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 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.
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.
Copyright Jeffrey O’Callaghan 2012
Vol. 3 — 2012
The concept of a field was developed when physicists learned that they could simplify the calculations of the forces involved in planetary motion by assuming or imagining the existence of a continuous gravitational field. They defined this field in such a way that if another planet were put at any point in that field the resulting force between any other planets would be exactly the Newtonian one. This simplified the calculations of planetary motion because it allowed them to isolate and analyze the forces of one planet on another instead of trying to analyze the forces exerted on a planet by the others at the same time.
Originally, many thought this was just a trick to simplify calculations.
But Michael Faraday, while researching electromagnetism discovered that a continuous field has real physical properties and therefore was able to convince others that is was more the just a calculating device.
However quantum mechanical assumes that all forces both attractive and repulsive are propagated by particles.
It is easy to understand how particles can be responsible for repulsive forces because our every day experiences tell us that a force is generated when two objects collide that causes them to move apart or repel each other.
However this is not the case with attractive forces because no has ever observed two objects moving towards or being attracted to each other after a collision.
Therefore scientists have to create or imagine what are called "virtual particles" which by their own admission do not exist, except in the math to explain attractive forces in terms of particle interaction.
Granted they assume that virtual particles exhibit some of the properties that "real" particles do, such as obedience to the conservation laws however they differ in that they when they collide or interact with "real" particles they cause them to attract instead of repulsing each other as is the case when two real particles interact.
One problem with this assumption is that no has or ever will observe a virtual photon because as mentioned earlier by definition they do not exist. Another more damaging one is that it is very difficult to devise a realistic mechanism based on observations that can account for how something that does not exist in the real world can interact with something that does to cause the observed properties of a repulsive force.
However one can define the mechanism responsible for both the attractive and repulsive forces of files by extrapolating observations of a classical three-dimensional environment to a fourth *spatial* dimension.
The reason why is because the force of a field effects the spatial not the time or space-time properties of an environment.
Einstein gave us the ability to do this when he used the constant velocity of light to define the geometric properties of space-time because it provided a method of converting a unit of time in a space-time environment to unit of space 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 advantage of this is that it allows one to define the physicality of faraday fields in terms of their observable spatial instead of their unobservable time properties.
For example the article "What is electromagnetic energy" Sep 27, 2009 showed one can physically derive the forces of electromagnetism by extrapolating the physical properties of a three-dimensional environment to a matter wave moving on a "surface" of a three-dimensional space with respect to a fourth *spatial* dimension.
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.
In other words one can explain both the attractive and repulsive properties of electromagnetic fields field by without the need of assuming the existence of virtual particle by extrapolating observations of our three dimensional environment to a fourth spatial dimension.
However it also provides a method of linking electromagnetic field to their quantum mechanical properties because as the article "Why is energy/mass quantized?" Oct. 4, 2007 showed one can also explain them by extrapolating resonant properties of a field in classical a three-dimensional environment to a matter wave moving on a "surface" of a three-dimensional field with respect to a fourth *spatial* dimension.
Briefly it showed the four conditions required for resonance to occur in a classical field, 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 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 field (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 field to be established in four *spatial* dimensions.
Observations of a three-dimensional environment tell us that the energy of a resonant field 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 fields are responsible for the quantum mechanical properties of field
As article What is electromagnetic energy" Sep 27, 2009 showed one can derived both the attractive and repulsive properties of electromagnetic fields in terms of differential displacements created by a matter wave moving on a "surface" of a three-dimensional field with respect to a fourth *spatial* dimension. While the article "Why is energy/mass quantized?" showed one can also derive their quantum mechanical properties of fields by extrapolating the laws governing resonance in a classical three-dimensional field to the differential displacement caused by a matter wave on that same surface of three dimensional space manifold with fourth *spatial* dimensions.
As was mentioned earlier scientists have to create or imagine what are called "virtual particles" which by their own admission do not exist, to explain attractive forces in terms of particle interaction.
However one does not have image anything to explain the repulsive properties of forces of fields and the quantum mechanical properties particles because as was shown above one can use the real physical properties of a continuous one made up of four *spatial* dimension.
Copyright 2012 Jeffrey O’Callaghan
Vol. 3 — 2012