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.

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

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

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

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

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

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

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

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

“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.

But what does the discovery of the Higgs Boson tell us about the reality of the Higgs field.
This is an import question because its existence is based on abstract mathematical constructs which may or may not describe its reality.  In other words even though they may have predicted its existence it has not yet been connected it to the observable reality of what we can see and touch.

The importance of connecting a theoretical idea to the observable properties of our world was demonstrated by Einstein 200 years after Newton realized that his gravitational theory meant “one body may act upon another at a distance”.

“It is inconceivable 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 he was unable to tell us what mass is, he was only able tell us how mass interacts with space-time.

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

This is similar to Newton in that he was able to mathematically define how mass gravitational interacts with other masses but was unable to understand or define a physical mechanism that could account for that interaction.

Einstein was often quoted as saying “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.”

In other words to fully understand the theoretical significance of the Higgs Field and why it is responsible for mass one should be able to describe how it interacts with mass in terms of a physical image based on what we can see and touch in our three-dimensional world much as Einstein was able describe how space and time interacted with each other to cause gravity.

Most scientists would agree that the best way to accomplish this would be by observing how mass interacts with space-time.

Unfortunately mass does not directly interact with time because we do not see a change in it no matter how long we wait however we can observe how its position in space can change with time.

This suggests that we may be able to form a physical image of the reality of the Higgs field if we could redefine Einstein space-time geometry associated with forces in terms of the spatial properties of position we associated  with mass.

Einstein gave us the ability to do this when he defined the geometric properties of a space-time universe in terms of the balance between mass and energy defined by 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 energy to its equivalent spatial  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.

This was the bases for assuming as was done in the article “Defining energy” Nov 27, 2007 that all forms of energy including thermo and that associated with mass can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of one in a space-time environment.

However changing ones perspective on the geometric structure of the universe form one of space-time to four *spatial* dimensions, 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* dimension creates mass and why it is quantized in the fundamental particles of the Standard Model in terms of a physical image formed by 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 in a 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 classical resonance to occur.

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

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

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

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

This suggest that the Higgs field is made up of the field properties of four *spatial* dimensions and that the magnitude of a mass would be dependent on its geometrical configuration.

If true one should be able to use those field concepts to explain why the mass of 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 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 properties of classical resonance and the field properties of four *spatial* dimensions.

This shows how one can use the field properties of four *spatial* dimension 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.

However assuming the Higgs Field is created by the geometry of four *spatial* dimensional allows one to understand the dynamics of the mass of the Higgs boson in same terms as the fundamental particles defined above.

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 conceptually understand how it interacts with space to create its potential energy in terms of the physical image formed by water in a dam. This is because the potential energy of water is defined by its spatial separation with respect to the bottom of a dam.  Therefore according to the above theoretical model, the potential energy or mass contained in the Higgs boson would be defined by its spatial separation 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 energy and therefore the mass of the Higgs bosom and where it should be located in an environment consisting of four *spatial* dimension in terms of the physical image of water in a dam.  This is because as mentioned earlier the potential energy of water in a dam is solely dependent on the height of the dam while that of the Higgs Boson would be dependent on magnitude of the spatial separation of the three-dimension space manifold it is occupying with respect to a fourth *spatial* dimension.

This shows how it is possible to understand the reality of the Higgs Field in terms of a physical image by reformatting (as was done in the article “Reformulating space-time” Oct 1, 2013) Einstein General Theory of Relativity in terms of four *spatial* dimensions.

It should be remember that Einstein’s genius allows us to chose 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 2013 

The post The “reality” of the Higgs field 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.