The "Shadows" of four spatial dimensions®

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.

Authors: Jeffrey O’Callaghan (Author) the_imagineers@yahoo.com IM The_imagineers, Juan Echaurren (Co-Author, Collaborator) jechaurren@hotmail.com, Christian Mills (Co-Author, Collaborator, Editor) captain_mills@yahoo.com, Stefan von Weber (Collaborator) webers@fh-furtwangen.de, Tjipto Juwono (Collaborator).

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 a common mechanism related to the existence four *spatial* dimensions and a continuous non-quantized form of mass.

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. However, this indicates that a continuous non-quantized medium must exist because his theories indicate that even the smallest possible particle must have a wave component. But, macroscopic observations of waves 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.)

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 space and time in terms of a distortion or curvature 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

Imaginations search
Intellects explore

Contents


The Imagineer's Chronicles	A Theoretical blog
Shadows PDF format
Abstract
Contents	Individual Chapter web sites
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".

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.

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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 have a wave component. His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer. However, this indicates that a continuous non-quantized medium must exist because his theories indicate that even the smallest possible particle must have a wave component. But, macroscopic observations of waves 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.

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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.

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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?"

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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.

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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.

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.

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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.

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.

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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.

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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.

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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.

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