Webster’s dictionary defines curiosity, an attribute which most educational systems tries to develop in their students as the eagerness to learn, understand, question or ask why.

Why then is it that the degree of curiosity seems to decline in many students as they move through the educational system.

Granted that is a subjective statement because as of yet there is no objective test to quantify curiosity in a given student.  However as our children move though an education system their eagerness to find answers to questions like "Why is yellow yellow?" seems to wane.

One reason may be because many educators focus on the answers instead of the questions.

Many parents try to answer the unbounded curiosity of their preschooler or first grader by simply answering their questions.  However many times they continue to ask why the answer is what it is because they have not yet developed the concept of finality. 

For example I can remember asking my one of my teachers "Why is yellow yellow?".  However instead of answering she said "You tell me".  Wanting to impress her I began looking for the answer.   After a while I told her the reason is because it was no other color.  She said that I was correct.  I wore a proud smile as I told my mother and farther what I had done.  However that feeling did not last very long because I soon realized that looking for the answer had keep me occupied for quite some time.  A few days later she brought my smile back when she asked me "Why is yellow not any other color?"  That question has kept me occupied for my entire life.  Not the question but the realization that there is no finality to answers and ones curiosity regarding them.

Finality is the enemy of curiosity because it prevents the mind from going further than it normal would and an educational system that is based on it systematically inhibits it because it teaches students not to look beyond the answers.

For example, traditionally educators measure the progress of students in terms of his or her ability to answer questions based in many cases on lectures or reading assignments.  If a student does not define the answer in those terms he or she in most cases does not get credit for it.  The finality of this testing procedure conditions many to accept answers and not to question or be curious why those answers are what they are.

One cannot teach curiosity one must plant the seed.

The first step is understanding that curiosity is not defined only by the desire to find answers but a desire to look beyond them towards the future. 

One way of accomplishing this is by not asking questions that have a predefined answer.

For example asking a student "Why yellow is yellow" will force him or her to question why things are what they are.   Additionally the fact that he or she cannot find the answer in books requires him or her to look beyond traditional mental patterns developed by our educational system and devise creative solutions based on an internal conceptual analysis.

However what makes this question uniquely different from the standard questions on many tests such as "Why is the sky blue?" is that it does not have a predefined answer.   As mentioned earlier our traditional educational system expects students to define the answers to questions such as "Why is the sky is blue?" in terms of the predefined answers found in his or her text book.  This "my way or the highway" approach to education inhibits the development of curiosity because most students know that if they use it to devise a more creative solution they will most likely not get credit for their answer.  This conditions students to focus their curiosity only on what they can find in books in instead using it for creative proposes.

However the question "Why is yellow yellow?" forces the mind to create conceptual solutions based non-factual attributes of what defines a color which are not predefined in books.

Yet the most productive and beneficial forms curiosity usually begin and end in an environment external to its participants.  For example, Einstein’s Theories of Relativity began when he became curious about what the world would look like to someone riding on a beam of light, a non physical environment he could never participant in.

However most of the questions on the standard tests given by modern educators have a predefine beginning and end in a physical environment students can participate in.

For example the question "Why the sky blue?" has a beginning in the question why and an ending in the scientific explanation of the properties of light given in the physically accessible  environment of a text book. 

However the question "Why is yellow yellow?" does not have a predefined beginning because the due to its circular properties the answer in part defines the question.  Additionally because the answer cannot be found in a book students must rely on his or her ability to conceptualize the question in the non-physical environment of his intellect.

Curiosity and the ability to conceptualize solutions go hand in hand.  One can exist with the other however they support and enhance each other.

The educational value of questions like "Why is yellow yellow?" is that it forces students to rely on their internal ability to conceptualize solutions instead of their ability to find answers in a book or on the internet.

One way to keep curiosity and its creative potential alive in students as they move through an educational system is to reward them by giving them credit for internally conceptualized creative solutions that are developed independently of factual information they can derive from a book or internet.

Doctors tell us that our muscles will atrophy if one does not exercise.  Similarly the curiosity and creativity of our students atrophy if they are not exercise.

We as educators have a responsibility to allow their curiosity to roam through environments that have not already been traveled and recorded in our textbooks by asking questions that they do not contain the answers to and giving credit for independently created solutions.

Later Jeff

Copyright 2012 Jeffrey O’Callaghan

We have shown throughout the Imagineer’s Chronicles there would be many theoretical advantages to defining the universe in terms four *spatial* dimensions instead of four dimensions space-time. 

One is that it would allow one to derive a common mechanism responsible for all the forces found in nature by extrapolating observations made in a three-dimensional environment to a fourth *spatial* dimension.

Presently the Standard Model of Particle Physics links the strong and weak forces with electromagnetism through the abstract mathematical formulation called gauge symmetry.

However, for the past 50 years brightest minds in the scientist community have been unable to verify the integration of gravity through observations into its theoretical structure. 

There can be only two reasons for this.

The first is that nature has made the graviton or the gauge symmetric particle the proponents of standard model say is responsible of gravity so elusive as to make it undetectable with modern instrumentation. The second is that gauge symmetry is not responsible for gravity.

However as time goes by the first scenario becomes less and less creditable because with the increasing sensitivity of our measurement technologies and the ability modern computers to create accurate theoretical models that tell us exactly where to look for the graviton it is difficult to understand why it has not yet been observed.

Some say that the reason is because it interacts so weakly with matter that modern instruments are not sensitive enough to detect it even with, as mentioned earlier the recent exponential increase in their sensitivity.  However the proponents of the standard model will eventually have to face the reality that if it is not observed soon it may not exist and therefore the gauge symmetric foundation of the Standard Model is invalid with respect to gravitational forces.

Yet what is even more damaging to the creditability of the Standard Model is that there is an alternative explanation for the origins of the four forces that is based on the observable and therefore verifiable properties of a three-dimensional environment instead of on the unobservable abstract mathematical properties of gauge symmetry. 

As mentioned earlier one of the theoretical advantages to assuming space is composed of four *spatial* dimensions instead of four dimension space-time is that it would allow one to define a common mechanism responsible for the all of the forces of nature by extrapolating observations of a three-dimensional environment to a fourth *spatial* dimension.

For example in the article "The “Relativity” of four spatial dimensions" Dec.  1, 2007 it was shown that one can derive gravitational forces in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension in a manner that makes prediction identical to those of General Relativity without having to assume existence of the graviton.

Later the article "What is electromagnetic energy" Sep 27, 2009 showed one can derive electromagnetic forces in terms of the displacement created by a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension by extrapolating the classical laws of three-dimensional wave mechanics to a fourth *spatial* dimension.

This would enable one to define a theoretical connection between electromagnetic and gravitational forces in terms of a displacement in a "surface" of a three dimensional space manifold with respect to a four *spatial* dimension.

For example a wave on the two-dimensional surface of water causes a point on that surface to be become displaced or rise above or below the equilibrium point that existed before the wave was present.  A force will be developed by the differential displacement of the surfaces, which will result in the elevated and depressed portions of the water moving towards or become "attracted" to each other and the surface of the water.

Similarly a matter wave on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would cause a point on that "surface" to become displaced or rise above and below the equilibrium point that existed before the wave was present.

Therefore, classical wave mechanics, if extrapolated to four *spatial* dimensions tells us the force developed by the differential displacements caused by a matter wave moving on a "surface" of three-dimensional space with respect to a fourth *spatial* dimension will result in its elevated and depressed portions moving towards or become "attracted" to each other. 

However, it also provides a classical mechanism for understanding why similar charges repel each other because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement. 

Similarly the magnitude of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by two similar charges will be greater than that caused by a single one.  Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two similar charges than it would be for a single charge. 

One can define the causality of electrical component of electromagnetic radiation in terms of the energy associated with its "peaks" and "troughs" that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement. 

However, Classical Mechanics tells us a horizontal force will be developed by that perpendicular or vertical displacement which will always be 90 degrees out of phase with it.  This force is called magnetism.

This is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls matter horizontally towards from the apex of that displacement

This shows how and why a theoretical model based on the existence of four *spatial* dimension instead of four dimensional space-time would allow one to derive a physical link between electromagnetic and gravitational forces because, as the articles “The “Relativity” of four spatial dimensions" and "What is electromagnetic energy" showed on can derive both in terms of a displacement in the "surface" of three-dimensional space by extrapolating the laws of classical mechanics in a three dimensional environment to a fourth *spatial* dimension. 

This cannot be done in terms of four-dimensional space time because a time or a space-time dimension is only observed to move in one direction forward and therefore could not support the bidirectional movement required to create a differential displacement.

However it also provides a method of linking electromagnetic and gravitational forces to their quantum mechanical properties because as the article "Why is energy/mass quantized?" Oct.  4, 2007 showed one can derive their quantum mechanical properties by extrapolating the laws of classical resonance in a three-dimensional environment to a matter wave moving on a "surface" of a three dimensional space manifold with respect to a fourth *spatial* dimension. 

Briefly it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet by a matter wave in an environment consisting of four *spatial* dimensions. 

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the "surface" of a three-dimensional space (the substance) to oscillate with respect to a fourth *spatial* dimension at the frequency associated with the energy of that event.

The oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in four *spatial* dimensions.

Observations of a three-dimensional environment tell us that the energy of a resonant system can only take on the discrete or quantized values associated with the fundamental or a harmonic of its fundamental resonant

Similarly the energy of a resonant system in an environment consisting of four *spatial* dimensional environment could only take on the discrete or quantized values associated with the fundamental or a harmonic of a resonant system in that environment. 

These resonant systems are responsible for the quantum mechanical properties the energy/mass.

Yet one can also derive "The Strong and Weak forces by extrapolating the properties of resonance in three-dimensional environment to a fourth *spatial* dimension

The weak force manifests itself in the transmutation of a quark from one flavor or color to another when nuclear particles decays and is responsible for changing one quark to another quark, or a lepton to another lepton,

The mechanism responsible was for this was derived in the article the "The geometry of quarks" Mar 15, 2009.

Observations of particles indicate they are made up of distinct components called quarks of which there are six types, the 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.  Scientists have also determined that quarks can take on one of three different configurations they have designated by the colors red, blue, and green

The mechanism responsible for the fractional charge of quarks can be found in article "Embedded dimensions" which showed it is possible to define all forms of energy including electrical in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, we as three-dimensional beings can only observe three of the four *spatial* dimensions.  Therefore, the energy associated with a displacement in its "surface" with respect to a fourth *spatial* dimension will be observed by us as being directed along that "surface".

However, because two of the three-dimensions we can observe are parallel to that surface we will observe it to have 2/3 of the total energy associated with that displacement and we will observe the other 1/3 as being directed along the signal dimension that is perpendicular to that surface. 

This means the 2/3 fractional charge of the Up, Charm and Top may be related to the energy directed along a "surface" of a displaced three-dimensional space manifold with respect to a four *spatial* dimension while the -1/3 charge of The Down, Strange and Bottom may be associated with the energy that is directed perpendicular to that "surface".

The reason why quarks come in three configurations or colors with a fractional charge of 1/3 or 2/3 is be because, as was shown in the article "Embedded dimensions" there are three ways the individual axis of three-dimensional space can be oriented with respect to a fourth *spatial* dimension.  Therefore, the configuration or "colors" of each quark may be related to how its energy is distributed in three-dimensional space with respect to a fourth *spatial* dimension. 

However, it also explains why it takes three quarks of different "colors" to form a particle because, as mentioned earlier one can define a particle in terms of a resonant system on a "surface" a three-dimensional space manifold with respect to a fourth *spatial* dimension.  If the colors of each quark represent the central axis associated with its charge then to form a stable resonate system would require three quarks that have different central axis to balance its energy with respect to the axes of three-dimensional space.  A particle could not exist if two quarks have the same central axis or color because it would cause an energy imbalance along that axis.  Therefore, a particle consisting of anything but quarks of three different colors would not be stable. 

As mentioned earlier the weak force manifests itself in the transmutation of a quark or lepton from one flavor or color to another when particles decay.

However this is what one would expect if their stability was related, as shown above to the geometric configuration of their central axis because the only thing that distinguishes their color or flavor is how their central axes in the fourth *spatial* dimension orientated with respect to three-dimensional space.  If the individual quark components of a particle were not in the lowest energy configuration they would rotate around that axis until they were. 

Therefore the weak force could be derived in terms of the force required to produce the lowest energy configuration possible by the transmutation or the change of a quark or lepton from one flavor or color to another by the rotation of its central axis with respect to a fourth *spatial* dimension.

This suggests that the stability of the energy/mass components of particles such as a proton and neutrons are related to a resonant interaction between the components of three and fourth *spatial* dimensions. 

However, the fact the resonant interaction between the components of three and fourth *spatial* dimensions is strong enough overcome the repulsive electrical energy of the two up Quarks in a proton also defines the causality of the strong force and the stability of a nucleus.

The strong force is a result of the spatial separation between the protons in a nucleus becoming small enough so the excess resonant binding energy associated with their individual dimensional properties can interact.  The sharing of this excess binding energy allows the up quark of one of the adjacent protons to be replaced with a down quark resulting in the formation of a neutron consisting of one up quark and two down quarks

However, the addition of a neutron to a nucleus adds the excess binding energy associated with its resonant system without the repulsive effects associated with of the positive charge of a proton. 

Therefore, the existence of neutrons in a nucleus allows for creation of larger ones consisting of multiple positively charged protons because they add the binding energy associated with their resonant system without adding any repulsive electrical charge. 

Yet this indicates that the magnitude of the strong nuclear force would be related to the size of the nucleus. 

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

However, 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 its structure.  This will result in that nucleus expelling the energy/mass required to reduce its physical size to a point where a stable nucleonic structure can be maintained.  Therefore, any nucleus that is physically larger than this critical value will be unstable and radioactive.

Additionally, the nucleus of atoms that have an atomic weight less than the critical value would increase its weight and size by "absorbing" energy/mass from an external source.  This will result in increasing the size and atomic number of that nucleus.

This indicates that the effectiveness of the strong nuclear force in absorbing or emitting energy/mass would drop rapidly off as the distance from the nucleus increases.

This shows how one can derive mechanism responsible for the strong nuclear and weak forces by extrapolating the classical laws governing resonance in a three-dimensional environment to an environment consisting of four *spatial* dimensions.

However it also provide a physical link between them, gravitational and electromagnetic forces because it defines them in terms of a common mechanism associated with displacements in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension created by either the rest mass of an object or a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

Briefly the article "The “Relativity” of four spatial dimensions" extrapolated the laws of classical dynamics to derive gravitational forces in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension while the article "What is electromagnetic energy" Sep 27, 2009 derived electromagnetic forces in terms of the differential displacements created by a matter wave moving on a "surface" of a three dimensional space manifold with respect to a fourth *spatial* dimension.  Additionally the article "Why is energy/mass quantized?" showed one can also derive their quantum mechanical properties and those of  energy/mass and by extrapolating  the laws governing resonance in a classical three-dimensional environment to a matter wave in four *spatial* dimensions while as was just shown the strong and weak forces can also be derived in terms of a resonant properties associated with a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension

This demonstrates that if one assumes as was done here that space is composed of four *spatial* dimension instead of four dimension space-time one can theoretical unify the four forces of nature by extrapolating the classical laws of a our three-dimensional environment to displacements in  a "surface" of a three dimensional space manifold with respect to a fourth *spatial* dimension.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

We have shown throughout the Imagineer’s Chronicles and its companion book "The Reality of the Fourth *Spatial* Dimension" there would many theoretical advantages to defining the universe in terms of four *spatial* dimensions instead of four dimensional space time.

One is that it would allow one to understand the arrangement of electrons in a atom and why the four quantum numbers define them by extrapolating the properties of a classical three-dimensional environment to a fourth *spatial* dimension.

In other words one can derive the physicality of the Principal Quantum number (n),  the Angular Momentum "ℓ"  (l), Magnetic (m) and Spin Quantum Number(+1/2 and -1/2) by extrapolating the laws of a classical Newtonian environment to a fourth *spatial* dimension.

In the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown that one can derive the quantum mechanical properties of energy/mass by extrapolating the observable properties of a three-dimensional environment to a fourth *spatial* dimension.

Briefly it showed the four conditions required for resonance to occur in a classical Newtonian environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in one consisting of four spatial dimensions

The existence of four *spatial* dimensions would give the "surface" of a three-dimensional space manifold (the substance) the ability to oscillate spatially with respect to it thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

Therefore, these oscillations on a "surface" of three-dimensional space, would meet the requirements mentioned above for the formation of a resonant system or "structure" in space.

Observations of a three-dimensional environment show the energy associated with resonant system can only take on the incremental or discreet values associated with a fundamental or a harmonic of the fundamental frequency of its environment.

Similarly the energy associated with resonant systems in four *spatial* dimensions could only take on the incremental or discreet values associated a fundamental or a harmonic of the fundamental frequency of its environment.

These resonant systems in four *spatial* dimensions are responsible for the incremental or discreet energy associated with quantum mechanical systems.

However the fact that one can derive the quantum mechanical properties of energy/mass by extrapolating the resonant properties of a wave in three-dimensional environment to a fourth *spatial* dimension means that one should be able to derive the quantum numbers that define the properties of the atomic orbitals in those same terms.

As mentioned earlier there are four quantum numbers.  The first the Principal Quantum number is designated by the letter "n", the second or Angular Momentum by the letter "ℓ" the third or Magnetic by the letter "m" and the last is the Spin or "s" Quantum Number.

In three-dimensional space the frequency or energy of a resonant system is defined by the vibrating medium and the boundaries of its environment.

For example the resonant energy of a standing wave generated when a violin string plucked is determined in part by the length and tension of its strings.

Similarly the energy of the resonant system the article "Why is energy/mass quantized?" associated with atom orbitals would be defined by the "length" or circumference of the three-dimensional volume it is occupying and the tension on the space it is occupying.

Therefore the physicality of "n" or the principal quantum number would be defined by the fundamental vibrational energy of three-dimensional space that article associated with the quantum mechanical properties of energy/mass.

The circumference of its orbital would correspond to length of the individual strings on a violin while the tension on its spatial components would be created by the electrical attraction of the positive charge of the proton.

Therefore the integer representing the first quantum number would correspond to the physical length associated with the wavelength of its fundamental resonant frequency.

However, classical mechanics tells us that each environment has a unique fundamental resonant frequency which is not shared by others.

This defines physicality of the environment associated with the first quantum number and why it is unique for each subdivision of electron orbitals. Additionally observations tell us that resonance can only occur in an environment that contains an integral or half multiples of the wavelength associated with its resonant frequency and that the energy content of its harmonics are always greater the those of its fundamental resonate energy.

This allows one to derive the  physicality of the second "ℓ" or azimuth quantum number in terms of how many harmonics of the fundament frequency a given orbital can support. 

In the case of a violin the number of harmonics a given string can support is in part determined by its length.   As the length increase so does the number of harmonics because its greater length can support a wider verity of frequencies and wavelengths.  However, as mentioned earlier each additional harmonic requires more energy than the one before it.  Therefore there is a limit to the number of harmonics that a violin string can support which is determined in part by its length.

Similarly each quantum orbital can only support harmonics of their fundamental frequency that will "fit" with the circumference of the volume it occupies.

For example the first harmonic of the 1s orbital would have energy that would be greater than that of the first because as mentioned earlier the energy associated with a harmonic of a resonant system is always greater than that of its fundamental frequency.  Therefore it would not "fit" into the volume of space enclosed by the 1s orbital because of its relatively high energy content.  Therefore second quantum number of the first orbital will be is 0. 

However it also defines why in terms of classical wave mechanics the number of suborbital associated with the second quantum number increases as one move outward from the nucleus because a larger number of harmonics will be able to "fit" with the circumference of the orbitals as they increase is size.

This also shows that the reason the orbitals are filled in the order 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, 5s is because the energy of the 3d or second harmonic of the third orbital is higher in energy than the energy of the fundamental resonant frequency of the 4th orbital.  In other words Classical wave mechanics tells us the energy of the harmonics of the higher quantum orbitals may be less than that of the energy of the fundamental frequency of preceding one so their harmonics would "fit" into circumference of the lower orbitals

The third or Magnetic (m) quantum number physical defines how the energy associated with each harmonic in each quantum orbital is physically oriented with respect to axis of three-dimensional space.

For example it tells us that the individual energies of 3 "p" orbitals are physically distributed along each of the three axis of three-dimensional space.

The physicality of the fourth quantum or spin number has nothing to do with the resonant properties of space however as was shown in the article "Pauli’s Exclusion Principal: a classical interpretation" Feb. 15, 2012 one can derive its physicality by extrapolating the laws of a three-dimensional environment to a fourth *spatial* dimension.

Briefly the article "Defining potential and kinetic energy?" Nov. 26, 2007 showed all forms of energy including the angular momentum of particles can be defined in terms of a displacement in a "surface* of three-dimensional space manifold with respect to a fourth *spatial* dimension.  In three-dimensional space one can use the right hand rule to define the direction of the angular momentum of charged particles.  Similarly the direction of that displacement with respect to a fourth *spatial* dimension can be understood in term of the right hand rule.  In other words the angular momentum or energy of an electron with a positive spin would be directed "upward" with respect to a fourth *spatial* dimension while one with a negative spin would be associated with a "downwardly" directed one.

Using your right-hand: Curl your fingers into a half-circle around the wire, they point in the direction of the magnetic field, B Point your thumb in the direction of the conventional current

Therefore one can define the physically of the fourth or spin quantum number in terms of the direction a "surface" of three-dimensional space is displaced with respect to a fourth *spatial* dimension.  For example if one defines energy of a electron with a spin of -1/2 in terms of a downward directed displacement one would define a +1/2 spin as an upwardly directed one.

The physical reason why only two electrons can occupy a quantum orbital and why they have slightly different energies can also be derived by extrapolating the laws of a classical three-dimensional environment to a fourth *spatial* dimension.

There a two ways to fill a bucket.  One is by pushing it down and allowing the water to flow over its edge or by using a cup to raise it to the level of the buckets rim.

Similarly there would be two ways fill an atomic orbital according to the concepts presented in the article "Defining potential and kinetic energy?".  One would be by creating a downward displacement on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* to the level associated with the electron in that orbital while the other would be raise it up to that energy level .

However the energy required by each method will not be identical for the same reason that it requires slightly less energy to fill a bucket of water by pushing it down below its surface than using a cup to fill it.

However it also explains why no two quantum particles can have the same quantum number because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement. 

Similarly the magnitude of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by two quantum particles with similar quantum numbers would greater than that caused by a single one.  Therefore, they will repel each other and seek the lower energy state associated with a different quantum number because the magnitude of the force resisting the displacement will be less for them if they had the same number.

This shows how one can derive the physicality of the four quantum numbers by extrapolating the laws of a classical three dimensional environment to a fourth *spatial* dimension.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

We have shown throughout "The Imagineer’s Chronicles" and its companion book "The Reality of the Fourth Spatial Dimension" there would be many theoretical advantages to assuming the universe is made up of four *spatial* dimensions instead of four-dimensional space-time and that Dark matter is, in part composed of a continuous non-quantized field of energy/mass.

One of them is that, as was shown in the article "What is Dark Matter?" Sept 10, 2007 it would give a logically consistent explanation for why the gravitational component of Dark Matter is invisible.  This is because if it was composed of a continuous non-quantized field energy/mass it would be undetectable by modern scientific instrumentation which are only calibrated to detect mass in its particle or discontinuous form.  However, because this field would be made up energy/mass it would exert gravitational force.

Therefore the gravitational forces associated with that component of Dark Matter would be "dark" or invisible.

However, if Dark Matter or a continuous non-quantized field of energy/mass did make up a significant percentage of the universe’s mass, as observations suggest it would have an effect on our understanding of the evolution of the universe for two reasons.  The first is because its attractive properties would affect the evolution of the large scale structures of the universe such as galaxies and galactic clusters.  The second is because of the effect it would have on the propagation of light.

Yet before we begin to address the reason for those effects it would be beneficial to discuss some other observations that support its existence.

For example the fact that electromagnetic energy in itself is not quantized because a photon can have any frequency and therefore any energy greater than zero or less than infinity.  Additionally the equation defining the relationship between mass and energy, E=m*c^2 indicates that mass is completely convertible to one or more photons with energies greater than zero or less than infinity.  This suggests that a continuous non-quantized field of energy/mass must be available to support the continuous properties associated with the energy of the electromagnetic spectrum and that of the mathematical equation that defines the relationship between energy and mass.

Another is the confirmation in 1927 by Davisson and Germer of Louis de Broglie theory that all particles have a wave component. This is observational proof of the existence of a continuous field of energy/mass because waves are by definition a continuous form of energy and therefore the existence of a continuous field of energy/mass is necessary to support the internal wave component of particles.

However one of the strongest arguments that can be made for its existence when combined with four *spatial* dimensions instead of four dimensional space-time is that it allows one to theoretically derive the quantum mechanical properties of energy/mass and electromagnetic waves by extrapolating the observations of a three-dimensional environment to a fourth *spatial* dimension.

In the article "Why is energy/mass quantized?" Oct. 4, 2007 it was shown that one can derived the quantum mechanical properties of energy/mass and a photon by extrapolating the laws of classical resonance in a three dimensional environment to the discrete energies associated with a resonant "system" formed in four *spatial* dimensions created by a matter wave in a continuous non-quantized field of energy/mass.  However, it also showed all energy must be propagated through space in these quantized resonant systems.

Briefly it showed the four conditions required for resonance to occur in a classical three-dimensional environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in one consisting of four *spatial* dimensions.

The existence of four *spatial* dimensions would give the continuous field of energy/mass (the substance) the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the continuous field of energy/mass to oscillate with respect to a fourth *spatial* dimension at the frequency associated with the energy of that event.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in a continuous field of energy/mass.

Classical mechanics tells us the energy of a resonant system can only take on the quantized values associated with its resonant or a harmonic of its resonant frequency.

As the article "Why is energy/mass quantized?"  showed these resonant systems in a continuous field of energy/mass are responsible for the quantum mechanical properties of a photon and energy/mass.

This cannot be done in four-dimensional space-time because time is only observed to move in one direction forward and therefore it could not support the bi directional movement required for resonance to occur.

However, it is also possible to use the existence of a continuous non-quantized form of energy/mass and four *spatial* dimension to explain the internal electromagnetic wave properties of a photon in terms of the matter wave that the article "Why is energy/mass quantized?" showed was responsible for its quantum mechanical properties.

In the article "Electromagnetism in four *spatial* dimensions" Sept.27, 2007 it was shown that one can derive the electromagnetic properties of electromagnetic wave energy in terms of oscillations in a continuous non-quantized field of energy/mass generated by a matter wave moving at the velocity of light on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This can be understood by comparing a matter wave in a continuous field of energy/mass that article hypothesizes is responsible for electromagnetic energy to a wave on water.

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

Additionally, classical wave mechanics tells us a force will be developed by the differential displacement of its surfaces, which will result in the elevated and depressed portions of the water moving towards or become "attracted" to each other and the surface of the water.

Similarly, the "trough" of a matter wave in a continuous field of energy/mass would displace a volume of three-dimensional space below its "surface" with a component of four-dimensional space.  While its "peak" would displace a "volume" of four-dimensional space above a "surface" of a three-dimensional space manifold with three-dimensional space.

However, as mentioned earlier classical wave mechanics when extrapolated to a fourth *spatial* dimension tells us that a force would be developed by the differential displacements of the continuous field of energy/mass, which will result in the elevated and depressed portions "moving" towards or becoming "attracted" to each other.

Therefore, by extrapolating the laws of classical wave mechanics to four *spatial* dimensions one can derive the causality of the attractive forces of unlike electromagnetic charges in terms of a force developed by the differential displacement of a continuous field of energy/mass caused by a matter wave on that "surface".

However, it also provides a classical mechanism for understanding why similar charges repel each other because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement.

Similarly, the magnitude of a displacement in a continuous field of energy/mass caused by two similar charges will be greater than that caused by a single one.  Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two similar charges than it would be for one.

The reason electromagnetic energy is observed to be made up of discrete quantized units called photons and not a continuous wave is because, as mentioned earlier article "Why is energy/mass quantized?" showed the energy of a matter wave forms resonant "system" formed in four dimensional space.  Therefore, its energy will propagated in the quantized resonant systems called photons.

Yet if it is true that a electromagnetic waves are propagated in a continuous field of energy/mass it would affect our present understanding of the evolution of the universe because the most accepted theoretical model (the Standard Model) hypothesis the universe evolved from a small compact "ball" of energy/mass which began a rapid expansion based in part on a frequency shift in the spectral lines in light called the red shift.

In 1929 Edwin Hubble observed the characteristic colors, or spectral lines emitted by the stars in the galaxies do not have exactly the same wavelengths observed in the laboratory; rather they are systematically shifted to longer wavelengths, toward the red end of the spectrum.

He correctly assumed this change in the observed frequency of light occurs in part because its source i.e. galaxies and observer are in motion relative to each other, with the frequency increasing when the source and observer approach each other and decreasing when they move apart.  Therefore, he assumed the red shift he observed in the spectrum of galaxies meant that they were moving way.

However, he also found the further a galaxy is away from the Earth the larger its redshift and therefore its recessional velocity form the Earth is proportional to their distance from it.  Astronomers still use the formula called Hubble law he derived from these observations to predict the rate at which the universe is expanding.  It states that it is directly related to distance times a constant known as the Hubble Constant.  

Yet, as mentioned earlier the existence of Dark Matter or a continuous non-quantized field of energy/mass would affect our understanding of the evolution of the universe because it would interact with the wave properties of a photon causing them to be red shifted.  How and why this interaction occurs requires an understanding of how and why it would interact with a photon to generate a red shift which as mentioned earlier is the basis for many of the currently accepted cosmological models of its origin.

(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.)

One way of accomplishing this would be to compare the interaction of the matter wave component of a photon derived in the article "Electromagnetism in four *spatial* dimensions" with a continuous non-quantized form of energy/mass to the interaction of a wave on water to water.

The frequency and energy content of a water wave decreases as it moves along its surface due, in part, to its interaction with the inertial mass of the water.  The greater the distance it travels on the water the greater the decrease in its energy and frequency.

Similarly the frequency of the matter wave component of a photon would decrease as it moved along a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension due to its interaction with a continuous non-quantized energy/mass component of space.  The greater the distance it travels the greater the decrease in its energy and frequency.

However this "Tired Light" concept of the energy loss associated with the red shifting of photons by its interaction with space has been dismissed by many because no Compton scattering is observed in them.

Compton scattering is a type of scattering that X-rays and gamma rays undergo in matter.  The inelastic scattering of photons in matter results in a decrease in energy (increase in wavelength) of an X-ray or gamma ray photon, called the Compton Effect.  Part of the energy of the X/gamma ray is transferred to a scattering electron, which recoils and is ejected from its atom (which becomes ionized), and the rest of the energy is taken by the scattered, "degraded" photon.

Inverse Compton scattering also exists, where the photon gains energy (decreasing in wavelength) upon interaction with matter.  Since the wavelength of the scattered light is different from the incident radiation, Compton scattering is an example of inelastic scattering, but the origin of the effect can be considered as an elastic collision between a photon and an electron.  The amount the wavelength changes by is called the Compton shift.  Although nuclear Compton scattering exists Compton scattering usually refers to the interaction involving only the electrons of an atom.  The Compton Effect was observed by Arthur Holly Compton in 1923 at Washington University in St. Louis and further verified by his graduate student Y. H. Woo in the years following.  Compton earned the 1927 Nobel Prize in Physics for the discovery.

Many feel it demonstrates that light cannot be explained purely as a wave phenomenon.  Thomson scattering, the classical theory of an electromagnetic wave scattered by charged particles, cannot explain low intensity shifts in wavelength (Classically, light of sufficient intensity for the electric field to accelerate a charged particle to a relativistic speed will cause radiation-pressure recoil and an associated Doppler shift of the scattered light, but the effect would become arbitrarily small at sufficiently low light intensities regardless of wavelength.)  Light must behave as if it consists of particles to explain the low-intensity Compton scattering.  Compton’s experiment convinced physicists that light can behave as a stream of particle-like objects (quanta) whose energy is proportional to the frequency.

The reason why many astronomers believe the entire redshift of a star is the result of its movement away from an observer is, as just mentioned 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 Compton scattering in red shifted light.  Since no Compton scattering is observed in light coming from a star it is assumed by many astronomers it can only be caused by the movement of an object away from an observer because as mentioned earlier it is the only way they can explain it.

Yet as was shown in the article "Why is energy/mass quantized?" if the quantum mechanical properties of electromagnetic energy are a result of a resonant system generated by a matter wave in a continuous non-quantized field of energy/mass then Classical Wave theory tells us that a portion of the redshift may be caused by the interaction of its wave properties with a continuous non-quantized energy/mass component of space.

This would mean that the assumption that the entire redshift in a star’s spectrum is a result of its movement away from us may be invalid because the energy loss due to the interaction of the wave component of a photon with a dark matter or a continuous non-quantized field of energy/mass would result in it being redshifted.

(The article "Unifying Quantum Mechanics and the velocity of light" Feb 01, 2008 define the reason why the velocity light is constant in a vacuum despite the fact it is propagated on a continuous non-quantized field of energy/mass in terms of the geometry of four spatial dimensions.)

However the law of conservation of energy/mass tells us that it must be conserved.  Therefore, if a electromagnetic energy is redshifted or loses energy due to an interaction with a continuous non-quantized field of mass as it moves through an environment the continuous non-quantized mass component of that environment must increase. This is becuase that law and the experimentally verified equation E=mc^2 tells us that if the energy component of a close environment decrease its mass component must increase.

However it also tells us the magnitude of this interaction is quantified by the experimentally verified equation E=mc^2.

Yet as has been showed throughout the Imaginers Chronicles a magnitude of continuous non-quantized field of mass of space with respect to its continuous non-quantized energy field component determines the volume of three-dimensional space.   Therefore if one increases this ratio in a given region of space the volume associated with that region will expand.

Therefore the rate of expansion of the universe due to a conversion electromagnetic energy to a continuous non-quantized field of mass would be related to the non-linear formula of E=mc^2 because it defines their ratio in any environment.

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 its 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 the calculated rate of expansion which is based on the assumption that the entire energy loss of associated with the red shift in light is due to the recessional velocity of galaxies.

However, as mentioned earlier it should be remember we are not saying that the universe is not expanding, but we are saying that rate of that expansion may be less than predict by many of today’s cosmologists.

Presently the universe appears to be in an overall state of expansion with respect to a fourth *spatial* dimension, due to the recessional velocity of galaxies.

However, someday this expansion will crease and it will enter a contraction phase.

This is primarily due to the mechanism defined earlier in which light or electromagnetic energy is converted to continuous non-quantized field of mass.  This will result in increasing in the total mass content of the universe, with a corresponding increase in its total gravitational contractive forces.

The universe will begin to contract when the contractive force associated with the gravitational potential of this increase mass exceeds the expansive forces associated with the 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.

The heat of a contracting gas generates an expansive force that opposes further contraction.

Similarly, the heat generated by the contraction of the universe will cause an expansive force that will oppose the 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 generated by its contraction.

At this point in time the total expansive energy of the universe would be equal to the total mass equivalent of that energy or E=mc^2, where "E" equals the total expansive energy of the universe and "m" equals the total energy/mass content of the universe.  From this point on the velocity of the contraction will slow and be maintained by the momentum associated with its remaining energy/mass component.

However, after a certain point in time the heat generated by its contraction will cause its mass component to be converted back to a continuous non-quantized field of energy.  This will reduce the total mass content of the universe and attractive gravitational forces associated with it.

This will result in the universe entering an expansive phase because the radiation pressure generated by heat of its collapse will exceed the contractive forces associated with its remaining mass. 

Earlier it was shown that the interaction of an electromagnetic wave with a continuous non-quantized field of energy/mass results in increasing the quantity of a continuous non-quantized field of mass in the volume of space where the interaction occurred.

Therefore, the quantity of a continuous non-quantized field of mass in the universe will increase as it expands due to its interaction with an electromagnetic wave.

Hence the expansion will continue until the total gravitational attractive forces associated with the continuous non quantized field of mass exceeds the total expansive forces cause by the heat generated by its contraction.

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 in a closed system remains constant.

This results in the universe experiencing in a never-ending cycle of expansions and contractions of equal magnitudes.

Many cosmologists do not accept the cyclical scenario of expansion and contractions because they believe a collapsing universe would end in the formation of a singularity similar to the ones found in a black hole and therefore, it could not re-expand.

However, according to the first law of thermodynamic the universe would have to begin expanding before it reached a singularity because that law states that in an isolated system energy can neither be created nor destroyed.

Therefore, because the universe is by definition an isolated system; the energy generated by its gravitational collapse cannot be radiated to another volume but must remain within it.  This means the radiation pressure exerted by its collapse must eventually exceed momentum of its contraction and the universe would have to enter an expansion phase.  This will cause the mass/energy of the universe to oscillate around a point in space. 

This would be analogous to the how momentum of a mass on a spring causes it spring to stretch beyond its equilibrium point resulting it osculating around it. 

There can be no other interoperation if one assumes the validity of the first law of thermodynamics which states that the total energy of the universe is defined in terms of heat and the momentum of its components.  Therefore, when one decreases the other must increase and the universe must oscillate around a point in space if it does enter a contraction phase.

The reason a singularity can form in black hole is because it is not an isolate system therefore the thermal radiation associated with its collapse can be radiated into the surrounding space.  Therefore, its collapse can continue because momentum of its mass can exceed the radiation pressure cause by its collapse in the volume of space surrounding a black hole.

According to this scenario the heat generated by its collapse would have to raise the temperature enough to completely ionize its energy/mass, making it opaque to radiation to account for the observer properties of the Cosmic Background Radiation and the consistency of the laws of physics in each cycle. 

This would make the Cosmic Background Radiation an integral part of each cycle and provides for observation method to quantify the process.  This is because one could use the first law of thermodynamics to determine if the momentum of the collapsing of energy/mass of the universe would generate enough heat to ionize enough of the universe’s baryonic matter to account for its observed properties.

This shows how and why the existence of Dark matter or a continuous non-quantized field of energy/mass would affect our understanding of our universe’s evolution.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

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Richard Feynman on pages 24 and 25 of his book “The Character of Physical Laws” describes how both gravitational and electrical forces are linked in terms of a 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/(4.17 X 10^42) Now therein lies a very deep mystery.  Where could such a tremendous number come from?  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."

However, one may be able to show that gravity and electricity are different aspect of the same thing and derive "this fantastic ratio" if one extrapolates the laws of classical physics in a three-dimensional environment to a fourth *spatial* dimension as done in "The Imagineer’s Chronicles".

Because as the article "Why is energy/mass quantized?" Oct. 4, 2007 showed one can derive the quantum mechanical properties of electrical forces by extrapolating the laws governing resonance in a three-dimensional environment to a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

There are four conditions required for resonance to occur in a classical Newtonian environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial.

The existence of four *spatial* dimensions would give the "surface" of three-dimensional space (the substance) the ability to oscillate spatially between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

Therefore, these bi-directional oscillations in a "surface" of a three dimensional space would meet the requirements mentioned above for the formation of a resonant system or "structure" in space.

Observations of a three-dimensional environment show us the energy associated with resonant system can only take on the incremental or discreet values associated with a fundamental or a harmonic of the fundamental frequency of its environment.

Similarly the energy associated with resonant systems in four *spatial* dimensions could only take on the incremental or discreet values associated a fundamental or a harmonic of the fundamental frequency of its environment.

This shows that one can understand the origins of the quantum mechanical properties of an electromagnetic wave in terms of classical mechanics if one assumes that it is a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth "spatial" dimension.

However as the article "The Photon: a matter wave?" Oct. 1, 2007 one can also understand the origins electrical forces and their quantum mechanical properties by extrapolating the laws of classical wave mechanics in a three-dimensional environment to a matter wave moving on a "surface" of a three-dimensional space manifold with respect to  fourth *spatial* dimension.

Briefly a wave on the two-dimensional surface of water causes a point on that surface to be become displaced or rise above or below the equilibrium point that existed before the wave was present. A force will be developed by the differential displacement of the surfaces, which will result in the elevated and depressed portions of the water moving towards or become "attracted" to each other and the surface of the water.

Similarly a matter wave on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would cause a point on that "surface" to become displaced or rise above and below the equilibrium point that existed before the wave was present.

Therefore, classical wave mechanics, if extrapolated to four *spatial* dimensions tells us a force would be developed by the differential displacements caused by a matter wave moving on a "surface" of three-dimensional space with respect to a fourth *spatial* dimension which will result in its elevated and depressed portions moving towards or become "attracted" to each other.

This would define the causality of the attractive forces of unlike charges associated with the electromagnetic wave component of a photon because it tells us a force would be developed by a differential displacement of a point on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, it also provides a classical mechanism for understanding why similar charges repel each other because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement.

Similarly the magnitude of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by two similar charges will be greater than that caused by a single one. Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two similar charges than it would be for a single charge.

One can define the causality of electrical component of an electromagnetic wave in terms of the energy associated with the "peaks" and "troughs" that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement.

However, Classical Mechanics tells us a horizontal force will be developed by that perpendicular or vertical displacement which will always be 90 degrees out of phase with it. This force is called magnetism.

This is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls matter horizontally towards from the apex of that displacement.

This shows how one can understand electric and magnetic forces by extrapolating laws of classical mechanics in a three-dimensional environment to a displacement in a "surface" of a three-dimensional space with respect to a fourth *spatial* dimension.

The reason why electrical forces are quantized is because as mentioned earlier its energy is propagated through space in quantized resonant systems defined in the article "Why is energy/mass quantized?"

However as the article "Gravity in four *spatial* dimensions" Dec. 15, 2007 showed one also can derive gravitational forces in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension by extrapolating the laws of classical physics in a three-dimensional environment to a fourth "spatial" dimension

One can understand how by comparing the forces on objects would experience in four *spatial* dimensions to those experienced by a marble on a rubber diaphragm with a rod pushing down it.

The surface of the diaphragm will represent the "surface" of three-dimensional space the marble, the energy/mass of an object and the rod will represent the “W” axis of a fourth *spatial* dimension.

(The "W" axis of the fourth *spatial* dimension was defined in the article "Embedded dimensions Oct. 27, 2007")

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 displaced and will no longer be perpendicular to the rod.

Gravitational forces will then have a tangential component along the displacement in 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

Similarly objects interacting with a displacement in "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension will experience a differential force directed towards the apex of that curvature. This force is called gravity.

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

This would make gravitational and electrical forces different aspects of the same thing because it defines both in terms of the physical properties of a displacement in a "surface" of a three-dimensional space manifold with respect to a four *spatial* dimensions.

However, they also share a common property defined by the E=mc^2 because it defines the ratio of all forms of energy including electrical to the gravitational energy contained in mass

If true one should be able to define a mechanism responsible for why "The ratio of the gravitational attraction to electrical repulsions is given by a number with 42 digits tailing off" in terms of the equation E=mc^2 and the fact that they are both have a common origin in a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Solving the equation E=m*c^2 for "m" gives m=E/c^2. This would define the ratio of electrical to its gravitational energy/mass equivalent because as mentioned earlier it defines the ratio of electrical to the gravitational energy associated with mass.

The law of gravitation states that the forces between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them or m x m/d^2

If one then substitutes E/c^2 for “m” in that equation one gets F=(E/c^2)^2/r^2.  This would define the ratio of the attractive properties of gravity to the repulsive properties of electrical energy in terms of the geometry of four *spatial* dimensions.

Using 3.0 x 10^10 cm/sec for the speed of light (c) and substituting we obtain for the ratio of electrical to gravitation forces to be F=E/(3.010^10 cm/sec)^4/r^2 or F=E/(8.1X 10^41 cm/sec).

This value represents 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 to electrical forces.

The theoretical result of 1/8.1 X 10^41 differs from the experimental value of 1/(4.17 X 10^42) because the equation of E=mc^2 that defines the ratio between gravitational and electrical energy tells us that some of the electrical energy in a system is derived from its mass or gravitational component.  Therefore, one must subtract the quantity of the gravitational equivalent of the electrical forces associated with that mass from the above derived value to obtain the experimental value.

Therefore it appears one can 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 the same thing” if one assume as we have done they are both caused by a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension and answers Mr. Feynman’s question as to "how could they (gravitational and electrical forces) come in such disproportion".

Later Jeff

Copyright Jeffrey O’Callaghan 2012