The Higgs Boson which was tentatively confirmed to exist on 14 March 2013 appears to confirm the existence of the Higgs field. Its discovery is pivotal to the Standard Model and other theories within particle physics because it explains why some fundamental particles have mass when the symmetries controlling their interactions should require them to be massless, It should allow physicists to finally validate the last untested area of the Standard Model’s approach to fundamental particles and forces, guide other theories and discoveries in particle physics, and potentially lead to developments in.
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.
| Family 1 | Family 2 | Family 3 | |||
| Particle | Mass | Particle | Mass | Particle | Mass |
| Electron | .00054 | Muon | .11 | Tau | 1.9 |
| Electron Neutrino | < 10^-8 | Muon Neutrino | < .0003 | Tau Neutrino | < .033 |
| Up Quark | .0047 | Charm Quark | 1.6 | Top Quark | 189 |
| Down Quark | .0074 | Strange Quark | .16 | Bottom Quark | 5.2 |
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