The Higgs boson discovered at the CERN particle physics laboratory near Geneva, Switzerland, in 2012, is what, according to the Standard Model of particle physics gives all other fundamental particles mass. However, despite the work of thousands of researchers around the world, nobody has been able to figure out exactly how it does that or why some particles are more massive than others.

However, there is another way to understand mass and its resistance to acceleration based solely on the field concepts of Einstein’s theories.

For example, Einstein defined the physicality of mass in terms of the energy density associated with a displacement in space-time which he quantified by the equation E=mc^2. This means he also defined the reason some particles are heavier than others is because they have a greater displacement and therefore a greater energy content than other masses. Pitting it another way the equation E=mc^2 not only defines physicality of mass but also quantifies why some particles are heavier that others in terms of in terms of the field properties of space-time.

However, his equations and the observations of particles in particle accelerators tell us the relativistic mass of a body increases over its finite rest mass as it is accelerated with respect to an observer and that energy must be added to it to do so.

He also tells us the rate at which energy can added to a mass is limited by the speed of light. This means according to Relativity, the reason why mass resists acceleration is because the speed at which energy can be added to it is limited. Putting it another way according to it, the reason for its resistance to acceleration MAY not be related to the field properties of a Higgs boson but to the field properties of space-time that limits the rate at which energy can be added to it.

This conclusion is supported by the fact that because Einstein’s relativistic equations tell us that mass or its energy content increases as it approaches the velocity of light it will take more energy to make an incremental change in it. Therefore, because it limits the speed at which energy can be added to it, it will resist acceleration more than one that is at rest with respect to an observer.

In other words, one does not need the Higgs boson to explain a particles mass and why it resists a change in motion because one can use the OBSERVABLE properties of our environment and of Einstein’s theories to do so.

The post 4. Explaining mass and its resistance to acceleration in terms of the field properties of space time. appeared first on Unifying Quantum and Relativistic Theories.

Einstein told us that energy and mass are interchangeable however he did not define what mass is.  He only told us how mass interacts with space-time.

As Steven Weinberg said “Mass tells space-time how to curve while space-time tells mass how to move”.

However Einstein’s inability to define or derive the casualty of mass is can be traced to the fact that he chose to define the energy associated with it in terms of four dimension space-time instead of defining the mass associated with energy in terms four *spatial* dimensions.

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

In other words because he defined the geometric relationship between energy and mass in terms of the constant velocity of light means that one can quantitatively and qualitatively define a one to one between the properties of energy in a space-time universe to the physical properties of mass four *spatial* dimensions.

This was the bases for assuming as was done in the article “Defining energy” Nov 27, 2007 that all forms of energy including thermo and inertia or momentum of mass can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of one in a space-time environment.
However changing ones perspective on the geometric structure of the universe form one of space-time to four *spatial* dimensions not only gives one the ability to understand the causality of mass but also give one the ability derive its quantum mechanical properties as was done in the article “Why is energy/mass quantized?” Oct. 4, 2007″ in terms of its wave component and the resonant properties of four *spatial* dimensions.

(Louis de Broglie was the first to predict the existence of the wave properties of mass when he theorized that all particles have a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer).

Briefly that article 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 in one consisting of four.

The existence of four *spatial* dimensions would give a matter wave that Louis de Broglie associated with a particle the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the “surface” of a three-dimensional space manifold to oscillate with respect to a fourth *spatial* dimension at a 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 four *spatial* dimensions.

Classical mechanics tells us that resonant systems can only take on the discrete or quantized energies associated with a fundamental or a harmonic of their fundamental frequency.

However, this does not explain how the boundaries of a particleâ€s resonant structure are defined.

In classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space. 

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate “up” or “down” with respect to a fourth *spatial* dimension.

The confinement of the “upward” and “downward” oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the geometric boundaries of the resonant system associated with a particle.

Therefore, these resonant systems in a four *spatial* dimensions would define mass and its quantum mechanical properties because of the fact that the volumes of space containing them would have a higher concentration of energy and therefore the mass associated with those volumes would be greater.

This would allow one to, not only understand the causality of the absolute properties of mass such as inertia but it would allow us to derive all of its relativistic ones.

For example one can use these concepts to explain why the corresponding particle types across the three fundamental families of particles in the Standard Model listed in the table below have identical properties except for their mass, which grows larger in each successive family.

As mentioned earlier the article “Why is energy/mass quantized?” showed that one can derive the mass of a particle in terms of the energy contained within a resonant system generated by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension while the article “Defining energy” showed that one can derive the energy of its environment in terms a displacement in the same three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore using the concepts developed in those articles one could derive the total mass of a particle in terms of the sum of the energies associated with that resonant structure and the displacement in the “surface” of three-dimensional space associated with the energy of the environment it is occupying.

Yet Classical Mechanics tells us there will be specific points in space where the matter wave that Louis de Broglie associated with a particle can interact with the energy content or temperature of its environment to form a resonant system.

Therefore, the mass of each family member would not only be dependent on the energy associated with the resonant system that defined their quantum mechanical properties in the article “Why is energy/mass quantized?” but also on temperature of the environment they are occupying.

Thus suggest the reason “The corresponding particle types across the three families have identical properties except for their mass, which grows larger in each successive family.” is because of an interaction between the resonant properties defined in the article “Why is energy/mass quantized?” and the energy content of the environment they are occupying.

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

The relative masses of the fundamental particles increases in each successive family because the higher-energy environments where they occupy would result in the corresponding particles in each successive family to be formed with a greater relative “separation” in the “surfaces” of a three-dimensional space manifold with respect to a fourth *spatial* dimension..

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

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

Additionally the corresponding particle types across the three families have “identical properties” because as shown in the article “The geometry of quarks” Mar. 15, 2009 they are related to the orientation of the “W” axis of the fourth *spatial* dimension with the axis of three-dimensional space.  Therefore, each corresponding particle across the three families will have similar properties because the orientation of the “W” axis of the fourth *spatial* dimension with respect to the axis of three-dimensional space is the same for the corresponding particles in all of the families.

This explains why “The corresponding particle types across the three families having identical properties except for their mass, which grows larger in each successive family” in terms of the properties of classical resonance and the existence of four *spatial* dimensions.

However it also allows one to derive the absolute properties of mass associated with Newton’s first and second laws of motion because as was shown in the article “The Equivalence Principal: an alternative to space-time” July 15, 2008 all accelerations or forces (including gravitational) can be derive in terms of a curvature in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

(This curvature is analogous to the curvature in space-time Einstein assumed was responsible for gravitational forces.)

Newton’s first law of motion which defines the inertial properties of the mass of an object or particle states that “Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it”

However this is what one would expect if one assumes, as mentioned earlier the momentum of an object is caused by a displacement of a “surface” of a three-dimension space manifold with respect to a fourth *spatial* dimension because according those concepts it would tent to stay rest or once in motion would tend to stay in motion because its displacement would remain constant unless it interacted with an external force or as was shown in the article “The Equivalence Principal: an alternative to space-time” a three dimensional “surface” that was curved with respect to a fourth *spatial* dimension.

However it also allows on to understand the causality of Newton’s second law which defines the relationship between an object’s mass “m”, its acceleration “a”, and why the change in velocity of an object or particle is define by the equation is F = ma because as mentioned earlier, the rest mass of an object is directly proportional to a displacement a “surface” of three-dimensional space manifold with respect to fourth *spatial* dimension.  Therefore, as was shown in the article “Defining energy” there will be a 1 to 1 correspondence between it and the curvature in space associated with the energy required to make a unit change in its displacement with respect to a fourth *spatial* dimension.  Therefore the inertia of an object or its resistance to change in velocity would be directly related to its mass. 

In other words using Einstein’s field equations to redefine his space-time universe in terms of four *spatial* dimension allows one to not only understand and derive the causality of the relativistic properties of mass but also the absolute properties associated with its inertia without the need of assuming the existence of the Higgs Boson.

Later Jeff

Copyright Jeffrey O’Callaghan 2013

The post Deriving mass without the Higgs Boson appeared first on Unifying Quantum and Relativistic Theories.

One is that it would allow one to understand why a proton and an election have different masses even though the absolute magnitude of their charge is the same in terms of the laws of classical three-dimensional space.
In the article “Why is energy/mass quantized?” Oct. 4, 2007 it was showed one can derive its quantum mechanical properties by extrapolating the laws of classical resonance in a three-dimensional environment to a matter wave in a continuous non-quantized field of energy/mass moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

(Louis de Broglie was the first to predict the existence of a continuous field of energy/mass when he theorized that all particles had a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.)

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 a matter wave the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimension 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.

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 discrete quantized values associated with its resonant or a harmonic of its resonant frequency.

The article “Why is energy/mass quantized?” showed why these resonant systems in four *spatial* dimensions are responsible for the discrete quantized energies associated with protons and electrons.

However, one can also use the above concept of four *spatial* dimensions to understand the physical boundaries of a proton and electron.  

In classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space. 

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate “up” or “down” with respect to a fourth *spatial* dimension.

The confinement of the “upward” and “downward” oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries associated with a particle in the article “Why is energy/mass quantized?“

(The internal structure of quarks, a fundament component of particles was derived in the article “The geometry of quarks” Mar. 15, 2009 in terms of an interaction between a continuous energy/mass component of space and the geometry of four *spatial* dimensions.)

Meanwhile in the article “The reality of the fourth *spatial* dimension” Dec. 1, 2010 it was shown that one can derive all forms of energy including gravity in terms of a displacement or curvature in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This curvature is analogous to the space-time curvature “The General Theory of Relativity” hypothesized is responsible for gravitational energy.

One advantage, as will be shown below to defining the universe in terms of four *spatial* dimensions is that allows for a bidirectional spatial movement of a “surface” of a three-dimensional space manifold whereas defining it in terms of four dimensional space-time does not.  This is because one can move in two directions up or down, forwards or backwards in a spatial dimension but in only one direction, forward in a time dimension.

For example in the article “Electromagnetism in four *spatial* dimensions” Sept. 27, 2007 showed one can derive the polarity and absolute magnitude of the charge on a proton and electron in terms of a bidirectional displacement of a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

It derived the positive charge of a proton in terms of a “downward” displacement  in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  While the negative the charge of an electron will be derived in terms of oppositely directed “upward” displacement in that surface.

One can understand how these displacements would define their electrical properties by extrapolating the laws of classical mechanics of displacements in water to it.

Classical mechanics tell us that if one lifts a bucket full of water or pushes down on an empty one a force will be developed that will cause the bucket raised above or the one that was pushed down below its surface to move or become “attracted” to its surface.

Similarly if one lifts or pushed down on a “surface” of three-dimensional space manifold a force will be developed that will cause the raised or depressed regions to become attracted to its surface.

Therefore, one could derive why the unlike charges attract each other in terms of a classical mechanism if one assumes that they are a result oppositely directed of a displacement  in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

Additional classical mechanics also tells us there is a direct relationship between the magnitudes of a displacement in the surface of water to the magnitude of the energy resisting that displacement.

For example the force resisting the further displacement of an empty bucket in water is directly related to the depth of that displacement.

This defines why like charges repel each other because the displacement in a “surface” of a three-dimensional space manifold 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 energy resisting the displacement will be greater for two identical charges than it would be for a single charge.

The mechanism responsible for generating this movement was defined in the article “The reality of the fourth *spatial* dimension” were it was shown when mass is converted to energy or energy to mass, the “surface” of a three-dimensional space manifold either “expands” or “contracts” with respect to a fourth *spatial* dimension.  This would result in the movement of that “surface” respect to it.

The effects these movements have on the density of continuous energy/mass component of the resonant systems that defined the quantum mechanical properties of a proton and electron in the article “Why is energy/mass quantized?” are analogous to the effects high and low pressure areas in the earth’s atmosphere have on density of air molecules.

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

Conversely, in a low-pressure area the energy of the air molecules is directed upward away from the surface of the earth which results in their density at the apex of a low-pressure area to be less than the density of the air molecules in the volume of air adjacent to it.

A similar effect would occur in space with respect to the density of their continuous energy/mass component

In a dimensional “high-energy volume” associated with the positive charge of a proton, the energy of the continuous energy/mass component of space would be directed “downward” with respect to a fourth *spatial* dimension, towards the “surface” of a three-dimension space manifold.  This results in its density in the resonant system of a proton to be greater relative to its density in the volume adjacent to it.

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

Conversely in a dimensional “low-energy volume” associated with the negative charge of an electron, the energy of the continuous energy/mass component of space would be directed “upward” with respect to a fourth *spatial* dimension, away from the “surface” of a three-dimension space manifold.  This results in its density in the resonant system of an electron to be less relative to its density in the volume adjacent to it.

Therefore, the density of the continuous energy/mass component of the resonant system of a proton will be greater than that of an electron even though the absolute magnitude electrical energy or charge is the same.

This is analogous to why the density of air molecules in a high-pressure area is greater that in a low-pressure area even though the magnitude of their energy is same but oppositely directed.

In the article “Gravity and electromagnetism linked in four *spatial* dimensions” Dec 14, 2007 it was shown that the mass of a particle or object is directly related to the density or concentration of the continuous field of energy/mass contained in the volume of a particle or object.

Therefore because the density, as mentioned earlier of the continuous non-quantized field of energy/mass is greater in a proton than that of an electron its mass will also be greater than that of an electron.

This shows that one of the theoretical advantages to define the space in terms of a continuous field of energy/mass and four *spatial* dimensions instead of four dimensional space time is that it would allow one to understand why the relative mass of a proton is greater than that of an electron even though the absolute magnitude of their charge is the same by extrapolating the laws of a classical environment to four *spatial* dimensions.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

The post The relative masses of a proton and electron appeared first on Unifying Quantum and Relativistic Theories.

If so one should be able to derive the strong force in those terms.

The strong force, also known as the strong interaction, is the strongest force in the universe, 10³⁸ times stronger than gravity and 100 times stronger than the electromagnetic force.  However, it is only effective on length-scales of the atomic nucleus and drops rapidly off as the distance from the nucleus increases.

Earlier 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 laws of classical resonance in a three-dimensional environment to a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
(Louis de Broglie was the first to predict the existence of a matter wave when he theorized that all particles have a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.)

Briefly it was shown 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 manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

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

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

Later in the article “The geometry of quarks” Mar. 15, 2009 it was shown that one can understand why a particle is made up of three quarks of different “colors” again by extrapolating the geometric of three-dimensional space to a fourth while the article “Embedded dimensions” Oct. 22. 2007 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.

Using the concepts developed in those articles one derive the mechanism responsible for why observe of particles 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 explanation is based in part on the fact that 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 may 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.

A proton contains two up Quarks with a +2/3 charge and one down quark with a -1/3 charge.  This tells us because they are stable that the resonant interaction of their geometries contains more energy that the electrical repulsive energy associated with their positive charge.

It is this excess resonant binding energy associated with their dimensional properties defines the causality of the strong force and the stability of a nucleus.

However, its components or protons and neutrons must be physically close enough for them to share this excess energy to create a stable one.

The sharing of this excess binding energy is also responsible for the creation of neutrons because geometrically it takes less energy for a volume to contain the two up quarks and two down quarks of a proton and neutron instead of four up quarks and two down quarks of two protons. In other words their electrical repulsive energy associated with the quarks is cut in half when the volume contains a proton and neutron instead of two protons and therefore energy/mass component of that volume will be in the lowest energy state possible.

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 binding energy of the strong force would be related to the size of the nucleus 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 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 only be effective on length-scales of the atomic nucleus and would drop rapidly off as the distance from the nucleus increases.

This shows how one can derive mechanism responsible for the strong nuclear force by extrapolating the classical laws governing resonance in a three-dimensional environment to one made up of four.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

The post The Strong force in four *spatial* dimensions appeared first on Unifying Quantum and Relativistic Theories.

If so one should be able to define the weak force in those terms.

The weak force is responsible for changing to one quark to another or a lepton to another lepton – the so-called “flavor changes” when particles undergo radioactive decay.  In Physics speak the weak interaction involves the exchange of the intermediate vector bosons, the W and the Z.

Earlier 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 laws of classical resonance in three-dimensional space to a matter wave on a surface of a three dimensional space manifold with respect to four *spatial* dimension.
(Louis de Broglie was the first to predict the existence of a matter wave when he theorized that all particles have a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer. )

Briefly it was shown 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 manifold with respect to a fourth *spatial* dimension to oscillate 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 four *spatial* dimensions.

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

Later in the article “The geometry of quarks” Mar. 15, 2009 it was shown that one can understand why a particle is made up of three quarks of different “colors” again by extrapolating the geometric of three-dimensional space to a fourth while the article “Embedded dimensions” Oct. 22. 2007 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.

Using the concepts developed in those articles one derive the mechanism responsible for why observe of particles 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 explanation is based in part on the fact that 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 may 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 stable.

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

As mentioned earlier the weak force manifests itself in the transmutation of a quark from one flavor or color to another when nuclear particles decays and manifest itself by changing one quark to another, or a lepton to another lepton, the so-called “flavor or color changes”.

However this is what one would expect if their stability was related to, as mentioned above 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. 

However, as mentioned earlier a particleâ€s stability is related to how the central axis of its component quarks are oriented with respect to a fourth *spatial* dimension.  Therefore the weak force could be defined in terms of the energy associated with their most stable geometric configuration.  In other words to form a stable particle the central axis of its quarks would have to rotate around their fourth dimensional axis until the particle they were a part of had obtained the lowest geometric energy configuration possible with respect to a fourth *spatial* dimension. 

Hence one could derive the casualty of the transmutation or the flavor or color change of quarks from to another in terms of the reconfiguration of its central axis with respect to a fourth *spatial* dimension required to form a stable particle.

This is analogous to the central axis of a wind vane rotates in three-dimensional towards the direction of the wind to reduce the amount of force or energy on its two-dimensional surface by the wind.

Similarly the three-dimension axis of quarks will rotate in four *spatial* dimensions to reduce the energy content of a particle to its lowest level.

As mentioned earlier the binding energy holding quarks together is dependent on the resonant interaction their central axis.  Therefore, magnitude of weak nuclear force binding them together would be associated with the flavor or color change that occurs when an atomic decay takes place.

The reasons the weak force manifests itself in the exchange the vector particles called the W and  Z bosons is because as was shown in the article “Why is energy/mass quantized?” all energy is propagated in discrete resonant structures.  Therefore, it will have particle properties that article associates with them.

This shows how one can derive mechanism responsible for the weak force by extrapolating the classical laws governing resonance in a three-dimensional environment to one made up of four *spatial* dimensions.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

The post The weak force in four *spatial* dimensions appeared first on Unifying Quantum and Relativistic Theories.

One of them is that it would provide an alternative explanation that is more consistent with the observed properties of Dark Matter than can be found based solely on the quantum mechanical assumption that all energy/mass exists in quantized particle form.

Wikipedia tells us “The first person to provide evidence and infer the presence of dark matter was Swiss astrophysicist Fritz Zwicky, of the California Institute of Technology in 1933.  He applied Newton’s law of gravity to the Coma cluster of galaxies and obtained evidence of unseen mass.  Zwicky estimated the cluster’s total mass based on the motions of galaxies near its edge and compared that estimate to one based on the number of galaxies and total brightness of the cluster.  He found that there was about 400 times more estimated mass than was visually observable.  The gravity of the visible galaxies in the cluster would be far too small for such fast orbits, so something extra was required.  This is known as the “missing mass problem”.  Based on these conclusions, Zwicky inferred that there must be some non-visible form of matter which would provide enough of the mass and gravity to hold the cluster together.”

Many physicists believe the vast majority of the dark matter is in a non-baryonic form such as entities such as axions, supersymmetric particles, or WIMPs and baryonic neutrino.

However, as Lee Smolin points out in his book “The Trouble with Physics” none of these scenarios is supported by observations.

Neutrinos because of their mass would be characterized by high random speeds in the early universe.  However, observations of the early universe indicate the matter that condensed to form galaxies was not hot enough to support the energy that would be associated with those high speeds.

The other particles, which could provide the missing mass fall into two classes: those which have been proposed for other reasons but happen to solve the dark matter problem, and those which have been proposed specifically to provide the missing dark matter.

Examples of objects in the first class are axions and the supersymmetric particles.  Their properties are defined by the theory, which predicts them, by virtue of their mass; they can solve the dark matter problem only if they exist in the correct abundance.

The second class of particles contains entities such as the WIMP or “Weakly Interacting Mass Particle” whose properties are not specified.  However, they are assumed to have properties that would allow them to explain the missing mass associated with dark matter along with other “ad hoc” ones that would explain why they have not yet been observed experimentally.

However, the existence of them along with axions and the supersymmetric particles is not based on observations so therefore there is no way to either confirm their existence or that they are responsible for the gravitational force associated with dark matter.

However, as mentioned earlier there is another theoretical possibility that is based on theory and observations that has been overlooked by the scientific community.

In the article “What is Dark Matter?” Sept 10, 2007 it was shown that one could theoretically explain and predict the gravitational forces associated with Dark Matter in terms of the continuous field properties of energy/mass because it would have all of its observed properties. In others words being a non particle form of energy/mass in would not interact with electromagnetic forces and therefore it would be invisible or “Dark” to instrumentation that is calibrated to detect electromagnetic energy. Yet because it is made up of energy/mass it would add to the gravitational force of the particle matter in the universe.

Louis de Broglie was the first to realize the reality of the field properties of energy/mass when in 1924 he proposed that all forms of particle matter have a wave component. This was fully confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.  (This discovery served as the basis for developing the general theory nowadays known by the name of wave mechanics.)  However it also tells us that all matter and energy posses the continuous or field properties associated with waves. 

However, the most significant theoretical advantage to assuming the existence of a continuous field of energy/mass is that it would allow one understand, in terms of the laws of classical wave mechanics the quantum mechanical properties of energy/mass.

In the article “Why is mass and energy quantized?” Oct. 4, 2007 it was shown one can derive the quantum mechanical properties of energy/mass by extrapolating the resonant properties of a classical three-dimensional environment to a matter wave in a continuous field of energy/mass on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

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

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

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

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

This provides yet another theoretical basis for its existence because as shown above one can derive the quantum mechanical properties of energy/mass in terms of a resonant system formed by a matter wave in a continuous field of energy/mass.

However as mentioned earlier because it is made up of energy/mass it would have add to the gravitational potential of the particle forms of matter in the universe and as was also mentioned earlier it  would not interact with electromagnetic forces and therefore it would be invisible or “Dark” to instrumentation that is calibrated to detect electromagnetic energy

This shows a viable alternative based on both theoretical arguments and experimental observations to the assumption that dark matter is made up of particles while at the same time providing a very strong argument for defining its properties in terms of a continuous field of energy/mass.

Later Jeff

Copyright 2010 Jeffrey O’Callaghan

The post The field properties of Dark Matter appeared first on Unifying Quantum and Relativistic Theories.