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.

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

In other words Einstein was only able to explain how the field properties of space interact to create gravity while the Standard Model defines how the asymmetry of those fields gives particles their mass.

However this suggests that one may be able to integrate the Standard Model into Einstein’s concept of gravity if one can define a common physical mechanism responsible for how Higgs field breaks the symmetry of space-time to create mass while at the same time explaining how and why its field properties interact to create gravity.

Einstein gave us a method for accomplishing this when he said “If a new theory (such as that associated with the Higgs boson) was not based on a physical image simple enough for a child to understand, it was probably worthless.”

For example Newton was troubled by the fact that that his gravitational theory meant .” that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact…That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.”

However Einstein realized that one can understand how gravity “may act upon another at a distance through a vacuum” by extrapolating the physical image of how objects move on a curve surface in a three-dimensional environment to a curved four dimensional space-time manifold. This allowed him to conceptually understand gravity in terms of a physical image based on our three-dimension environment.

In other words the mathematics developed by Newton was only able to quantitatively predict gravitational forces while Einstein gave us the ability to conceptually understand why “one body may act upon another at a distance” by physically connecting it to the reality of what we can see and touch.

However, as mentioned earlier he was unable to tell us what mass is, he was only able tell us how mass interacts with space-time.

Similarly the Standard Model is able to define mass in terms of the symmetry breaking properties of the Higgs field however it is unable to define in terms of a physical image of how it interacts with the field properties of space-time to create gravity or the forces associated with mass.

This fact is difficult to understand because the Standard model is based on a Relativistic Quantum Field theory which has its foundation in Einstein’s Theories.  Therefore one would think that it would be easy to integrate it into them.

However Einstein’s and modern scientist’s inability to connect the Standard Models explanation for mass to Einstein’s explanation of gravity can be traced to the fact that they chose to define the universe in terms of energy instead of mass.

Einstein told us that a curvature in the field properties of space-time is responsible for gravitational energy and because of the equivalence between energy and mass defined by his equation E=mc^2 one must also assume that it is responsible for mass.

This suggest that one may be able to incorporate Einstein’s explanation of the gravity into the Standard Model if one converts or transposes the his space-time universe which defines field properties of energy in terms of geometry of space-time to one that defines mass of in terms of its field properties.

Einstein gave us the ability to do this when he used the constant velocity of light and the equation E=mc^2 to define the dynamic balance between mass and energy because that provided a method of converting the space-time displacement he associated with energy in a space-time universe to one we believe he would have associated with mass in a universe consisting of only four *spatial* dimensions.  Additionally because the velocity of light is constant he also allows us to defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

The fact that the equation E=mc^2 allows us to both qualitatively and quantitatively derive the spatial properties of energy in a space-time universe in terms of its spatial properties in four *spatial* dimensions is the bases for assuming as was done in the article “Defining energy” Nov 27, 2007 that all forms of energy/mass, including that associated with the Higgs field 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 changing ones perspective on the geometric structure of the universe form one of space-time to four *spatial* dimensions, as was just shown to be possible gives one the ability to define the physical mechanism by which the Higgs Field or the field properties of four *spatial* dimensions interacts with particles to create mass and why they are quantized in terms of a physical image formed in our three-dimensional environment.

For example one can form a physical image of why mass is quantized, as was done in the article “Why is energy/mass quantized?” Oct. 4, 2007 by extrapolating the image of a wave and its resonant properties in three dimension environment to one made up of four *spatial* dimensions.

This would be analogous to how Einstein, as mentioned earlier was able to explain gravity by extrapolating the physical image of how objects move on a curved surface of three-dimension space to one consisting of four dimensional space-time.

(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 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.

Physical observations of our three dimensional environment tell us that resonant systems can only take on the discrete or quantized energies associated with a fundamental or a harmonic of their fundamental frequency

Therefore, these resonant systems in the field properties of four *spatial* dimensions would define mass and its quantum mechanical properties in terms of the Standard Model 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.

However can also understand in terms of a “physical image” of the boundaries of the point particles of the Standard Model using the above concepts.

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 “box” containing the resonant system the article “Why is energy/mass quantized?” associated with a particle.

(The reasons why particles can be treated as a mathematical points in the Standard Model is because according to the above theoretical model the components of their energy/mass and forces associated with them would be evenly distributed around the centre of mass or the resonant structure in the article “Why is energy/mass quantized?” Oct. 4, 2007)

However this suggest the symmetry breaking properties the Standard Model associates with the Higgs field may be related to the geometric properties of four *spatial* dimensions.

If true one should be able to use those field concepts to explain how it interacts with particles to give them mass and why the mass of the corresponding particle types across the three fundamental families of particles in the Standard Model listed in the table below 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 or temperature of an 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 or energy of the environment they are occupying.

Thus suggest the reason “The corresponding particle types across the three families in the Standard Model 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 mass 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 asymmetrical field of four *spatial* dimensions.

However it also shows how one can use the asymmetrical field properties of four *spatial* dimensions or the Higgs Field to understand the causality of the masses of the fundamental particles in the Standard model in terms of a physical image based on the “reality” of what we can see and touch in our three dimensional environment.  This is similar to how Einstein, as mentioned earlier was able to shown that a mass “may act upon another at a distance through a vacuum” by extrapolating the physical image of how objects move on a curve surface in a three-dimensional environment to a curved four dimensional space-time manifold.

As mentioned earlier the article “Why is energy/mass quantized?” showed that one can derive the total mass of all particles in terms of the sum of 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 and the energy associated with displacement in the “surface” of three-dimensional space associated the environment it is occupying.

However if one assumes, as was done above the Higgs field is created by a spatial displacement in the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension one can also understand how its asymmetric properties interacts with particles to create their mass in terms of the physical image formed by water in a dam.

This is because the potential energy of water molecule in a dam is defined by its asymmetrical spatial separation with respect to the bottom of the dam.

Similarly, according to the above theoretical model, the potential energy or mass contained in particles would be defined by an asymmetrical displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

In other words it gives one the ability to define the asymmetrical properties the Standard Model associates with the Higgs field in terms of a physical image of water in a dam because as mentioned earlier its potential energy is in part dependent on the height of the dam while that of a particle would be dependent on magnitude of the spatial separation or the “height” of the three-dimension space manifold it is occupying with respect to a fourth *spatial* dimension.

However, as was mentioned earlier Einstein also defined gravity in terms of an asymmetrical displacement or curvature or a “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension or a space-time manifold.

This suggest that one may be able to unite the Standard Model with Einstein’s concept of gravity with if one can find a way of integrating the effects an asymmetrical curvature in “surface” of a three-dimensional manifold with respect to either space-time or a higher or fourth *spatial* dimension would have on a particle with the asymmetrical properties of the Higgs field.

It should be remember that Einstein’s genius allows us to choose whether to view the reality of the Higgs Field in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of energy/mass and the constant velocity of light.

Later Jeff

Copyright Jeffrey O’Callaghan 2014

The post Integrating the Standard Model into Einstein’s gravitational theory appeared first on Unifying Quantum and Relativistic Theories.

“However far the quantum physical phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms. The argument is simply that by the word “experiment” we refer to a situation where we can tell others what we have learned and that, therefore, the account of the experimental arrangements and of the results of the observations must be expressed in unambiguous language with suitable application of the terminology of classical physics.

This crucial point…implies the impossibility of any sharp separation between the behavior of atomic objects and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear…. Consequently, evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be regarded as complementary in the sense that only the totality of the phenomena exhausts the possible information about the object.”

In other words he did not think that it was possible to use classical concepts to integrate the wave and particle characteristics of a quantum particle into a single picture therefore he felt that there exits a physical division between the macroscopic world of classical objects and the microscopic world of quantum particles. 

However this may not be the true and one can understand why if one views the universe in terms of four *spatial* dimensions instead of four dimensional space-time.

(The reason will become obvious later.)

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 space-time universe to a unit of a *spatial* dimension identical to those in our three-dimensional universe .  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 a space-time universe 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 Einstein’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. 

One of the advantage to doing is that allows one to understand the wave particle duality of energy/mass or its complementary property in terms of the concepts of classical physics.

For example the article, “Why is energy/mass quantized?” Oct. 4, 2007 showed that one can explain and understand the physicality of its particle properties in terms of the classical concept of waves by extrapolating the laws of resonance in a three-dimensional environment to a matter wave moving on “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension.  It also explains why all energy must be quantized or exist in these discrete resonant systems when observed.

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 a matter wave moving in 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.

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.

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.

Therefore these resonant systems in would be responsible incremental or discreet energy associated with quantum mechanical systems.

This allows one to define the particle properties of energy/mass in terms of the classical concepts of a wave.

However, one can define its wave properties in terms of the classical concepts of a particle in terms of the boundaries of its resonant structure.

For example 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 of the resonant system associated with a particle in the article “Why is energy/mass quantized?“

However it also provides the ability to understand the inseparability of the wave and particle properties of energy/mass because it clearly demonstrates how one is depend on the other.

However it also explains why quantum systems either display the properties of a particle or a wave when measured because if one wants to measure the total energy contained in a given volume of space one will observe it as a particle while if one want to measure how it is propagated through space one must observe its wave properties.

Additionally it defines a classical reason why particles sometimes behave like wave and sometimes like particle and why it is impossible simultaneously observe them.

As shown earlier the energy contained in a quanta of space associated with a particle would be defined by the energy associated with the wavelength of its resonate structure.  In other words to observe or measure the particle properties of a given volume of space one has to sample all of its energy leaving nothing of its wave component to measure.  Similarly if one wants to observe or measure fully the wave energy of a quantum of space one would have to sample all of its energy leaving none of its particle properties.

(If one does not want to observe all of the energy in a given volume of space then one would expect that the difference would be made up by the emission of a photon or other particle whose energy would correspond to that difference.)

The reason why one cannot simultaneously measure both its wave and particle properties is because as mentioned the energy of a particle is defined by the wave properties of its resonant structure.  Since the resonant system that defines a particle is the smallest unit of its resonate structure if one measures its particle properties there would be no wave energy left for measuring its wave proprieties while if someone measure its wave energy there would be no energy left to support its particle properties. Therefore making one of these measurements precludes the other.

This demonstrates how one can integrate the wave and particle characteristics of a quantum particle into a single picture and why the  physical division between the macroscopic world of classical objects and the microscopic world of quantum particles as was assumed by Bohr many not exist. 

Later Jeff

Copyright Jeffrey O’Callaghan 2014

The post Mass from first principles appeared first on Unifying Quantum and Relativistic Theories.

In other words even though one can find equations to accurately quantify or define an environment does not mean that they have found an valid explanation as to how and why it is what it is.

For example both Quantum Mechanics and the Standard Model of Particle Physics define and quantify the environment of particles in terms of what could be considered the mystical properties of a non-dimensional mathematical point.

Mystical in the sense that the definition of mysticism as being or having vague speculation: a belief without sound basis could be applied to it.  This is because by definition no one has or ever will be able to observe the non-dimensional mathematical point they use to define a particle therefore we do not have an observational and therefore a sound basis for assuming its existence.

Most who have study the history of science are aware of the fact that many medieval and Renaissance astronomers assumed the planets were imbedded in rigid celestial spheres whose movement was guided celestial intelligences, souls or impressed forces.

Today many would classify that concept as being mystical because there is no observation evidence to support the assumption that the motion of the planets is control by some form of intelligence.

However many modern scientists would disagree with the assertion that a non-dimensional particle has similarities to the mystical ones we now associate with the Renaissance astronomer’s celestial intelligences by pointing to the fact that it permits them to accurately quantify its environment within the limit of our modern observational capabilities.

Yet the same argument could and most probably was used by them to justify their belief in idea that a celestial intelligence were guiding the planet because it also permitted them to accurately define and quantify the orbital environment of the planets within the limits of their observational capabilities.

The Standard Model of particle physics uses the concept of point particle only because it makes its mathematical description of their properties possible.   However it assumes that a point is appropriate representation of any object whose size, shape, and structure are irrelevant in a given context. For example, from far enough away, an object of any shape will look and behave as a point-like object.

While Quantum Mechanics derives the world of the very small in terms of the probability function based on mathematical representation of particle as a non dimension point for reason similar to why the standard model does.  In other words the only way to define the position of a particle in terms of a probably function is buy assuming that it does not have any spatial properties.  Therefore it also assumes that it size, shape, and structure are irrelevant in a given context.

Unfortunately for the proponents of Quantum Mechanics the concept of a point particle is complicated by the Heisenberg uncertainty principle, which tells us even in the domain of quantum mechanics an elementary particle, with no internal structure, occupies a nonzero volume because of the uncertainty involved in determine the exact point where it is located in space.

As mentioned earlier both of these theoretical models assume that non-dimensional point is an appropriate representation of a particle because its size, shape, and structure are irrelevant in a given context.

But what if it is relevant?

For example what if the Heisenberg’s Uncertainty Principle which asserts there is a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position x and momentum p, can be simultaneously known is related to the spatial extension of a particle and not to its point properties as quantum theory assumes.

As was shown in the article “Why is energy/mass quantized?” Oct. 4, 2007 it is possible to understand the quantum mechanical properties of energy/mass in terms of an extended object 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. 

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

The existence of four *spatial* dimensions would give three dimensional 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.

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

Therefore the discrete or quantized energy of resonant systems in a continuous form of energy/mass would be responsible for the discrete quantized quantum mechanical properties of particles.

However, it did not explain how the spatial boundaries or volume of these resonant structures is 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 “box” containing the resonant system the article “Why is energy/mass quantized?” associated with a particle.

The mathematics of Quantum mechanics support the assumption that a particle occupies a finite volume berceuse it defines the smallest possible unit of space and increment of energy in terms of Planck’s length “h” while defining the size of an individual quantum of force in terms of the equation E = h c / L. 

As mentioned earlier both the standard model of particle physics and quantum mechanics assume that a point particle is an appropriate representation of any object whose size, shape, and structure is irrelevant in a given context.

However, even though the size and shape of a particle may be irrelevant to someone looking at it from the macroscopic perspective of a human observer it may be very relevant to the process and mechanisms reasonable for what a human observes.

For example if one assumes, as quantum mechanics does that a particle is a non-dimensional point then according to the above concepts there would be an uncertainty in determining its position because that non-dimensional point could be found any with the volume of the three-dimensional “box” mentioned above.

Yet one could come to the same conclusion if one assumes that the quantum properties of a particle are a result of resonate system in four spatial dimensions because according to the above concepts there would be an uncertainty in determining its position because that non dimensional point could be found anywhere within the volume of the “box” mentioned above.

Planckâ€s length is one of fundamental components of Quantum Physics and along with Heisenbergâ€s Uncertainty Principle it defines the uncertainty in the ability to measure more than one quantum variable at a time.  For example attempting to measure an elementary particleâ€s position (â–²x) to the highest degree of accuracy leads to an increasing uncertainty in being able to measure the particleâ€s momentum (â–²p) to an equally high degree of accuracy.  Heisenbergâ€s Principle is typically written mathematically as â–²xâ–²p  Â³ h / 2  where h represents Planck constant

As mentioned earlier the resonant wave that corresponds to the quantum mechanical wave function defined in the article “Why is energy/mass quantized?” predicts that a particle will most likely be found in the quantum mechanical “box” whose dimensions would be defined by that resonant wave.  However quantum mechanics treats particles as a one dimensional points and because it could be anywhere in it there would be an inherent uncertainty involved in determining the exact position of a particle in that “box”.

For examine the formula give above ( â–²xâ–²p  Â³ h / 2 ) tells us that uncertainty of measuring the exact position of the point in that “box” defined by its wavefunction would be equal to â–²xâ–²p  Â³ h / 2.   However because we are only interested in determining its exact position we can eliminate all references to its momentum.

However if we eliminate the momentum component from the uncertainty in a particle position become 6.626068 × 10^-34 meters or Planckâ€s constant.

As mentioned earlier the uncertainty involved in determining the exact position of a particle is because it is impossible to determine were in the “box” defined earlier the quantum mechanical point representing that particle is located.  However as mentioned earlier Planckâ€s constant tells us that one cannot determine the position of a particle to an accuracy greater that 6.626068 × 10^-34.  This suggest that Planck constant 6.626068 × 10^-34 defines the physical parameters or dimensions of that “box” because it defines the parameters of where in a given volume of space a quantum particle can be found.

Classical mechanics uses also uses the existence of a point at the center of mass to calculate the position of an extended object and to predict how it would interact with other objects in a gravitational field.  Similar to quantum mechanics it assumes that the object position can be determined by measuring it from a point defining its center because from a distance they feel it gives them an appropriate representation of the size, shape, and structure of the object. 

Therefore they can define the position of an irregular shaped object such as an asteroid by determining the distance from that point to whatever reference point they chose.

However Classical mechanics accepts the fact that there are limitation to the concept of using the center of an object to predict its position and how it will interact with other objects because as the resolution of the measurements increase or distance between decreases between it and the measure device it accepts the fact that the object shape has an effect on those measurements.

Similarly fact that Quantum mechanics tells us the individual quanta of energy/mass have a spatial extension defined by the equation E = h c / L means that there would always be an uncertainty in determining its position related to its shape because as mentioned earlier the resonant structure defining its particle properties is made up of the dynamic components of a matter wave and therefore there would be a predictable randomness when interacting with a measurement device.

Therefore on a quantum scale the size, shape, and structure of a particle would be relevant in determining a particle reality

This shows how one can not only mathematical describe the quantitative “reality” of a particles environment but also define how and why we observe them to interact the way we do based on the observable and therefore the verifiably properties of a three-dimensional environment instead speculating on the existence of a mystical non-dimensional particle.

As mentioned earlier assuming non-dimensional point particle can describe the quantum world is mystical in the same sense as the assumption made in the middle ages that celestial intelligences, souls or impressed forces were guiding the planets because there is no sound observational basis for their existence.

However history has shown that the greatest advances in science are made when one eliminates mysticism from the description of reality

As mentioned earlier Scientist especially physicists should always remember that describing reality is different from defining it.

Later Jeff

Copyright Jeffrey O’Callaghan 2013 

The post The Mysticism of a non-dimensional particle appeared first on Unifying Quantum and Relativistic Theories.

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

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

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

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

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

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

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

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

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

Unfortunately one cannot use the same logic to explain the potential energy of mass in the Standard Model because it defines in terms of a space-time environment which is not computable with one based solely on the properties of a spatial one as is the above example.

This would be true if Einstein had not used the equation E=mc^2 and the constant velocity of light to define the geometric properties of a space-time because that provided a method of converting a unit of space-time he associated with energy to unit of space associated with position in four *spatial* dimensions.  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 according to the concepts in that article one could define the inertial or rest mass of an object or particle by extrapolating the observations of the potential energy of the water in a bucket resting on the surface of a table to a displacement in a “surface” of a three-dimensional volume with respect to a fourth *spatial* dimension.  In other words one could define the energy associated with mass in terms of a spatial displacement of a three-dimensional volume with respect to a fourth *spatial* dimension for the same reason as one can define the energy of the water in the bucket as being related to its displacement with respect to the table top.

In other words one can define the physicality of the Higgs field in terms of a displacement in the field properties of a four *spatial* dimension or space-time.

However if as was shown above one assumes that the Higgs field is made up geometric properties of four *spatial* dimensions or four dimensional space-time allows one to understand why it does what it does in terms of a physical image based our three dimension environment.

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

This is because also allows one to derive the energy associated with the momentum or constant relative velocity of an object or particle in terms of those scalar field properties buy adding the displacement associated with its rest mass to the one the article “Defining energy?” Nov 27, 2007 associated with constant velocity. (The relative velocity of an object at rest with respect to other objects is zero so the displacement of three-dimensional space with respect to those objects would also be zero.) 

In other words it allows on to understand in terms of a physical image based on our three dimensional environment how a  “linear” displacement in the field properties of a three-dimension space with respect to a fourth *spatial* dimension or the Higgs field is responsible for why particle have mass and the energy associated with its relative motion.

However it can also explain why an object or particle resists acceleration and why that resistance is directly proportional to its mass because as that article showed a curvature in a “surface” of a three dimensional space manifold with respect to a four *spatial* dimensions is responsible for all accelerations.  However because as was shown earlier there is a one to one correspondence between it and the space-time curvature Einstein indicated was responsible for mass it would be directly proportional to it.  Therefore the interaction of mass with the slope of a curvature in a “surface” of a three-dimensional space and it would be directly proportional to its mass.  This means the acceleration a mass experiences when it interacts a curvature in either in either an environment consisting of space-time or four *spatial dimensions proportional to its mass.  In other words there should according to these concepts outline above be a one to one correspondence between the mass of an object or particle and the acceleration it experiences for a given force.

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

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

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

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

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

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

Later Jeff

Copyright Jeffrey O’Callaghan 2012

The post The physicality of the Higgs fields appeared first on Unifying Quantum and Relativistic Theories.

However, for the past 50 years brightest minds in the scientist community have been unable to observe the Gravitron or the particle it assumes it responsible for the force of gravity.

Some say this is because it interacts so weakly with matter that modern instruments are not sensitive enough to detect it even with, as mentioned earlier the recent exponential increase in their sensitivity. 
However the reason may be because we have been looking in the wrong direction.

For example in the article ” Linking Gravity with electromagnetism in four *spatial* dimensions”  Dec. 15, 2007 it was shown that one can derive quantum properties of gravitational and electrical forces in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension in a manner that makes prediction identical to those of General Relativity.

Einstein gave us the ability to derive gravity in terms of a displacement a “surface” of a three dimensional space manifold with respect to a fourth spatial dimension when he defined the geometric properties of a space-time universe in terms of the equation E=mc^2 and the constant velocity of light because that provided a method of converting the displacement in space-time he associated with gravity to its equivalent displacement in four *spatial* dimensions.  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.

However as that article one also can derive electromagnetism in terms of spatial displacement of a “surface” of a three dimensional space manifold with respect to fourth *spatial* dimension

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

However the above theoretical model shows that the quantum unit of both gravity or the Gravitron and electromagnetism; the photon share a common origin in a resonant system and therefore would interact with each other. This suggests that instead of looking for gravitons effect on matter one would be more likely to find it by observe the random effects it would have on the movement of extremely light particles such as low frequency photons.

This random effect would be amplified by the distance traveled so with our advanced technologies if it exists we should be able to observe a difference between photons with nearby verse ones with far away origins.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

The post Finally, someone found a physical link between the graviton and the photon appeared first on Unifying Quantum and Relativistic Theories.

One is that it would allow physicists to define a particles mass and inertia by using one’s imagination to extrapolate observations made in a three-dimensional environment to a fourth *spatial* dimension.

For the past 50 years, the Standard Model of particle physics has given us a complete mathematical description of the particles and forces that shape our world.  It predicts with so much accuracy the microscopic properties of particles and the macroscopic ones of stars and galaxies that many physicists feel that it is the ultimate theory of matter and energy.
But as Charles Seife mentions on page 142 of his bookAlpha & Omega “Taken literally the plain vanilla form of the Standard model does not say anything about particle mass at all: in fact if theorists try to put mass in to its equations they blowup and become meaningless.”

In 1964 Peter Higgsshowed that one can solve this problem and explain why particles have inertial or rest mass if one assumes space is permeated by what is called a Higgs field.

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

The only problem is that the Higgs boson has never been observed.

This is problematic for its proponents primarily because The Large Hadron Collider (LHC) the world’s most expensive and highest-energy particle accelerator has been able to attain the energy levels which most believe should make it observable.

However, if it cannot be observed in the high energy environment presently generated by the LCH, scientists are going to have to make a decision as to whether or not to continue to expend the resources looking for something that may not exist or expend even more to create a more powerful accelerator.

This is especially relevant because as mentioned earlier there is an alternative explanation for mass that is based on the observable and therefore verifiable properties of three-dimensional space which does not require the large expenditures in time and money as would be required for verifying the existence of the Higgs boson.

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

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

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

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

This means that one could define the potential, inertial or rest energy of mass by extrapolating the observations of the potential energy of the water in a bucket resting on the surface of a table to a displacement in a “surface” of a three-dimensional manifold with respect to  a fourth *spatial* dimension.  In other words one could define the potential energy associated with inertial mass in terms of the displacement of a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension for the same reason as one can define the potential energy of the water in the bucket as being related to its displacement with respect to the table top.

However the article “Defining energy” Nov 26, 2007 derived the energy associated with the relative velocities in terms of a differential displacement of a volume of an object or particle with respect to a fourth “spatial” dimension.  In other words it was able to show the energy associated with velocities are a result of a differential displacement in a “surface” of a three-dimensional space manifold with respect to a fourth “spatial” dimension.

(The energy associated with relative velocities would be associated with the displacement of the surface of the table with respect to the floor in the example mentioned earlier.)

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

This means, one could define the potential energy associated with the velocity or momentum of an object or particle in terms of the displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension associated with its rest mass plus that associated with its relative velocity because according to the concepts presented in those articles it would be defined by the sum of those components.

The first would be magnitude of the displacement in a “surface” of a three-dimensional space associated with the rest mass of an object.  The second would be the magnitude of the displacement of that “surface” with respect to a fourth *spatial* dimension caused by the energy of its relative motion.  (The momentum of an object at rest with respect to other objects is zero so the displacement of three-dimensional space with respect to those objects would also be zero.) 

This also defines why the “relativistic” mass or inertia of an object or particle increase as its velocity approaches that of light because its total energy/mass would, according to the concepts presented here be related to the relative magnitude of the total displacement in a “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension which in turn would be related to their relative velocities.

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

Therefore,  if as mentioned earlier the momentum of a particle or object is caused by a displacement of a “surface” of a three-dimension space manifold it would tent to stay rest or ones in motion would tend to stay in motion unless it interacted with a “surface” that was curved with respect to a fourth *spatial* dimension.

This means that one does not have to assume the existence of the Higgs Boson to explain why particles have both mass and inertia because it shows how one can use his or her imagination to explain it by extrapolating observations of a three-dimensional environment to a fourth *spatial* dimension.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

The post Mass, inertia, and the Higgs Boson 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 is that it would allow one to quantifiably derive the origins of our present universe in terms of a cycle of expansions and contractions by extrapolating the laws of a classical environment to four *spatial" dimensions.

The Standard Cosmological Model of the Universe hypothesis the universe evolved from a small compact "ball" of energy/mass which began a rapid expansion based in part on a frequency shift in the spectral lines in light called the red shift.

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

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

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

As mentioned earlier there are several theoretical advantages to assuming the existence of four *spatial* dimension and a continuous non-quantized field of energy/mass.

The first, as was shown in the article "What is Dark Matter?" Sept 10, 2007 is that it would allow one to explain the invisible gravitational component of Dark matter because being up of mass it would exert a gravitational potential yet being continuous it would be invisible to modern instrumentation which are only calibrated to detect mass in its particle form.

That article listed several other observations that support its existence such as the fact that electromagnetic energy in itself is not quantized because a photon can have any frequency and therefore any energy greater than zero or less than infinity and the equation defining the relationship between mass and energy, E=m*c^2 indicates that mass is completely convertible to one or more photons with energies greater than zero or less than infinity.

This suggests that a continuous non-quantized field of energy/mass must be available to support the continuous properties associated with energy of the electromagnetic spectrum.

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

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

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

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

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

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

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

It was shown these resonant systems in a continuous field of energy/mass are responsible for the quantum mechanical properties of a photon and energy/mass.

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

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

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

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

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

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

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

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

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

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

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

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

(It should be remember, we do agree with many cosmologists that the universe is presently in an overall state of expansion however, we disagree with the currently accepted rates at which this expansion is occurring and define this expansion not in terms of a "big bang" but in terms of cycle of expansions and contractions in four *spatial* dimension.)

One way of accomplishing this is to compare the interaction of the matter wave component of a photon with a continuous non-quantized form of energy/mass to the interaction of a wave on water to water.

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

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

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

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

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

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

The reason why many astronomers believe the entire redshift of a star is the result of its movement away from an observer is as just mentioned classical theory of charged particles interacting with an electromagnetic wave, cannot explain any shift in wavelength.

Therefore, if the red shift was caused by a particle interaction one should observed Compton scattering in red shifted light.  Since no Compton scattering is observed in light coming from a star it is assumed by many astronomers it can only be caused by the movement of an object away from an observer because as mentioned earlier it is the only way they can explain it.

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

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

However the law of conservation of energy/mass tells us that it must be conserved.  In other words if a photon is redshifted or loses energy to a continuous non-quantized form of mass as it move through an environment it tells us the mass component of that environment must increase.

Yet this means that interaction will result in an increase the continuous non-quantized mass component in the environment where that energy loss took place.  The magnitude of this interaction is quantified by the experimentally verified equation E=mc^2.

However as has been showed throughout the Imaginers Chronicles a volume of three-dimensional space is made up of a continuous field of mass therefore if one increases the quantity of it in a given region of space the volume associated with that region will expand.

Therefore the rate of expansion of the universe due to a conversion electromagnetic energy to a continuous non-quantized field of mass would be related to the non-linear formula of E=mc^2.

Therefore, if this mechanism does define one of the expansive components of the universe the rate of the expansion would be less than that predicted by many cosmologists because one of its components would be defined by the non-linear formula of E=mc^2 and not by the linear recessional velocity of galaxies.  This would result in a reduction of the calculated rate of expansion which is based on the assumption that the entire energy loss of associated with the red shift in light is due to the recessional velocity of galaxies.

(The force called Dark Energy is a result of the fact that one must add the non-linear expansion caused by the creation of a continuous non-quantized field mass to the linear expansion associated with the recessional velocity of galaxies making it appears as though the expansion of the universe is accelerating.)

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

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

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

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

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

However, the contraction or "compression" of the universe will generate heat for the same reason as heat is generated by the "contraction" or compression of a gas.

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

Similarly, the heat generated by the contraction of the universe will cause an expansive force that will oppose gravitationally forces that are causing the universe to contact.

The velocity of contraction will increase until the momentum of the galaxies, planets, and the continuous non-quantized mass components of the universe equals the expansive forces generated by the heat generated by its contraction.

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

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

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

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

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

Hence the expansion will continue until the total gravitational attractive forces of the mass in the universe exceeds the total expansive forces cause by the heat generated by its contraction.

At this point, the contraction phase will begin again.

Since the universe is a closed system, the amplitude of the expansions and contractions will remain constant because the law of conservation of mass/energy dictates the total mass and energy in a closed system remains constant.

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

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

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

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

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

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

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

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

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

Later Jeff

Copyright Jeffrey O’Callaghan 2011

The post Dark Matter and the Evolution of the universe appeared first on Unifying Quantum and Relativistic Theories.

 has shown it is possible to define a universe in terms of four *spatial* dimensions in a manner that makes predictions identical with those of Einsteinâ€s General and Special Theories of Relativity by extrapolating observations of three-dimensional environment to a fourth *spatial* dimension while defining the theoretical advantages to adopting this perspective over that of his theories.

One is that it would allow one to define the abstract mathematical “realities” of the Standard Model of Particle Physics in terms of the observable reality of our three-dimensional environment.

For the past 25 years, the Standard Model of Particle Physics has given us a complete mathematical description of the particles and forces that shape our world.  Its predictions have matched experimental data, decimal place for decimal place, with amazing precision. However, most of its predictions are based on abstract mathematics. 

They indicate the laws of nature are symmetrical with respect to production of particles and antiparticles.  In other words when one creates a particle in an accelerator one must also create an antiparticle whose energy/mass is equal and opposite to it.

However, mathematical symmetry is defined as an attribute of a shape or relation which is an exact reflection of form on opposite sides of a dividing line or plane.

Therefore, if the standard model does describe the particles and forces that shape our world then it should be able to physically define what the dividing line is between a particle and antiparticle because our world is not made up of equations but physical objects.

This is extremely difficult to do in terms of the space-time geometry of Relativity because time is only observed to move in one direction forward and therefore could not provide a dividing line required to define symmetry.

Therefore, one cannot define the reality of the negative or opposite directed energy the Standard Model ascribes to anti-particles without assuming they are made up of negative mass.  This is because the only term other than mass in relativistic formula that define energy or E=mc^2 is squared and therefore is always positive.  This means the only way one can define the physical reality of negative energy in terms of space-time geometry is to assume the existence of negative mass.  Unfortunately, the abstract mathematics of the Standard Model does not permit the existence of negative mass.

Granted some like Richard Feynman have tried to use vectors to define negative energy/mass associated with anti-particles by assuming time moves backwards in them with respect to particles.  However, this methodology cannot define its reality in terms of General Relativity because the time component of energy in Relativistic formulas is also squared which means that energy must always be positive. 

Additionally even thought the equations of Relativity permit time to move backwards no one has ever observed that to happen.

As mentioned earlier this blog showed it is possible to define a universe in terms of four *spatial* dimensions in a manner that makes predictions identical to those of Einsteinâ€s General and Special Theories of Relativity by extrapolating the laws of a three-dimensional environment to a fourth *spatial* dimension.

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

We have all observed the symmetry in a three-dimensional environment with respect to a dimensional plain.  For example we can observe the symmetry imposed by a two-dimensional plane or boundary in our three-dimensional environment.

However if it is true, as we are suggesting that energy/mass is caused by a displacement in a “surface” of a three dimensional space manifold with respect to fourth *spatial* dimensions one could extrapolate the symmetrical properties associated with a two-dimensional plane or boundary in three-dimensions to the boundary between a third and fourth *spatial* dimension.

In other words one could define the abstract mathematical symmetry of the standard model in terms of the “reality” of a boundary between the third and fourth *spatial* dimension.

This means the proponents of the Standard Model could define the mathematical symmetry it associates with the energy/mass of particles and anti-particles terms of oppositely directed displacements in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of having to rely purely on the abstract “reality” of mathematical logic.

However, it also would allow them to define a physical mechanism for why an antiparticle is created whenever a particle is based on observations of our three-dimensional environment.

Classical hydrodynamics tells us if we push down on a small area on the surface of water in a closed container it will become displaced.  However, it also tells us that the volume of water displaced by that downward pressure will be offset by a equal but opposite volume displaced in the upward direction.

However, as mentioned earlier the article “The reality of the fourth *spatial* dimension” showed one can define all forms of energy/mass in terms of a spatial displacement in a “surface” of a three dimensional space manifold.

Therefore if mass is a result of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension any downward displacement in its “surface” will be
offset by a equal but oppositely “upward” directed displacement.

Therefore, according to classical hydrodynamics a particle could not be created without the creation of antiparticles because as mentioned earlier it tells us that when a surface undergoes a displacement an equal but opposite or a symmetrical one must be created on that surface.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

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