http://www.nasa.gov/

Gravity is the central dilemma of the theory of everything, and it so happens that it is the central chapter of this model as well. In addition, I will offer an explanation for the unexplained Planck Constant in the paragraphs to come. An explanation is also proposed for the nature of the mass of subatomic particles. The explanations are verified by experimental findings in nuclear physics and the standard model of sub-atomic particles.

Mass 
By definition mass is the resistance of a particle to acceleration. This property is also called inertia. The true nature of mass is not completely understood.
The standard model of particles postulates that sub-atomic particles by themselves do not posses mass. Mass is defined only by inertia. The Newton equation for inertia is F = ma, where m is mass of an object, F is the force needed to accelerate it with the magnitude a.

Gravity
Newton’s law of universal gravitation denotes that all objects attract each other. The force of attraction is directly related to the object’s gravitational mass.
It is astonishing that these seemingly different properties of objects, namely inertial mass and gravitational mass, are equal. This phenomenon is called the Equivalence Principle.
At this point, let us look at the main existing theories, which try to explain inertia and mass.

Higgs Mechanism
The most popular belief for a description of the origin for mass is the Higgs Mechanism.  As mentioned before, the standard model of particles postulates that particles by themselves do not posses mass.  The equation for mass acquisition through Higgs mechanism is given by:

 mi = Γ ћω²c/2πc²

Where Γ is Abraham –Lorentz damping constant.  Ћ is Dirac's constant and ωc is cutoff frequency (the frequency at which a mass respond to and starts oscillating). Please note that, everything else being fixed, in Higgs mechanism, the mass is directly related to the cutoff frequency of the wave-particle.
The Higgs postulate assumes a universal field called Higgs field that is carried by the Higgs Boson. Higgs Boson is a hypothetical particle that supposedly introduces mass to other particles through Higgs mechanism.
“The Higgs idea comes directly from the Physics of Solids. A solid contains a lattice of positively charged crystal atoms. When an electron moves through the lattice, the atoms are attracted to it, (therefore slowing it down) causing the electron's effective mass to be as much as 40 times bigger than the mass of a free electron.”⁶⁴
This concept has been extended to define the nature of mass acquisition by particles.
The Higgs particles supposedly create crowding and traffic in a particle’s way. Although they are not affecting the homogenous motion of particles they some how resist against particles acceleration. This is proposed as the reason behind resistance of the particle to change of trajectory and acceleration. So far, hard work in the Cern and Fermi lab and other accelerators and colliders throughout the world failed to find Higg’s boson. In fact, the Dec 2001 issue of the New Scientist published an article titled “No sign of the Higgs boson” with a strong suggestion that the Higgs boson does not exist.
Even if we find such a boson, we still have to find an explanation for the way that it actually creates inertia.
David Miller from Dept. Physics and Astronomy, University College London says: “A crystal lattice can carry waves of clustering without needing an electron to move and attract the atoms. They are called phonons”
Dr. Miller continues, “there could be a Higgs mechanism, and a Higgs field throughout our Universe, without there being a Higgs boson.”64
The amount of energy added by Higgs field is:

E= M²h² + Ah⁴

Where A is a positive but unknown constant, h is the size of Higgs field, and M is the mass of Higgs particle.
Dirac's Electron and Higgs Mechanism
The Dirac equation for electron is obtained by:

Ψ = (a _A , b _A' )

It represents a pair of 2-spinors. We can interpret its physical reality as follows. An electron actually consists of two separate particles (a _A and b _A'). By definition b A' is an antiparticle. These two particles have opposite charges and continually convert to each other. In case of electron, the anti particle is called positron. Positron has been actually detected.

Roger Penrose, Road to Reality⁵⁶

The conversion coupling constant is 2^-1/2 M. The quantity M = ħ/ m₀ , where ħ is Dirac’s constant and m₀ is the rest mass. In Higgs view 2^-1/2M is a field where particles drop and acquire mass again.

There are controversies about Higg’s Mechanism. Even Martinus Veltman, a Higgs architects himself, call it a rug under which we sweep our ignorance. Sheldon Glashow is less kind, calling it a toilet in which we flush away the inconsistencies of our present theories.⁷⁰
The researchers at California Institute for Physics and Astrophysics question Higg’s postulate of mass acquisition as:
“Why does the energy "soaked up" from the Higgs field resist acceleration? Perhaps that is not a legitimate question. Perhaps mass and energy intrinsically possess the property of inertia and that is the end of the story.” ⁶⁵ 

Stochastic Electrodynamics
Semi-classic stochastic electrodynamics has been well developed since 1960. It postulates that at a microscopic level, the field is filled with numerous plane waves that extend in every direction.
It hypothesizes that the waves come from the Zero Point Field (ZPF).
 “Stochastic electrodynamics postulates that the ZPF is as real as any other radiation field. In such a view the existence of a real ZPF is as fundamental as the existence of the universe itself. The only difference between stochastic electrodynamics and ordinary classical physics is the single assumption of the presence of this all-pervasive, real ZPF, which happens to be an intrinsic part of the universe.” ⁶⁵
Knowledge about zero point energy is needed to comprehend the mass explanation in The Stochastic electrodynamics view.  Thus, I will elaborate more about ZPE in following paragraphs.

Zero Point Energy
As mentioned before, quantum mechanics predicts the existence of Zero Point Energy.  The Casimir effect and Lamb shift phenomena are evidence for ZPE. Additionally, the one- dimensional harmonic oscillator also argues in favor of its presence.
 “The theory of electromagnetic radiation is quantized by treating each mode as an equivalent harmonic oscillator. From this analogy, every mode of the field must have hf/2 as its average minimum energy.” ⁶⁵
The phenomenon has been described in Singularity chapter.
P.S. Wesson from the University of Waterloo among other physicists infers: “Search into zero-point physics is justified and should be supported” ⁶⁶
At least on paper the use of ZPF to extract energy is possible. In fact Haisch and Rueda have presented a paper to NASA conference on space craft propulsion in 1997, suggesting the use of ZPF for future space drives.⁶⁷
The followings are the beliefs of the researchers in California Institute for Physics and Astrophysics about ZPF and stochastic electrodynamics:
“In fact, two distinct views about it exist today.
One justification for making such an assumption is that by adding the ZPF to classical physics many quantum phenomena can be derived without invoking the usual laws or logic of quantum mechanics. It is premature to claim that all quantum phenomena could be explained by stochastic electrodynamics (that is, classical physics plus the ZPF), but that claim may one day turn out to be the case. In that event, one would have to make a choice. One could accept the laws of classical physics as only partly true, with a wholly different set of quantum laws required to complete the laws of physics; that is essentially what is done in physics now. Or one could accept the laws of classical physics as the only necessary laws, provided they are supplemented by the presence of the ZPF” ⁶⁶
According to Equivalence Principle, if the ZPF gives rise to the phenomenon of inertia, it must also generate the effect of gravity in some way.
There are outstanding issues regarding ZPE; for instance, if there is such a field in space-time, the gravitational effect must be enormous. 
If we take ZPE as an internal element to space-time, its gravitational effect would be enormous. Paul Wesson writes:
“It is also claimed that if the ZPF really exists, it would be such an enormous source of gravitational force that the radius of curvature of the universe would be several orders of magnitude smaller than the nucleus of an atom. Of course, such a conclusion directly conflicts with everyday experience. The fallacy in the argument is that in the Sakharov-Puthoff model the ZPF as a whole would not itself gravitate. The gravitational force results from perturbations of the ZPF in the presence of matter. In the Sakharov-Puthoff model, then, the uniform ZPF is not a gravitational source and hence would not contribute to curving the universe.” ⁶⁶
  For more detailed information about ZPF please check http://www.calphysics.org/.
In addition, this field must affect the electromagnetic radiation wavebands.  This effects have not been observed.

Quantum Vacuum Inertia Hypothesis
Quantum Vacuum Inertia Hypothesis mainly developed by California Institute for Physics and Astrophysics (CIPA). CIPA takes (ZPF) as virtual because if real it has to have certain cosmological effect that is not consistent with observations. The hypothesis speculates that the electromagnetic quantum vacuum (ZPF) contributes to the inertial mass of a matter. The nature of this effect is explained under the name Rindler Flux (Please check http://www.calphysics.org/rindler.html). In Rindler frame model the resulting force is proportionate to acceleration.

Rest Mass in Quantum Vacuum Inertia Hypothesis (QVIH)
Since a particle continuously interacts with the ZPE fluctuations, it exhibits Brownian-like motion.  In the CIPA interpretation, this is the origin for quantum foam. A tiny bit of the quantum vacuum energy is diverted into the kinetic energy. This gives the Compton frequency and therefore the rest mass to the particle.  In the CIPA view, “one could think of a particle as a localized concentration of zero-point energy which gravitates and resists acceleration” ⁶⁵

Inertia in QVIH
From Newton’s second law of motion we know that a stationary mass (m) subject to a force (f), will accelerated (a) in the direction of the force. This acceleration is proportional to exerted force. F =ma.
The inertial mass in CIPA model is described as the effect of ZPE on accelerating objects. The accelerating objects interact with electromagnetic random waves of ZPE described above. The movement generates a drag force that is proportionate to acceleration. In CIPA view, this drag force is the origin of inertia and it is called acceleration-dependent drag force.
Therefore, In CIPA model, when force is applied to an object, it prevents it from following its own trajectory. This is called inertia and is the origin of the notion of mass. 

Particle’s Frequency
In (CIPA) model, the particle is actually traveling along the wave that is a geodetic trajectory in space-time. The frequency of particles depends on the energy of wave that carries it. So a force is needed to prevent the object from following its trajectory. 
“The waves are fact ripples in space-time. These waves do carry energy, and each wave has a specific direction, frequency and polarization state. This is called a "propagating mode of the electromagnetic field.” ⁶⁵
In this model the waves are present and a particle by getting involved in any specific wave obtain the specific energy and frequency. The frequency identifies the nature of the particle. This is the way that particle get their identification.  Authors Bernard Haisch, Alfonso Rueda, L. J. Nickisch, Jules Mollere postulate:
“Zero-point fluctuations give rise to space-time micro-curvature effects yielding a complementary perspective on the origin of inertia. Numerical simulations of this effect demonstrate the manner in which a mass-less fundamental particle, e.g. an electron, acquires inertial properties.” ⁷⁰
One may ask why there are just three main stable fermions (up quark, down quark, and electron) and a handful of unstable particles. Why the mass of proton and neutron are not proportionate to their constituents whereas, bigger objects mass is incremental?  CIPA researchers believe,
“The quantum vacuum inertia hypothesis strongly suggests that the interaction between the quantum vacuum and charged fundamental particles (quarks and electrons) takes place at specific frequencies or resonance.” ⁶⁵

Gravity in Quantum Vacuum Inertia Hypothesis (QVIH)
We feel and observe the effect of gravity constantly. However, the nature and dynamics of gravity is not well understood. The mainstream physics classifies gravity as one of the four main forces of nature (along with electromagnetic, strong and weak nuclear forces). Uphill efforts to unify the gravity with three other forces (grand unify theory) has not been fruitful so far.
Dr. H. E. Puthoff one of the researchers of CIPA describes the nature of gravity from the QVIH standpoint:
“Taking a completely different track … the well-known Russian physicist Andrei Sakharov put forward the somewhat radical hypothesis that gravitation might not be a fundamental interaction at all, but rather a secondary or residual effect associated with other (non- gravitational) fields.
Specifically, Sakharov suggested that gravity might be an induced effect brought about by changes in the zero-point energy of the vacuum, due to the presence of matter. If correct, gravity would then be understood as a variation on the Casimir theme, in which background zero-point-energy pressures were again responsible. Although Sakharov did not develop the concept much further, he did outline certain criteria such a theory would have to meet such as predicting the value of the gravitational constant G in terms of zero-point-energy parameters.” ²²
Dr. Puthoff and CIPA researchers followed the above lead and developed it further. Their efforts provided the following positive results.
“The gravitational interaction is shown to begin with the fact that a particle situated in the sea of electromagnetic zero-point fluctuations develops a "jitter" motion, or ZITTERBEWEGUNG as it is called. When there are two or more particles, they are each influenced not only by the fluctuating background field, but also by the fields generated by the other particles, all similarly undergoing ZITTERBEWEGUNG motion, and the inter-particle coupling due to these fields’ results in the attractive gravitational force.
Gravity can thus be understood as a kind of long-range Casimir force. Because of its electromagnetic underpinning, gravitational theory in this form constitutes what is known in the literature as an "already-unified" theory. The major benefit of the new approach is that it provides a basis for understanding various characteristics of the gravitational interaction hitherto unexplained. These include the relative weakness of the gravitational force under ordinary circumstances (shown to be due to the fact that the coupling constant G depends inversely on the large value of the high-frequency cutoff of the zero-point-fluctuation spectrum); the existence of positive but not negative mass (traceable to a positive-only kinetic-energy basis for the mass parameter); and the fact that gravity cannot be shielded (a consequence of the fact that quantum zero-point-fluctuation "noise" in general cannot be shielded, a factor which in other contexts sets a lower limit on the detectability of electromagnetic signals).” ²²
The CIPA conjecture for the nature of gravity force between two objects is:
“The secondary electromagnetic fields turn out to have a remarkable property. Between any two particles they give rise to an attractive force. The force is much weaker than the ordinary attractive or repulsive forces between two stationary electric charges, and it is always attractive, whether the charges are positive or negative. The result is that the secondary fields give rise to an attractive force we propose may be identified with gravity.” ⁶⁵
The CIPA researchers believe that inertial and gravitational mass are the identical thing. Inertia is felt as an object accelerates through the electromagnetic quantum vacuum. The gravitation is actually acceleration of the electromagnetic quantum vacuum past a fixed object.
“The latter case occurs when an object is held fixed in a gravitational field and the quantum vacuum radiation associated with the freely-falling frame instantaneously co-moving with the object follows curved geodesics as prescribed by general relativity.” ⁷⁰
For detailed and updated description of Quantum Vacuum Inertia Hypothesis Please check reference # 65.

ZPE in our Model

There are similarities between what I am going to present here and the CIPA model, because in both models ZPE is the origin for mass and gravity. In our model though, the origin of the ZPE is esoteric (external) but the resulting fields are intrinsic of the universe. So there will be some fundamental differences.
If we take ZPE as being out of space time and accept it as a property of proposed singularity. Then it can provide answers to questions like why the it does not affect the wave bands such as isotropy of microwave back ground, infra-red, optical and ultraviolet rays.
The particles carry a minute portion of the external ZPE inside the space-time.

Rest Mass in this Model
Einstein’s Special Relativity implies that a particle’s mass in motion increases proportionate to its speed. Lorentz equation for transforming mass in motion is:

m = m₀/ √ (1-v² /c ²)

Where m is mass in motion, m₀ is the rest mass. V is the speed of object and c is the speed of light. Because the speed is the main variable here, is it fair to conclude that the nature of mass has something to do with kinetic energy of the object?
Underneath I quote from Professor Wesson of university of Waterloo and take the lead from following statement:
“Haisch and Rueda (1999a) returned to the issue of non-linearities, arguing that the observed masses of particles (e.g., the electron mass at 512 keV) are due to resonances in the electromagnetic ZPF. They also suggested that the scattering of the ZPF by a charged particle takes place at the Compton wavelength … and that this leads to the de Broglie relation characterizing the wave description of the particle in terms of ¸deB = h=p (where p is the momentum and h is Planck constant.). This extension of their previous work is interesting; but in terms of making contact with the testable aspects of wave-mechanics, needs to be extended to a full discussion of the wave”66
In 1920, De Broglie proposed that every object has a wave like motion. In accordance with De Broglie’s postulate, larger objects follow shorter wavelength and have higher frequencies. Quantum mechanics on the other hand tells us that the smaller the scale the more turbulence is observed in fabric of space.
In previous chapters, we postulated that in sine wave motion a real  particle actually moves along a wave. In this scenario, if we take the speed along the x-axis, fixed at all times the actual velocity of the particle increases with the raise of the tangent of the angle a.

V = Vx tang. a

Thus as particle gets close to x-axis, somewhere along the line, it reaches the light speed (c = 300.000 km/s) and has to disappear from space-time (because according to Einstein’s postulate, universe cannot accommodate speeds more that c).  We have speculated that the particle has to exit space-time and enter singularity. In addition, somewhere below x-axis the particle will reappear because its speed decreases to c again and then reduces further to its ordinary propagation speed.
A plane wave equation can be written as:

Ψ(x_a)=e^-ipa^xa/h

Where p is momentum. Adding 2pħ to the p_ax^a will not change its quantity. The equation has a time-like period of 2pħ /p₀ and a space-like period of 2pħ /p1.
So we may conclude that at each period there are times that momentum is zero.
On the other hand p = mv. So, at zero momentum moments either m or v has to be zero.
2pħ /p1 tells us that along x direction, momentum is also periodic. This means momentum appears and disappears during each period as well.
In addition, wave function is a complex function and has an imaginary (out of space-time component in it). In the same chapter, we also have speculated that the mechanics of particles in this movement mimics a bouncing ball.

The two forces, which are acting on a bouncing ball, are attractive force of gravity and repulsive force of electromagnetic from molecules (electrons) at the surface of the earth. If the wave particle movement mimics the bouncing ball, in our model singularity has to have a repulsive force, which ejects the particles, and throw it to space-time. This gives the maximum kinetic energy at the time of entrance to space-time. For bouncing ball model to operate an opposite force is also needed. One can speculate that in wave particle scenario, the elasticity of displaced fabric of space provides the opposite force.

 

When the particle immerges into the space-time, it pushes the fabric of space and creates a bulge. As the energy of particle is used up, its speed decreases and particle reaches the peak of the wave. At this point, the elasticity of space-time pushes the particle down and back to singularity again.

Frequency in this Model
Please note that the frequency of each wave is proportionate to its magnitude square:

f ~A²  

Where f is frequency and A is magnitude. This only sounds right. The more energy a particle has the higher it can jump and the bigger would be the distortion of space-time. In this scenario we do not have to assume pre-existing wave in fabric of space, rather we may hypothesize that if the amount of energy is harmonic with oscillation of space-time it creates the waves observed in micro scale. Any other energy level which is not harmonious with fabric of space either can not create wave or it will create short-life waves which belongs to unstable particles of standard model.
Therefore, unlike CIPA model, I am suggesting that energy belongs to object. The magnitude of object emergence inside space-time dictates its Compton Frequency (f ~A²) and therefore its identification.
Traveling back to singularity replenishes the energy of the particle and another cycle will start.  This scenario is similar to water waves. Suppose a stone is thrown into a pond. The impact energy obtained by water molecules raises the wave but at the peak the gravity drags the molecules down back to the pond. There are no preexisting waves before the stone is dropped into the pond.
There are similarities between Sakharov-Puthoff model and the above scenario. In Sakharov-Puthoff model, the perturbation of particles in ZPE presence creates the mass and curvature of space. In the model in hand, the presence of matter (and its travel to singularity) is needed for transferring ZP energy to space-time.
In CIPA model, because the numbers of wave modes are enormous, and increases as the square of the frequency. The sum of tiny energy per mode times the huge spatial density of modes yields a very high energy density, which is not experienced. In our model, we confine the ZPE delivery just to individual particle-waves and not plane (waves that carry particles) and not all possible waves in microcosm. Therefore, this problem does not arise. This can only happen if ZPE exists outside and its energy being carried by particles into the space-time.

Preexisting Waves
Alternatively, we may postulate that plane waves introduced in Higg’s Mechanism and QVIH may actually exist. The attractive and deflective force of zero point fluctuation may create randomly phased plane waves (shapes) in space-time.
Roger Penrose indicates that Einstein field equations:
“Predict a spectrum of quantum fluctuations in space-time. It also has a precise Planck-scale description, which makes use of very elegant mathematics connected to the invariants of graphs and knots.” ⁵
We may further assume that a particle according to its energy level gets involved with a harmonic wave-like curvature of space and continues its journey just like a planet or any other object traveling in a gravitational field or just like a car following the path of a curved road.

 Bodies and Waves
The fundamental particles (fermions) have longer wavelengths. Therefore, in this scenario the waves in bigger scales belong to fundamental particles. Since the known particles are numbered and have specific frequencies, the micro–curvature of space cannot be completely random phased, rather the space waves created by ZPE at least in bigger wavelengths have to be numbered with specific frequencies. In addition, Pauli’s Exclusion principle indicates that just a handful of useable waves in larger scales are formed.  According to Pauli’s principle particles occupy their territory exclusively. They do not share their trajectory with any other similar particles.
As we get to smaller wavelengths, we gradually get closer to the territory of hadrons and atoms and molecules and then larger objects. Bigger objects oscillate in smaller wavelengths. If you had a bowling ball with a mass, of say one kilogram, moving at one meter per second, its wavelength would be about a septillionth of a nanometer. This is so ridiculously small compared to the size of the bowling ball itself. That is why we never notice any wavelike motion while looking at a bigger object.
Here we can get philosophical and postulate that each one of us just like any other object have a wave like motion and enter and exit singularity in each period of our wave motion. Then this can explain some of the strange findings in transpersonal psychology experiments.

Mass and Wave Function
In the previous chapter, we presented the detailed format for particle-wave function in this model. Above, I also explained my conjecture about the nature of the rest mass of particles.

In following paragraphs, I apply the above format to actual particles to see if the above model is in line with observations and experiments.

Fundamental Constants 
Previously, I have mentioned that this chapter is the center- piece of this model. Here I offer explanations for the nature of Planck Constant, hierarchy problem and masses of fundamental particles as we go along.
First, let us discuss the fundamental constants. There are some numbers which frequently being encountered in mathematical calculations related to different astrophysical and quantum mechanical experiments in laboratories. We do not know where they come from. It seems that they are natural and originated from fundamentals that created our universe. That is why they are called Fundamental constants.
The most famous one is the light speed denoted by (c). Nobody knows why light constantly travels at approximately 300.000 km/s. Another major one is Planck constant (denoted as h) with the value of 

6.626 0693 x 10^-34 J s.

There are also others, like Gravitational constant, Boltzmann constant, Dirac’s constant (h/2p) and the Columb Force constant. Masses of fundamental particles are also considered constant because apparently we do not know where their value comes from.
Unlike CIPA model, in this model energy does not belong to waves in the field. If it did, such energetic waves had to interfere with propagation of testable rays in space and would show their signatures in experiments. Such an effect has not been observed.
I believe energy accompanies the particles, which are traveling along the wave. I will take the lead from CIPA researchers postulate that,
“The energy of the ZPF continues to rise sharply with the frequency of the radiation quantitatively, the energy density is proportional to the cube of the frequency; double the frequency, and the energy increases by a factor of eight. At what frequency the ZPF spectrum finally cuts off or loses its ability to interact with matter are important and still unresolved issues?” ⁶⁵
What if particles scoop up energy from singularity twice during each period of their wavelength? Can this be the reason for energy to be proportionate to frequency of objects? Let’s review it.
For the wavelength of a particle, we may write:

λX = h / m_X C

Where λ is the wavelength of the object, h is Planck constant, C is the speed of light, and m is the mass of the particle.  Because,
λ_X  = C/f_X, we may write:⁴⁰
 
C/f_x = h / m_X C
f_x = m_X  C²/ h

So, we conclude that the frequency of any object is proportionately related to its mass. Having the above scenario in mind, how do we explain the relationship?
Here we may postulate that, the mass is the kinetic energy obtained from singularity and delivered by an object each time it appears in space-time. Because in above model particle hits singularity twice in each wavelength, so the energy delivered is twice its frequency (f).

E_k = E_s 2f   (1)

Where E_k is the total  kinetic energy of the particle, E_s is the unit of kinetic energy delivered in each trespassing. So objects with higher frequency deliver more kinetic energy and thus they are more massive.
To calculate E_s of different particles we used the Einstein equation,  E_k = m₀c2 . Where m₀ is the rest mass of the particle and c is the light speed. Then we write the total energy as product of Compton frequency of the particle and E_s;

E_e = E_s *f com

Thus the energy derived from singularity is calculated as:

E_s = *f com /E_e

Below, we calculated the E_s for electron and muon as examples. Please note that values for Compton frequency and mass of the particles are obtained by experiments in Fermi lab and elsewhere.

E_e = m₀ c² = 9.109826 *10^-31*9*1016=81.988434*10^-15
E_e = E_s *f com
f com=c/l com=3* 10⁸/2.426310215 *10^-12=1.236445357*10 ²⁰

The Thing
It seems that the particles are essentially made of one entity (a thing).  The energy and therefore the path chosen by that thing (wavelengths) specify the identity of it and this is how we differentiate and name it as different fundamental particle. In beta decay (transformation of neutron to proton) a d quark changes to a u quark and releases a W boson which means releasing energy.
In the above model, we may postulate that in beta decay, a d quark with higher frequency looses some of it kinetic energy and therefore moves to another path with longer wavelength. This is when we call it u quark.
This can be an explanation for particles changing to each other. This is observed in accelerators everyday. Therefore we may speculate that different particles are actually the same thing.  We distinguish and differentiate the thing by measuring the amount of kinetic energy and the path it follows (Compton wavelength).
Assumption MG #3; Fundamental particles are essentially the same entity except that their kinetic energy and therefore the wavelength adopted will differentiate them from each other.
 Compton Wavelength
How would a particle choose which wave to follow? De Broglie introduced the Compton frequency as an intrinsic character of each particle or mass.
The Compton wavelength of a particle x is obtained by 
λX = h / mXC and Compton frequency by  fX= mXC/h where mXis the mass of particle and h is the Planck constant. 
Everything else being constant, mass is directly proportionate to frequency.
Previously, I have assumed that particles in their wave like motion enter and exit singularity relative to their frequency. We may assume that from here kinetic and potential energy will cause the wave motion to continue as long as they are not disturbed.  Obviously as long as Compton wavelength of a particle does not change its character stays the same, But if Compton wavelength changes we are dealing with a new particle. Changing the Compton frequency is possible in high energy accelerators.

High Energy Accelerators

In accelerators the new particles are constantly formed and interchange to each other.
Inversely, we can postulate that the wave chosen depends on the amount of energy (kinetic energy) which is delivered in by a specific particle. Combining it with the assumption of preexisting plane waves we may conclude:
Assumption MG #4 Fundamental particles only associate with the waves which are harmonic to their Compton frequency.
Relativistic Mass 
So far, we have been dealing with the mass of a particle at rest. Relativistic mass (the mass of an object that is traveling with high velocity in relation to an observer) is a different issue altogether.
When an observer is measuring a rest mass in his lab, since both observer and the mass are almost stationary to each other in the same frame of reference, the measured mass is rest mass (m0). We may call the lab frame of reference A. But if the mass starts to move with velocity v, it is residing in a new frame of reference, we may call it frame of reference B. The two frames have a velocity relative to each other which is due to kinetic energy of frames of references. The Lorentz transformation equation for relativistic mass is as follows: m = m0/ √ 1-v2/c2
The equation suggests that as speed increases the mass increase as well.
How are we going to explain this difference in mass measurement?

Previously we have assumed that the nature of mass is kinetic energy. When the observer in frame A (a scientist in Kennedy Space Station) is going to measure the mass of an object which is moving in frame B (the flying shuttle), he has to take the extra kinetic energy of moving shuttle into his account. While moving, the inertia (the force needed to move the said object) has changed proportionate to the velocity (extra kinetic energy) of the shuttle.
If an astronaut inside the shuttle measures the same object, he will get the rest mass that is less than the mass that scientists on earth will record. The extra kinetic energy cannot be measured inside the shuttle, because the astronaut and the object are stationary relative to each other.
Dirac's Electron and this Model
In our interpretation mass is defined by kinetic energy. This kinetic energy is obtained from singularity. Clearly, there are some similarities between this model and Dirac’s electron in Higgs mechanism although they are fundamentally different.

Roger Penrose, Road to Reality⁵⁶

The birth and rebirth of electron is in line with our model. Also for a charged particle, the second portion of the phase (below x-axis) has the opposite charge that acts as anti-particle.
On the other hand, the instantaneous speed of Dirac particles is always constant and equal to speed of light. The variation in propagation speed comes from zigzag motion of two components as they average out. In our model, the speed along the propagation line is constant but instantaneous speed of the particle changes between propagation speed and speed of light in 2-dimension wave plane. Vanishing and rebirth comes by entering and rising from singularity.

Gravity in this Model

 

 

 

 

 

 

 

 

I undertake Sakharov-Puthoff model claims that the particle interaction with ZPE and perturbation of it is the origin of gravity and curving the space-time, as a lead to present an alternative model for gravity.
The Newton’s law of universal gravitation conveys that massive objects attract each other. Newton’s gravitational force is governed by the following equation:
F = G m1m2/r²

Where F is the attractive force between two masses, m1 and m2.   The distance between them is shown by r.
In contrast, Einstein’s General Relativity denotes that a massive object curves the space-time and the free falling objects follow the curved space-time.
Mark McCutcheon, in his book The Final Theory, raised a very valid question. The gravitational force is constantly at work. As such, its energy is being constantly consumed. Therefore, one will expect that the force diminishes and disappear by the passage of time. This is against observations. Small energy loss through gravitational waves does not reflect the tremendous energy needed to constantly curve the space along the path of heavenly bodies.   The earth‘s gravitational pull continuously curves a new portion of space as it moves along its orbit around the sun. The curved space has kept the moon in an orbit around the earth for more than four billion years with no major change. For the gravitational pull to stay unchanged, the force has to replenish constantly. We need an unending source of energy to provide the gravity that exists throughout the universe.
The true nature of gravity is not yet understood but we have the Principle of Equivalence that tells us that the gravitational force corresponds to masses involved. 
The Einstein field equations imply that any accelerated mass radiates energy. Similarly, the Maxwell equations indicate that any accelerated charge radiates electromagnetic energy.

Previously, I have used a bouncing ball analogy for the particle-wave function. Please note that the velocity of a bouncing ball is always changing. In our model, particles are constantly accelerating or decelerating while following the path of their wavelength. Therefore, we can assume that the radiated energy exert the attractive force. We call this attractive force, gravity.
This force is also proportionate to particles frequency and thus it’s mass. This will satisfy the gravitational/mass equivalence principle.
In another scenario, if a particle strikes into space-time network, the network bulges in and its lines concave. The created dent depends on the elasticity of the network proper and the force applied. We can look at the sewing machine operation as an analogy. Frequent penetration of the needle of sewing machine creates a depression or dent in the fabric being stitched. If the frequency is high enough the concavity remains steady. This is an analogy for how a colliding particle can create curves similar to gravitational fields in space-time.
Please refer to the Wave-Particle Function chapter to see how, in this model, a particle is assumed to smack into thespace-time network and create gravitational fields during its wave function.

 

 

 

 

 

 

 

 

 

 

In this model, the long sought after and never found graviton is not needed to create the gravitational curvature of space. Graviton is the assumed particle responsible for the gravity field in quantum mechanics. Conversely, the General Relativity theory asserts that any object in the gravitational field follows a straight-line trajectory in space. According to it, gravitation happens because the mass curves the space-time itself and objects follow this curve.  
Therefore, graviton is not necessary to create the gravitational field in general relativity. In my conjecture the wave function of a massive object (by either radiating energy or mechanically striking the fabric of space-time) creates the curvature needed for the gravity effect in Einstein’s theory of General Relativity. The frequent penetration of space-time by a massive object also creates the gravitational wave, which spreads throughout the universe.
Equivalence Principle
Looking at presented model for wave-particle, we find a good explanation for the equivalence of gravitational and inertial mass.
The Compton frequency is proportionate to the mass of the object. The energy of the object is also directly related to its frequency and the total mass that it caries. A wave function as described above would deliver a force to the fabric of space-time that is proportional to its mass and energy.
In the sewing machine analogy, the force on the needle creates the concavity and frequency of penetration if high enough can hold the concavity in place. We will have a steady depression if frequency 0vercomes the elasticity of the fabric. 
Therefore, the mass of an object is directly related to the curvature produced in the space-time and as a result to the gravitational field.
In reality, the gravity is not only related to the mass of an object. More precisely, the gravity is related to the mass and the energy carried by it. For example, a compressed spring has more energy and therefore, creates more gravity. 
The model presented above explains the above phenomenon. In our model, the curvature created is related to the total force inserted at the time of smashing into the fabric not just to the mass of the object. 
The arguments presented are open for debate. The reader is encouraged to email his/her inputs to correct, modify or develop the contents. Please send your emails to; zpfields@yahoo.ca

The arguments presented are open for debate. The reader is encouraged to email his/her inputs to correct, modify or develop the contents. Please send your emails to; zpfields@yahoo.ca