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.

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.

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.