properties of the microscopic universe in terms of the existence of four *spatial* dimensions and a continuous non-quantized form of mass.

Introduction:  Common sense sometimes gives a false indication of reality.  As a result, "Shadows" of other truths go unnoticed.

For example, many people of the fifteenth century believed the earth was flat, even though they could see the circular shadow of the earth moving across the moon during a lunar eclipse.

However, Christopher Columbus along with many educated people of that time realized this to be an indication that the earth might be spherical.

He trusted both his intellect and his senses more than the conventional wisdom of the time and sailed to a new world of knowledge and understanding.

Abstract:  Quantum mechanics and Einstein's Relativistic Theories of have been the most successful scientific theories of modern times however, attempts to unify them and define "A Theory of Everything" have been unsuccessful.

This is because their exists an incompatibility between the microscopic universe described by quantum mechanics and the macroscopic universe described by Einstein's theories regarding its physical structure.

Einstein's theories define the macroscopic universe in terms of the existence of a continuous space-time metric  while quantum theories define the microscopic universe in terms of discontinuous particles. Therefore, these two theories are inherently incompatible because the physical structure of the universe cannot be both continuous and discontinuous at the same time

However, "Shadows" demonstrates the relativistic properties of space and time and the quantum properties of mass, energy, momentum and position can be explained and predicted by defining the universe in terms of four *spatial* dimensions and the existence of a continuous non-quantized form of mass.  This would allow physicists to define a common unifying mechanism responsible for both the quantum properties of microscopic universe and the relativistic properties of the macroscopic universe.

Chapter one will postulate that space is composed four *spatial* dimensions and a continuous non-quantized form of mass.

Chapter two will derive the quantum or particle properties of mass in terms of integral energies associated with a resonant "structure" formed in space by "oscillations" in a continuous non-quantized form of mass.

Chapter three will define the particle called a photon in terms of "oscillations" in a continuous non-quantized form of mass caused by a matter wave moving at the velocity of light on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, Chapters two and three provide a bridge between discontinuous or particle properties of the microscopic universe to the continuous properties of the macroscopic universe in terms of a continuous non-quantized form of mass.

(Louis de Broglie was the first to theorize 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.)

Time will be defined as only being a measure of the sequential ordering of the causality of an event, while the causality of gravity, momentum and the quantum properties of mass and energy will be defined in terms of the physical properties of four *spatial* dimensions.  Time will then be individually linked to each coordinate plane of four-dimensional space by the mathematical and experimental observed sequential ordering of events that occur in each coordinate plane

Chapter fifteen will derive the relativistic properties of gravity, space and time in terms of a distortion in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This indicates redefining the physical structure of the universe in terms of a geometry of four *spatial* dimensions and the existence of a continuous non-quantized form of mass may enable physicists to define a common unifying mechanism responsible for both the quantum and relativistic properties of our universe.

Conclusion:  "Shadows" demonstrates the power that changing one's perspective can have in helping humankind understand the mechanisms responsible for the physical laws and forces of nature.

*****************

"I am enough of an artist to draw freely on my imagination.
Imagination is more important than knowledge. Knowledge is limited.
Imagination circles the world."
Einstein

"Intuitive thinkers have made many of the breakthroughs in science"
Louis de Broglie

"The universe's most powerful enabling tool is
not knowledge or understanding
but imagination"
Jeff

*****************

Contents

Abstract

Chapter One

A Universe of Four *Spatial* Dimensions

Chapter Two

The Causality of the Quantum properties of mass & energy

Chapter Three

Electromagnetic Energy in terms of Four *Spatial* Dimensions

Chapter Four

The Photon a Particle or Wave?

Chapter Five

Bell's theory and the EPR Paradox

Chapter Six

Heisenberg's uncertainty principle and four spatial dimensions

Chapter Seven

The Photon, a matterenergy wave?

Chapter Eight

The relative masses of subatomic particles in terms of a Fourth *Spatial* Dimension

Chapter Nine

Electrical Potential Energy and Four *Spatial* Dimensions

Chapter Ten

The boundary between a Third and Fourth *Spatial* Dimension

Chapter Eleven

Propagation of electromagnetic energy in terms of Four *Spatial* Dimensions

Chapter Twelve

Gravity and the Fourth *Spatial* Dimension

Chapter Thirteen

The relative mass of a unit electric charge

Chapter Fourteen

A Link between Gravitational and Electrical forces

Chapter Fifteen

The relativistic properties of Four *Spatial* Dimensions

Chapter Sixteen

A link between Relativity and Quantum mechanics

Chapter Seventeen

Gravitational and Kinetic Energies Linked by a Fourth *Spatial* Dimension

Chapter Eighteen

The Principal of Equivalence & Absolute Reference Frames with respect to Four *Spatial* Dimension

Chapter Nineteen

The composition and structure of Quarks with respect to Four *Spatial* Dimensions

Chapter Twenty

The Fundamental Quantum Particles

Chapter Twenty-One

The Origin of the Positron in terms of a Fourth *Spatial* Dimension

Chapter Twenty-Two

Dimensional Mechanics

Chapter Twenty-Three

Experimental Verification of Shadows

Chapter Twenty-Four

Maxwell's equations in terms of Four *Spatial* Dimensions

Chapter Twenty-Five

"Evolution" of the universe in terms of Four *Spatial* Dimensions

Conclusion

Chapter One
A Universe of Four Spatial Dimensions

Defining the properties of a universe consisting of time and four *spatial* dimensions is not possible until we have an understanding of the causality of the forces that are responsible for those properties.

First, time will be defined as only being a measure of the sequential ordering of the causality of an event, then the causality of the forces associated with gravity, electromagnetism, momentum and the quantum properties of mass and energy will be defined in terms of the physical properties of four *spatial* dimensions.  Time will then be individually linked to each coordinate plane of four *spatial* dimensions by the experimentally observed sequential ordering of events that occur in each coordinate plane.

The relativistic properties of time and space will be derived in Chapter fifteen in terms four *spatial* dimensions.

"Shadows" postulates a volume of space is composed of a continuous non-quantized form or “field” of mass and energy and that interactions between these fields and four *spatial* dimensions is responsible for the casualty of the forces found in nature.

There are four types of forces associated with a continuous non-quantized field of mass and energy, a positive and negative matterfield and a positive and negative energyfield.  The interactions of these four forces are responsible for the geometric structure of the universe. 

The combination of matter and energy form matterenergy.

Most are familiar with three out of four forces that define the geometric structure of the universe.

Mass and the attractive force of gravity are associated with a positive matterfield component of space while positive and negative electrical charges are associated with a positive and negative energyfield component of space.

However, some may not be familiar with force associated with a negative matterfield component of space.  It will be shown latter this field is related to a mass component of anti-particles.  Additionally it will be shown a negative matterfield component of space is not associated with anti-gravity.

(The physical mechanism responsible for a negative matterfield component of space and the mass associated with the anti particle called the positron will be developed in Chapter twenty-one in terms of the geometry of four spatial dimensions.)

All the forces of nature will be derived in terms of a geometric distortion or "displacement* in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

It will be shown the forces associated with mass of a particle is generated by a "depression" or curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

The forces associated with antiparticles is a result of an "elevation" in a "surface" of a three-dimensional space manifold with respect to a four *spatial* dimension.

It will be shown that electric and magnetic forces have a common origin in terms of energy gradients generated in three-dimensional space.  The attractive and repulsive properties of electric and magnetic fields will be shown to be related to interactions of the "surfaces" of a three-dimensional space manifold with the geometry four *spatial* dimensions.

It will be shown how and why the forces associated with two similar electrical charges will oppose each other, while the forces associated two similar matter or "gravity fields" will attract each other in terms of the geometry of four spatial dimension and the existence of a continuous non-quantized form of mass. .

These four forces interact to produce the geometric properties of space.

However, it should be remembered these four forces are generated out of only one continuous non-quantized form of mass and energy. 

In Chapter three, the propagation of a photon will be derived in terms of a matter wave moving  on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

In Chapter two, the quantum or particle characteristics of a photon, mass, and energy will be derived in terms of a resonant system or "structure" formed in space by "vibrations" generated by a matter wave in a continuous non-quantized form of mass. 

These resonant structures will be called a "quantum mass unit of space".

(Louis de Broglie was the first to theorize that all particles had a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.  However, this means there must be a continuous non-quantized medium for it to be propagated on because even the smallest possible particle must have a wave component. Therefore, there must exist a continuous non-quantized medium to propagate the wave of the smallest possible particle. However, macroscopic observations of wave energy indicate that it can only be propagated on a medium made up of mass. Therefore, the success of Louis de Broglie theory indicates that a continuous non-quantized form of mass exists.)

Therefore, Chapters two and three define a common mechanism responsible for both the quantum and wave properties of mass, energy and a photon because they define them in terms of resonant system or "structure" generated by a matter wave in continuous non-quantized form of mass.

In Chapter three the energy of individual photons will be derived in terms of a rate of the frequency of "vibrations" in a continuous non-quantized form of mass that produce a resonant or "standing" matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

It will be shown that a photon's energy can be defined in terms of the equation for the Kinetic energy of an object or E=1/2*m*v^2.  Where "E" equals the magnitude of the energyfield and "m" equals the magnitude of the matterfield component of a matter wave associated with a photon, and "v" would equal the "velocity" of the matter wave.

Additionally Chapter fifteen will shown the velocity of light is universally constant, despite the fact that it is transmitted on a physical medium consisting of a continuous non-quantized form of mass, because of a relativistic property of time and four *spatial* dimensions.

Another physical property of a continuous non-quantized form of mass can be illustrated by comparing it to different forms of water in the air.

Water vapor is difficult to detect with the eye because it is composed of relatively small particles, while the condensed particles of water vapor or fog is easier to detect because its particles are physically larger.

The matterenergy fields of space have similar properties.

In the "vapor" state, a continuous non-quantized form of mass is difficult to detect because it is not made up of particles.  However, in a "condensed state" or the state where a resonant "structures" defined in Chapter two exists in a volume of space, the particles or quanta of matterenergy associated with those resonant structures, (such as electron or proton) are detectable because they are physical larger.

For example, fog is composed of an aggregation of water vapor thereby making the particles of water vapor detectable to the eye because they are larger.

Similarly, all quantum particles are composed of "aggregations" of the matterenergy fields of space thereby making these “particles” or “quanta” of matterenergy detectable because they are physically larger.

Mass and the gravitational forces will be derived in Chapter twelve to be the result of a distortion, curvature or "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This curvature or "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is analogous to the curvature or "depression" in a space-time manifold that Einstein's General Theory of Relativity postulates is responsible for mass.

In Chapter thirteen the polarity and magnitude of a positive and negative unit electric charge will be derived in terms of an energy gradient in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, because all the forces of nature including the gravitational and electrical forces have properties associated with the matterenergy fields of space any force acting on a closed spatial system will cause a change in the physical relationships between the matter and energy components of that volume of space.  This will result in that force becoming predominant or observable in that volume of space.

The water analogy can again be used to illustrate this property of the matterenergy fields of space.

If a cold surface is introduced into a humid environment, water vapor will condense to form water droplets.

An effect similar to this occurs in space.

If an entity with a less positive matterenergy field, such as an electron, is introduced into the matterenergy fields of space, the force or energy associated with that matterenergy field will "condense" out of the “fabric” of space and become observable.

In Chapter eight, the mass of a proton will be derived in terms of a distortion or “depression” in a “surface” of a three-dimensional space manifold with respect to the fourth "spatial" dimension.

The mass of an electron will be derived in terms of an “opposite” distortion or “elevation” in a “surface” of a three-dimensional space manifold with respect to the fourth "spatial" dimension.

The “strong nuclear force" that "binds" a nucleus of an atom together can be derived in terms of a resonant "structure", defined in Chapter two, and the attractive forces are associated with the continuous non-quantized mass component of a proton and neutron.

As mentioned earlier Chapter two will derive the quantum properties of all particles in terms of a resonant "structure" formed in space by "vibrations" of a continuous non-quantized form of mass. 

"Shadows" postulates the strong nuclear force is the result of the spatial separation between protons and neutrons in a nucleus becoming small enough so their resonant energies can interact to form one homogenous stable resonant "structure" or particle composed of a continuous non-quantized form of mass.

These larger stable resonant "structures" are called atomic nuclei.

The presence of a neutron in the nucleus of atoms containing more than one proton is necessary to form a stable nucleonic "structure" because the added the attractive forces of the continuous non-quantized form of mass of the neutron interacts with the continuous non-quantized mass component of a proton.  This increases the ratio of the attractive or binding forces of the continuous non-quantized form of mass in a nucleus with respect to the repulsive force associated with the electrical component in a nucleus.  This allows the protons and neutron in the nucleus to become spatially close enough so their resonant energies can interact to form a single stable resonant "structure" in space.

(The internal structure, stability and electrical neutrality of a neutron will be derived in Chapter nineteen in terms of an interaction between the matter and energy components of space and a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension .)

This suggest a nucleus of an atom is not composed of individual protons and neutrons but of one homogenous resonant particle "structure" made up of a continuous non-quantized form of mass.

The magnitude of the strong nuclear force is related to the size of the homogenous resonant structure associated with a nucleus.

The size or diameter of a nucleus increases as is the atomic weight increases.

Therefore, after a certain atomic weight is reached a nucleus will become physically too large for the individual resonant "structures" associated with the protons and neutron to uniformly share the energy require to maintain the stable resonant "structure" associated with that nucleus.  This will result in that nucleus expelling the energy required to reduce its physical size to a point where a stable resonant "structure" can be maintained.  Therefore, any nucleus that is physically large that this will be radioactive.

Additionally, the nucleus of atoms that have an atomic weight less that the critical value for establishing homogenous resonant structure would increase its weight and size by "absorbing" energy from an external source if the energy were allowed to get spatial close enough to the nucleus so that it could become part of the internal resonant structure of that nucleus.  This will result in increasing the size and atomic number of that nucleus.

This indicates that the effectiveness of the stronger nuclear force in absorbing or emitting a particle will be dependent on the distance from the center of the nucleus of an atom.

The exact composition of space now becomes relevant to the study.

“Shadows” postulates space is made up, in part, of mass because it defines the physical structure of space in terms of a dynamic relationship between the forces associated with a continuous non-quantized form of mass and energy.  Therefore, a volume of space must have properties associated with mass because is, in part, made up of mass.

Following this logic, a question is presented: Why hasn't this mass been detected?

Stepping back in history may shed light on the answer to this question.

Many people of the fifteenth century did not realize the Earth was spherical because its curvature was small compared to their scope of their vision.  However, the shadow of the earth on the moon during a lunar eclipse gave them an opportunity to view the spherical shape of the earth from a distance.

Similarly, the reason we may not have detected the mass associated with a continuous non-quantized mass component of space is that its effects are small compared to our scope of our "vision".

There are however, “Shadows” that gives us an opportunity to "view" the properties of a continuous non-quantized mass component of space in terms of the red shift of spectral lines emanating from galaxies.

Astronomers have noted that our universe appears to be expanding.  This idea is based on the shifting of the spectral lines coming from galaxies called the red shift.

One interpretation is that galaxies are moving away from the earth and the greater the distance a galaxies is from the earth the faster it is moving away.

This observation of light is similar to that of sound.  The pitch of a train's whistle is lower when it is moving away and its velocity determines the difference in pitch.

Astronomers have interpreted the red shift in a similar manner.

They assume the greater the red shift in a galaxies spectrum the faster the galaxies is moving away from the earth.

However, another explanation is possible.  The frequency of spectral lines is an indication of the energy they possessed at the point it was generated.  The frequency of light is also an indication of the energy it has at the point it is observed.  Red light has less energy than blue light.  If space were composed of a continuous non-quantized form of mass, as this paper postulates light would dissipate energy due to the "dampening" effects of its inertial properties.

Therefore, each spectral line would lose energy due to the properties of a continuous non-quantized mass component of space causing it to shift towards the red end of the spectrum.

This indicates the magnitude of the red shift may not be entirely a result of the movement of galaxies away from us.

Instead, a portion of the energy loss associated with a red shift may be a result of light interacting with a continuous non-quantized form of mass.

If space is composed of a continuous non-quantized form of mass then the assumption that the greater the distance a galaxies is from us the faster it is moving away may not be valid.

It may be because the further light travels the more time it would have to dissipate energy to a continuous non-quantized form of mass as it traveled through space.

(A blue shift could be observed in a galaxies spectrum if the velocity of a galaxies moving in our direction imparted more energy to the spectral lines than was dissipated by a continuous non-quantized mass component of space it traveled through.)

This "Tired Light" concept of the energy loss associated with the red shifting of photons by it's interaction with particles in space has been dismissed by many because no Compton scattering is observed in red shifted photons. 

Compton scattering is caused by an interaction between high energy particles such as photons and electrons which results in the electron being given part of the energy (making it recoil), and a photon containing the remaining energy being emitted in a different direction from the original, so that the overall momentum of the system is conserved.  If the photon still has enough energy left, the process may be repeated.  This process would result in a scattering of the energy of a photon.

The reason why many astronomers believe the entire redshift of a galaxie is the result of its movement away from an observer is that classical theory of charged particles interacting with an electromagnetic wave, cannot explain any shift in wavelength.

Therefore, if the red shift was caused by a particle interaction one should observed the Compton scattering of light that would be associated with a particle interaction.  Since no Compton scattering is observed in the red shift coming form a galaxy it is assumed by many astronomers it can only be caused by the movement of an object away from an observer.

However, as will be shown in Chapter three the particle properties of a photon are the result of a resonant "system" generated by a matter wave in a continuous non-quantized form of mass moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, because a photon is made up of a matter wave in a continuous non-quantized form of mass a portion of the redshift may be the result of an interaction between the matter wave responsible for it particle properties and a continuous non-quantized form of mass.

This would mean that the assumption that the entire redshift in a galaxies spectrum is a result of its movement away from us might be invalid.

The Cosmological Principal that the universe should appear the same in all directions supports the hypothesis that a portion of the energy loss associated with the red shift is a result of the properties of a continuous non-quantized mass component of space. 

Since the energy loss of light associated with a continuous non-quantized mass component of space would only be dependent on the distance it traveled, the universe would appear to be the same in all directions as long as one kept the observational distance constant.

In addition, there is direct observational evidence that supports the hypothesis that a volume of space has contains a measurable quantity of a continuous non-quantized form of mass.

Recently it has been determined by astronomers the universe must contain a large amounts of "dark matter" that cannot be seen directly but which we know exists because of the influence its gravitational mass has on the orbits of stars in galaxies.

However, the physical properties that astronomers have associated with "Dark Matter" share the same physical properties of a continuous non-quantized form of mass.  They are both composed of mass and therefore would generate gravitational energy, which would influence the orbits of stars in galaxies and because it is a continuous form of mass, it would not be detectable by modern instrumentation because they are calibrated to detect mass in its particle form.

This strongly suggests the observed properties associated with "Dark Matter" may be the result of a continuous non-quantized mass component of space.

Later in Chapter twenty-three, an experimental technique for the direct measurement and observation of the continuous non-quantized mass component of space.

Return to Contents

Chapter Two
The Quantum properties of
mass and energy

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

This is the basis for postulating in Chapter one that space is composed of four *spatial* dimensions and a continuous non-quantized form of mass and energy.

However, it can and will be shown that resonant systems or "structures" in a continuous non-quantized form of mass are responsible for the quantum properties of mass and energy.

First, we will define the mechanism responsible for generating the resonant "structures" of a quantum particle and then mathematically derive the density of a continuous non-quantized form of mass in a vacuum in terms of Planck's Length.

In Chapter one an analogy involving the formation of water particles in the earth's atmosphere was used to define the formation of a quantum particle.

Water vapor in the atmosphere condenses to create particles of fog.

This was shown to be analogous to a continuous non-quantized form of mass "condensing" to form quantum particles in space.

However, space also posses another physical property associated with water.

A particle or molecule of water is made up of a discrete resonant structure formed by the electrical properties of atoms of hydrogen and oxygen.

Similarly, a quantum particle is made up of a discrete resonant "structure" formed by the oscillatory properties of a continuous non-quantized form of mass.

In Chapter three it will be shown that the propagation of a photon is the result of a matter wave moving on a surface of a three-dimensional space manifold with respect to a fourth *spatial* dimension. The oscillations caused by this matter wave on the "surface" of a three-dimensional space manifold with respect to a four *spatial* dimension is responsible for generating the resonant structure of all quantum particles.

(Louis de Broglie was the first to theorize that all particles had a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.  However, this means there must be a continuous non-quantized medium for it to be propagated on because even the smallest possible particle must have a wave component. Therefore, there must exist a continuous non-quantized medium to propagate the wave of the smallest possible particle. However, macroscopic observations of wave energy indicate that it can only be propagated on a medium made up of mass. Therefore, the success of Louis de Broglie theory indicates that a continuous non-quantized form of mass exists.)

The mechanism responsible for the formation of the resonant "structure" of a quantum particle is similar to the mechanism responsible for the formation of all classically resonating systems.

In a closed classically resonating system a vibrational pattern is created in space when the inertial properties of a mass vibrate in a manner that allows the reflected waves from one end of the medium to interfere with incident waves from the source in such a manner that those specific points along the medium appear to be standing still.

Similarly, in a closed resonating "system" defining a quantum particle, a vibrational pattern is created in space by the inertial properties of a continuous non-quantized form of mass that allows the reflected matter wave to interfere in such a manner that specific points along the medium appear to be standing still.

How "vibrations" in a continuous non-quantized form of mass can generate the energy associated with a quantum particle can be understood by comparing it to the vibrations of a wave on the surface of water.

The trough of a standing wave on water displaces the vertical volume of water with air and the peak of the wave displaces the air above the surface of the water with water.

If space was composed of four *spatial* dimensions as was postulated earlier in Chapter one a matter wave in a continuous non-quantized form of mass could establish a resonate or "standing" wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

The trough of a "standing" matter wave on a "surface" of a three-dimensional space manifold would "displace" a continuous non-quantized mass component of space "below" a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension with a component of a fourth *spatial* dimension.

The peak of a resonant or "standing" matter wave on "surface" of a three-dimensional space manifold would "displace" a component of a fourth *spatial* dimension "above" a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension with a continuous non-quantized mass component of three-dimensional space.

Chapter Ten will derive all forms of energy in terms of a "displacement" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, the displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension generated by a "standing" matter wave on a "surface" of a three-dimensional space manifold would be responsible for the internal energy associated with all quantum particles.

We will now derive the relative density of a continuous non-quantized form of mass in a vacuum in terms of the quantum fluctuations describe on page 169 of John A Wheeler's book, "At Home in the Universe" were he defines the fundamental length of a quantum particle to be universally constant and unchanging.

"There is only one truly fundamental length in nature a length free of all reference to the dimensions and rate of revolution of the planet on which we happen to live, free of any appeal to the complex properties of any solid or gas: free of every reference to the mysterious properties of any elementary particle: what we call today the Planck length,

L= (hG/C^3)1/2= 1.6X10^-33 cm

And what we identify with the characteristic scale of quantum fluctuations in the geometry of space".

Since the quantum fluctuations mentioned in John A Wheeler's book define the fundamental quantum component of a vacuum it can be used to define density of the continuous non-quantized mass in a vacuum.

In Chapter three the energy associated with the resonant vibrations in the continuous non-quantized form of mass responsible for the internal energy of a photon and all quantum particles will be derived in terms of the equation E=hf. Where “E” equals the energy of the photon “h” is Planck's constant (6.547 X 10^-27 erg sec) and “f” is the frequency of the vibrations in the continuous non-quantized form of mass.

In classical physics the internal energy of resonant system is, in part, related to the kinetic energy associated with the velocity of the mass component of that system or 1/2mv^2.

This indicates the equation E=hf defining a photon's energy could be redefined in terms of the kinetic energy of a continuous non-quantized of mass component of a photon to be equal to 1/2mc^2=hf, where "m" equals the magnitude of the continuous non-quantized mass component of the photon.

However, a photon's energy is moving at the velocity of "c" with respect to an observer who is measuring the length of the "standing" matter wave that was shown earlier to be responsible for the quantum fluctuations mentioned in John A Wheeler's book.

Therefore, an observer must divide the observed length of a standing matter wave of a photon by the velocity of light "c" to define the physical length of a fundamental quantum fluctuation associated with a photon in terms of Planck's length.

This indicates the equation 1/2mc^2=(h/c)*f would define the length of the quantum fluctuations in a continuous non-quantized form of mass and energy responsible for the energy of a photon with respect to an observer who is stationary with respect to movement of a photon through space.

However, the value of Planck's length 1.6X10^-33 cm is the spatial length associated with Planck's constant.

Therefore the above equation can be rewritten, using the value for Planck's length and solving for "m", as m= 2*(1.6X10^-33 cm/c^3)f.

The minimum possible quantum fluctuation in space would have a frequency of one.

This means the density of a continuous non-quantized form of mass in a vacuum would be m=3.2X10^-33 grams/c^3sec or 3.2X10^-33 grams per cubic light second or a cube that has the dimensions of the distance light travels in one second.

Return to Contents

Chapter Three
Electromagnetic Energy
and Four Spatial Dimensions

EM radiation is propagated through space by a matter wave, supported by vibrations in a continuous non-quantized form of mass moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Chapter one postulated that space is composed of four *spatial* dimensions and a continuous non-quantized form of mass and energy.

In Chapter two, the quantum properties of mass, energy were derived in terms of resonant "system" formed in space by oscillations or vibrations in a continuous non-quantized form of mass.

It was shown that a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would generate a "standing" or resonant wave in a continuous non-quantized form of mass. 

This indicates the quantum or particle properties a photon of EM radiation are the result of a resonant "structure" or system generated in a continuous non-quantized form of mass by a matter wave moving at the velocity of light on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. It will now be shown that "contractions" in a "surface" of a three-dimensional space manifold caused by matter wave moving at the velocity of light on its "surface" are responsible for the energy of a photon. The magnitude of these "contractions" will be derived in terms of the frequency of a matter wave and the relationship between mass and energy defined by the equation E=mc^2.

The "contractions" in a "surface" of a three-dimensional space manifold caused by a matter wave on a "surface" of a three-dimensional space manifold would be analogous to how a wave on the two-dimensional "surface" of water contracts or shortens the two-dimensional distance between two points on the surface of the water.

The mechanism responsible for causing these "contractions" can be derived from the equation E=h*f which defines a photon's energy in terms of its frequency.

As mentioned earlier, Chapter two defined the energy of all quantum particles, including a photon, in terms of resonate "structures" or systems formed by oscillations in a continuous non-quantized form of mass.

However, the kinetic energy of a system is defined by the equation E=mv^2 where "E" equals the energy of the system "m" equals its mass and "v" is the velocity of the mass in that system. 

Therefore, the energy in the resonant system of a photon could be defined in terms of the mass of the continuous non-quantized mass component of a photon times it's velocity or E=mc^2f, where "E" equals the energy of a photon "m" equals the mass of its continuous non-quantized mass component and "f"` equals the frequency of the interchange between the mass and energy components of the matter wave. The energy is directly related to its frequency because the velocity of the interactions between the mass and energy components of a photon would be directly related to the frequency of those interactions.

This indicates the equation E=h*f can be rewritten as E=mc^2*f because it would define the energy of a photon in terms of the velocity of the oscillations in a continuous non-quantized form of mass and energy that are responsible for a photon's energy.

This means the equation of E=mc^2f would also to define the magnitude of the "contractions" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension responsible for a photon's energy.

However, equation of E=m*c^2*f defining a photon's energy will have to be modified to E=m*c^2*(v/F).

This is because a photon's energy will be derived in terms of a ratio of a "contraction" in a length of a "surface" of a three-dimensional space manifold caused by the passage of a matter wave with respect to the length of a three-dimensional space manifold with no matter wave present.

The term (v/F) in the equation E=m*c^2*(v/F) defines the ratio of a shortening of a length of a "surface" of a three-dimensional space manifold caused by the passage of a "standing" matter wave associated with a photon or EM radiation. Because "v" equals the "distance" between two points on a "surface" of a three-dimensional space manifold with NO EM radiation traveling though it minus the distance between two points separated by one wavelength on a "surface" of a three-dimensional space manifold with a matter wave moving though it, while "F" equals the length of a three-dimensional space manifold with respect to a fourth *spatial* dimension with a matter wave of "0" frequency passing through it. Therefore, the dimensionless term (v/F) defines the ratio of the shortening of the length of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the passage of the matter wave responsible for EM radiation. 

However, before we begin our discussion regarding the "contractions" in a "surface" of a three-dimensional space manifold responsible for a photon's energy we must first understand the difference between the "dynamic" and "static" component of a photon's energy.

The "dynamic" component of a photon's energy is related to the effects it has on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

In Chapter twelve the magnitude of a mass will be derived in terms of a "curvature" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. This "curvature" shortens or "contracts" the three-dimensional distance on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension because the "chord" of the "arc" caused by this "curvature" is shorter than the "arc" itself.

Chapter twelve indicates that the energy associated with the mass of a moving particle is, in part related to a "curvature" in a "surface" of a three-dimensional space manifold.

Therefore, because the energy of a photon can only come from a conversion of mass to the energy associated with a curvature in the "surface" of a three-dimensional space manifold this curvature must move at the same velocity as that of the photon. This means a portion of a photon's energy is propagated by a dynamic contraction of space at the velocity of light. This contraction of space due to the movement of a photon though space would be the dynamic component of a photon's energy.

However the particle properties of a photon were define earlier in terms of resonant system on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

This means that a portion of a photon's energy would be contained internally to its particle or resonant "structure" while a portion of its energy, as mentioned earlier would be propagated by a dynamic contraction of space.

The internal energy of the resonant "system" associated with the particle properties of a photon would be considered the "static" form of a photon's energy because its energy is moving at the same velocity as the photon and therefore it would be "static" relative to it.

Earlier these discussions showed the "contractions" in a "surface" of a three-dimensional space manifold responsible for the "static" component of a photon's energy are caused by oscillations in a continuous non-quantized form of matter defined by the equation E=m*c^2*(v/F).

However, as mentioned earlier the "contractions" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the internal oscillations of the continuous non-quantized mass component of a photon does not contribute to "dynamic" energy of a photon associated with its movement through of space at the velocity of light. Therefore to define the contractions in a "surface" of a three-dimensional space manifold associated internal energy of a photon one must factor the velocity of light or "c out of the equation E=m*c^2*(v/F) defining the total energy of a photon.

This indicates, the energy associated with the "contraction" of a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension by a photon would be quantified by the equation E=m*c*(v/F) or E=m*c*(Mr-Mc)/F). 

The term (Mr-Mc)/F) in the equation E=m*c*(Mr-Mc)/F) defines the magnitude of a contraction in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension in terms of the frequency of a matter wave responsible for a photon's energy. This is because the term "Mr" represents the distance between two points on a three-dimensional space manifold with respect to a fourth *spatial* dimension with NO matter wave traveling thought it and the term "Mc" represents the distance two points occupy on a three-dimensional space manifold with respect to a fourth *spatial* dimension with a matter wave moving through it and "F" equals the length of a three-dimensional space manifold with respect to a fourth *spatial* dimension with a matter wave of "0" frequency moving through it. Therefore, the dimensionless term (v/F) or (Mr-Mc)/F) defines the "shortening" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension by the passage of a matter wave responsible for EM radiation.

Earlier it was mention that Chapter twelve defined gravitational energy in terms of a "shortening" or contraction in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However the equation of E=m*c*(Mr-Mc)/F) indicates that EM radiation and the energy of a photon is also the result of a "shortening" or contraction in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This provide a physical link between the quantum properties of a photon and gravitational energy because if defines both in terms of the physical properties of a continuous non-quantized form of mass and energy and four *spatial* dimensions. 

The finial equation defining EM radiation would be E=m*c*c*(Mr-Mc)/F) or E=mc^2*(Mr-Mc)/F) because as mentioned earlier the dynamic lengthening of space at the speed of light associated with mass to energy conversions responsible for the formation of a photon contributes to the total energy associated with a photon and EM radiation.

This completes the derivation of EM radiation in terms of a matter wave in a continuous non-quantized form of mass and energy moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Return to Contents

Chapter Four
The Photon a Particle or Wave?

Why does a photon behave at times like a particle and at other times like a wave?

The answer to this question can be found by examining the resonant "structures" defined in Chapter two responsible for the particle characteristics of a photon and the matter wave that Chapter three showed was responsible for the propagation of a photon's energy.

Chapter two derived the particle characteristics of a photon in terms of the discrete energy associated with a resonant "system" formed in space by oscillations in a continuous non-quantized form of mass.

Chapter three defined the resonant "system" of a photon in terms of the characteristics of a matter wave moving in a continuous non-quantized form of mass.

Therefore, Chapters two and three define a common mechanism responsible for both the particle and wave characteristics of a photon in terms of a resonant "system" caused by a matter wave in a continuous non-quantized form of mass.

The photoelectric effect demonstrates one of the particle characteristics of a photon. 

The photoelectric effect is the emission of electrons from matter upon the absorption of electromagnetic energy.  The emission of electrons from matter is observed to begin as soon as the electromagnetic energy strikes it.

This supports the particle aspect of a photon because wave theory predicts delayed emissions of electrons.  In addition, it was observed that varying the intensity of the light does not change the velocity of the electrons ejected but only their numbers.

Einstein based his quantum or particle theory of electromagnetic radiation, in part, on these photoelectric observations.  He realized these observations could only be explained by assuming photons consist of discrete "packets" or quanta of energy that is depended on their frequency.

The reason delayed emission is not observed in the photoelectric effect is because, as mentioned earlier Chapter two showed the energy of individual photons is the result of a resonant "system" caused by oscillations in a continuous non-quantized form of mass

Therefore, the energy of a specific photon would be directly dependent on the frequency of the resonant "system" that defines its energy.

If the energy associated with a resonant "system" of a photon of a given frequency is sufficient it will instantly eject an individual electron off a photoelectric surface.

The velocity of an electron leaving a photoelectric surface is not affected by the intensity of the light because varying its intensity will only cause an increase or decrease in the number of photons of a specific frequency striking the photoelectric surface.  Since the energy of the resonate "system" associated with a photon of is directly dependent on it's frequency, the energy and therefore the velocity of electrons ejected off the surface of a photoelectric material by photons with identical frequencies will also be identical.

However, increasing or decreasing the intensity of the light striking the photoelectric surface will increase or decrease the number of elections ejected from the surface because the number of resonate "structures" of sufficient energy to eject electrons from the surface will increase or decrease.

Therefore, the particle characteristics of a photon associated with the photoelectric effect can be explained in terms of a resonate "system" generated by a matter wave in a continuous non-quantized form of mass.

However, light also posses the non-particle characteristics of a wave.

Thomas Young demonstrated this 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 hole covered, the light impacts the wall in a line between the source and hole in the screen.  However, when both holes are open the light impacts the wall generating 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.

Additionally when a device was used to determine which silt the individual photons passed thought the interference disappeared.  This indicates that act of measuring which silt a photon passes result in destroying the interference pattern.

This appears to contradict the particle characteristics of a photon because a series of individual photons can generate an interference pattern associated with a wave when passing thought a screen with two slits, therefore, each individual photon, also posses the characteristics of a wave.

The wave characteristics of individual photons is due to the fact that its energy, as was shown in Chapter three is propagated though space by a resonant "system" generated by a matter wave in a continuous non-quantized form of mass.

When a single photon passes through a screen with a single slit, the spatial component associated with the wavelength of its resonant "system" can only be transmitted along velocity vector of the photon and the direction of the photon will not be altered.  The photon will strike the screen on straight line between the source and hole in the screen.

However, a “torque” will be generated on a single photon if it is allowed to pass though one slit in a screen with two opened slits because the spatial component associated with the wavelength of its resonant "system" can simultaneously pass or be transmitted through the two spatially separated slits in the screen.  This will generate a torque on the direction of a photon after passing through the silts in the screen because of the different spatial path lengths between the slits.

Because the resonant "system" of a photon is transmitted by a matter wave, the orientation of its spatial component will vary sinusoidally with respect to time.  This means the direction of the “torque” and therefore the direction of the photon as it moves through the two slits will vary sinusoidally with respect to time. 

Therefore, a series of single individual photons passing through a screen with two opened slits will generate a interference pattern on the screen because the torque generated by the sinusoidal varying direction of the spatial component associated with a matter wave will cause a sinusoidal variation in the direction of each photon that transverses the screen.

This is the mechanism responsible for the wave characteristics of individual photons as observed in the Thomas Young experiment.

However, when attempts are made to measure which slit a photon passed through the interference pattern disappears and it behaves like a particle.

This is because attempts to measure which silt a photon passes through changes the characteristics of the matter wave passing through that slit.  Therefore, that component of the matter wave responsible for its resonant "structure" will no longer interfere with component that is passing though the other slit.  This will result in the collapse of the wave function and the disappearance of the interference pattern that is observed when no attempt is made to determine which slit the photon passed through.

Therefore defining the propagation of a photon in terms of a resonant matter wave in a continuous non-quantized form of mass answers the question "Why does a photon behave at times like a particle and at other times like a wave?"

Return to Contents

Chapter Five
Bell's Theorem and the EPR paradox

Tjipto Juwono contributed the following explanation of a 1935 paper co-authored by Einstein, Podolsky, and Rosen, which presented what has been called the EPR paradox.

"In 1935, Einstein co-authored a paper which was intended to show that Quantum Mechanics could not be a complete theory of nature.  The first thing to notice is that Einstein was not trying to disprove Quantum Mechanics in any way.  In fact, he was well aware of its power to predict the outcomes of various experiments.  What he was trying to show was that there must be a "hidden variable" that would allow Quantum Mechanics to become a complete theory of nature

The argument begins by assuming that there are two systems, A and B (which might be two free particles), whose wave functions are known.  Then, if A and B interact for a short period of time, one can determine the wave function which results after this interaction via the Schrödinger equation or some other Quantum Mechanical equation of state.  Now, let us assume that A and B move far apart, so far apart that they can no longer interact in any fashion.  In other words, A and B have moved outside of each other's light cones and therefore are spacelike separated.

With this situation in mind, Einstein asked the question: what happens if one makes a measurement on system A?  Say, for example, one measures the momentum value for system A.  Then, using the conservation of momentum and our knowledge of the system before the interaction, one can infer the momentum of system B.  Thus, by making a momentum measurement of A, one can also measure the momentum of B.  Recall now that A and B are spacelike separated, and thus they cannot communicate in any way.  This separation means that B must have had the inferred value of momentum not only in the instant after one makes a measurement at A, but also in the few moments before the measurement was made.  If, on the other hand, it were the case that the measurement at A had somehow caused B to enter into a particular momentum state, then there would need to be a way for A to signal B and tell it that a measurement took place.  However, the two systems cannot communicate in any way!

If one examines the wave function at the moment just before the measurement at A is made, one finds that there is no certainty as to the momentum of B because the combined system is in a superposition of multiple momentum eigenstates of A and B.  So, even though system B must be in a definite state before the measurement at A takes place, the wave function description of this system cannot tell us what that momentum is!  Therefore, since system B has a definite momentum and since Quantum Mechanics cannot predict this momentum, Quantum Mechanics must be incomplete.

In response to Einstein's argument about incompleteness of Quantum Mechanics, John Bell derived a mathematical formula that quantified what you would get if you made measurements of the superposition of the multiple momentum eigenstates of two particles. If local realism was correct, the correlation between measurements made on one of the pair and those made on its partner could not exceed a certain amount, because of each particle's limited influence.

This gave physicists the ability to test the whether particles can instantly influence other particles when they are "spacelike separated" or exist in different local reality.

The "hidden variable" that Einstein was referring to in the previous article that would "make quantum mechanics complete" may be related to the existence of a continuous non-quantized form of mass.

Chapter one postulated that space is composed of a continuous non-quantized form of mass and four *spatial* dimensions instead of four dimensional space-time .

Later in Chapter two, a quantum particle was defined in terms of a resonant system or "structure" formed in space by "oscillations" in a continuous non-quantized form of mass and energy.

Chapter three derived the propagation of EM radiation in terms of a matter or matterenergy wave "moving" at the velocity of light on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  It was shown this matterenergy wave is generated by oscillations in a continuous non-quantized form of mass. 

How the existence of a continuous non-quantized form of mass would allow for communications between two quantum particles that are "spacelike separated" would be analogous to how "information" can be "communicated" from one pool ball to another on the surface of a pool table.

The pool balls will represent the resonant "structures" in a continuous non-quantized form of mass and energy that defined a quantum particle in Chapter two.

Pool is a game in which a ball called a cue ball is struck and as a result, the cue ball travels on the surface of the pool table until it collides with an object ball.  This collision results in the “information" regarding the cue balls momentum to be "communicated" to the object ball.  The object ball then begins to travel across the table until it collides with and "communicates" the "information" on its momentum to the next ball in line.  The speed at which the "information" is "communicated" between the cue ball and the object ball is, in part, dependent on the time required to travel the distance between the individual balls on the table.

However if the pool balls are physically contacting each other the "communication" or "information" transfer from the first to the last ball in line will be almost instantaneous because the time required for them to travel the distance between them would be minimal.

Chapter three derived the velocity of EM radiation and the information it carries in terms of a conversion of a continuous non-quantized form of mass to a continuous non-quantized form of energy and a conversion of a continuous non-quantized form of energy to a continuous non-quantized form of mass.

Therefore, the speed or velocity of electromagnetic energy and the "information" it contains is due, in part, to the time required for this conversion to take place.

This would be analogous to the speed of "communication" or "information" transfer in the earlier example of the pool balls in that the time required for information to be transferred from the first to the last pool ball in the line was dependent on the time required for them to travel through the space between them.  This is because speed of the transfer of information by EM radiation would be dependent on the time required for a continuous non-quantized form of mass to "travel the distance" required for it to interact with a continuous non-quantized form of energy.

However, both the EPR paradox and Bells theorem deal with rate at which the information regarding the momentum of quantum particles can be communicated between different local realities.

Since the momentum of a quantum particle would be directly related to its continuous non-quantized mass component, the "hidden variable" which would allow the transferring of information regarding its momentum from different "spatially separated" local realities at speeds greater than that of light may be related to the existence of a continuous non-quantized form of mass.

If space were made up of a continuous non-quantized form of mass as is postulated in Chapter one each resonant "structure" that defined a quantum particle in Chapter two would be in direct physical contact with other quantum particles through the continuous non-quantized form of mass that makes up the space between them.  Therefore the transfer of the information related their momentum would be almost instantaneous for the same reason as the information transfer between the pool balls that were physically connect or touching was almost instantaneous in the earlier example.

This indicates two quantum particles may be "spacelike separated" with respect to the electromagnetic energy but not with respect to the information carried by a continuous non-quantized mass component of space. 

This defines a physical mechanism explaining why Bell's theorem may provide mathematical verification for the instantaneous communication between quantum particles that exist in different local realities in terms of the existence of a continuous non-quantized form of mass and energy.

Return to Contents

Chapter Six
Heisenberg's uncertainty principle
 and four spatial dimensions

The Heisenberg uncertainty principle states that locating a particle in a small region of space makes the momentum of the particle uncertain; and conversely, that measuring the momentum of a particle precisely makes the position uncertain.

However, it can be shown the uncertainty of the position and momentum of a particle is physically related to the internal structure of the resonant system that defines a particle in Chapter two.

Chapter one postulated a volume of space is composed of four *spatial* dimensions and a continuous non-quantized form of mass.

In Chapter two, a particle was defined in terms of a resonant system or "structure" formed in space by oscillations in a continuous non-quantized form of mass.

Chapter three showed the energy or momentum of a particle is related to oscillations in a continuous non-quantized form of mass generated by a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

(Louis de Broglie was the first to theorize that all particles had a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.  However, this means there must be a continuous non-quantized medium for it to be propagated on because even the smallest possible particle must have a wave component. Therefore, there must exist a continuous non-quantized medium to propagate the wave of the smallest possible particle. However, macroscopic observations of wave energy indicate that it can only be propagated on a medium made up of mass. Therefore, the success of Louis de Broglie theory indicates that a continuous non-quantized form of mass exists.)

Therefore, both the momentum and position of a particle is related to a matter wave in a continuous non-quantized form of mass.

This is because, as was shown in Chapter Three momentum of a particle is related to the wavelength of a matter wave in a continuous non-quantized form of mass.  While, as was shown in Chapter two the position of a particle is related to where in space resonant "structure" associated with the matter wave component of that particle can be found.  However, the probability of finding a specific value for the momentum of a particle is dependent on the energy distribution of the matter wave that defines its energy while the probability of finding a specific value for the position of a particle will be dependent on the spatial distribution of the resonant system that defines it position. 

The uncertainty involved in simultaneously measuring both the momentum and position of a particle is related to fact that both of their values are dependent on the same matter wave in a continuous non-quantized form of mass. 

The accuracy of a measurement is determined by how much of the measurement parameter is accessed.  For example, one must access more of the wavelength component of the matter wave responsible for the momentum of a particle as he or she increase the accuracy of the measurement of its momentum.

However, this means that there is less of the matter wave responsible for a particle's position accessible for measurement, thereby increasing its uncertainty.

This is because the same matter wave responsible for a particle's momentum is also responsible for generating the resonant system responsible for a particle's position.  Therefore if a portion of it is used to measure its momentum there will be less available to measure its position thereby making that measurement less accurate

Similarly, one must access more of the resonant system responsible for the position of a particle as he or she increase the accuracy of the measurement of its position.

However. because the resonant system associated with a particle's position is generated by a matter wave, there will be less of the matter wave component accessible for the measurement of its momentum, thereby increasing its uncertainty.

This means the uncertainty involved in the simultaneous measurement of the position or momentum of a quantum particle or "The Heisenberg's uncertainty principle" is due to the internal structure of a particle and the existence of a matter wave in a continuous non-quantized form of mass.

Additionally defining particle such as an electron in terms of a resonant "structure" in a continuous non-quantized form of mass as was done in Chapter two, also explains why quantum particles appear to randomly "move" or "jump" to different positions in space without ever moving though the intervening space.

An electron can "jump" from one atomic orbital to the next without going thought the intervening space because the resonant "structure" associated with an electron does not move from one atomic orbital to the next.

Instead the resonant "structure" associated with an electron collapses in its initial atomic orbital and is then reformed in a new atomic orbital.  Because no resonant system is generated in the intervening space between the atomic orbital no electrons will be found there.

Defining a quantum particle in terms of resonant system formed by matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension also provides a physical mechanism responsible for probability of finding an electron at a certain position or Schrödinger's probability wave function.

This is because the position of an electron in an atomic orbital would be dependent on how the energy associated the matter wave responsible for generating the resonant system is distributed around the nucleus of an atom.

This defines a physical mechanism responsible Schrödinger's wave function in terms of a matter wave and the existence four *spatial* dimensions.

Therefore, defining a particle in terms of resonant "structure" formed by a matter wave in a continuous non-quantized form of mass allows one to define a physical mechanism responsible for Heisenberg's uncertainty principle and Schrödinger's probability wave function.

Return to Contents

Chapter Seven
The Photon, a matterenergy wave?

It is possible to understand how and why a photon can have of both the particle and wave properties described by Richard P Feynman in his book "QED The Strange Theory of Light and Matter" by defining it in terms of a resonant "system" in four *spatial* dimension.

On pages 17 thru 23 he discusses what happens when light is partially reflected by two surfaces.  He demonstrates by placing two glass surfaces exactly parallel to each other one can observe how the photons of light reflected from the bottom surface interact with those reflected from the top surface.  Depending on the distance between the glass surfaces he can determine, by using a photo detector, that four percent or 4 out of 100 photons reflected from the lower surface of the glass could add up to as many as 16 or none at all when they interact with the photons reflected from the upper surface of the glass.

These observations by Mr. Feynman support a wave theory of electromagnetic radiation.  Because according to wave theory, the energy associated with the interference of 4 photons with 4 other photons will result in energy variations that corresponds to the energy associated with 0 to 16 photons.

However, wave theory also predicts the energy variations should be continuous.

In other words, the energy of the reflected photons should be able to take on any value between 0 and the combined energies associated with 16 photons.

Unfortunately, for the wave theory of light, the energy of the reflected photons Richard Feynman observed in the above experiment only take on integral or quantum values equal to the energy of the photons that originally struck the surface of the glass.  This indicates that a photon's energy is not transmitted by a wave but by a quantum unit or particle of energy.

However, this apparent contraction between the wave and particle properties of a photon can be resolved if a photon is, as mentioned earlier viewed in terms of a resonant "system" generated by the passage of matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Chapter one postulated that space is composed of four *spatial* dimensions and a continuous non-quantized form of mass.

In Chapter two, the particle properties of a photon were derived in terms of discrete resonant "systems" formed in space by oscillations in a continuous non-quantized form of mass.

Chapter three derived the propagation of a photon's energy in terms of a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by oscillations in a continuous non-quantized form of mass.

(Louis de Broglie was the first to theorize that all particles had a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.  However, this means there must be a continuous non-quantized medium for it to be propagated on because even the smallest possible particle must have a wave component. Therefore, there must exist a continuous non-quantized medium to propagate the wave of the smallest possible particle. However, macroscopic observations of wave energy indicate that it can only be propagated on a medium made up of mass. Therefore, the success of Louis de Broglie theory indicates that a continuous non-quantized form of mass exists.)

Therefore, Chapters two and three answers the question regarding how and why a photon can behave at times like a wave and at other times like a particle because it defines both its wave and particle properties in terms of a common mechanism related to matter wave in a continuous non-quantized form of mass.

The wave like interference of photons observed by Mr. Feynman would be due to the wave properties of the oscillations responsible for the formation of the resonant "system" of a photon defined in Chapter two.

If the distance between the two glass surfaces in Richard Feynman's experiment is equal to half of the wavelength of the oscillations in the continuous non-quantized mass component of a photon, the interference of the wave properties of those oscillations will yield the energy associated with 0 photons.

If the distance between two glass surfaces is equal to the wavelength of the oscillations in a continuous non-quantized mass component of a photon, the interference of their wave properties of those oscillations will yield the energy associated with 16 photons.

However, this does not explain how and why the energy variations caused by the interference of photons are quantized and not continuous as wave theory predicts they should.

The reason the energy of interfering photons is not continuous is because as, mentioned earlier, the oscillations in a continuous non-quantized form of mass form resonant "systems" that define the energy of a photon.

Since the energy of the resonant "system" of each photon is fixed by its resonant parameters it can only interact or interfere  with the wave prosperities of other photon to generate photons with those same resonant parameters.

Therefore, energy variations caused by the interference of the wave properties of a photon can only have the discrete or quantum values associated with the resonant "systems" of the those photons.

This indicates viewing a photon in terms of a resonant "system" formed by oscillations in a continuous non-quantized form of mass can define a mechanism that can explain and predict both the observed particle and wave properties of a photon.

However, defining the energy of a photon in terms of a resonant property of a matter wave also makes it possible to analyze the path of individual photons between two reflective surfaces in terms of their energy amplitudes, as Richard P Feynman did in his book "QED".

In Richard Feynman’s book "QED", he analyzed the process by which 4 photons are reflected from bottom surface of two pieces of glass in terms of the direction of their energy amplitudes.  When light is reflected from a single surface, the directions of energy amplitudes of the reflected photons are randomly varying with respect to photons impacting the surface.  However, when photons are reflected from two surfaces the timing or direction of the energy amplitude can be synchronize between the top and bottom surfaces so they can be made to cancel or reinforce each other.  As a result 4 photons reflected form the bottom surface can cause as few as 0 photons or as many as 8 photons to arrive at the top surface. 

When the directional energy amplitudes of the 4 photons reflected from the top surface are opposite to those that are impacting the bottom surface, they will cancel and no photons reflected from the bottom surface will arrive at the top surface.  When the directional energy amplitudes of the photons reflected from the bottom surface are the same as to those that are impacting the bottom surface, they will add and 8 photons reflected from the bottom surface will arrive at the top surface.

The vector properties of the energy amplitude or energy component of a matter wave define the mechanism responsible for the synchronization of the energy amplitude of photons. 

The direction of energy of the continuous non-quantized mass component of a matter wave varies sinusoidally with respect to distance.  This means that it would be possible to synchronize the direction and amplitude of it between the top and bottom reflective surfaces so that as few as 0 photons or as many as 8 photons to arrive at the top surface. 

Therefore defining a photon in terms of a matter wave in a continuous non-quantized mass component of space defines a mechanism that allowed Mr. Richard Feynman to analyze the process by which 4 photons are reflected from two surfaces in terms of the direction of their energy amplitudes.

Return to Contents

Chapter Eight
The relative masses of the Proton and Electron
in terms of Four Spatial Dimensions

Why do a proton and an election have different masses even though the absolute magnitude of their charge is the same?

The answer to this question can be found in terms of energy "gradients" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the charges of the proton and electron.

Chapter one postulated a volume of space is composed of four *spatial* dimensions and a continuous non-quantized form of mass.

Chapter thirteen will derive the polarity and absolute magnitude of the unit electric charge of a proton and electron in terms of energy "gradients" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

The positive charge of a proton and will be derived in terms of an energy gradient in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  While the negative the charge of an electron will be derived in terms of oppositely directed an energy "gradient" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension

Chapter Ten will define how these energy "gradients" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension effect the density of a continuous non-quantized mass component of space.  It will show that they would affect its similar to the way energy or pressure gradients called high and low pressure areas in the earth's atmosphere effect the density of air.

In a high-pressure area, the energy of air molecules is directed downward towards the surface of the earth.  This results in the density of the air molecules at the apex of a high-pressure area to be greater than the density of the air molecules in the volume of air adjacent to the apex of a high-pressure area.

Conversely, in a low-pressure area the energy of the air molecules is directed upward away form the surface of the earth.  This result in the density of the air molecules at the apex of a low-pressure area to be less than the density of the air molecules in the volume of air adjacent to the apex of a low-pressure area.

This means density of the air molecules will be greater at the apex of a high-pressure area than at the apex of a low-pressure area even though the absolute value of the total energy the air molecules are equal.

A similar effect would occur in space with respect to the density of a continuous non-quantized form of mass.

In a dimensional “high-energy volume” associated with the positive charge of a proton, the energy of the continuous non-quantized mass component of space would be directed “downward” with respect to a fourth *spatial* dimension, towards the “surface” of a three-dimension space manifold.  This would result in the density of the continuous non-quantized mass component of space at the apex of a dimensional “high-energy volume” to be greater than the density of the continuous non-quantized form of mass in the volume of space adjacent to the apex of the dimensional “high-energy volume”.

This is analogous to how the air molecules at the apex of a high-pressure area in the earth's atmosphere would be denser than the air molecules in the volume of air adjacent to the apex of a high-pressure area.

Conversely In a dimensional “low-energy volume” associated with  the negative charge of an electron, the energy of the continuous non-quantized mass component of space would be directed “upward” with respect to a fourth *spatial* dimension, away form the “surface” of a three-dimension space manifold.  This results in the density of the continuous non-quantized mass component of space at the apex of a dimensional “low-energy volume” to be less than the density of the continuous non-quantized form of mass in the volume of space adjacent to the apex of the dimensional “low-energy volume”.

This is analogous to how the air molecules at the apex of a low-pressure area would be less dense than air molecules in the volume of air adjacent to the apex of a low-pressure area.

Therefore the density of a continuous non-quantized form of mass will be greater at the apex of a dimensional "high-energy volume" than at the apex of dimensional "low-energy volume" even though the absolute value of their electrical energies associated with both a dimensional "high and low energy volumes" are equal.  This is true for the same reason the density of the air molecules is greater at the apex of a high-pressure area than a low-pressure area even though the absolute values of the energies are equal.

Chapter twelve will shown that the mass of a particle or object is dependent on the density or concentration of a continuous non-quantized form of mass contained in the volume of that particle or object.

Therefore the relative mass of a proton will be greater that the mass of an electron even though the absolute magnitude of their charge is the same because the density of the continuous non-quantized form of mass is greater in the volume occupied by a proton than an electron.

Return to Contents

Chapter Nine
Electrical Potential Energy and
 Four Spatial Dimensions

An electrical potential is caused by energy gradients in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Chapter one postulated space is composed of four *spatial* dimensions and a continuous non-quantized form of mass and energy.

in Chapter eight the relative masses of a proton and electron were derived in terms the existence of three-dimensional "high and low energy volumes" caused by energy gradients in the "surface" of a three-dimensional space manifold with respect to a fourth *spatial dimension.  It was shown the relative mass of a proton and electron are related to the density of a continuous non-quantized form of mass in these "energy volumes"

Chapter Ten will show these energy "gradients" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would effect its "surface" similar to the way the energy or pressure gradients called high and low pressure areas in the earth's atmosphere effect the surface of mercury in a barometer.

A barometer consists of a U shaped glass tube filled with mercury that has one side sealed with the air removed so the air pressure on that side of the U tube is close to zero.

The energy gradients in the earth's atmosphere called high or low pressure areas cause the surface of the mercury in the open tube upward or downward with respect to the surface of the mercury in the sealed end of the tube.  The direction of the energy of air molecules determines which way the mercury moves.  In a high pressure area the mercury moves downward because the energy of the air molecules is directed downward.  While in a low pressure area the mercury move upward relative to where it would be in a high pressure area because the downward energy of the air molecules is less than it is in a high pressure area.

The magnitude of the atmospheric energy of a high or low pressure area can be determined by measuring the separation in the surfaces of the two columns of mercury and calculating the energy or pressure required to cause that separation.

Chapter thirteen will derive the polarity of a unit charge in terms of how dimensional "high and low energy volumes" effects the "surfaces" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

It will be shown that in a three-dimensional "high energy volume" the "surface" of a three-dimensional space manifold moves "downward" because the pressure of a continuous non-quantized form of mass is directed downward towards the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  This would be analogous to how the air molecules in a high pressure area cause the surface of mercury to move downward in a barometer.

Similarly, in three-dimensional "low energy volume" the "surface" of a three-dimensional space manifold moves "upward" with respect to where it would be in a three-dimensional high energy volume because the pressure of a continuous non-quantized form of mass is directed upward towards the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  This would be analogous to how the air molecules in a low pressure area cause the surface of mercury to move upward in a barometer with respect to where it was in a high pressure area.

The magnitude of electrical energy or potential would be determined by the magnitude of the spatial separation between two "surfaces" of a three-dimensional space manifold with respect to a fourth *spatial* dimension similar to how the magnitude of the pressure of energy of high and low pressure areas is determined by the separation of the two columns of mercury.

Chapter ten will demonstrate there is a direct relationship between the magnitude of a spatial "separation" between two "surfaces" of a three-dimensional space manifold with respect to a fourth *spatial* dimension and the magnitude of the energy differential associated with that "separation".

Therefore, the relative "separation" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the "upward" or "downward" "movement" of a "surface" of a three-dimensional space manifold  associated with a positive or negative charge will result in an energy differential to be developed along a "surface" of a three-dimensional space manifold.

This spatial separation between the “surfaces” of a three-dimensional space manifold is the casualty of an electrical potential.

The relative "positions" of the "surfaces" of a three-dimensional space manifold with respect to a fourth *spatial* dimension determines the polarity of the electric potential.  If one defines the energy associated with a "surface" of a three-dimensional manifold "above" another one with respect to a fourth *spatial* dimension as positive electric potential one would define the energy associated with a "surface" of a three-dimensional manifold "below" it with respect to a fourth *spatial* dimension as negative electric potential.

This completes the derivation of an electrical potential in terms of an energy gradient in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Additionally it shows an electrical potential and the relative masses of a proton and electron share a common casualty in terms energy gradients in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension because, as was mentioned earlier, Chapter eight derived the relative masses of a proton and electron in terms of an energy gradient in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Return to Contents

Chapter Ten
The boundary between a
Third and Fourth Spatial Dimensions

We have postulated that the universe is composed of only four *spatial* dimensions and that all of the forces of nature are due to a distortion or curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

We can use an analogy of a two-dimensional creature living on surface of a piece of paper to explain how and why a curvature in a "surface" of at three-dimensional space manifold is responsible for the force of nature.

A two dimensional creature "living" on the surface of a piece of paper would not be aware the paper he was living on existed in a three-dimensional universe because his field of vision would be limited to surface or length and width of the paper.

Therefore, he or she would not be aware of the existence of the dimension of height or the third *spatial* dimension because he or she could not look in the direction of a third *spatial* dimension.

As will be shown latter, the energy three-dimensional beings use to activate their senses does NOT travel through a fourth *spatial* dimension but only on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, similar to the two-dimensional creature, the field of vision of three-dimensional beings would be limited to the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This means three-dimensional beings would not be aware of the existence of a fourth *spatial* dimension because they cannot "look" in the "direction" of a fourth *spatial* dimension.

But before we begin exploring a universe consisting of four *spatial* dimensions we must first have an understanding of how they are orientated.

We observe that we can move independently in any direction in three-dimensional space.  This indicates that the axes of three-dimensional space are not fixed to each other but are embedded into each other.

This is why we are not limited in how we can move or change the orientation of a two-dimensional plane such as the surface of a piece of paper in three-dimensional space.

Our three-dimensional space is embedded in a universe consisting of four *spatial* dimensions in a similar manner.  In other words the origins of the axes of a four dimensional universe is not rigidly fix to each other but are embedded in it allowing for the independent movement of each individual axis of four *spatial* dimensions with respect to the other axis of four *spatial* dimensions.  Therefore, it would be possible to orient each axes of a "surface" of a three-dimensional space manifold independently of its orientation to the axes of four *spatial* dimensions.  This would be analogous to how it is possible to orient a two-dimensional surface of piece of a paper in any way we chose in three-dimensional space.

If we accelerate a two-dimensional surface of a piece of paper through three-dimensional space by pushing on its center, its surface will develop a curvature with respect to three-dimensional space because of the drag generated by the space it is moving through.  A two dimensional creature living on the "surface" of the paper would not realize that the surface of the paper is curved with respect to three-dimensional space because he or she could not "look" in that direction.

Similarly if a three-dimensional object is accelerated through a fourth *spatial* dimension, its three-dimensional "surface" will develop a curvature due to the "drag" generated by its movement through four *spatial* dimensions.  This is similar to how the surface of the paper developed a curvature due to it movement through three-dimensional space.  It will be shown in Chapter fifteen that this  curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is the causality of kinetic forces.

We as three-dimensional beings would not be aware the "surface" of a three-dimensional space manifold was curved with respect to a fourth *spatial* dimension because we could not look in the direction of a fourth *spatial* dimension.

We also observe that it is possible to curl a two-dimensional surface into a sphere forming a balloon in three-dimensional space because as mentioned earlier the axes of a two-dimensional surface are not fixed to the axis of our three-dimensional space.  Additionally we observe that we can increase or decrease the magnitude of the curvature of the "surface" of the balloon by increasing or decreasing its internal pressure.

Similarly, a "surface" of three-dimensional space manifold can be curled to form a three-dimensional "sphere" in four *spatial* dimensions because axes of the "surface" of a three-dimensional space manifold are not fixed to the axes four *spatial* dimensions.  This is analogous to how a two-dimensional surface can be curled to forum a three-dimensional sphere in three spatial dimensions.  The force developed by this spherical curvature is responsible for gravitational forces.

Similar to the spherical surface of the balloon curvature in the "surface" of three-dimensional sphere will contract or expand if mass is added to or removed from its center.  This will result in increasing or decreasing the magnitude of the curvature in the surface of the three-dimensional sphere. 

It will be shown in Chapter twelve this spherical curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is responsible for gravitational forces.

In Chapter one it was postulated that space is composed four *spatial* dimension and a continuous non-quantized form of mass.

it will be shown that a curvature or distortion in a "surface" of a three-dimensional manifold caused energy gradients in four *spatial* dimensions is the causality of all forms of energy.

How and why an energy gradient in four *spatial* dimensions can distort a "surface" of a three-dimensional space manifold would be analogous to how and why the "surface" of a liquid in a barometer is distorted by the energy of air molecules in high and low pressure areas in the earth's atmosphere.

Although high and low-pressure areas have properties of three-dimensional space because they extend vertically into the atmosphere, they affect the two-dimensional surface of a liquid in a barometer.

In a high-pressure area, the surface of the liquid in a barometer becomes depressed or distorted because the energy of the air molecules is directed downward towards the surface of the liquid.

While in areas of low atmospheric pressure, the surface of the liquid in a barometer becomes elevated with respect to where it would be in a high-pressure area because the pressure is directed upward away from the surface of the liquid.

This is a result of the transfer of the energy associated with the three-dimensional high or low-pressure areas to the two-dimensional surface of the liquid. 

Similarly, the energy of a continuous non-quantized form of mass will generate four dimensional high and low "energy volumes"  in a three-dimensional space similar to the high and low pressure areas in the earth's atmosphere.

In a four-dimensional “high-energy volume”, the "surface" of a three-dimensional space manifold becomes "depressed" with respect to a fourth *spatial* dimension because the “energy pressure" is directed “downward” towards the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This would be analogous downward force of the three-dimensional high-pressure area in the earlier example depressing the two-dimensional surface of the liquid in a barometer.

Conversely in a four dimensional “low energy volume” the "surface" of a three-dimensional space manifold becomes "elevated" with respect to where it would be in a four-dimensional high energy volume because the "energy pressure" is directed “upward” away from the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

These "elevations" or "depressions" in a "surface" of a three-dimension space manifold with respect to a fourth *spatial* dimension are the causality of all of the forces of nature.

How and why this is true can be understood by using the earlier analogy involving the paper.

As mentioned earlier the orientation of the x and y plains of a surface of a piece of paper are not fixed to the dimension of height or the vertical plain of three-dimensional space because the paper can be pick up, rotated, or distorted with respect to three-dimensional space.

This causes its surface to become distorted with respect to the z or third dimension plain.  The force of gravity would then have tangential components relative to its surface because it surface it curved or distorted with respect to the three-dimensional forces associated with gravity.

Similarly as mentioned earlier the x, y, and z planes of three-dimensional space fixed to the axis of four-dimensional space.  Therefore, a "surface" of a three-dimensional space manifold could be "curled" or distorted with respect to the axis of four-dimensional space.

The tangential component of the energy associated with a distortion in "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is responsible for the forces of nature. 

This would be analogous to how gravitational forces would be developed along a distorted surface of a piece of paper in the earlier example. 

 (This "curvature" or distortion in the "surface" of a three-dimensional space manifold with respect to the fourth *spatial* dimension is analogous to the space-time curvature that Einstein postulated was responsible for the force of gravity in his General Theory of Relativity.)

One might ask how the geometry of four-dimensional space can be altered from three-dimensional space to account for the forces of nature.

This question can be answered by using the earlier analogy involving a barometer.

If the liquid in the barometer used in the earlier analogy were allowed to boil, the pressure on the two-dimensional surface of the liquid would increase because the boiling liquid, in the form of vapor, would expand towards the three-dimensional volume above the surface of the water.  This would increase the pressure on the surface of the water and cause it to move downward or become "distorted" with respect to three-dimensional space.

Similarly Chapter twelve will show that when mass is converted to energy, the energy "expands" towards a fourth *spatial* dimension.  This results in increasing the "pressure" on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension causing it to become distorted with respect to a "vertical" or "W" axis of the fourth *spatial* dimension.

If the "expansion" of mass to energy is directed only along one of the three axes of three-dimensional space, the "pressure" and the force this "pressure" causes will result in acceleration along that axis.

Another way of describing how objects in a third *spatial* dimension can have an affect on a fourth *spatial* dimension is by comparing the mechanism responsible for their interactions with a fourth *spatial* dimension to that of a steam engine.

In a steam engine, water expands in the form of steam from the two-dimensional surface of the water.  This expanding steam generates a force that distorts the two-dimensional geometry of the surface of a piston by causing it to move with respect to vertical axis of four *spatial* dimensions.

As mentioned earlier when mass is converted to energy, it “expands", in the form of energy, from the three-dimensional "surface" of the mass in the "direction" of a fourth *spatial* dimension.  This expanding mass, in the form of energy generates a force on a "surface" of a three-dimensional causing it to "move" with respect to the "vertical" or "W" axis of the fourth *spatial* dimensional.

This is analogous to how the steam in a steam engine generates the force on the surface of the piston that results in the two-dimensional surface of a piston to move or become distorted with respect three-dimensional space.

Again, we can use the analogy of a two-dimensional creature to understand how and why the energy "contained" a three-dimensional mass can alter the geometry of three-dimensional space with respect to the fourth *spatial* dimension.

However instead of "living" on the surface of a piece of paper as in the earlier example, the two-dimensional creature will be “living” on the surface of water which will also be considered the surface of a piston in a steam engine.

If the water were heated to the boiling point the steam would expand towards the volume above the surface of the water putting pressure on the surface of the water or piston causing it to move with respect to vertical axis of three-dimensional space. 

However, the two-dimensional creature living on the surface of the water or piston could not directly tell where the steam had originated that was causing the geometry of the surface of the piston to move with respect to three-dimensional space because, as mentioned earlier he or she could not "look" down in the direction that it was coming from.

But, if the two-dimensional creature had placed marks on the wall of the piston he or she could indirectly tell the geometry of the surface of the water or piston had changed by looking along the surface at those marks as the piston moved passed them.

He or she could determine the distance the surface of the piston had moved because he or she could "see" and count the marks on the wall of the piston as the surface of the piston passed them.  Since the magnitude of the force on the surface of the piston determines the distance it would move the two-dimensional creature would then have a way of determine the total force on the surface of the piston by counting these marks.

Just as a two dimensional creature cannot look down to see the volume of water below its surface where the steam originates from, we as three-dimensional beings cannot look “down” to see the "volume" of mass below a "surface" of a three-dimensional space manifold where energy originates from.

When mass "expands" to energy it generates a force on a "surface" of a three-dimensional space manifold, which results in its "surface" "moving" with respect to a fourth *spatial* dimension.

The "separation" in the "surfaces" of two three-dimensional space manifolds with respect to a fourth *spatial* dimension caused by this movement defines the relative energy volume or "energy position" between two different volumes of three-dimensional space.

In addition, three-dimensional beings could not directly tell the "surface" of a three-dimensional space manifold had "moved" or become distorted with respect to a fourth *spatial* dimension because three-dimensional beings cannot look in the direction of a fourth *spatial* dimension.

It has been and will be demonstrated throughout this paper that all forces are associated with a "curvature" , distortion or a "spatial separation" in a "surface" of a three-dimensional space manifold with respect to a  fourth *spatial* dimension.  The depth or magnitude of this "curvature" determines the relative magnitude of the forces between two points in space.

Return to Contents

Chapter Eleven
Electromagnetic energy:
a matterenergy wave?

Electromagnetic energy is propagated by a matter wave moving at the velocity of light on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Chapter one postulated that space is composed of four *spatial* dimensions and a continuous non-quantized form of mass.

In Chapter two, the quantum or particle properties of mass, energy, and electromagnetic energy were derived in terms of discrete resonant "structures" formed in space by oscillations in a continuous non-quantized form of mass.

Chapter three derived the propagation of a electromagnetic energy in terms of a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by oscillations in a continuous non-quantized form of mass.

(Louis de Broglie was the first to theorize that all particles had a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.  However, this means there must be a continuous non-quantized medium for it to be propagated on because even the smallest possible particle must have a wave component. Therefore, there must exist a continuous non-quantized medium to propagate the wave of the smallest possible particle. However, macroscopic observations of wave energy indicate that it can only be propagated on a medium made up of mass. Therefore, the success of Louis de Broglie theory indicates that a continuous non-quantized form of mass exists.)

Therefore, Chapters two and three define the mechanism response for both the wave and particle characteristics of electromagnetic energy because it defines both its wave and particle properties in terms of a common mechanism related to oscillations in a continuous non-quantized form of mass.

However, Chapters two and three did not define the mechanism responsible for the movement of a matter wave across a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

It can be shown an inertial component of a continuous non-quantized form of mass is responsible for its propagation.

The reason can be understood by comparing it to why the inertial property of a block of wood floating on the surface of water is responsible for the propagation of wave on a surface of water.

The surface of the water will represent a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension and the mass of the wood will represent the mass associated with a continuous non-quantized form of mass.

(Later in Chapter fifteen it will be shown the reason the velocity of light is universally constant, despite the fact that it is transmitted on a physical medium consisting of a continuous non-quantized of mass is because of a relativistic property of time and four *spatial* dimensions.)

When an energy source applies a force to one side of the block of wood, part of its surface will become depressed while part of it will become elevated with respect to the surface of the water.  The buoyancy of the water would force the part of the wood that was depressed back to the surface.  The momentum due to the inertia associated with the mass of the wood would cause the part that was depressed to become elevated above the surface of the water.  Gravity would then force the elevated portion of the wood back to the surface of the water.  The block of wood would oscillate back and forth in this manner generating a wave on the surface of the water.

Electromagnetic energy is propagated by a similar mechanism.

Chapter ten showed how a force applied to a "surface" of a three-dimensional space manifold will cause it to become either "depressed" or "elevated" with respect to a fourth *spatial* dimension.  The energy associated with a "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would cause the "depressed" portion back to the "surface" of that three-dimensional manifold.  The momentum due to the inertial properties of a continuous non-quantized mass component of three-dimensional space will then cause that "surface" to become "elevated" with respect to a fourth *spatial* dimension.  Then the energy associated with the "elevated" "surface" of a three-dimensional space manifold will cause it to return to the "surface" of that three-dimensional space manifold.  This will cause the "surface" of a three-dimensional space manifold to oscillate back and forth generating a wave on the "surface" of a three-dimensional space manifold.

These alternating "elevations" and "depressions" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would cause a matter wave to move across the a "surface" of a three-dimensional space manifold.

In Chapter ten all forms of energy were derived in terms of a "slope" generated in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension by a distortion or "displacement" in a "surface" of that manifold.

The "displacements" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the peaks and valleys of a matter wave would result the formation of a three-dimensional distortion in the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

The electrical component of electromagnetic energy is a result of the force associated with the "slope" of a distortion in a "surface" of a three-dimensional space manifold that is parallel to the velocity vector of the matter wave.

However, the magnetic component of electromagnetic energy is a result of the force associated with a "slope" of a distortion in a "surface" of a three-dimensional space manifold that is perpendicular to the velocity vector of the matter wave.

The reason why the electrical and magnetic components of Electromagnetic energy are always 90 degrees out of phase is because the slopes associated with these distortions with respect to a fourth *spatial* dimension will always 90 degrees out of phase with each other.

Return to Contents

Chapter Twelve
Gravity and the
Fourth Spatial Dimension

Gravitational forces are caused by a "depression" or curvature in four *spatial* dimensions and not by a curvature in a space-time manifold as postulated by the "General Theory of Relativity".

Chapter one postulated space is composed of four *spatial* dimensions and a continuous non-quantized form of mass.

Chapter eight showed the relative masses of a proton and electron were the result of a curvature in a "surface" of a three-dimensional space manifold caused by energy gradients in a continuous non-quantized form of mass.

How and why energy gradients cause a curvature in a "surface" of three-dimensional space manifold with respect to a fourth *spatial* dimension can be understood by comparing them to the energy gradients called high pressure areas in the earth's atmosphere.

The downward movement of the air molecules in high-pressure area generates a downward force on the "surface" it contacts causing it to become depressed or curved.

A similar affect occurs in four *spatial* dimensions where the energy of a continuous non-quantized form of mass is directed "downward" towards the "surface" of a three-dimensional space manifold.

The energy that is directed "downward" or "perpendicular" to a "surface" of a three-dimensional space manifold will cause its "surface" to become "curved" with respect to a fourth *spatial* dimension. 

(The curvature in space is analogous to the space-time curvature "The General Theory of Relativity" uses to define the force of gravity.  However, they differ in that "Shadows" defines this curvature in terms of four *spatial* dimensions instead of four-dimensional space-time.)

How a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension effects objects in three-dimensional space can be understood by comparing it to a marble and a rod on surface of a rubber diaphragm.

The marble on the diaphragm will represent a particle or object on a "surface" of a three-dimensional space manifold and the rod will represent the “W” axis of a fourth *spatial* dimension.

(The "W" axis of a fourth *spatial* dimension was defined earlier in Chapter ten.)

If the end of the rod is orientated perpendicular to the "surface" of the diaphragm and is allowed to touch it without putting any pressure on it, the surface of the diaphragm will remain flat.  The marble on the flat diaphragm would not move.

However, if pressure is applied to the rod, the "surface" of the diaphragm will become depressed and will no longer be perpendicular to the rod.

Gravitational forces will then have a tangential component along the "surface" of the rubber diaphragm.  The tangential component of the gravitational force directed along the "surface" of the diaphragm will cause the marble to move towards the apex of the depression.

In Chapter ten, the magnitude of all forms of energy was derived in terms of a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

As mentioned earlier "downward" pressure of a continuous non-quantized form of mass will generated a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

The energy (defined in Chapter ten) directed along a curvature in a "surface" of a three-dimensional space manifold is responsible for gravitational forces.  It causes particles and objects to "roll" towards the apex of that curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

This is analogous to the marble rolling along the "surface" of the apex of the depression in rubber diaphragm. 

The accumulation of a particles at the apex of a "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is responsible for the mass of planets, stars and galaxies.

Some say that is it impossible to define gravitational forces in terms of only four *spatial* dimensions.

However, observations of our environment indicate otherwise.

We observe that we can move independently in any direction in three-dimensional space.  This indicates that the axes of three-dimensional space are not fixed to each other but are embedded into each other.

This is why we are not limited in how we can move or change the orientation of a two-dimensional plane such as the surface of a piece of paper in three-dimensional space.

This indicates that our three-dimensional space is embedded in a universe consisting of four *spatial* dimensions in a similar manner.  In other words the origins of the axes of a four dimensional universe is not rigidly fix to each other but are embedded in it allowing for the independent movement of each individual axis of four *spatial* dimensions with respect to the other axis of four *spatial* dimensions.  Therefore, it would be possible to orient each axes of a "surface" of a three-dimensional space manifold independently of its orientation to the axes of four *spatial* dimensions.  This would be analogous to how it is possible to orient a two-dimensional surface of piece of a paper in any way we chose in three-dimensional space.

If we accelerate a two-dimensional surface of a piece of paper through three-dimensional space by pushing on its center, its surface will develop a curvature with respect to three-dimensional space because of the drag generated by the space it is moving through.  A two dimensional creature living on the "surface" of the paper would not realize that the surface of the paper is curved with respect to three-dimensional space because he or she could not "look" in that direction.

Similarly if a three-dimensional object is accelerated through a fourth *spatial* dimension, its three-dimensional "surface" will develop a curvature due to the "drag" generated by its movement through four *spatial* dimensions.  This is similar to how the surface of the paper developed a curvature due to it movement through three-dimensional space.  This curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is the causality of kinetic forces.

We as three-dimensional beings would not be aware the "surface" of a three-dimensional space manifold was curved with respect to a fourth *spatial* dimension because we could not look in the direction of a fourth *spatial* dimension.

We also observe that it is possible to curl a two-dimensional surface into a sphere forming a balloon in three-dimensional space because as mentioned earlier the axes of a two-dimensional surface are not fixed to the axis of our three-dimensional space.  Additionally we observe that we can increase or decrease the magnitude of the curvature of the "surface" of the balloon by increasing or decreasing its internal pressure.

Similarly, a "surface" of three-dimensional space manifold can be curled to form a three-dimensional "sphere" in four *spatial* dimensions because axes of the "surface" of a three-dimensional space manifold are not fixed to the axes four *spatial* dimensions.  This is analogous to how a two-dimensional surface can be curled to forum a three-dimensional sphere in three spatial dimensions.  The force developed by this spherical curvature is responsible for gravitational forces.

Similar to the spherical surface of the balloon curvature in the "surface" of three-dimensional sphere will contract or expand if mass is added to or removed from its center.  This will result in increasing or decreasing the magnitude of the curvature in the surface of the three-dimensional sphere.  This spherical curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is responsible for gravitational forces.

This indicates  that gravitational energy could be defined in terms of a magnitude of a spherical curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

The difference between gravitational and electromagnetic force is related to the causality of the physical mechanism responsible for the generation.

Electromagnetic forces were defined in Chapter eleven in terms a slope caused by the "peaks" and "valleys" of a matterenergy wave moving at the velocity of light on a "surface" of a three-dimensional space manifold with respect to a fourth "spatial" dimension.  This would cause a tangential "movement" with respect to a "surface" of three-dimensional space of objects affected by a by the "peaks" and "valleys" of a matterenergy wave. 

However, gravity is caused by a "perpendicular" force on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension by a stationary "depression" in a "surface" of a three-dimensional space manifold.  This will cause the movement of an object along a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension towards the apex of the cone generated in a "surface" of a three-dimensional space manifold.

Return to Contents

Chapter Thirteen
The relative mass of a
Unit Electric Charge

The relative masses of a proton and electron are different despite the fact that the absolute value electrical charge is the same because of the existence of a continuous non-quantized form of mass and a fourth *spatial* dimension.

In Chapter one "Shadows" postulated space is composed of four *spatial* dimensions and a continuous non-quantized form of mass.

Chapter nine derived an electrical potential in terms of displacements in four *spatial* dimensions caused by an interaction of continuous non-quantized form of mass with a "surface" of a three-dimensional space manifold.  It showed that a downward “pressure” of a continuous non-quantized form of mass would cause a “depression” in a “surface” of a three-dimensional space manifold while the upward pressure of a continuous non-quantized form of mass would cause an “elevation”.

Chapter Ten derived all forms of energy in terms of a "displacement" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, the relative "displacements" in the "surfaces" of a three-dimensional space manifold with respect to a fourth *spatial* dimension determines the polarity of an electric potential.  If one defines the energy associated with a "surface" of a three-dimensional space manifold as being "depressed" with respect to another one as positive electric potential, one would define a "surface" of a three-dimensional manifold, which was "elevated" relative to another as a negative electric potential.

This indicates that the absolute magnitude of the "displacements" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the energy of a continuous non-quantized form of mass would be responsible magnitude of electrical potential.

The mechanism responsible for generating a "displacement" between two "surfaces" of a three-dimensional space manifold can be understood by comparing the effects the energy of continuous non-quantized form of mass has on its surface to the effects the energy of air molecules in high and low pressure areas in the earth's atmosphere have on the surface of a liquid in a barometer.

A barometer is an instrument that measures atmospheric pressure by determining the separation between two surfaces of a liquid in U shaped tube. 

In a high-pressure area, one surface of the liquid becomes depressed with respect to the other because energy of the air molecules in a high-pressure area is directed downward towards the surface of the liquid.  However, in a low-pressure area that same surface of the liquid would become elevated because energy of the molecules in a low-pressure area is directed upwards away from the surface of the liquid.

Similarly, the downward or upward energy with respect to a fourth *spatial* dimension of a continuous non-quantized form of mass would cause a "surface" of a three-dimensional space manifold to become either "depressed" or "elevated" .

As mentioned earlier Chapter ten derived all forms of energy including electrical in terms of a relative displacement in the "surfaces" of a three-dimensional space manifold caused by a "depression" or "elevation" in the "surfaces" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

In Chapter two, it was shown that a particle's energy was related to a resonant system in a continuous non-quantized form of mass.  Therefore, the energy of a fundamental or unit electric charge would be related to the fundamental harmonic of that resonant system. 

Therefore, because the energy of the fundamental resonant frequency of a continuous non-quantized form of mass is identical the electrical energy associated with an "elevation" or "depression" in a "surface" of a three-dimensional space manifold with respect a four *spatial* dimension will be identical. 

This means that the magnitude of both a positive and negative unit charge will be identical.

Chapter eight derived the relative masses of a proton and electron in terms of the density of a continuous non-quantized form of mass in the "depressions" and "elevations" in a "surface" of a three-dimensional space manifold associated with a charged particle.  It was shown the density of a continuous non-quantized form of mass at the apex of a "depression" or "elevation" associated with the energy of a charge particle is related to a directional component of that energy.  The downward directed, with respect to a fourth *spatial* dimension of the electrical energy of a proton causes the density of a continuous non-quantized form of mass to be greater at the apex of the "depression" than the density a continuous non-quantized form of mass at the apex of the "elevation" caused by upward directed energy component of an electron.

Chapter twelve derived the mass of particle in terms of the quantity of a continuous non-quantized form of mass that it contained. 

Therefore, the mass of a proton will be relatively greater that the mass of an electron because the density of a continuous non-quantized form of mass is greater in the "depression" in a "surface" of a three-dimensional space manifold associated with the charge of a proton than in the "elevation" associated with the charge of an electron.

This completes the explanation of why the relative masses of a proton and electron are different despite the fact that the absolute value electrical charge is the same in terms of the existence of a continuous non-quantized form of mass and four *spatial* dimension.

Return to Contents

Chapter Fourteen
The Link between
Gravitational and Electrical forces

A link between gravitational and electrical forces can be established by analyzing a physical relationship between a continuous non-quantized form of mass responsible for gravitational forces and a slope of a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimensions responsible for electrical forces

Chapter one postulated space is composed of four *spatial* dimensions and a continuous non-quantized form of mass.

Chapter twelve derived gravitational forces in terms of the quantity of a continuous non-quantized form of mass contained a curvature or "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth "spatial" dimension.

(This curvature is analogous to the space-time curvature Einstein postulated is responsible for the force of gravity.)

Chapter nine derived electrical forces in terms of the energy associated with a slope of a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension

Chapter two defined the physical relationship between a continuous non-quantized form of mass and the energy associated with a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension in terms of the equation E=mc^2. 

This indicates that gravitational and electrical forces share a common physical link in terms of a curvature in "surface" of a three-dimensional space manifold and the relationship defined by the equation E=mc^2.

However, as Richard Feynman points out on pages 24 and 25 of in his book “The Character of Physical Laws” both gravitational and electrical forces also share another common relationship with respect to the inverse square law.

"The inverse square law appears again in the electrical laws, for instance, Electricity also exerts forces inversely as the square of the distance, this time between charges, and one thinks perhaps that the inverse square of distance has some deep significance.  No one has ever succeeded in making electricity and gravity different aspects of the same thing."

Later he talks about the ratio of gravitational attraction to electrical repulsions:

"The ratio of the gravitational attraction to electrical repulsions is given by a number with 42 digits tailing off.  (The exact number was given in a diagram as Gravitation attraction / Electrical repulsion = 1/(417 X 10^42) Now therein lies a very deep mystery.  Where could such a tremendous number come form?  If you ever had a theory from which both of these things are to come how could they come in such disproportion?  What equation has a solution which has for two kinds of forces an attraction and repulsion with that fantastic ratio."

The solution of the equation defining why the ratio of gravitational attraction to electrical repulsions have such a "fantastic ratio" can be found by analyzing the relationship between mass and electrical forces defined in Chapter two in terms of the equation E=mc^2.  Were "E" equals the magnitude of the "slope" in four-dimensional space "m" equals the magnitude of the continuous non-quantized form of mass associated with a slope in four-dimensional space and "c" equals the speed of light.

Therefore, one should be able derive an equation that will define “The ratio of the gravitational attraction to electrical repulsions” in terms of the equation E=mc^2.

Solving the equation E=m*c^2 for "m" or the continuous non-quantized form of mass responsible for gravitation forces gives m=E/c^2.

The law of gravitation states that F=g*m*m/r^2.

Substituting the equation that defines the magnitude of a continuous non-quantized form of mass in terms of the electrical energy of associated with that mass or E/c^2 into the equation that defines the law of gravitation F=g*m*m/r^2 gives F=(E/c^2)^2/r^2.

Since, as mentioned earlier the quantity of a continuous non-quantized form of mass in a "depression" in a "surface" of a three-dimensional space manifold is responsible for gravitational forces and the slope in the "surface" of a three-dimensional space manifold is responsible for electrical energy, the equation F=(E/c^2)^2/r^2 would define the ratio of the magnitude of gravitation force to the magnitude of the electrical energy associated with that continuous non-quantized form of mass. 

Using 9.0 x 20 cm/sec for the speed of light (c) squared and substituting we obtain F=E/(9.0 X 20)^2/r^2 or F=E/(8.1 X 10^41).

The value of 1/(8.1 X 10^41) represents the value of the ratio of “Gravitation attraction / Electrical repulsion” Richard Feynman was referring to in the earlier quote from his book “The Character of Physical Laws” because it numerically defines the ratio of gravitational energy to electrical energy.

However it appears to have solved the “very deep mystery” as to why the inverse square law can be applied to both gravitational and electric forces by “making electricity and gravity different aspects” of a common interaction between a continuous non-quantized form of mass responsible for gravitation force and the slope of a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension responsible for electric force and answered Mr. Feynman's question as to "how could they (gravitational and electrical forces) come in such disproportion".

Return to Contents

Chapter Fifteen
The “Relativity” of
Four Spatial Dimensions

Einstein’s "Theory of Relativity" has been one of the most successful theories in the history of modern science.

It has had remarkable success in explaining and predicting the causality of gravitational forces and the experimentally observed time dilation and mass increase associated with velocities based primarily on the consistency of the velocity of light.

However, it has also had some remarkable failures in that it has been unable to define a mechanism that can simultaneously explain or predict both the quantum properties of mass and energy and the relativistic properties of space and time.

This paper has and will shown that it is possible to explain and predict both the relativistic properties of space, time and the quantum properties of mass and energy in terms of a common mechanism with respect to the geometry of four *spatial* dimensions and the existence of a continuous non-quantized form of mass and energy.

Chapter one postulated that space was composed of four *spatial* dimensions and a continuous non-quantized form of mass and energy.

Chapter two showed how and why the quantum characteristics of mass could be explained and predicted terms of a resonant "structure" formed in a continuous non-quantized form of mass and energy.

This chapter will shown how and why the relativistic properties of space, time, mass and energy can be explained and predicted in terms of four *spatial* dimensions and the existence of a continuous non-quantized form of mass.

The "dimension" of time will be defined as only being a measure of the sequential ordering of the causality of an event and is linked to each coordinate plane of four-dimensional space by the mathematical and experimentally observed sequential ordering of events that occur in each coordinate plane.  It will be shown the geometric properties of four *spatial* dimensions is responsible for time dilation.

(The justification for defining a time only in terms of a measure of the sequential ordering of the causality of an event is because there are no mathematical or experimental observations that contradict this definition.)

Chapter twelve defined the gravitational force in terms of a curvature or "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  The magnitude of the "rest" mass of an object was derived in terms of a quantity of a continuous non-quantized form of mass "contained" in a displacement or “depression” a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by that curvature.

(The curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension this paper postulates is responsible for gravitation force would be analogous to the space-time curvature the "General Theory of Relativity" postulates is responsible for gravitational forces.)

However, Chapter ten showed a "displacement" between two "surfaces" of a three-dimensional space manifold with respect to a fourth "spatial" dimension is the casualty of all forms of energy and that the magnitude of a displacement in a "surface" of a three-dimensional space manifold determines the magnitude of the energy of a system.

Therefore, if all energy is related to a displacement in a "surface of a three-dimensional space manifold one can define the kinetic energy of a velocity in terms of a "elevation" in a "surface" of a three-dimensional space manifold.

This is because Observations show that it is possible to move in only one direction in time but two in space.  For example, it is possible to move up or down, backwards or forwards in space but only move forward in time.

However, kinetic and gravitational energy posses a similar type of symmetry in that the kinetic energy of a mass opposes or is oppositely directed from the gravitational energy of a mass.  For example, the kinetic energy of the mass of an orbiting satellite opposes the gravitation energy of the mass it is orbiting. 

Therefore, if the mechanism responsible for gravitational energy is definable in terms of a "depression" in a "surface" of a three-dimensional space manifold, kinetic energy would be definable in terms of a symmetrically opposite "elevation" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  This is possible because observations of spatial dimensions tell us the surface of a spatial dimension can move in two directions, "up" and become "elevated" or "down" and become depressed.

This means that the total mass of an object in motion would sum of two components.

The first will be the rest mass of the object defined in Chapter twelve or the quantity of a continuous non-quantized form of mass "contained" displacement associated with the "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension responsible for a gravitational field.

The second will be the quantity of a continuous non-quantized form of mass "contained" in the displacement    between the different "surfaces" of a three-dimensional space manifold caused by the kinetic energy of the relative velocity of the objects.

Therefore, the mass of an object viewed by an observer who is in motion relative to that object will be greater that the rest mass of that object and the difference will be dependent on the kinetic energy or velocity of the object.

This defines the mechanism responsible for why the mass of an object is increase when viewed by an observer who is in relative motion to that mass.

The following analogy can be used to understand and define the relationship between time, length, and velocities.

Assume that two “2 dimensional creatures” are living on the surface of two pieces of paper resting on a desktop.

Also, assume the two creatures can view the surfaces of the other piece of paper, which are separated a pencil.

If the diameter of the pencil is increased, the curvature between the surfaces of the two pieces of paper will increase.

Each of these creatures, when viewing the other piece of paper will only perceive the two-dimensional translation of the three-dimensional curvature generated by the pencil.

Therefore, each will view the distance between two points on the surface of the other as shorter since they will view that distance as a two-dimensional translation of a three-dimensional curvature in the surface of the paper.

The "movement" of “time” on both surfaces will also be affected.

Each will view the others “time” as moving slower because they will view a two-dimensional translation of its "movement" through a curvature in three-dimensional space.

Similarly, because three-dimensional beings can only view a three-dimensional translation of a "curvature" or displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the motion of an object they will view the length of an object to be shorter with respect to a similar object that is not in motion.

This is analogous to why the length of a line would appear shorter to the two-dimensional "creature" viewing the surface of the paper that was separated by the pencil.

Time will also appear to "move" slower or become dilated for objects that are motion because three-dimensional beings can only view a three-dimensional translation of a "curvature" or displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the motion of an object they will view the passage of time on that object to be slower that it would be if the object were not moving.

This is analogous to why the passage of time would appear slower to the two-dimensional "creature" viewing the surface of the paper that was separated by the pencil.

Therefore, because the magnitude of the displacement or the "curvature" an object generates in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is dependent on its velocity the magnitude of the time dilation and the foreshortening of length will be related to its relative velocity of an object.

The velocity of light is constant despite the relative motion of an observer because the foreshortening of the length or distance the light travels is proportional to the motion of the observer.  Therefore, the velocity of light will be same in all reference frames despite the relative velocities of the observers to those reference frames.

It should be remember this scenario applies to all forms of energy because, as Chapter ten showed, three-dimensional beings perceive energy in terms of the magnitude of a relative "curvature" in  "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

The Lorentz transformations derived from this theoretical model will take on the same form as the Lorentz transformations derived from Relativity.

This is because this theoretical model postulates that a displacement or curvature in "surface" of a three-dimensional space manifold, with respect to a fourth *spatial* dimension caused by the kinetic energy of an object is proportional to the velocity of light.

Therefore, because both Relativity and the above mechanism predict a physical shortening of length and a slowing of time are the result of a "curvature" or displacement in space related velocity of light, the form of the Lorentz transformations associated with the foreshortening of an object and slowing of time will be identical for both of these models.

However, this theoretical model defines the magnitude of a foreshortening of length and a slowing or dilation of time in terms of a "curvature" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of curvature in four dimensional space-time manifold as Einstein did.

Gravitational energy will also cause time to slow and length to decrease for the same reason a relative velocity causes time to slow and length to decrease.

Chapter twelve derived the mechanism responsible for gravitational energy in terms of a "curvature" caused by a "depression” in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Earlier the mechanism responsible for kinetic energy or velocity was derived in terms of a “curvature” caused by an “displacement” in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, because both gravitational and kinetic energies are derived from a common "curvature" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension they will have a similar effect on physical properties of length and time.

This means both Relativity and this paper predict an observer in a gravitational field will measure the length of an object to be shorter and passage of time to be slower with respect to an observer who is located outside of a gravitational field.

However, this paper defines this shortening of length and slowing of time in a gravitational field  in terms of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of four-dimensional space-time manifold.

The "relative" characteristics of a "curvature" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension associated with kinetic and gravitational energy would also make it impossible for an observer to determine if an acceleration is caused by a gravitational field or kinetic energy such as that from an exhaust of a rockets engine.

This is because the mechanism defined above indicates the magnitude of a force associated with both gravitational and kinetic energy is related to the absolute magnitude of a "curvature" a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension between two points in space.

Therefore, an observer could only "view" the absolute magnitude of a "curvature"  in a three-dimensional space manifold with respect to a fourth *spatial* dimension associated with an acceleration he or she was experiencing and therefore he or she would have no way to determine if it was caused by a gravitational field or an accelerated reference frame. 

Therefore, both this paper and Relativity make identical predictions with respect to the relativistic properties of space and time and the inability to determine what is causing acceleration.

However, the model presented here is a broader based because it has and will define a common mechanism responsible for both the relativistic properties of space and time and the quantum properties of mass and energy in terms four spatial dimensions and a continuous non-quantized mass and energy component of space.

Return to Contents

Chapter Sixteen
A link between Relativity and
Quantum Mechanics

One of the primary goals of a "Theory of Everything" is to provide a physical link between the relativistic properties of space and time and the quantum properties of mass and energy.  We have shown in this paper that the best way of achieving this goal may be to define the universe in terms of the existence of a continuous non-quantized form of mass and four *spatial* dimensions .

However, this would require one to redefine time in only in terms of a measure of the sequential ordering of the causality of events because the relativistic properties of space and time would be defined in terms four *spatial* dimension instead of the physical properties of a space-time dimension.

Chapter one postulated that space is composed of a continuous non-quantized form of mass and four *spatial* dimensions instead of four-dimensional space-time.

Chapter two defined the quantum properties of mass and energy in terms of a resonant system formed on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension by oscillations a continuous non-quantized form of mass.

Chapter three showed the propagation of electromagnetic energy is a result of matter wave moving at the velocity of light on a "surface" of a three-dimensional space manifold with respect to a fourth "spatial" dimension.  This matter wave generates oscillations in a continuous non-quantized form of mass that Chapter two showed would result the formation of the resonant system responsible for a photon or particle properties of electromagnetic radiation.

(Louis de Broglie was the first to theorize that all particles had a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.  However, this means there must be a continuous non-quantized medium for it to be propagated on because even the smallest possible particle must have a wave component. Therefore, there must exist a continuous non-quantized medium to propagate the wave of the smallest possible particle. However, macroscopic observations of wave energy indicate that it can only be propagated on a medium made up of mass. Therefore, the success of Louis de Broglie theory indicates that a continuous non-quantized form of mass exists.)

This provides a physical link between the wave and particle characteristics of mass, energy and electromagnetic radiation because it defines them in terms of a common mechanism related to the existence of a continuous non-quantized form of mass and four *spatial* dimensions.

Chapter twelve defined mass and gravitational force in terms of the quantity of a continuous non-quantized form of mass contained a "curvature" in a "surface" of a three-dimensional space manifold with respect to a fourth "spatial" dimension.

This provides a link between gravitational force and the quantum properties of mass and energy because it defines them in terms of a common mechanism related to the existence of a continuous non-quantized form of mass and four *spatial* dimensions.

Chapter fifteen showed that a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is responsible for the relativistic properties of space and time.  It demonstrates the Lorentz transformations that define the relativistic properties of space and time would be identical for a universe consisting of four *spatial* dimension as for one that consisted of four-dimensional space-time.

This provides a physical link between the wave and quantum properties of mass and energy and relativistic properties of space, time, and gravity because Chapters fifteen, twelve, two, and three defined them in terms of a common mechanism related to the existence of a continuous non-quantized form of mass and four *spatial* dimensions.

Adopting this theoretical model over the present quantum and relativistic theories for scientific investigations would have several advantages in achieving modern science goal of define a "Theory of Everything", primarily because it would enable scientists to define a common mechanism responsible for the both quantum and relativistic properties of all of the forces and laws of nature in terms of the existence of a continuous non-quantized form of mass and energy and four *spatial* dimensions.

Return to Contents

Chapter Seventeen
A link between Gravitational
and non-gravitational forces 

To establish a physical link between gravitational and kinetic energy requires an understanding of their causality.

Chapter one postulated the universe is made up of four *spatial* dimension instead of four-dimensional space-time. 

Chapter fifteen defined the causality of kinetic energy in terms of a "slope' of a curvature of an "elevation" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Chapter twelve derived the causality gravitational forces in terms of a "slope" of a curvature of a “depression” in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

(This "curvature" or "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension responsible for gravitational forces is analogous to a curvature in a space-time manifold that Relativity postulates is responsible for gravitational forces.)

The link between gravitational and kinetic forces can be understood by comparing the effects a “slope” in a "surface" of a three-dimensional space manifold have on an object in three-dimensional space to the effects the slope an inclined plane have on a marble.

The direction of the downward force or acceleration experienced by a marble on an incline is proportional to the slope of the incline which in tern is proportional the magnitude of the elevation in the incline.

Chapter fifteen showed the magnitude of a "slope" of the "elevation" in a "surface" of a three-dimensional space manifold would be directly related to velocity or kinetic energy of an object.

This means the forces or accelerations caused by the interaction of the kinetic energy of two moving objects would be directed away from those objects because the direction of the force would be away from the apex of the "elevation" in a "surface" of a three-dimensional space manifold.  Additionally, the magnitude of those forces would be directly related to the kinetic energy of the interacting objects because the magnitude of the "slope" in a "surface" of a three-dimensional space manifold is directly related to the magnitude of the kinetic energy of an object.

This is analogous to how the magnitude and direction of the downward acceleration of the marble on the incline in the earlier example was proportional to the slope of the incline.

Chapter twelve derived gravitational force in terms of a "slope" generated by “depression” in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  It was shown the magnitude of a "slope" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension generated by that "depression" is proportional to mass of an object.

Therefore, the magnitude of force or acceleration experienced by an object in three-dimensional space due to an interaction with the "slope" of a gravitational "depression" in a "surface" of a three-dimensional space manifold would be proportional to the mass of that object.

However, the direction of the forces or accelerations associated with the "slope" of a gravitational "depression” in a "surface" of a three-dimensional space manifold will be oppositely directed with respect to the accelerations or forces generated by a Kinetic energy "elevation" in a "surface" of a three-dimensional space manifold.

This is because an object interacting with a gravitational "depression" would attain acceleration towards, not away, from the object it is interacting with. 

This defines causality of gravitational and kinetic forces in terms of common “incline” or "slope" in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

The mechanism responsible for gravitational forces is derived in terms of an "incline" caused by a “depression” in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  This results in a force being directed towards the apex of the "depression" in a three-dimensional space manifold associated with the mass of an object.

While the mechanism responsible for forces associated with kinetic energy is derived in terms of a similar "incline" caused by a "elevation" in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  This results in a force being directed away from the apex of the "elevation" in a three-dimensional space manifold associated with the velocity of an object.

Principle of Equivalence or the inability to distinguish gravitational and kinetic or non-gravitational forces is due to the relative characteristics of the "inclines" generated by a kinetic energy "elevation" and a gravitational "depression" in a "surface" of  a three-dimensional space manifold with respect to a fourth *spatial* dimension .

In Chapter fifteen, the forces associated with kinetic energy or non-gravitational forces such as those generated by a rocket engine were defined in terms of the absolute magnitude of a *slope* in a three-dimensional space manifold caused by an "elevation" in a "surface" of a three-dimensional space with respect to a fourth *spatial* dimension.

In Chapter twelve, the forces associated with gravitational forces were defined in terms of the absolute magnitude of a "slope" in a three-dimensional space manifold generated by a "depression" in a "surface" of a three-dimensional space with respect to a fourth *spatial* dimension.

Since the absolute magnitude of a "negative slope" generated by a "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would be indistinguishable form the absolute magnitude of a "positive slope" generated by an "elevation" in the "surface" of a three-dimensional space manifold gravitational and non-gravitational or kinetic forces are indistinguishable. 

This defines a physical link between gravitational and kinetic energies in terms of their casualty and in terms of the absolute magnitude of a slope in a common curvature in four *spatial* dimensions.

Return to Contents

Chapter Eighteen
The Principal of Equivalence, Inertia
& Absolute Reference Frames with respect to
Four Spatial Dimensions

Why "The Principal of Equivalence" or the fact that the laws of physics are the same in a gravitational field as in an accelerated reference frame can be understood in by examining the causality of the forces responsible of the laws of physics in terms of four *spatial* dimensions.

Chapter twelve defined the causality of gravitational accelerations in terms of a "slope" of a "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

(This "depression" in a "surface" of the three-dimensional space manifold with respect to a fourth *spatial* dimension is analogous to a depression or curvature in a space-time manifold the General Theory of Relativity is postulates is responsible for gravitational accelerations.)

Chapter seventeen derived causality of non-gravitational accelerations in terms of the "slope" of an "elevation" a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

The laws of physics are the same in a gravitational field as in an accelerated reference frame because, as was shown in Chapters twelve and seventeen the forces responsible for those laws are generated by the absolute value of a "slope" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Since the absolute magnitude of a "negative slope" generated by a "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would be indistinguishable form the absolute magnitude of a "positive slope" generated by an "elevation" in the "surface" of a three-dimensional space manifold the laws of physics will be the same in a gravitational field and as in an accelerated reference frame.

Another aspect of "The Principal of Equivalence" is that all mass free falls with the same acceleration in a gravitational field.

The mechanism responsible for this can be understood by examining how a particle defined in Chapter two interacts with four *spatial* dimensions.

Chapter one postulated a volume of space is composed of four *spatial* dimensions and a continuous non-quantized form of mass.

Chapter two derived the quantum properties of particles in terms of resonant "systems" formed in space by oscillations in a continuous non-quantized mass.

The reason all masses free fall with the same acceleration in a gravitational field can be understood by comparing the forces generated by a gravitational field to the forces in an accelerated reference frame such as that generated by a rockets exhaust on a box of marbles.

The box will represent a mass and the marbles in the box will represent the individual quantum particles in that mass.

If a constant force, such as that produced from rocket's exhaust were applied to a box containing marbles it would move with a constant acceleration.  However, the rate of acceleration of the box would be inversely proportional to the number of marbles in the box because the mass of the box is directly proportional to the number of marbles in the box.

Another way of describing this would be to attach a string to each marble and apply a force to the strings.

If the total force applied to all of the strings were kept constant, the rate of acceleration of the box of marbles would be inversely related to the number of marbles in the box.

However, if a constant uniform force was applied individually to each string the total force on the box will vary in direct proportion to the number of marbles in the box and the rate of acceleration of the box will remain unchanged no matter how many marbles it contained.

Attaching a string to each marble in a box and applying constant uniform force individually to each string illustrates why all masses "freefall" with the same acceleration in a uniform gravitational field. 

The string will represent the "attachment" or interaction each individual quantum particle in an object has with a "surface" of three-dimensional space manifold with respect to a fourth *spatial* dimension.

As mentioned earlier Chapter twelve derived the magnitude of gravitational force to be directly related to the magnitude of the "slope" of a "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Additionally, it was shown the mass of an object was directly related to the number of quantum particles it contained.

Because each individual quantum particle in an object would be "attached" to a "surface" of a three-dimension space manifold associated with a gravitational field the total force experienced by an object in gravitational field will be a directly proportional to the number of quantum particles is contains.

This is analogous to why the total force experienced by the box of marbles with the strings attached in the earlier example varied in direct proportion the number of marbles contained in the box.

The reason all masses free fall with the same acceleration in a gravitational field is that the mass of an object would be directly proportional to the number of quantum particles it contains, the total gravitational force on an object will be directly proportional to is mass.  Therefore, all masses will freefall in a gravitational field with the same acceleration.

This explains another aspect of "The Principal of Equivalence", that an observer inside a laboratory could not determine if he or she was in a gravitational field or was in constant accelerated motion.  This is because each quantum particle that makes up a laboratory in a gravitational field or an accelerated reference frame will be interacting "freely" with the curvature in space associated with that form of acceleration.

This means an observer inside a laboratory could not determine if his or her laboratory was in uniform accelerated motion or in a gravitational field is that as mentioned earlier the absolute value of the "slope" in a "surface" of a three-dimensional space manifold with respect to fourth *spatial* dimension caused by a gravitational or non-gravitational acceleration is indistinguishable. 

However, this also means that an observable absolute reference cannot exist is because an observer cannot determine if his or her laboratory is in motion relative to another.  Therefore, because this is true for every laboratory regardless of it size every laboratory can be considered as is own absolute reference frame relative to itself.  However because every laboratory in space is a subset of the space it is occupying it cannot consider itself to be an absolute reference frame relative to the space outside of itself.

Return to Contents

Chapter Nineteen
The composition and structure of Quarks
with respect to Four Spatial Dimensions

The propose of this discussion is to derive the electrical properties of quarks in terms of pressure gradients in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

It is based on the following definitions.

There are six types of quarks UP/Down, Charm/Strange and Top/Bottom.  The Up, Charm and Top have a fractional charge of 2/3.  The Down, Strange and Bottom have a fractional charge of -1/3.

A proton is made up of two Up and one Down quark, so two quarks of 2/3, which add up to 4/3, is balanced by a quark of -1/3, to give the proton an electrical charge of +1.  By contrast, neutrons are made up of one Up quark (2/3) and two Down quarks (-1/3 + -1/3), so they add up to 0.  Thus, the neutron has electrical charge of zero.

Chapter one postulated space is composed of four *spatial* dimensions and a continuous non-quantized form of mass and energy.

Chapter thirteen derived the magnitude of a unit electric charge in terms of a "pressure gradient" in a continuous non-quantized form of mass and the effects it has on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Additionally it was shown these "pressure gradients" in a continuous non-quantized form of mass responsible for a unit electric charge has characteristics of four *spatial* dimensions therefore, it's energy will be distributed over the coordinate planes of a three-dimensional space manifold with respect to its orientation to a fourth *spatial* dimension.

The component of the "pressure gradient" is that is directed parallel to the force of that "pressure gradient" will be directed along a single coordinate plane of a three-dimensional space manifold.

However, the component of the "pressure gradient" is that is perpendicular to the force of that "pressure gradient" will be directed along the two coordinate planes of a three-dimensional space manifold that are perpendicular to the direction of the force.

In other words 2/3's of the total energy of these gradients in a continuous non-quantized form of mass would be directed along the two three-dimensional coordinate planes that are perpendicular to the "pressure gradient" in a continuous non-quantized form of mass.

The remaining, 1/3 of the total energy of the gradients in a continuous non-quantized form of mass responsible for a unit electrical charge would be directed along a single coordinate plane of three-dimensional space that was parallel to the direction of the "pressure gradient" a in continuous non-quantized form of mass.

Chapter ten defined the orientation of the axes of four-dimensional space and derived the casualty all forces in terms of a distortion or curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Therefore, a distortion generated in each individual coordinate plane of a three-dimensional space manifold by "pressure gradients" in a continuous non-quantized form of mass would define the causality of the fractional charge of quarks.

The fractional charge of Up, Charm and Top quarks would be caused by the energy of the "pressure gradients" in a continuous non-quantized form of mass that is directed along the two three-dimensional coordinate planes that are perpendicular to the direction of the force of those "pressure gradients".

Therefore, they would posses 2/3 of the total charge or energy responsible for a unit electrical charge.

The fractional charge of Down, Strange and Bottom quarks would be caused by the energy of "pressure gradients" a continuous non-quantized form of mass that is directed along a single three-dimensional coordinate plane that is parallel in to the direction of the force generated by the pressured gradient.

Therefore, they would posses 1/3 of the total charge and energy of a continuous non-quantized form of mass responsible for a unit electrical charge.

A proton is made up of two Up and one Down Quark.

One of these Up Quarks is a result of a summation of the force in a continuous non-quantized form of mass associated with a positive unit charge of a proton that is directed along the two three-dimensional coordinate planes that are perpendicular to the direction of the force generated by the pressure gradient.  Therefore, it will have a charge of 2/3 of the total positive electrical energy of the proton.

However, this results in an imbalance in the continuous non-quantized form of mass associated with the positive electrical energy of a proton that is directed along the single coordinate plane of a three-dimensional space that is parallel to the direction of the force of the energy gradients with respect to a fourth *spatial* dimension.

This is because, as mentioned earlier, the energy of a unit electric energy of a proton is distributed between all three coordinate planes of three-dimensional space.

Therefore, to balance the positive electrical energy of a proton directed along the single coordinate plane that is parallel to the direction of the force of the pressure gradient, a proton attracts an electron or a down Quark whose negative electrical energy is oppositely directed along that single coordinate plane.

This balances and restores the symmetry of the "pressure gradient" in a continuous non-quantized form of mass with respect to the single coordinate plane that is parallel to the positive electrical energy of the proton directed along that coordinate plane.

However, as mentioned earlier the "pressure gradients" in a continuous non-quantized form of mass of both a unit negative and positive electric charge are divided or distributed between all the coordinate planes of three-dimensional space.

This means there would be an imbalance in the "pressure gradient" in a continuous non-quantized form of mass associated with a proton that is directed along the two coordinate planes of three-dimensional space that are perpendicular to the "pressure gradient" in a continuous non-quantized form of mass associated with an electron or down Quark.

Therefore, to balance the energy of a continuous non-quantized mass component of a proton directed along the two coordinate planes of three-dimensional space that are perpendicular to the force generated by the pressure gradient the proton "attacks" another Up quark.

Therefore, a proton consists of two Up quarks with a charge of +2/3 and one Down quark with a charge -1/3 leaving the proton with the "pressure gradients" in an electrical charge of plus one.

A neutron is the result of a proton "absorbing" the electrical energy or combining the "pressure gradient" of a down quark that is directed along the single coordinate plane of three-dimensional space that is parallel to the "pressure gradient" of the positive electrical energy of a proton.  This results in the cancellation of the electrical energy responsible for the positive and negative electrical charges of a proton and electron along that coordinate plane of three-dimensional space.

However, the energy of the pressure gradient of an electron or down quark is also distributed along the two axes that are perpendicular to the force generated by the pressure gradient.  Therefore, the "pressure gradients" in the negative charge of an electron directed along these axes combines with the energy of the positive electrical pressure of a proton to form another down quark.

Therefore, a neutron would consist of two Down quarks and one Up quark.

This defines a physical mechanism responsible for the electrical structure of Quarks and how they combine to form protons and neutrons in terms of the geometry of fourth *spatial* dimensions and the existence of a continuous non-quantized form of mass. 

Return to Contents

Chapter Twenty
The relative masses of the
Fundamental Quantum Particles

As Brian Greene pointed out in his book "The Elegant Universe", one of the unsolved mysteries of modern particle physics is why every fundamental particle encountered to date can be group into three families.

"Physicists have recognized a pattern among these particles displayed in the following table.  The matter particles neatly fall into three groups, which are often called families.  Each family contains two of the quarks an electron or one of its cousins and one of their neutrino species.  The corresponding particle types across the three families have identical properties except for their mass, which grows larger in each successive family."

The answer to Brian Greene's question regarding why the particles in the above table have “identical properties" except for their mass, which grows larger in each successive family” is related to the resonant "structures" that defined a fundamental quantum particle in Chapter two, and a mechanism defining mass in Chapters eight and twelve.

In Chapter one "Shadows" postulated a volume of space is composed of four *spatial* dimensions and a continuous non-quantized form of mass.

Later, in Chapter two, the quantum properties of mass and energy were derived in terms of the integral energies associated with resonant "structures" formed in space by "oscillations" in a continuous non-quantized form of mass.

In Chapter twelve, the relative mass of a macroscopic object, such as a star or planet was derived in terms of a quantity of a continuous non-quantized form of mass contained in a "depression" in "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  It was shown the magnitude of a mass was related to the magnitude of a spatial *separation* or "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

(This curvature caused by a "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension this paper postulates is responsible for the mass of an object is analogous to the space-time curvature the Einstein postulated is responsible for the mass of an object mass.)

In Chapter eight the relative masses of a proton and electron were derived in terms of the relative "separation" between two "surfaces" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Chapter ten derived all forms of energy, including gravitational, electrical and thermal, in terms of the relative magnitude of a spatial "separation" with respect to a fourth *spatial* dimension of two different "surfaces" of three-dimensional space manifolds.

Together Chapters eight, twelve and ten define the relative masses and the energy of all objects, such as stars and planets and quantum particles including the fundamental ones in terms of a common mechanism related to a "separation" between two "surfaces" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This means the relative masses of the families of the fundamental quantum particles in the above table would be dependent on energy content of the environment where they are created because as Chapter ten indicated, the energy content of an environment is one of the factors that determines the spatial "separation" between two "surfaces" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, Chapter two and ten showed the masses of fundamental quantum particles cannot take on any random value because the mass associated with the particles in each family would be the result of a resonant relationship between a continuous non-quantized form of mass and energy and the energy of the environment in which they were generated.

Therefore, because there are only specific points in space where a continuous non-quantized form of mass and energy and the energy content of their environment can resonant, each of the corresponding particle type across the three families must have a specific mass related to the energy of the environment in which they were created.

The particles in the first family are found in relativity low energy environments, are relatively stable, and for the most part can be observed in nature.  However, the particles in the second and third families are for the most part unstable and can be observed only in high-energy environments of particle accelerators.  The exception is the Muon in the second family of fundamental particles, which is only observed in the high-energy environment of cosmic radiation.

The relative masses of the fundamental particles increases in each successive family because as shown in Chapter ten the higher-energy environments were they are generated in result in the corresponding particles in each successive family to be formed with a greater relative "separation" in the “surfaces” of a three-dimensional space manifold with respect to a fourth *spatial* dimension than the particle in the preceding families.

Therefore, the corresponding particles in the second family will have a greater mass than the particles in the first family because the "separation", with respect to a fourth *spatial* dimension of the three-dimensional space manifold associated with the second family is greater then the "separation", with respect to a fourth *spatial* dimension, of the three-dimensional space manifold associated with the first family.

Similarly, the corresponding particles in the third family will have a greater mass than those in the second family because the "separation", with respect to a fourth *spatial* dimension, of the three-dimensional space manifold associated with the third family is greater then the spatial "separation", with respect to a fourth *spatial* dimension, of the three-dimensional space manifold associated with the second family.

This defines the mechanism responsible for the increase in mass of the fundamental quantum particles across the three families in terms of a "separation" in surface of a three-dimensional space manifold with respect to a fourth *spatial* dimensions and the resonant properties associated with a continuous non-quantized form of mass.

The corresponding particle types across the three families have similar electrical properties because as shown in Chapter nineteen the electrical properties of a fundamental quantum particle are related to the orientation of the "W" axis of the fourth *spatial* dimension with the axis of three-dimensional space.  Therefore, each corresponding particle across the three families will have similar electrical properties because the orientation of the "W" axis of the fourth spatial dimension with respect to the axis of three-dimensional space is the same for the corresponding particles in all of the families.

This defines the physical mechanism for “The corresponding particle types across the three families having identical properties except for their mass, which grows larger in each successive family”.

Return to Contents

Chapter Twenty-One
The Origin of the Positron in
terms of Four Spatial Dimensions

The origin of the positron can be traced to an interaction between a fourth *spatial* dimension and a continuous non-quantized form of mass.

Chapter one postulated of space is composed of four *spatial* dimensions and a continuous non-quantized form of mass.

Chapter two derived the quantum properties of mass and a photon in terms of integral energies associated with a resonant "structure" formed in space by oscillations in a continuous non-quantized mass component of space.

Chapter three derived the transmission of a photon in terms of a matter wave moving at the velocity of light on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  It was shown this matter wave is formed by oscillations in a continuous non-quantized mass component of space.

(The fourth *spatial* dimension was defined in Chapter ten.)

Therefore, Chapters two and three define the mechanism responsible for both the wave and quantum properties of a photon because they define both in terms oscillations in a continuous non-quantized form of mass and energy. 

(Louis de Broglie was the first to theorize that all particles had a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.  However, this means there must be a continuous non-quantized medium for it to be propagated on because even the smallest possible particle must have a wave component. Therefore, there must exist a continuous non-quantized medium to propagate the wave of the smallest possible particle. However, macroscopic observations of wave energy indicate that it can only be propagated on a medium made up of mass. Therefore, the success of Louis de Broglie theory indicates that a continuous non-quantized form of mass exists.)

However, Chapters two and three also provide the basis for defining a physical mechanism responsible for the generation of an electron-positron pair,  described in the following article provided by Elsharony Hemetis in terms of the existence of four *spatial* dimensions and a continuous non-quantized form of mass.

"As is known electrons and positrons are identical twins with anti rotations.  This infers that the physical structure of electrons and positrons are polar structures.  Yes they are.  A Photon is a magnetic field tornado of double conical structure with the Electron and positron connected at the base.  If a Photon hits or enters the premises of a (super intensity) magnetic field, it breaks up forming a positron-electron pair.  The electric charge is a function of the direction of the magnetic flux entering the base of the tornado or leaving out from it.  Think of positrons as a magnetic flux pump made of magnetic flux similar to air and tornadoes.  This theory infers that there is nothing such as elementary particles.  The word elementary is a relatively absolute or a temporarily absolute that reflects the latest scientific analysis of physical structures."

The mechanism responsible for generating an electron positron pair can be understood by comparing the oscillations in a continuous non-quantized form of mass to the oscillations associated with a wave on a surface of water.

Oscillations of water generate a wave on its surface, which displaces the vertical volume of water below the surface with air while the peak of the wave displaces the air above the surface of the water with water.

Similarly, oscillations of a continuous non-quantized form of mass would generate a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

The trough of a matter wave would displace a continuous non-quantized mass component of three-dimensional space below a "surface" of a three-dimensional space manifold with a component of four-dimensional space.  While the peak of a matter wave would displace a "volume" of four-dimensional space above a "surface" of a three-dimensional space manifold with a quantity of a continuous non-quantized mass component of three-dimensional space.

In Chapter eleven, the electrical and magnetic components of a photon were derived in terms of the "direction" of the forces associated with oscillations in a continuous non-quantized form of mass.

The electrical component of a photon’s energy was derived in terms of the energy associated with the sinusoidal oscillations in a continuous non-quantized form of mass that are parallel to the velocity vector of a photon and the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

While the magnetic component of a photon’s energy was derived in terms of the energy associated with sinusoidal oscillations in continuous non-quantized form of mass that are perpendicular or tangential to the velocity vector of a photon and a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

The formation of an electron-positron pair described in Hemetis's article is caused by a "torque" generated by a super intense magnetic field on the polar magnetic field of the matter wave responsible for the propagation of a photon's energy.

Because of the orientation of the magnetic component of a matter wave it will experience a force while transversing a magnetic field which will cause a “twisting” of its "orientation" so that its energy will no longer be moving parallel to the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Because the energy of the matter wave will no longer moving parallel to the "surface" of a three-dimensional space manifold a portion of a continuous non-quantized form of mass component of space will become "elevated" with respect to a fourth *spatial* dimension while a portion will become "depressed".   The "elevated" portion of a continuous non-quantized of mass component of space "above" a surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension will be identical but oppositely directed from the one "below" a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Chapter nine, derived a negative charge in terms of the energy associated with a separation in a "surface" of a non-quantized mass component of three-dimensional space, while a positive electrical charge was defined in terms of an oppositely "directed" separation in a "surface" of a non-quantized mass component of three-dimensional space

As mentioned earlier, when a photon passes through a supper intense magnetic field a twisting force or torque will be generated on a matter wave associated with the propagation of a photon's energy.

As was shown eariler, "torque" will result in a portion of the "surface" of a continuous non-quantized mass components of space to become "elevated" and a portion to become "depressed" with respect to a fourth spatial dimension.

The continuous non-quantized mass component of space "above" the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension will have all of the electrical properties associated with an electron defined in Chapter thirteen. 

However, the continuous non-quantized mass component of space "below" the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension will be oppositely directed with respect to the one associated with an electron  "above" the "surface" of a three-dimensional space manifold.  Therefore, it will have a positive electric charge associated with a positron.

In Chapter eight the mass of an electron was derived in terms of the “quantity” of a continuous non-quantized mass component of space contained “elevation” in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

As mentioned earlier the "torque" caused by the passage of a photon through a supper intense magnetic field would generate two oppositely but identical displacements in continuous non-quantized form of mass; one  "above" and one below a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

The continuous non-quantized mass component of space contained in an "elevation" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension generated when a photon passes through a super intense magnetic is responsible for the mass of an electron.

However, as previously mentioned, the torque generated on a photon as it transverses a super intense magnetic field will generate an oppositely directed displacement or "depression" in a "surface" of a three-dimensional space manifold that is equal in magnitude to the "elevation" associated with an electron.

This means it will have the same quantity of a continuous non-quantized mass component of space as an electron but it will be oppositely "directed" with respect to a "surface" of a three-dimensional space manifold.  Therefore, it will have the mass associated with positron.

Chapter ten derived energy in terms of the absolute magnitude of a displacement caused by an "elevation" or "depression" in a "surface" of a three-dimensional space manifold with respect to fourth *spatial* dimension. 

Therefore, when a positron and electron combine they will release the energy associated with absolute value of their combined mass.

This defines the origin and physical characteristics of the positron in terms of an interaction between a fourth *spatial* dimension and a continuous non-quantized form of mass and energy.

Return to Contents

Chapter Twenty-Two
Dimensional Mechanics in terms
 of four *spatial* dimensions

Einstein predicted the relativistic properties of space, time and that E=Mc^2 based primarily on the observation that the velocity of light remained constant despite the motion of an observer.  He used conceptual thought experiments and mathematical arguments to justify the equation E=mc^2.  His arguments were credible enough for some to expend the energy necessary to see if his predication that mass could be converted to energy was possible.

This resulted in the development of nuclear power.

This paper also uses mathematical and conceptual thought experiments similar to those of Einstein to demonstrate the universe is composed of a four-dimensional *spatial* manifold instead of four-dimensional space-time.

Additionally Chapters two, three, and fifteen derives the relativistic properties of space and time, the quantum properties of mass and the consistency of the velocity of light in terms of a common physical mechanism with respect to four *spatial* dimensions.

Unfortunately, Einstein's theories could only derive a mechanism responsible for the relativistic properties of space and time and not one that could account for the quantum properties of mass and energy.

Therefore, the arguments presented in this paper would appear to be more credible and universally applicable than those presented by Einstein because they define a common mechanism responsible for both relativistic properties of space and time and the quantum prosperities of mass where his theories could not.

What humankind must determine is if the arguments presented in this paper are credible enough to justify expending the energy necessary to examine the all of the possibilities, including high-speed inter-dimensional communications systems and energy “wave guides" for transporting energy from one point in three-dimensional space to another through a fourth *spatial* dimension.

However, the development of a device called a "Magnetic Resonator" may be another potential benefit that could arise from analyzing the concepts presented this paper.

Chapter eleven derived the accelerations associated with magnetic forces in terms of a tangential force on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

If one could fabricate a "Magnetic Resonator", a device that generates two concentric independently rotating spherical magnetic fields it MAY be possible to use power generated by this device to accelerate objects to velocities close to that of light.

It must be designed so that the orientation of the rotational axes of the magnetic spheres can be change with respect to each other.

According to the concepts developed in Chapter eleven if one misaligns the orientation of the rotational axis of the two magnetic spheres so that their magnetic poles do not line up a differential "force" with respect to a fourth *spatial* dimension, will be developed between the internal and external volumes of space associated with the "Magnetic Resonator".  This will result in accelerating the "Magnetic Resonator" and its contents through space.

If the generators of the magnetic fields were located internal to the spheres, the acceleration could be maintained as the magnetic spheres moved thought space.

Additionally, if the strength of the magnetic fields is large enough it may be possible to "lift" the "Magnetic Resonator" and its contents "out" of a three-dimensional space into a fourth *spatial* dimension were according to the theoretical predictions of this paper it could travel faster than the speed of light.

It should be pointed out that traveling through space is different from traveling in space.

This can be understood by comparing space travel using these concepts to traveling in an aircraft.

When an aircraft is flying only the external parts of an aircraft, the wings and fuselage, are traveling in the atmosphere and are exposed to the forces associated with the velocity of the wind.  However, the people in the cabin of the aircraft are flying through atmosphere and therefore do not experience the forces associated with the wind.

In other words, the wings and fuselage absorb all of the forces associated with the wind generated by the motion of the aircraft shielding the people traveling in the cabin are from them.

A similar effect would occur when a “"Magnetic Resonator"” is moving in space.

Only the external parts or the magnetic shells of the "Magnetic Resonator", which are traveling in space, will be exposed to the forces associated with acceleration and motion.  However, the objects internal to the magnetic spheres would be moving through space and therefore would not experience the forces associated with acceleration.

This is analogous to how objects and people in the cabin of an aircraft do not feel the forces associated with the wind.

In other words, the magnetic spheres of a "Magnetic Resonator" will absorb some, if not all, of the forces associated with the accelerations generated by the motion of a "Magnetic Resonator" through space.

Unfortunately, human civilization presently does not have the technology or access to the large energy resources required to make this mode of transportation practical.

However, there are a number of ways in which the dimensional properties of space can be developed with present technologies for the benefit of humankind such as the development of high speed communications networks by using the faster than light data transfer speeds in the fourth *spatial* dimension and inter-dimensional energy "wave guides" for directly "tapping" the internal energy of stars.

The explanation of the "Magnetic Resonator" was not meant to show us how to build it, but to give a very basic understanding of the dimensional mechanics associated with a universe of four *spatial* dimensions and give direction to our imagination and intellect.

However, the number of benefits of these ideas can bring to humankind is only limited by the imagination and intellect of those who explore them.

Return to Contents

Chapter Twenty-Three
The Unification of Quantum
 and Relativistic Theories

The theoretical model presented in this paper has and will shown it is possible to define a common unifying mechanism responsible both the quantum and wave properties of mass and energy and relativistic properties of space and time in terms of the existence of four *spatial* dimensions and a continuous non-quantized form of mass and energy.

In this chapter an experimental procedure will be outlined that will allow for a quantitative measurement of the physical properties associated with a fundamental component of this theoretical model, a continuous non-quantized form mass and will enable verification of the mechanisms and processes presented in this paper.

Chapter one postulated a volume of space is composed of four *spatial* dimensions and a continuous non-quantized form of mass.

Chapter two derived the quantum characteristics of mass in terms of integral energies associated with a resonant "system" formed in space by "oscillations" in a continuous non-quantized form of mass and energy.

Chapter three derived the propagation of a photon in terms of a matter wave moving at the velocity of light on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  It was shown this matter wave is the result of "oscillations" in a continuous non-quantized form of mass.

Therefore, Chapters two and three define a common mechanism responsible for both the quantum and wave characteristics of a photon because they define both in terms of "oscillations" in continuous non-quantized form of mass.

(Louis de Broglie was the first to theorize that all particles had a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.  However, this means there must be a continuous non-quantized medium for it to be propagated on because even the smallest possible particle must have a wave component. Therefore, there must exist a continuous non-quantized medium to propagate the wave of the smallest possible particle. However, macroscopic observations of wave energy indicate that it can only be propagated on a medium made up of mass. Therefore, the success of Louis de Broglie theory indicates that a continuous non-quantized form of mass exists.)

Chapter fifteen derived the relativistic properties of space and time in terms of a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Chapter twelve derived gravitational forces in terms of the quantity of a continuous non-quantized form of mass contained in a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, Chapters two,  three,  fifteen and twelve define a common mechanism responsible for both the quantum and wave properties mass, energy, and the relativistic properties of gravity, space and time by defining them in terms of the existence of four *spatial* dimensions and a continuous non-quantized form of mass and energy. 

The following discussion will describe an experimental technique, which will allow for direct observation and quantification of a continuous non-quantized form of mass this theoretical model postulates is fundamentally responsible for both the quantum properties and mass and energy and the relativistic properties of space and time. 

In the following article which appeared in the Physics News Update The American Institute of Physics Bulletin of Physics News http://www.aip.org/physnews/update/ Number 391, September 15, 1998 by Phillip F.  Schewe and Ben Stein of NASA reported observing an anomalous acceleration in several of its space probes that is consistent with this paper concept of a continuous non-quantized form of mass.  (These findings of Phillip F Schewe and Ben Stein were confirmed in Physics News update http://www.aip.org/physnews/update/ article 447)

ANOMALOUS ACCELERATION Data from several spacecraft, including Pioneer 10 and 11, Galileo, and Ulysses provide evidence for an unexplained, weak, long-range acceleration, a new report shows.  Position and velocity information is derived from radio signals sent from the craft to the Deep Space Network back on Earth.  Any change in velocity over time can be ascribed to a variety of known sources: the sun and planets, the solar wind, the Milky Way, the Kuiper belt, etc.  But even after taking this all into account, as well as other possibilities such as the presence of dark mass in the solar system (only a millionth of a solar mass of dark mass could reside within the orbit of Uranus, it is estimated) or gas leakage from the vehicles themselves, a small acceleration in the direction of the Sun---8 x 10-8 cm/sec^2 for Pioneer 10---remains unaccounted for.  Signs of this anomaly first appeared in the Pioneer tracking as long ago as 1980 Pioneer 10 was launched in 1972 and is presently 70 astronomical units from Earth.  Now six space scientists, armed with many years of Pioneer data, supplemented with trajectory information from Galileo and Ulysses, have carried out the first thorough analysis of the problem and find the anomaly to be as persistent as ever.  (The Voyager spacecraft are less useful for determining acceleration anomalies.)   The researchers doubt but do not rule out the possibility of a novel gravitational effect or other kind of new physics.  Alternative explanations include subtle systematic errors in the data analysis or unexpected aspects of space navigation.  Further work on this problem may extend to the observed motions of planets, comets, and the proposed Pluto Express craft.  (John D.  Anderson et al., Physical Review Letters, 5 October 1998 contact John Anderson at JPL, 818-354-3956, john.d.anderson@jpl.nasa.gov or Michael Nieto at Los Alamos, 505-667-6127, mmn@mmn.lanl.gov journalists can obtain copies of the article from AIP Public Information.)"

As mentioned earlier Chapter one, postulated a volume of space is composed of a continuous non-quantized form of mass.

If space was composed of a continuous non-quantized form of mass, it could be responsible for the anomalous decelerations observed in NASA's space probes.

The deceleration caused by a continuous non-quantized form of mass would be analogous to the slowing or decelerating effects air has on the movement of aircraft.

Air provides resistance to the movement of an aircraft causing it to slow or decelerate.

Similarly, the existence of a continuous non-quantized form of mass would provide "resistance" to a space probes movement causing it to slow or decelerate.

It should be possible to analytically verify a connection between the anomalous acceleration NASA has observed on several of its deep space probes to the existence of a continuous non-quantized form of mass by comparing the energy loss observed in NASA's space probes to the red shift observed in the emission spectra of stars.

Chapter one postulated a portion of the energy loss associated with a red shift observed in star's spectra may be due to the "resistive" or decelerative properties this paper associates with a continuous non-quantized form of mass.

Therefore if the deceleration of NASA's space probes is due to a resistive property of a continuous non-quantized form of mass, it should be possible to correlate it to the energy loss or red shift that Chapter one associates with a continuous non-quantized form of mass because they would both be related to the existence of a continuous non-quantized form of mass.

One could determine a "drag coefficient" for a continuous non-quantized form of mass by measuring the percentage of energy loss per unit of distance due to a decelerative property of a continuous non-quantized form of mass associated with the red shift of a star's spectra that was related only to the distance it traveled.  (The red shifted of light due to the relative motion of the object being observed must be factored out because it is not related to the decelerative properties of a continuous non-quantized form of mass.)

One could then use this "drag coefficient" to determine how much of observed deceleration in NASA's space probes was due to the existence of a continuous non-quantized form of mass.  If the value of the "drag coefficient' of space obtained in the above manner correlates with the anomalous energy loss or deceleration NASA has observed on its deep space probes it would have a tendency to verify the one of the fundamental postulates of this theoretical model; the existence of a continuous non-quantized form of mass.

As was pointed out in the above Physics News Update article even after taking into account "other possibilities such as the presence of "Dark Matter" in the solar system the observed deceleration of these space probes cannot be accounted for.

However, this theoretical model defines "Dark Matter" in a much broader sense than what was suggested in the article appearing in the Physics News Update regarding the deceleration of NASA space probes.  This is because it attributes existence of "Dark Matter" to a continuous non-quantized form of mass contained in a volume of space along with any other particular mass such as protons, neutrons, electrons or photons contained in that volume of space.

Therefore, one must add the decelerating properties this paper associates with a continuous non-quantized form of mass to the decelerating properties NASA associates with the particular "Dark Matter" mentioned in the above article to obtain the magnitude of the decelerations experience by the space probes.

The reason NASA's calculations regarding the decelerations on its space probes mentioned in the above article are "anomalous" is because they only used the decelerative properties they associated with the particular "Dark Matter" and did not factor in the deceleration that would be caused by the existence of a continuous non-quantized form of mass.

Chapter fifteen showed that time dilation and the foreshortening of length due to a velocity is related to a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension and not to a curvature in a four dimensional space-time manifold.

However, the "curvature" in a three-dimensional space manifold with respect to the fourth *spatial* dimension this theoretical model associates with gravitational fields also contributes to the current positions of NASA's in its Pioneer 10 and 11, Galileo, and Ulysses space probes.

In Chapter twelve, gravitational energy was derived in terms of a "curvature" or "depression" in a "surface" of a three-dimensional space with respect to the fourth spatial dimension.

It was shown this curvature in a "surface" of a three-dimension space manifold with respect to a fourth *spatial* dimension is analogous to the space-time curvature the Theory of Relativity predicts is the causality of gravity.

However, Chapter fifteen showed a universe consisting of four *spatial* dimensions instead of four-dimension space-time makes predictions identical in every respect, with regard to the relativistic properties of space and time, to those of the Special and General Theory of Relativity.

It defines the foreshorten of length and dilation of time due to a gravitational field in terms of a "curvature" in the "surface" of the third spatial dimension with respect to the fourth spatial dimension instead of a curvature in four dimensional space time.

Therefore, both this theoretical model and the Theory of Relativity make similar predictions regarding the positions of NASA’s Space probes with respect to the curvature in space both of these theories associate with a gravitational field.

However, this theoretical model also predicts the existence of a continuous non-quantized form of mass that if taken into account would allow NASA to make a more accurate prediction of the position of its space probes

Return to Contents

Chapter Twenty-Four
Maxwell's equations
in terms of Four Spatial Dimensions

Maxwell's equations can be derived from the existence of four *spatial* dimensions, a continuous non-quantized form of mass and the laws of classical physics.

Chapter one postulated space is composed of four *spatial* dimensions and a continuous non-quantized form of mass.

Chapter two derived the quantum characteristics of mass, energy and a photon in terms of the integral energies associated with a resonant "system" formed in space by "oscillations" in a continuous non-quantized form of mass.

Chapter three defined the propagation of a photon and electrical energy in terms of "oscillations" in a continuous non-quantized form of mass caused by a matter wave moving at the velocity of light in a continuous non-quantized form of mass.

(Chapter fifteen will shown the velocity of light is universally constant, despite the fact that it is transmitted on a physical medium consisting of a continuous non-quantized form of mass, because of a relativistic property of time and four *spatial* dimensions.)

Therefore, Chapters two and three define a common mechanism responsible for both the quantum and wave characteristics of an electrical energy because they define both in terms of "oscillations" caused by a matter wave in continuous non-quantized form of mass.

(Louis de Broglie was the first to theorize that all particles had a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.  However, this means there must be a continuous non-quantized medium for it to be propagated on because even the smallest possible particle must have a wave component. Therefore, there must exist a continuous non-quantized medium to propagate the wave of the smallest possible particle. However, macroscopic observations of wave energy indicate that it can only be propagated on a medium made up of mass. Therefore, the success of Louis de Broglie theory indicates that a continuous non-quantized form of mass exists.)

However, the existence of a continuous non-quantized form of mass and four spatial dimensions also provides the ability to define a mechanism responsible for Maxwell's equations in terms of the laws of classical physics

The "oscillations" in a continuous non-quantized form of mass responsible for generating a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is analogous to oscillations associated with a wave on the surface of water.

In a classical world, the trough of a wave on water displaces the vertical volume of water below the surface of the water with air while its peak displaces the air above the surface of the water with water.

Similarly, a "trough" of a matter wave on a "surface" of a three-dimensional space manifold would displace a volume of three-dimensional space below a "surface" of a three-dimensional space manifold with a component of four-dimensional space.  While a "peak" of a matter wave would displace a "volume" of four-dimensional space above a "surface" of a three-dimensional space manifold with a continuous non-quantized mass component of three-dimensional space.

Chapter ten derived all forms of energy in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This means the sinusoidal displacements in a "surface" of a three-dimensional space manifold caused by the "peaks" and "troughs" of a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would be responsible for the propagation of electromagnetic flux.

Electric flux is a result of the energy associated with a matter wave that is directed parallel to the velocity vector of the matter wave "along" a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, because of the geometry of four *spatial* dimensions the "peaks" and "troughs" of a matter wave will cause a force to be developed that will be tangential to the velocity vector of a matter wave on a "surface" of a three-dimensional space manifold.  This force is responsible for magnetic flux and will always be 90 degrees out of phase with the electrical flux component of the matter wave.

First the mechanism responsible for Gauss's law of Electricity, the total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity will be derived in terms of the geometric properties of four *spatial* dimensions.

Next Gauss's law of Magnetism, the net magnetic flux out of any closed surface is zero and that there are no magnetic monopoles will be defined in terms of the alignment of a "W" axis of a fourth *spatial* dimension with respect to the axes of three-dimensional space.

(The W axis of the fourth *spatial* dimension was defined in Chapter ten.)

Following that the physical mechanism responsible for Ampere's Law, the magnetic field in space around an electric current is proportional to the electric current that serves as its source will be derived in terms of an energy gradient in a three-dimensional space manifold that Chapter thirteen derived as being responsible for an electric charge. 

Then the fourth of Maxwell's equations or Faraday's law of induction that any change in a magnetic environment of a coil will cause a voltage to be "induced" in the coil that is equal to the negative rate of change of the magnetic flux times the number of turns of the coil will be derived in terms an energy gradient associated with a unit electric charge and inertial properties of a continuous non-quantized form of mass defined in Chapter one.

Gauss's law of electricity states the total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity or "integral of E*dA =Q / permittivity".

The mechanism responsible for the total electric flux out of a closed surface being equal to the charge enclosed is related to the "peaks" and "troughs" of a matter wave on a "surface" of a three-dimensional space manifold.

Chapter nine derived the magnitude of an electric charge in terms of separation between two surfaces" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  A positive electric charge was defined in terms of a "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension while a negative electric charge was defined in terms of an "elevation" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

As mentioned earlier the displacements in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the "peaks" or "elevations" and "troughs" or "depressions" of a matter wave are responsible for the propagation of electrical flux through space.

Therefore, as was shown in Chapter nine the displacements caused by the alternating "elevations" and "depressions" in a "surface" of a three-dimensional space manifold generated by a matter wave would be responsible for the transmission of positive and negative electrical energy through space.

However, as was shown in Chapter two and three the energy of a matter wave associated with charged particles form resonant "systems" or photons of electromagnetic energy in a continuous non-quantized form of mass.

Therefore the number photons of electric flux radiated through space will be dependent on the number of charged particles that generate those photons.

This indicates the total electric flux or energy out of a closed "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension surrounding an electrical charge will be equal, as Gauss's Law of Electricity states, to number of charge particles enclosed by that surface.

The fact that the total electric flux out of a closed surface must be divided by the permittivity of the volume of space an electric flux is transversing is related to the mechanism responsible for the propagating electric flux in space.

As mentioned earlier a electrical flux is propagated thought space by a matter wave in a continuous non-quantized form of mass moving at the velocity of light.

However, Chapter twelve showed there would be direct relationship between the density or permittivity of space and the density of a continuous non-quantized form of mass in that space. 

Therefore, the electric flux out of a closed surface must be divided by the permittivity of the volume of space because the attenuation of a matter wave moving though a continuous non-quantized form of mass would be directly related to the density of the continuous non-quantized form of mass that it was moving through.

This completes the derivation of the physical mechanism responsible for Gauss's law of electricity in terms of the existence of four *spatial* dimensions and a continuous non-quantized form of mass.

We will now derive the mechanism responsible for Gauss's law for magnetism, that the net magnetic flux out of any closed surface is zero and that magnetic monopoles do not exist or the integral of B*dA=0 in terms of the existence of four *spatial* dimensions.

The mechanism responsible for net magnetic flux out of a closed surface being equal to zero is related to the "alignment" or angle the "W" axis of a fourth *spatial* dimension has with respect to coordinate planes of a three-dimensional space.

(As mentioned earlier the "W" axis of the fourth *spatial* dimension was defined in Chapter ten.)

Chapter eleven indicated that magnetic flux was due a "tangential" force generated on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension by a "misalignment" of a "W" axis of a fourth *spatial* dimension with respect to the coordinate plains of three-dimensional space.

Therefore, the misalignment of a "surface" of a three-dimensional space manifold with respect to the "W" axis of a fourth *spatial* dimension caused by the "peaks" and "troughs" of a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would be responsible for the alternating polarity of the magnetic flux associated with propagation of electromagnetic energy.

However the "angle" or "alignment" a "W" axis of the fourth *spatial* dimension makes with a coordinate plain in a three-dimensional space manifold would be analogous to the angle a line makes when drawn through a plain on a coordinate graph.

A line will always make symmetrically equal and opposite angles above and below the coordinate plain it transverses.

Similarly, a “W” axis of a fourth *spatial* dimension will always make symmetrically equal and opposite angles "above" and "below" the coordinate plain in a three-dimensional space manifold it transverses.

Therefore, as was indicated in Chapter eleven the magnetic force or flux associated with a magnetic flux must always be equal and opposite "above" and "below" the three-dimensional coordinate plain it traverses.

This results in the net magnetic flux or force out of any closed surface always being equal to zero because the magnitude and "direction" of a force responsible for magnetic flux will be equal and opposite "above" and "below" a three-dimensional coordinate plain it is transversing.

This also defines the physical reason why magnetic monopoles cannot exist.

Magnetic monopoles cannot exist because the "W" axis of the fourth spatial dimension is infinite in length

This is analogous to how the each axis in three-dimensional space is infinite in length.

Therefore, magnetic monopoles do not exist because of the fact that the "W" axis of a fourth *spatial* dimension is infinite in length it must generate two magnetic fields of equal and opposite polarity "above" and "below" any coordinate plain in three-dimensional space it transverses.

This completes the derivation of the physical mechanism responsible for Gauss's law of Magnetism in terms of the orientation of "W" axis of the fourth *spatial* dimension with respect to the axes of three-dimensional space.

We will now move on and derive a physical mechanism responsible for Ampere's law that the magnetic field in space around an electric current is proportional to the electric current which serves as its source or the integral of B*ds=the permittivity of space times the current or “I”.

The mechanism responsible for Ampere's law can be derived from the "alignment" of a "W" axis of a fourth *spatial* dimension with respect to the tangential forces associated with an electron defined in Chapter thirteen.

Chapter thirteen derived electrical charges in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension while Chapter eleven defined the magnetic flux associated with a moving charge in terms of a tangential force on a "surface" of a three-dimension space manifold caused by this displacement.

In an electric current, the tangential forces associates with the magnetic flux of a charge will have a common "alignment" along the velocity vector associated with the electrically charged particles.

Therefore, the "tangential" force, which defines magnetic field in Chapter eleven, generated on a "surface" of a three-dimensional space manifold by an electric current will be aligned and additive because each will contribute  to the "tangential" force on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This results in the magnetic field in space around an electric current to be directly proportional to the electric current because, as was shown in Chapter eleven, the magnitude of a magnetic field is directly proportional to the magnitude of a "tangential" force along a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This completes the derivation of the mechanism responsible for Ampere's law in terms of the "alignment" of the "W" of the fourth *spatial* dimension and the existence of the existence of four *spatial* dimensions

Lastly we shall derive the mechanism responsible for Faraday's Law of Induction, that any change in a magnetic environment of a coil will cause a voltage to be "induced" in that coil that is equal to the negative rate of change of the magnetic flux times the number of turns of the coil or the integral of E*ds= -dB/dt.

The mechanism responsible for Faraday's Law of Induction is related to the inertial properties of a continuous non-quantized form of mass responsible for a unit electric charge defined in Chapter thirteen.

In the derivation of Gauss's law of Electricity it was shown why the total electric flux out of a closed surface is equal to the charge enclosed in terms of the existence of a continuous non-quantized form of mass and four *spatial* dimensions.

Therefore, each additional turn of a coil will add additional charges to the space effected the movement of those charges through that coil.  This will increase the total "tangential" or force generated on a continuous non-quantized form of mass in the space effected by those charges.

Later in the derivation of Ampere's law, it was shown the "tangential" force generated on a continuous non-quantized form of mass by the photon or electron in an electric current is directly related to the number of changed particle

This means each additional turn of a coil will make a proportional increase the magnitude of the magnetic flux or force associated with the current in that coil.

This defines the mechanism responsible for why the magnitude of the magnetic flux around that coil that is carrying an electric current is directly proportional to the number of turns in that coil. 

One aspect of electrical energy that has not yet been mentioned in this chapter is the mechanism responsible for the force or voltage associated with the unit electric charge.

Chapter nine derived the energy associated with the voltage and magnetic flux of an electric charge in terms of energy gradients, which as mentioned earlier, are caused by the "peaks" and "troughs" of a matter wave in a continuous non-quantized form of mass.

This suggests the change in the magnetic environment of a coil, which causes a voltage to be "induced" in that coil, may be related to the inertial properties of a continuous non-quantized form of mass associated with a charged particle.

This means that Newton’s third law of motion involving an interaction between masses which states "For every action there is an equal and opposite reaction" may be applied to the magnetic environment of a coil.

In other words, the voltage is induced in a coil is equal to the negative rate of change of the magnetic flux because a change in a continuous non-quantized component of space associated with a voltage could be considered to be an equal and opposite reaction to the change in a continuous non-quantized mass component space associated with a magnetic flux based on Newton's third law of motion.

This completes the derivation of the physical mechanism responsible for Faraday's law in terms of the energy gradient associated with the unit electric charge and inertial properties of the mass component of a "quantum mass unit of space".

This also completes the derivation of Maxwell's equations in terms of the existence of four *spatial* dimensions and a continuous non-quantized form of mass and the laws of classical physics..

Return to Contents

Chapter Twenty-Five
The Evolution of the universe in terms
of Four Spatial Dimensions

The Standard Cosmological Model of the Universe postulates the universe began as a small compact "ball" of mass that exploded producing a “big bang” and that the universe is expanding due to the aftermath of the "big bang" based, in part, on the frequency shifting of the spectral lines in EM radiation called the red shift.

Many astronomers have interpreted the red shift in EM radiation as an indication the galaxies are moving away from the earth and have calculated the rate of expansion of the universe based on the magnitude of this frequency shift.  They have assumed the frequency shift of EM radiation coming from galaxies is only due to their velocity with respect to the earth.

However, the recent observation that universe contains a measurable quantity of Dark Matter indicates that this assumption may not be valid because it would interact with EM radiation to cause a frequency shift which would not be related to the expansion of the universe.

To understand how Dark Matter or a continuous non-quantized form of mass would affect the rate of expansion of the universe and requires an understanding of how and why an interaction of EM radiation with a continuous non-quantized form of mass effects its propagation

(It should be remember, we do agree with many cosmologists that the universe is presently in an overall state of expansion however, we disagree with the currently accepted rates at which this expansion is occurring and define this expansion not in terms of a "big bang" but in terms of cycle of expansions and contractions in four *spatial* dimension.)

Chapter one postulated the universe is composed of a continuous non-quantized form of mass and four *spatial* dimensions instead of four-dimensional space-time.

Chapter two derived the quantum properties of a photon in terms of the discrete energies associated with a resonant "system" formed in space by oscillations in a continuous non-quantized mass component of space.

Chapter three defined a photon's energy in terms of oscillations in a continuous non-quantized form of mass caused by a matter wave moving on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension at the velocity of light. 

Therefore, Chapters two and three define a common mechanism responsible for both the quantum and wave characteristics of a photon and EM radiation because they define both in terms of matter wave in continuous non-quantized form of mass.

(Louis de Broglie was the first to theorize that all particles had a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.  However, this means there must be a continuous non-quantized medium for it to be propagated on because even the smallest possible particle must have a wave component. Therefore, there must exist a continuous non-quantized medium to propagate the wave of the smallest possible particle. However, macroscopic observations of wave energy indicate that it can only be propagated on a medium made up of mass. Therefore, the success of Louis de Broglie theory indicates that a continuous non-quantized form of mass exists.)

These oscillations in a continuous non-quantized form of mass responsible for generating a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would be analogous to the oscillations associated with a wave on the surface of water.

The trough of a water wave displaces a volume of water below its surface with air while the peak of a water wave displaces the air above the surface of the water with water.

Similarly a "trough" of a matter wave on a "surface" of a three-dimensional space manifold would displace a continuous non-quantized form of mass "below" a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension with a component of four-dimensional space while a "peak" of a matter wave would displace a "volume" of four-dimensional space above a "surface" of a three-dimensional space manifold with a component of three-dimensional space.

Chapter ten  showed all forms of energy were the result of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, the sinusoidal displacements in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the "peaks" and "troughs" of a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would be responsible of the propagation of EM radiation.

However, a matter wave and water wave would share another similarity in that they would both be effected by the interaction of their wave energy with the mass of the medium they are propagated on.

The frequency of a water wave decreases as it moves along the surface of the water due, in part, to an interaction with the mass of the water.  The greater the distance it travels on the water the greater the decrease in its frequency.

Similarly the frequency of a matter wave would decease as it moved along a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension due to it's interaction with a continuous non-quantized mass component of space.  The greater the distance it travels on a "surface" of a three-dimensional space manifold the greater the decrease in its frequency. 

However, it can be shown using the currently accepted laws of physics that a dissipation of EM energy resulting from a frequency shift due to its interaction with a continuous non-quantized form of mass will cause an increase the quantity of a continuous non-quantized mass component in the volume of space where that energy dissipation occurs.

Chapter two defined the quantum properties of a photon in terms of a closed resonant "system" generated by a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension.

In Chapter three, the “closed *spatial* system” defining the particle properties of a matter wave or photon was derived in terms of a dynamic interaction between a continuous non-quantized form of mass and four "spatial" dimensions.  It define the magnitude of the interactions terms of the equation E=mc^2 where "E" = the magnitude of the energy of the matter wave of a photon, m = the magnitude of a continuous non-quantized form of mass and c = the velocity of light.

According to the law of conservation of mass and energy, the sum of the mass and energy components of a close system must remain constant.

Therefore, due to the law of conservation of mass / energy, the dissipation of the energy of a matter wave due to its interaction with a continuous non-quantized form of mass MUST cause an increase in the quantity of a continuous non-quantized mass component of the space in the volume of space where that dissipation occurred.

However, Chapter two indicated a continuous non-quantized form of mass is responsible for the physical properties associated with spatial volume.

Therefore, the increase in the quantity of a continuous non-quantized form of mass will result in that volume of three-dimensional space physically "expanding" "towards" a fourth *spatial* dimension.

This means that a portion of the observed expansion of the universe associated with the energy loss of red shifted EM radiation may not be due to the recessional velocity of galaxies but instead may be due an increase in the physical volume of three-dimensional space with respect to a fourth *spatial* dimension caused by an increase in a continuous non-quantized form of mass.

However, the rate of expansion of the universe due to a conversion the energy of EM radiation to a continuous non-quantized form of mass would be related to the non-linear formula of E=mc^2.

Therefore, if this mechanism does define one of the expansive components of the universe the rate of the expansion would be less than that predicted by many cosmologists because one of the expansive components would be defined by the non-linear formula of E=mc^2 and not by the linear recessional velocity of galaxies.  This would result in a reduction of rate of expansion of the universe predicted by the assumption that the entire energy loss of EM radiation is due to the recessional velocity of galaxies.

However, it should be remember we are not sayng that the universe is not expanding, but we are saying that magnitude of the expansion may be less than predict by many of today’s cosmologists.

This model has been dismissed by many because of an observed time dilation in red shifted photons discussed at the “Errors in Tired EM radiation Cosmology” web page ( http://www.astro.ucla.edu/~wright/tiredlit.htm )

However, the fact that time dilation has been observed in red shifted photons supports the validity of this mechanism instead of refuting it because Chapter three derived the mechanism responsible for the energy loss associated with the red shifting of EM radiation in terms of a "relativistic" foreshortening or time dilation of space.

 Therefore, a time dilation should be observed if this were a valid mechanism.

Additionally, it was pointed out on the "Errors in Tired EM radiation Cosmology" page that the energy loss associated with the red shifting of EM radiation could not be cause by its interaction with particles because no "Compton effect is observed in red shifted photons.

(The "Compton Effect "is the term given to the blurring of distant objects that result from the interaction of EM radiation with particles in the space.)

The reason why many astronomers believe the entire redshift of observed in galaxies is the result of its movement away from an observer is because they assume the only way the wavelength of a photon of EM radiation can be shifted is by its interaction with another particle because classical theory of charged particles interacting with an electromagnetic wave, cannot explain any shift in wavelength.

Therefore, they assume because no Compton scattering is observed in red shifted EM energy from a star must be the result of its movement away from us.

However, this paper does not define the energy loss of EM radiation associated with a red shift in terms of an interaction with particles.

Chapter two derived the quantum properties of a photon in terms of the discrete energies associated with a resonant "system" formed in space by matter wave in a continuous non-quantized mass component of space.  Therefore, a portion of red shifting of a photon could be the result of its interaction between a continuous non-quantized form of mass and the matter wave responsible for it particle properties. Therefore it would be possible explain and predict the energy loss of the particle called a photon in terms of classical wave theory.

Presently the universe appears to be in an overall state of expansion with respect to a fourth *spatial* dimension, due to both the recessional velocity of galaxies and the physical expansion of a volume of space caused by a conversion of the energy of EM radiation to a continuous non-quantized form of mass discussed earlier.

However someday this expansion will crease and it will enter a contraction phase.

This is primarily due to the mechanism defined earlier in which EM radiation is converted to continuous non-quantized form of mass.  This will result in increasing in the total mass content of the universe and causing the total gravitational contractive forces associated with that mass to increase as time goes by.

The universe will begin to contract when the contractive forces associated with the increase mass of the universe exceeds the expansive forces associated with recessional velocity of the galaxies.

However, the contraction or "compression" of the universe will generate heat for the same reason as heat is generated by the "contraction" or compression of a gas.  But the heat of a contracting gas will generate an expansive force that will oppose the contraction of the gas.

Similarly, the heat generated by the contraction of the universe will cause an expansive force that will oppose gravitationally forces that are causing the universe to contact.

The velocity of contraction will increase until the momentum of the galaxies, planets, and the continuous non-quantized mass components of the universe equals the expansive forces generated by the heat caused by the contraction of the universe.

At this point in time the total energy of the universe would be equal to the total mass equivalent of that energy or E=mc^2, where "E" equals the total energy content of the universe and "m" equals the total mass content of the universe.  From this point on the velocity of the contraction will slow and be maintained by the momentum associated with the remaining mass component of the universe.

However, after a certain point in time the heat generated by the contraction of the universe will become great enough to convert the mass of the stars planets and the continuous non-quantized form of mass to EM radiation.  This will reduce the total mass of the universe and the total attractive gravitational forces associated with that mass.

This will result in the universe entering an expansive phase because the expansive forces associated with the heat generated by the contraction of the universe will exceed the contractive forces associated with the remaining mass of the universe.

Earlier it was shown that the interaction of EM radiation with the continuous non-quantized form of mass results in increasing the quantity of a continuous non-quantized mass contained in the volume of space where the interaction occurred.

Therefore, the quantity of a continuous non-quantized form of mass in the universe will increase as its expansion progresses.

This expansion will continue until the total gravitational attractive forces of the mass in the universe exceeds the total expansive forces cause by the heat generated by the contraction of the universe.

At this point, the contraction phase will begin again.

Since the universe is a closed system, the amplitude of the expansions and contractions will remain constant because the law of conservation of mass/energy dictates the total mass and energy of a closed system remains constant.

This results in the universe experiencing in a never-ending cycle of expansions and contractions of equal magnitudes.

Particle and star formation would not begin in the expansion phase until space had expanded enough to allow enough of the photons energy to be converted back into the continuous non-quantized form of mass to support their formation.

The Cosmic Background Radiation with the equivalent temperature of 3 degrees Kelvin discovered by Penzias and Wilson with the remnants of the energy that existed at the time when the universe changed over from an energy dominated to one containing both photons, subatomic particles and continuous non-quantized form of mass.  The sudden appearance of these “free” or subatomic particles that resulted from the conversion of a continuous non-quantized energy component of space to a continuous non-quantized form of mass destroyed the thermo equilibrium between the individual photons that had existed before the appearance of particles.  This Comic Background Radiation would appear to be almost a perfect Black Body Curve because at the instant this change over occurred the continuous non-quantized energy and mass components of space would be in thermo equilibrium because they would have been equally distributed throughout the entire volume of the universe.

Return to Contents

Conclusion

We have just begun a journey of intellect and imagination.

Just as Columbus did not know what he would find at the end of his voyage, we do not know what awaits us at the end of ours.

Many of the ideas and concepts outlined here will be modified because imagination is not reality. It will take the intellect and imagination of many to find and put all of the pieces of this puzzle together.

One person does not make a discovery; it is the result of a building of knowledge and understanding over the course of Humankind's existence.

Neil Armstrong was the first person to set foot on the moon. His voyage did not start on the lunch pad of Cape Kennedy. It began in the imagination of the first human to look at the moon and imagine what it would be like to set foot on it.

Imagination guides intellect and gives it the ability to discover reality.

If nobody had imagined traveling to the moon, no one would have tried to make the tools and devices required to make that journey a reality.

The ideas expressed in this paper allow us to imagine a universe different from the one that we are familiar with by bringing the "Shadows of another reality into clearer focus. Who knows where this imagination may take us.

By moving a piece of paper you can transport a two-dimensional creature "living" on its surface through three-dimensional space.

Just as our imagination guided our intellect to generate the tools and devices necessary to enable humankind to explore the moon it may guide us to generate the tools and devices necessary to transport humankind through four-dimensional space and allow us to explore a world limited only by our imagination.

Reality casts Shadows
Imagination illuminates Shadows
Intellect explores Shadows