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 defining the universe in terms of four *spatial* dimensions instead of four dimensional space-time.

One is that it would allow physicists to understand mass and inertia by extrapolating our experiences in a three-dimensional environment to a fourth *spatial* dimension.

For the past 50 years, the Standard Model of Particle Physics has given us a complete mathematical description of the particles and forces that shape our world. It predicts with so much accuracy the microscopic properties of particles and the macroscopic ones of stars and galaxies that many physicists feel that it is the ultimate theory of matter and energy.

But as Charles Seife mentions on page 142 of his book Alpha & Omega "Taken literally the plain vanilla form of the Standard model does not say anything about particle mass at all: in fact if theorists try to put mass in to its equations they blowup and become meaningless."

In 1964 Peter Higgs showed that one can solve this problem and explain the origins of inertial or rest mass is if one assumes space is permeated by what is called a Higgs field.

He was able to show that if a particle changes its velocity or accelerates, then the Higgs field should exert a certain amount of resistance or drag which according to his theory is the origin of mass. In a slightly more precise terminology, the origin of mass is an interaction between a particle and the (nonzero) Higgs field. It also assumes the disturbance created by mass as it moves through this field would have to generate the particle called the Higgs boson.

The only problem is that it is has been extremely difficult to identify the Higgs Boson (the particle The standard model associates with the Higgs field) because of the relatively few times it has been observed in the swam of particles created in modern particle accelerators.

This is problematic for its proponents because the Standard Model tells us it should be created more frequently than it has been in the high energy environments of particle accelerators like The Large Hadron Collider (LHC)

This means that scientists should be careful before saying that the particle they have discovered is the Higgs Boson predicted by the Standard Model.

Granted they may have used statistical analysis to determine that a few out of millions particles created in their accelerators has all of its properties however the existence of those particles may be associated with random events.

Therefore they should not only do a statistical analysis to determine if the observed particle has the properties of a Higgs Boson but they should also use the Standard Model to predict how frequently it should appear in the high energy environment they are observing.

If they find that it is not appearing as often as it should one must assume that it may be associated with randomly repeating event which is not connected to the Standard Models predictions.

This is especially relevant because there is an alternative explanation for mass that is based on the observable and therefore verifiable properties of three-dimensional space and does not require the analysis of a few isolated events as is required to verify the existence of the Higgs Field.

Observations of our three-dimensional environment tell us the total potential energy of an object or particle is related to the magnitude of its relative displacement. For example the potential energy of water in a bucket is in part determined by the height or displacement of its surface relative to the surface of the table it is resting on. However, its potential energy is greater if one measures it relative to the floor on which the table is resting.

In the following discussion the potential energy of the water in the bucket relative to the table top will represent the rest mass of an object or particle while its energy with respect to the floor will correspond to the energy associated with its relative velocity.

In the article "Why Space-time?" Sept. 27, 2007 it was showed one can derive the rest or inertial mass of an object or particle in terms of a displacement in a "surface" of a three-dimensional volume with respect to a fourth *spatial* dimension. Additionally it was shown one can derive the causality of all accelerations including gravitational in terms of an interaction of its mass with the slope of a curvature in a "surface" of a three-dimensional space caused by that displacement.

(This curvature is analogous to a curvature in a four-dimensional space-time Einstein theorized was responsible for gravitational accelerations)

However we know from observations that there is an equivalence between mass and energy and that all of the energy, except thermo in a volume of space that is not moving with respect to an external environment is contained in its mass component. This would be analogous to the fact that all of the potential energy in water in the earlier example is contained in the volume of the bucket on table.

Therefore according to the concepts in the article "Why Space-time?" one could define the inertial or rest mass of an object or particle by extrapolating the observations of the potential energy of the water in a bucket resting on the surface of a table to a displacement in a "surface" of a three-dimensional volume with respect to a fourth *spatial* dimension. In other words one could define the energy associated with mass in terms of the displacement of a three-dimensional volume with respect to a fourth *spatial* dimension for the same reason as one can define the energy of the water in the bucket as being related to its displacement with respect to the table top.

This shows how one can derive the inertial or rest mass of an object or particle by extrapolating the observable and verifiable properties of three-dimensional space to a fourth *spatial* dimension.

However the article "Defining energy" derived the energy associated with the relative velocities in terms of a differential displacement with respect to a fourth "spatial" dimension of the three-dimensional environment associated with each object or particle.

This means the energy associated with momentum or relative velocities would be analogous to the energy created by the displacement of the environment of the table top with respect to the floor in the example mentioned earlier.

Therefore if true one could derive the energy associated with the momentum or velocity of an object or particle in terms of a displacement in of a three-dimensional volume with respect to a fourth *spatial* dimension associated with its rest mass *plus* that associated with the displacement of its three-dimensional environment with respect to the fourth *spatial* dimension the article "Defining energy" associated with its relative velocity. (The momentum of an object at rest with respect to other objects is zero so the displacement of three-dimensional space with respect to those objects would also be zero.)

This would be analogous to how the total potential energy of water in a bucket would be as mentioned earlier determined by the height or displacement of its surface relative to the surface of the table it is resting on* plus* the height the table top is above the floor.

The reason mass increases as its velocity approaches that of light is because according to the concepts presented here its magnitude would be equal to the sum of the displacements in a "surface" of a three-dimensional space volume caused by its rest mass and that caused by its relative velocity. Therefore because as was shows in the article "Defining energy" its displacement with respect to a fourth *spatial* dimension would be directly related to its velocity its mass will increase along with its velocity.

Yet, as mentioned earlier the article "Why Space-time?" also showed that accelerations are caused by an object or particle interacting with a curved "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Isaac Newton defined inertia or mass as being responsible for why an object at rest will remain at rest, and an object in motion will remain in motion in a straight line at a constant speed.

Yet this is what one would expect if as mentioned earlier the momentum of a particle or object is caused by a "linear" displacement of a "surface" of a three-dimension space volume because it would tend to stay rest or ones in motion would tend to stay in motion unless it interacted with a three-dimensional "surface" that was curved with respect to a fourth *spatial* dimension.

This would also explain the resistance of an object or particle to an acceleration and why it would be directly proportional to its mass because as the article "Why Space-time?" showed the magnitude of the curvature in four *spatial* dimensions caused by mass would be directly proportional to it and since the causality of all accelerations are a result of an interaction of mass with the slope of a curvature in a "surface" of a three-dimensional space and it would be directly proportional to its mass. Therefore a mass will interact with the curvature in space that article also associated with an acceleration in proportion to its mass. In other words there should according to these concepts outline above be a one to one correspondence between the mass of an object or particle and the acceleration it experiences for a given force.

However this is exactly what Isaac Newton’s Second law of motion tells us that "The acceleration of a body is directly proportional to the net force F acting on the body, and is inversely proportional to the mass *m* of the body, i.e., F = *m*a.

*This not only provides an consistent explanation for the existence of mass based on verifiable observations made in our three-dimensional environment but also solves one of the major conceptual problems associated with the Higgs field and Newton’s first law of motion or an object at rest will remain at rest unless acted on by an unbalanced force while an object in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced force.*

*If one assumes the origin of mass is an interaction between a particle and the (nonzero) Higgs field and "that a disturbance created by mass as it moves through this field generates the particle called the Higgs boson" one also must assume that mass exchanges energy with the environment associated with the Higgs field. However this means that all objects will experience an unbalance force as it moves through that environment because that is the only way it can cause a disturbance in it.*

Yet this contradicts Newtown’s laws of motion and the observation that objects and particles maintain a constant velocity as they move through space because if it was true that mass is a result of an unbalance force or interaction between it and the Higgs field we would observe that they do not maintain a constant velocity while moving through space.

However according to the concepts outlined above mass and velocity are a result of an unchanging "linear" displacement in a "surface" of a three dimensional volume with respect to a fourth *spatial* dimension. Therefore these concepts conceptually agree with both observations of the movement of particles or objects and Newton laws because as just mentioned the displacement in the "surface" three dimensional space associated with both mass and velocity is unchanging and therefore does not require an interaction with its environment.

This demonstrates that one does not have to assume the existence of the Higgs field or Boson to explain why particles have mass and inertia because it can be explained by extrapolating observations made in our of a three-dimensional environment to a fourth *spatial* dimension.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

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

One is it would allow one define the "reality" of Faraday’s field and the strong, weak, electromagnetic, and gravitational forces by extrapolating properties of a classical three-dimensional environment to a fourth *spatial* dimension.

There are presently two methods science uses to define how forces are propagated.

The first assumes that all forces both attractive and repulsive are propagated by particles. For example it is assumed that electromagnetic forces are propagated though space by photons that are both real and virtual.

It is easy to understand how particles can be responsible for repulsive forces because our every day experiences tell us that a force is generated when two objects collide that causes them to move apart or repel each other.

However this is not the case with attractive forces because no has ever observed two objects moving towards or being attracted to each other after a collision.

Therefore scientists have to create or imagine what are called "virtual particles" which by their own admission do not exist, except in the math to explain attractive forces in terms of particle interaction.

Granted they assume that virtual particles exhibit some of the properties that "real" particles do, such as obedience to the conservation laws however they differ in that they when they collide or interact with "real" particles they cause them to attract instead of repulsing each other as is the case when two real particles interact.

When you ask a scientist how they know this all they can do is point to some abstract mathematical equations that they say demonstrates they have the physical properties associated with a repulsive field.

One problem with assuming this is that no has or ever will observe a virtual photon because as mentioned earlier by definition they do not exist. Another more damaging one is that it is very difficult to devise a realistic mechanism based on observations that can account for how something that does not exist in the real world can interact with something that does to cause the observed properties of a repulsive force.

The second assumption uses the concept of a field to explain how and why forces are propagated through space.

The only problem with this assumption is that no one has been able to define the physicality or reality of these fields in terms of four dimensional space-time.

*However as mentioned earlier one can define their "reality" and that of strong, weak, electromagnetic, and gravitational forces by extrapolating observations of a classical three-dimensional field to a fourth *spatial* dimension.*

The concept of a field was developed when physicists learned that they could simplify the calculations of the forces involved in planetary motion by assuming or imagining** **the existence of a continuous gravitational field. They defined this field in such a way that if another planet were put at any point in that field the resulting force between any other planets would be exactly the Newtonian one. This simplified the calculations of planetary motion because it allowed them to isolate and analyze the forces of one planet on another instead of trying to analyze the forces exerted on a planet by the others at the same time.

Originally, many thought this was just a trick to simplify calculations.

But Michael Faraday, while researching electromagnetism discovered that a continuous field has real physical properties and therefore was able to convince others that is was more the just a calculating device.

However unlike a virtual particles which cannot be defined in terms of their physicality one can define the physicality of faradays fields and the four forces of nature if one does, as mentioned earlier assume the existence of four *spatial* dimensions instead of four dimensional space-time.

For example the article "What is electromagnetic energy" Sep 27, 2009 showed one can physically derive the propagation of electromagnetic forces in by extrapolating the physical properties of a three-dimensional environment to a matter wave moving on a "surface" of a three-dimensional space with respect to a fourth *spatial* dimension.

This would enable one to define the physicality of both the attractive and repulsive properties electromagnetic forces in terms of *observable* field properties of a three-dimensional environment instead of the *imaginary* one of virtual particles.

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 surface 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 field 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 a three-dimensional field 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 field 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 fluctuations in the four dimensional field 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 cannot be done in terms of four dimensional space-time because time is only observed to move in one direction only forward and therefore could not support the bi directional movement required to account both attractive and repulsive forces.

This shows how and why a theoretical model based on the physical properties of a field consisting of four *spatial* dimension instead of four dimensional space-time would allow one to derive both the attractive and repulsive properties of faraday’s electromagnetic field.

However the article "The “Relativity” of four spatial dimensions" Dec. 1, 2007 showed that one can also derive gravitational forces in terms of the same field properties the article What is electromagnetic energy" associated with four *spatial* dimensions

Briefly it showed one can derive all forms of energy in terms of a displacement in a "surface" of a three-dimensional field with respect to a fourth *spatial* dimension.

Therefore, because mass is a form of energy it should, according to the concepts contained in that article cause a displacement in the field properties of three-dimensional space and objects interacting with it will experience a differential force directed towards the apex of that displacement. This force is called gravity.

Therefore the articles "What is electromagnetic energy" and “The “Relativity” of four spatial dimensions" define the physicality of the field properties of gravitational and electromagnetic force terms of a displacement in the "surface" of a three-dimensional field by extrapolating the physical properties of classical fields in a three-dimensional environment to a fourth *spatial* dimension.

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 them by extrapolating resonant properties of a field in classical a three-dimensional environment to a matter wave moving on a "surface" of a three-dimensional field with respect to a fourth *spatial* dimension.

Briefly it showed the four conditions required for resonance to occur in a classical field, 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 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 field (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 field to be established in four *spatial* dimensions.

Observations of a three-dimensional environment tell us that the energy of a resonant field 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 fields are responsible for the quantum mechanical properties the energy/mass.

Yet one can also derive the Strong and Weak forces by extrapolating the resonant properties of a three-dimensional field 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 forces including electrical in terms of a displacement of the field properties of a three-dimensional space with respect to a fourth *spatial* dimension.

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

However, it also explains why it takes quarks of three different "colors" to form a particle because, as mentioned earlier a particle is defined in terms of the resonant field properties of three-dimensional space. If the colors of each quark represent the central axis associated with its charge then to form a stable resonate field would require three quarks that have different central axis to balance its energy with respect to the axes of three-dimensional space. A stable 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 the central axis of the field properties of three-dimension space 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 field properties of three-dimensional space and a fourth *spatial* dimension.

However, the fact the resonant interaction between the components of a three-dimensional field 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 field 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 field 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 fields 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 fields 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 physicality or the "reality" of the field properties of the strong nuclear and weak forces by extrapolating the classical laws governing fields in a three-dimensional environment to one 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 three-dimensional field with respect to a fourth *spatial* dimension created by either the rest mass of an object or a matter wave moving is a three-dimensional field with respect to a fourth *spatial* dimension.

Briefly the article "The “Relativity” of four spatial dimensions" extrapolated the laws of classical fields to derive gravitational forces in terms of a displacement in a of a three-dimensional field 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 in the field properties of three-dimensional space created by a matter wave moving on a "surface" of a three-dimensional field 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 by extrapolating the laws governing resonance in a classical three-dimensional field 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 in that same a three-dimensional field.

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 observable field properties of our three-dimensional environment to fourth *spatial* dimensions.

Later Jeff

Copyright 2012 Jeffrey O’Callaghan