However it does not define how that force physically interacts with them to do that.  In other words it mathematically defines a SU(3) group but it does not define how it interacts with our observable environment to create that force.
Despite this shortfall some feel that a physical connection must exist between the math defining Quantum Chromodynamics, the Standard Model of Particle Physics and the physical reality of the observable environment humans occupy because their quantitative predictions so accurately describes the properties and forces associated with quarks.  This is true even though gravity which is part of that environment has yet to be incorporated into it.

However the fact that one can mathematically describe properties of an environment does not necessary mean that it accurately depicts its reality.

For example there are many ways to mathematically define why there are five apples on a table.  One could say that originally there were six and one was taken away or that there were four and one was added.  Both accurately described the observed number of apples on the table.  However if originally there were four apples the one that assumed there were six does not define the reality of their environment that produced them.

Similarly there may be several ways to describe the existence quarks.

If so how can we determine which one not only describes what we observe but also defines the reality of the environment that created them?

One way to increasing the possibility of getting it right would to define their environment based on what we observe and then derive its mathematical properties instead of defining them only in terms of its mathematical ones which is what Quantum Chromodynamics does.

For example, observations of the neutron and proton 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.  Additionally they tell us the binding energy associated with the strong force is only depended on the distance between them.  In other words it does not vary with time

This suggests, because that forces remain constant through time their existence is related to the spatial not the time properties of their environment.

This may be also be the reason why as was mentioned earlier gravity is has not yet been incorporated in it the Standard Model because presently the only viable theory we have; Einstein’s General Theory of Relativity defines it in term of the temporal properties of a space-time dimension. 

However Einstein gave us the ability resolve this conflict when defined his space-time environment  in terms of the constant velocity of light because that allows one to convert a unit of time in it to a unit of space in a one consisting of only 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 the symmetry of his mathematics provides a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

Doing so may allow one to define an environment which is responsible the forces and the fractional charge of quarks and how they interact to form particles in terms of the geometry four *spatial* dimension.

For example the article Defining energy Nov. 26, 2007 showed it is possible to define all forms of energy including electrical in terms of a physical displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension similar to how Einstein derived gravity in terms of a physical displacement in a space-time manifold.

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 one could define the environment responsible for 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 Nov. 22, 2007 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 can also explain why it takes three quarks of different “colors” to form a stable particle because, as the article “Why is energy/mass quantized?” Oct, 4 2007 showed one can define one 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.

(Briefly that article showed the four conditions required for resonance to occur in any 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 available in one consisting of four *spatial* dimensions,

The existence of four *spatial* dimensions would give a continuous non-quantized 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 “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 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.)

Yet this gives us a method of mathematically deriving the strong force in terms of the physical properties of predefined environment that it is a part of because we know two of its parameters; the electrical forces pushing them apart and the distance between them. Therefore we should be able to determine the magnitude strong force required to prevent that from happening using the geometric relationship describe above.

As was shown earlier the symmetry of Einstein’s mathematics provides a qualitative and quantitative means of redefining gravity in his space-time universe in terms of the geometry of four *spatial* dimensions.

Doing so would allow for the anchoring the mathematics defining both gravity and the strong force in terms of the physical properties a common environment something which Quantum Chromodynamics and the Standard Model of Particle Physics have been unable to do.

It should be remember Einsteinâ€s genius and the fact that he defined the geometry of space-time in terms of the constant velocity of light allows us to choose to define our universe in either a space-time environment or one consisting of four *spatial* dimension when. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the spatial as well as the temporal properties of our universe giving us a new perspective on how the forces it contains interacts with it.

Later Jeff

Copyright 2016 Jeffrey O’Callaghan

The post The Geometry of the Strong Force appeared first on Unifying Quantum and Relativistic Theories.

When the Copenhagen interpretation was first introduced Neils Bohr found it was necessary to assume the collapse of wave function to distinguish the quantum from the classical world.  This allowed it to develop without distractions from interpretational worries.  Nevertheless since then that it meaning has be hotly debated because if it is a fundamental properties of nature as many have assumed it would contradict the classical or Newton assumption that the world is deterministic.
However the science of physics is devoted to understanding the physical process responsible for creating the “reality” of our observable environment based on observing the physical interaction of its real not imagined components.

One of the reason it has been so difficult to understand what happens to the position component of a quantum system when it is observed may be because too much attention has been focused on the mathematical aspects of the wave function and not enough on its physical meaning in a space-time environment.  This is made even more difficult because the concept of superposition is defined in terms of the spatial properties of a quantum system instead of its space-time properties.

This suggest one be able to obtain a better understanding of what happens to it if one could view it in terms its spatial instead of it time or space-time properties.

Einstein gave us the ability to do this when he use the equation E=mc^2 and the constant velocity of light to define the geometric properties of space-time because it provided a method of converting a unit of time he associated with energy to unit of space associate with position. Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

The fact that one can use Einsteinâ€s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions is one bases for assuming as was done in the article “Defining energy?” Nov 27, 2007 that all forms of energy 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.

However defining the dimensional properties of quantum system in terms of its spatial instead of its time components would allow one to derive the physicality of the wave functioned associated with Schrödingerâ€s equation by extrapolating the observable properties of our reality to the quantum world it describes.

For example the article “Why is energy/mass quantized?” Oct. 4, 2007 showed one can derive its physicality by extrapolating the laws of classical wave mechanics 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.

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 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 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 space.

Therefore, these oscillations in a “surface” of a three-dimensional space manifold would meet the requirements mentioned above for the formation of a resonant system or “structure” in four-dimensional space if one extrapolated them to that environment. 

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

Hence, these resonant systems in four *spatial* dimensions would be responsible for the discrete quantized energy associated with the quantum mechanical systems.

(In the article “The geometry of quarks” Mar. 15, 2009 the internal structure of quarks, a fundament component of particles was derived in terms of a similar resonant interaction between three and four dimensional space.)

However assuming its energy is result of a displacement in four *spatial* dimension instead of four dimensional space-time as was done in the article “Defining energy?” Nov 27, 2007 allows one to not only derive the physicality of Schrödingerâ€s equation as was just done but also the physical reason why its particle components would be in superpositioned state before an observation is made.

Classical mechanics tell us that because of the continuous properties of waves, the energy the article “Why is energy/mass quantized?” associated with a quantum system would be distributed throughout the entire “surface” a three-dimensional space manifold with respect to a fourth *spatial* dimension similar to how the wave generated by a vibrating ball on a surface of a rubber diaphragm are disturbed over its entire surface while the magnitude of the displacement it causes will decrease as one moves away from the point of contact.

However, this means if one extrapolates the mechanics of the rubber diaphragm to a “surface” of three-dimensional space one must assume the oscillations associated with each individual quantum system must be disturbed thought the entire universe while the spatial displacement associated with its energy defined in the in the article “Defining energy?” Nov 27, 2007 would decrease as one moves away from its position.  This means there would be a non-zero probability they could be found anywhere in our three-dimensional environment because, as mentioned earlier the article “Why is energy/mass quantized?” shows that a quantum mechanical system is a result of a resonant structure formed by the oscillations on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Classical Wave Mechanics tells us a resonance would most probably occur on the surface of the rubber sheet were the magnitude of the vibrations is greatest and would diminish as one move away from that point,

Similarly an observer would most probably find a quantum system were the magnitude of the vibrations in a “surface” of a three-dimensional space manifold is greatest and would diminish as one move away from that point. 

However as mentioned earlier this is exactly what is predicted by Quantum mechanics in that one can define a particle’s exact position or momentum only in terms of the probabilistic values associated with vibrations of its wave function

Additionally this tells us that the wave function does not collapse but its energy is redirected towards the observer and as was shown in the article Why is energy/mass quantized? he would record its redirected energy in term of discrete quantized properties associated with a particle.

As mentioned earlier the science of physics is devoted to understanding the physical process responsible for creating the “reality” of our observable environment based on observing the physical interaction of its real not imagined components.

Yet even though we may never be able to directly observe the fourth *spatial* dimension we can verify its existence by observing the effects it has on our observable three-dimensional environment similar to how Einstein was able to conclude that gravity was a result of a curvature in a space time environment.

Later Jeff

Copyright Jeffrey O’Callaghan 2015

The post A classical interpretation of the wave function collapse appeared first on Unifying Quantum and Relativistic Theories.

Quantum theory defines the existence of particles in terms of a mathematically generated probability function created by Schrödinger’s wave equation and assumes that particles do not exist until a conscience observer looks at it.  In other words it assumes the act of observation or measurement creates their reality.

However because it is based on probabilities it also assumes that the predictability associated with the laws of causality that govern our macroscopic universe do not apply to a quantum world.

In other words in quantum theory, everything is unpredictable.

Einstein hated this uncertainty, famously dismissing it when he said “God does not play dice with the universe” even though he was unable to give a reason.

However he gave us a clue as to why God must play dice when he said “If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless”

In other words we may be able to understand why a quantum environment lacks causality if we can transform the abstract or non-physical aspects or the probabilities associated with Schrödinger’s wave equation to one that more closely resembles the physical properties of our classical world.

For example Einstein told us that our physical environment is made up of four dimensional space-time however no one has ever observed the physicality of time or a space-time dimension.

Therefore it is extremely difficult to form a physical image of the quantum world or any other based on the existence of time or a space-time dimension because it is not part of our sensory environment.

Granted Einstein’s theories give us a detailed and very accurate description of how an interaction of time with the three *spatial* dimensions is responsible for the “reality” of the sensory world we inhabit and he was able to give us a clear physical image how a curvature in space-time can be responsible for gravity.

For example the most common physical image use to explain gravity does not use time but instead extrapolates the image of an object moving on a curved two dimensional “surface” in a three dimensional environment to four dimensional space-time.  However this image only contains reference only to the sensory reality of the spatial dimensions and not a time or space-time dimension.

Yet, the fact that most humans define our physical “reality” in terms of the spatial dimensions instead of a time or space-time dimension suggests that one may be able to form a physical image of how and why the quantum world is what it is by viewing our universe in terms of its spatial instead of its time properties.

Einstein gave us the ability to do this when he used the velocity of light to define the geometric properties of space-time because it allows one to convert a unit of time in his four dimensional space-time universe to a unit of a space identical to those of our three-dimensional space.  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 by mathematically defining the geometric properties of space-time in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions.

The fact that one can use Einsteinâ€s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with gravity in terms of four *spatial* dimensions allows one to form an image of its causality in terms of the physical properties of the spatial dimension instead of the non-physical ones most of us associate with time or a space-time dimension. 

As was mentioned earlier one of the advantage to redefining Einstein space-time concepts in terms of four *spatial* dimensions is that it not only allows one to understand gravitational energy in more direct terms but also allows on to form a physical image in terms of a classical environment for the unpredictability of the quantum world.

For example in the article “Why is energy/mass quantized?” Oct 4, 2007 it was shown one can derive the quantum mechanical properties of a particle by extrapolating the laws governing resonance in a classically three-dimensional environment to a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Additionally, it was showed why all energy exists in these resonant systems and therefore must be quantized.

Briefly it was 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 its natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would also be found in one consisting of four.

The existence of four *spatial* dimensions would give three-dimensional space (the substance with a natural frequency) 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, these oscillations in a “surface” of a three-dimensional space manifold, according to classical mechanics would generate a resonant system or “structure” in space.  These resonant systems are known as particles.

(In an earlier article “The geometry of quarks” Mar. 2009 it will be shown how and why they join together to form these resonant systems in terms of the geometry of four *spatial* dimensions.)

The energy in a classically resonating system is discontinuous and can only take on the discrete values associated with its fundamental or a harmonic of its fundamental frequency.

However, these properties of a classically resonating system are the same as those found in a particle in that they are made up of discreet or discontinuous packets of energy/mass.  This is the basis for assuming, as was done in the article “Why is energy/mass quantized?” that its quantum mechanical properties are a result of a resonant system in four *spatial* dimensions.

The reason why we do not observe energy in its extended wave form is that, as mentioned earlier all energy is propagated through space in discrete components associated with its resonant structure.  Therefore, its energy appears to originate from a specific point in space associated with where an observer samples or observes that that energy.

This is analogous to how the energy of water in a sink is release by allowing it to go down the drain.  If all we could observe is the water coming out of the drain we would have to assume that it was concentrated in the region of space defined by the diameter of the drain.  However, in reality the water occupies a much larger region.

However, treating the quantum mechanical properties of energy/mass in terms of a resonant system generated by a matter wave also allows one to form a physical image of its unpredictability by extrapolating the laws of our classical three-dimensional world to a fourth *spatial* dimension.

Classical wave mechanics tells us a waveâ€s energy is instantaneously constant at its peaks and valleys or the 90 and 270-degree points as its slope changes from positive to negative while it changes most rapidly at the 180 and 360-degree points.

Therefore, the precise position of a particle quantum mechanics associates Schrödinger’s wave equation with could be only be defined in terms of the peaks and valleys of the matter wave responsible for its resonant structure because those points are the only places where its energy or “position” is stationary with respect to a fourth *spatial* dimension.  Whereas it’s precise momentum would only be definable with respect to where its energy change or velocity is maximum at the 180 and 360-degree points of that wave.  All points in between would only be definable in terms of a combination of its momentum and position.

However, to measure the exact position of a particle one would have to divert or “drain” all of the energy at the 90 or 270-degree points to the observing instrument leaving no energy associated with its momentum to be observed by another instrument.  Therefore, if one was able to determine precise position of a particle he or she could not determine anything about its momentum.  Similarly, to measure its precise momentum one would have to divert all of the energy at the 180 or 360 point of the wave to the observing instrument leaving none of its position information left to for an instrument which was attempting to measure it.  Therefore, if one was able to determine a particles exact momentum one could not say anything about its position.

The reason we observe a particle as a point mass instead of an extended object is because, as mentioned earlier the article “Why is energy/mass quantized?” showed its energy/mass must be packaged in terms of a resonant system.  Therefore, when we observe or “drain” the energy continued in its wave function, whether it be related to its position or momentum it will appear to come from a specific point in space similar how the energy of water flowing down a sink drain appears to be coming from a “point” source with respect the extended volume of water in the sink.

However, this allows one to form a physical image of the unpredictability of a quantum environment because it give us a Classical reason why we cannot precisely measure the both the momentum or position of a quantum object because the measurement of one effects the measurement of the other. 

For example, if one wants to measure the position of a particle to within a certain predefined distance “m” its wave energy or momentum will have to pass through that opening.  However, Classical Wave Mechanics tells us that as we reduce the error in our measurement by decreasing that predefine distance interference will cause its energy or momentum to be smeared our over a wider area.  Similarly, to measure its momentum one must observe a portion the wavelength associated with its momentum.  However, Classical wave mechanics tell us we must observe a larger portion of its wavelength to increase the accuracy of the measurement of its energy or momentum.  But this means that the accuracy of its position will be reduced because the boundaries determining its position within the measurement field are greater.

However, because of the dynamic interaction between the position and moment component of the matter wave responsible for generating the resonant system associated with a particle defined in the article a ”Why is energy/mass quantized?” the change or uncertainty of one with respect to the other would be defined by the product of those factors.

Another way of looking at this would be to allow a particle to pass through a slit and observe where it struck a screen on the other side.  One could get a more precise measurement of its position by narrowing the slit however classical wave mechanics tell us this will increase the interference of the wave properties associated with its resonant structure.  However this will cause the interference pattern defining its momentum to become more spread out and therefore make it more difficult to accurately determine its value.

Therefore, Classical wave mechanics, when extrapolated to Schrödinger’s wave equation in an environment consisting a fourth *spatial* dimension tells us the more precisely the momentum of a particle is known, the less precisely its position can be known while the more precisely its position is known, the less precisely its momentum can be determined.  In other words it tells us in terms of a physical image based on a classical environment the reason why God must play dice is because the physicality of a quantum environment prevents us from precisely determining the initial condition of a particle through observation.

Later Jeff

Copyright Jeffrey Oâ€Callaghan 2014

The post The causality of quantum probabilities or why God must play dice. appeared first on Unifying Quantum and Relativistic Theories.

To this point physicists have identified six types of quarks, called the UP/Down, Charm/Strange and Top/Bottom. The Up, Charm and Top have a fractional charge of 2/3 while the Down, Strange and Bottom have a fractional charge of -1/3.

They assume each quark carries a charge called “color” which like electric charge is always conserved. However, unlike electric charge, the color charge (the chromo in Chromodynamics) comes in three varieties or red, green, and blue and that each quark comprising a particle must have a different color, red, green, or blue.

The reason is because Pauliâ€s exclusion principle says no particle can be made up of components with identical quantum states.  They incorporate this principal into Quantum Chromodynamics theoretical structure by assigning a color to individual quarks and adopting a rule that says for a stable particle to exist the colors of their components must combine to make a colorless particle.  This requires particles to conform to Pauliâ€s exclusion principle because colorless or white light only exist if it is made up of one part red, blue, and green light.  Therefore a stable particle can only exist it is made up of three different types of quarks with colors of red blue and green.

However as of yet no one has been able to define the reason for their fractional charge or their color component in terms of the physicality of the environment they occupy.

Yet as was show in the article “The geometry of quarks” Mar. 15, 2009 one can derive a physical reason for their fractional charge and color properties if one assumes as was done in the article “Why is energy/mass quantized?” Oct 4, 2007 that the quantum mechanical properties of energy/mass can be derived in terms of a resonant structure formed by a matter wave on “surface” a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly that article 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 four spatial dimensions.

The existence of four *spatial* dimensions would give space (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 “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 in 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.

The only way to dampen the frequency of a classically resonating system is to add or remove energy from it, which results in changing the characteristics of that system.

Additionally the energy in a classically resonating system is, as mentioned earlier is discontinuous and can only take on the discrete values associated with its fundamental or harmonic of its fundamental frequency.

However, these properties of a classically resonating system are the same as those found in a particle in that they are made up of discreet or discontinuous packets of energy/mass and when energy is either added or removed from it, its characteristics changed.

But if space was made up of four *spatial* dimensions one should also be able to explain why quarks have a fractional charge and how their color properties interact to form stable particles in terms of the geometry four *spatial* dimension.

The article Defining energy Nov. 26, 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.

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 may be because, as was shown in the article Embedded Dimensions Nov. 22, 2007 there are three ways the individual axis of three-dimensional space can be oriented with respect to a fourth *spatial* dimension.  Therefore, the geometric configuration or “colors” of individual quarks may be related to how its energy is distributed in three-dimensional space with respect to a fourth *spatial* dimension.

However, it may also explain why it takes three quarks of different “colors” to form a stable 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 shows how one can put the color and therefore the Chromo in Quantum Chromodynamics by assuming that space is composed of four *spatial* dimensions instead of four dimensional space-time.

Later Jeff

Copyright 2012 Jeffrey O’Callaghan

The post Putting the Chromo in Quantum Chromodynamics appeared first on Unifying Quantum and Relativistic Theories.

One is that it would allow one to derive a physical link between gravity and the strong and weak forces by extrapolating the classical laws governing 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 theorize that all particle and forces have a matter wave component.  His theory was confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer;) 
In the article “The “Relativity” of four spatial dimensions” Dec. 1, 2007 it was shown that one can derive gravity in terms of a continuous curvature or 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.

One of the advantages to using this theoretical approach is that it would allow one to derive a physical link between it and the quantum mechanical properties of energy/mass because as was shown in the article “Why is energy/mass quantized?” Oct. 4, 2007 one can derive its quantum mechanical properties in terms of a resonant system generated by the displacements associated with a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  

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 displacements or oscillations with respect to a fourth *spatial* dimension 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.

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

Similarly these resonant systems in four *spatial* dimensions would be responsible for the quantum mechanical properties energy/mass because they could only take on the values associated with fundamental or a harmonic of its fundamental frequency.

Earlier it was mentioned that one can define gravitational energy in terms of a continuous curvature in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

However the article “Embedded dimensions” Oct. 22, 2007 also 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.

This would allow on to define a physical link between gravity, the quantum mechanical properties of energy/mass, and the weak force can be understood by integrating their geometric properties to the one responsible for the fractional charges of quarks as was done in the article “The geometry of quarks” Mar. 15, 2009.

Briefly it was showed one can derive the 2/3 fractional charge of the Up, Charm and Top and the 1/3 charge of UP/Down, Charm/Strange and Top/Bottom and 1/3 charge of The Down, Strange and Bottom in terms of the geometry of four spatial dimensions. 

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 may be because, as was shown in the article “Embedded dimensions” Oct. 4, 2007 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. 

The weak force manifests itself in the transmutation of a quark from one flavor or color to another when they decay with emission or absorption of W and Z bosons.

However this is what one would expect if their stability was related to, 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 is oriented with respect to four *spatial* dimensions.  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 quarkâ€s color is related to how its central axis is oriented with respect to a fourth *spatial* dimension.  Therefore the weak force could be defined as the energy required to produce the transmutation or the change of a quark 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 of the displacements in components of three and fourth *spatial* dimensions. 

One can also understand why a “W” or “Z” boson is either emitted or absorbed during the transmutation quarks in terms of the particle properties of the resonant system defined earlier in the article “Why is energy/mass quantized?” Oct. 4, 2007

In other words the same mechanism responsible for the quantum mechanical properties of energy/mass is also responsible for the particle properties of the forces associated with the “W” and “Z” boson.

However, the fact the resonant interaction between the components of three and four *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 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 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 neutrons to uniformly share the energy required 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 the mechanism responsible for the quantum mechanical properties of energy/mass, the strong and weak forces by extrapolating the classical laws governing resonance in a three-dimensional environment to the oscillatory displacements associated with a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However as mentioned earlier the article “The “Relativity” of four spatial dimensions” Dec. 1, 2007  it was shown that one can also derive gravitational energy in terms of a displacement in a continuous “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.

Therefore One can establish a link between it, and the strong and weak forces in terms of the continuous properties of four *spatial* dimensions because of the fact that the matter wave defining the resonant system responsible for  the strong and weak forces is by definition continuous which means the geometry supporting it must also be continuous.  Therefore this define a link between them in terms of the continuous geometry of four *spatial* dimensions.

This demonstrates how one can derive a theoretical connection between the strong and weak forces and gravity in terms of the continuous geometric properties of a “surface” of a three-dimensional space with a fourth *spatial* dimension. 

Later Jeff

Copyright Jeffrey O’Callaghan 2011

The post Gravity linked to the strong and weak forces appeared first on Unifying Quantum and Relativistic Theories.

One of them is that it would allow for theoretically defining a common mechanism for gravity and the color charge of quarks by extrapolating observations made in a three-dimensional environment to a fourth *spatial* dimension.
For example in the article “The geometry of quarks” Mar. 15, 2009 it was shown one can derive their electrical or color properties in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Quantum Chromodynamics, which is an integral part of the Standard Model of Particle Physics, defines how quarks interact with themselves and each other to form particles such as protons and neutrons.  The word quantum stands for the fact that interactions (forces between particles) on this level can be represented as things that occur only in chunks called quarks.  The word Chromodynamics stands for the color properties it associates with them.

In the article “Why is energy/mass quantized?” Oct. 4, 2007  it was shown the quantum mechanical properties of particles could be derived in terms of a resonant system formed on “surface” a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, 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.

But if space was made up of four *spatial* dimensions one should be able to explain why quarks have a fractional charge and how they interact to form particles in terms of the geometry four *spatial* dimension.

The article Defining energy Nov. 26, 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.

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 may be because, as was shown in the article Embedded Dimensions Nov. 22, 2007 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 may also explain 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 shows that it is possible to define the electrical properties of quarks and how they combine to form particles in terms of the geometry of four *spatial* dimensions.

The link between gravity and the electrical properties of quarks can be found by the fact that they are both a result of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

In the article “Why Space-time?” it was shown one can derive gravity in terms of a symmetrical curvature caused by a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimensions that article associated with gravity. Symmetrical in the sense that the magnitude of the deformation is equally distributed throughout each axis of three-dimensional space.

One can understand how by comparing effects this curvature has on objects in a three dimensional environment to the effects a rod pushing down on a surface of a rubber diaphragm that has on marble on it.

The marble on the diaphragm will represent the energy/mass of an object and the rod will represent the “W” axis of a fourth *spatial* dimension.

(The “W” axis of a 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 “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.

However, what makes electrical forces associated with quarks different from gravitational is that the displacement caused by them on a “surface” of a three-dimensional space manifold is not symmetrical as was shown earlier with respect to the axis of three-dimensional space whereas those of gravity are.

This shows that one of the theoretical advantages to defining the universe in terms of four *spatial* dimensional instead of four dimensional space time is that it allows one to physically connect the color charge of quark with gravity.

Later Jeff

Copyright 2011 Jeffrey O’Callaghan

The post Linking gravity to the color charge of quarks appeared first on Unifying Quantum and Relativistic Theories.

One of them is that it would allow one to explain the” reality” of the probabilities associated with quantum mechanical wave function in terms of the classical laws of three-dimensional space.
Quantum mechanics assumes that one cannot define a particle in terms of its exact position or momentum but only in terms of the probabilistic values associated with its wave function.  This is in stark contrast to the Classical “Newtonian” assumption that one can assign precise values of future events based on the knowledge of their past. 

For example In a quantum system Schrödinger wave equation plays the role of Newtonian laws in that it predicts the future position or momentum of a particle in terms of a probability distribution by assuming that it simultaneously exists everywhere in three-dimensional space. 

This accentuates the fundamental difference between quantum and classical mechanics because the latter defines the reality of future events in terms of the effects of pervious events whereas quantum mechanics defines them based on the “non-classical” reality of the sum total of all possible events that can occur.  

However, as mentioned earlier one can define the classical “reality” of quantum probabilities by extrapolating the laws of a classical three-dimension environment to one consisting of four *spatial* dimensions.

In the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown one can define why energy/mass is quantized by extrapolating the laws of classical wave mechanics 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.

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 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 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 space.

Therefore, these oscillations in a “surface” of a three-dimensional space manifold would meet the requirements mentioned above for the formation of a resonant system or “structure” in four-dimensional space if one extrapolated them to that environment. 

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

Hence, these resonant systems in four *spatial* dimensions would be responsible for the discrete quantized energy associated with the quantum mechanical systems.

This cannot be done in four-dimensional space-time because time or a space-time dimension is only observed to move in one direction forward therefore it cannot support the bidirectional movement require to define classical resonance.

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

In an earlier article “Embedded dimensions” Oct. 4, 2007 it was shown that one can derive all forms of energy including that of a quantum system in terms of displacement in a *surface* of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However assuming its energy is result of a displacement in four *spatial* dimension allows one to derive, as mentioned earlier the probability distribution associated with its wave function by extrapolating the laws of a three-dimensional environments to a fourth *spatial* dimension.

Classical mechanics tell us that because of the continuous properties of waves the energy the article “Why is energy/mass quantized?” associated with a quantum system would be distributed throughout the entire “surface” a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This would be analogous to what happens when one vibrates a rod on a rubber diaphragm.  The oscillations caused by the vibrations would be felt over its entire surface while their magnitudes would be greatest at the point of contact and decreases as one moves away from it.

However, this means if one extrapolates the mechanics of the rubber diaphragm to a “surface” of a three-dimensional space manifold one must assume the oscillations associated with each individual quantum system must simultaneously exists everywhere in three-dimensional space.  This also means there would be a non-zero probability they could be found anywhere in our three-dimensional environment.

As mentioned earlier the article “Why is energy/mass quantized?” shown a quantum mechanical system is a result of a resonant structure formed on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Yet Classical Wave Mechanics tells us a resonance would most probably occur on the surface of the rubber sheet were the magnitude of the vibrations is greatest and would diminish as one move away from that point,

Similarly a quantum system would most probably be found were the magnitude of the vibrations in a “surface” of a three-dimensional space manifold is greatest and would diminish as one move away from that point,

However as mentioned earlier this is exactly what is predicted by Quantum mechanics in that one can define a particle’s exact position or momentum only in terms of the probabilistic values associated with vibrations of its wave function.

This shows how one can define the classical “reality” of the quantum mechanical probability functions by extrapolating the laws of classical mechanics to four *spatial* dimensions.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

The post The *reality* of quantum probabilities 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.

However, it is unfortunate that some have not made an effort to find it in terms of its continuous properties instead of its quantum mechanical ones.

We observe that all particles have mass, which is associated with gravitational force.  However, for the past century the brightest minds of the scientific community have been unable to define how this force can be propagated by a particle using the current quantum mechanical paradigms.  Additionally, even with the recent advancements in observational technologies, no one has observed the graviton or particle that many feel is responsible for the propagation of gravitational forces.

However, the fact that we have been unable to define a unifying mechanism either mathematically or conceptually for the observed quantum mechanical and gravitational properties of nature in terms of the current paradigms may not be due to their theoretical structure but to how we are attempting to integrate them.

For example, the fundamental assumption of Quantum mechanics is that energy/mass is contained in discrete irreducible units or packets of energy/mass called quarks andleptons.

However, the graviton or particle many physics associated with gravitational force has not, as mentioned earlier been observed.  Some feel that this is due to the fact our instruments are not yet advance enough to detect it but it could also be because gravitational force is not propagated by a particle but by a continuous geometric property of energy/mass.

We have shown throughout this blog  that observations of our environment suggest that it would be possible to unify the quantum mechanical properties of energy/mass with the continuous properties of gravity if one assume the existence of four *spatial* dimensions instead of four-dimensional space-time.

In the article “Defining gravity” Dec. 15, 2007 it was shown that one can theoretically derive the relativistic properties of motion, space, time, gravity and the fact that it is equivalent to an accelerated reference frame in terms of a continuous geometric property of four *spatial* dimensions in a manner that makes predictions identical to those made in “The General and Special Theories of Relativity”.

While in the article “Why is mass and energy quantized?” Oct. 4, 2007 it was shown that one can derive the quantum mechanical properties of energy/mass by extrapolating the laws of resonance in a classical three-dimensional environment to a matter wave 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 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 be meet in one consisting of four *spatial* dimensions.

(In an earlier “The geometry of quarks” Mar. 15, 2009 it was shown how and why quarks join together to form these resonant systems in terms of the geometry of four *spatial* dimensions.)

The existence of four *spatial* dimensions would give the “surface” of three-dimensional space the ability to oscillate 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.

However, these oscillations in four *spatial* dimensions would, if one extrapolates the laws of three-dimensional space to it generate a resonant system or “structure” in it.  These resonant systems are what defined a particle in the article “Why is mass and energy quantized?“

This cannot be done in terms of four-dimensional space-time because time or a space-time dimension is only observed to move in one direction forwards and therefore could not support the bi-directional spatial movement required to establish classical resonance.

However, as mentioned earlier the article “Defining gravity” showed one can derive the properties of gravity in terms of a continuous geometric properties of four *spatial* dimensions while the article “Why is mass and energy quantized?” showed that one can derive the quantum mechanical properties of energy/mass in terms of a resonant system with that same geometry.

This suggest as mentioned earlier that one may be able to define a theory of everything by assuming that the quantum mechanical properties of energy/mass are a result of the continuous geometric properties of four *spatial* dimensions instead of assuming that the continuous properties of gravity and space are a result of the quantum properties of energy/mass

Later Jeff

Copyright Jeffrey O’Callaghan 2010

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