The inter-relation between consciousness and physical world is a great mystery. We know from quantum mechanics and special relativity that observer and consciousness play active roles in forming the reality as we know it. However, the mechanism of this role is the core question.
Evan Harris Walker ⁷³ postulates that,
“Physical reality is connected to consciousness by means of a single physically fundamental quantity.”
Underneath, I am suggesting a fundamental mechanism for this mysterious effect.

Electron in Relativistic quantum electrodynamics

Electron by definition is point like(has no volume). In classical physics definition, the energy associate with its electrostatic field increases as we get closer to it and the energy turn to infinity when the distance vanishes. But this is grossly against observations. Another flaw in classical physics. Here, Mass/energy equivalence ( E = mc² ) comes to rescue. Special Relativity suggests that as distance decreases and energy gets equal to 2mc² of mass of electron, a pair of electron/positron is formed that consumes the extra energy. Of course In closer distances energy is much more. But not to worry, infinite number of electron/positron is being formed, so that we end up with energy of just one electron. The conclusion, electron is made of a seed with heavy blanket of infinite positrons and another heavy dressing of infinite electrons on top. Infinite electrons and positrons need infinite space. What are we going to do now? Here again re normalization comes to rescue. The gigantic electron is not observed, then we close our eyes and renormalize the results.

Is it not easier to accept the exposure to an entity with infinite energy in smaller distances? Is it not easier to attribute the huge energy of electron field to this entity. Here is a model to introduce this entity to the equation?

Revisiting Wave/Particle duality
Wave function of particles was introduced as a model to describe the puzzle of The Heisenberg Uncertainty Principle. The Uncertainty Principal claims that we cannot be certain about the location and momentum of a particle simultaneously.
In this chapter we take wave function as a real motion of a particle along its wavelength in space. This model is in line with David Bohm’s model where particles have well defined positions and trajectories at every instant of time along their wavelength. However, here the trajectory in space-time is interrupted and periodically hits the non-local singularity along its each wavelength.
Polarization
According to Luis de Broglie every particle has an accompanying wave. For example a photon has an associated wave. Photon oscillates as it travels through space. The wave frequency of a photon differentiates various rays from each other. Photon wave frequency is dissimilar for different colors in optical band or other electromagnetic waves. Essentially photons can oscillate in any direction.  The orientation of oscillation is called polarization. Theoretically, particles can have polarization in all possible directions.
Transverse polarization
There are radial polarizations that stay inside an envelope of a circle perpendicular to the line of motion. These can always be specified by a particular pair of x , y and z values in a three coordinate system.

 

The above diagram shows a vertical and a horizontal polarization

This is the kind of particle polarization which is recognized and called physical.

Longitudinal polarization
In principle, there is a third polarization direction as well. It is the one that oscillates along the direction of motion.  Sound waves Oscillate in this direction.

But such oscillations are not recognized for particles. Longitudinal waves are labeled spurious (bogus) and non-physical. Although the theories of forces swing around this so called false polarization direction, current understanding of our physical world tells us that such non-perpendicular polarization should not exist. Therefore, currently the third direction is subject to filtering out and renormalization. However, to explain the symmetries in Einstein’s Special Relativity all oscillations have to be considered.
It is worth it to dwell on this third kind of polarization to see if it can help to resolve some of the existing paradoxes.

Complex Numbers
While looking at the quantum wave function from a mathematical point of view, Professor Roger Penrose indicates:
 “You cannot explain the wave like nature of quantum particles in term of probability waves of alternatives. They are complex waves of alternatives!” ⁵
In order to describe the wave particle function in this view, some knowledge about complex numbers is needed. Alternatively, just reviewing the assertions made in the complex number chapter should suffice to comprehend and follow topics that will be discussed.
As it was mentioned before, Complex Numbers are a combination of purely real and purely imaginary numbers.

Complex number = (x + iy)

Normally, we measure the elements of space-time by real numbers. The concept of the complex number implies that any of these elements should have an imaginary dimension in their nature.
Considering the notion of complex numbers, I have concluded that, the real axis value of elements in space-time periodically changes, disappears, and reappears. For example, if the real value in the X- axis denotes the mass of a particle, the mass has to appear and disappear in each period. This is what we see in the electrons around the nucleolus of each atom. The electron appears and disappears in a band like zone around the nucleolus. Erroneously, we call this zone orbit.

In this model, we take the imaginary number (i) as a factor which represents the singularity effect on different phenomenon. So any mass as it intermingles (multiplies) with singularity alternates and shifts in between its real value and imaginary value. In other words, the particle intermittently disappears from space and reappears along its wave path. We can generalize this concept and conclude,
Assertion WP #1; while traveling through the fabric of space, objects take a journey and alternate between singularity and space-time.

In a complex number diagram, as the Z passes the first quadrant, it enters a new arena where the real value is negative (second quadrant). So, it does not completely disappear but it enters into another domain. How are we going to interpret this negative value?

Modified Complex Plane

 

In the modified complex plane shown above, the real value reappears as the complex number rotates one 3/2p  and enters the fourth quadrant again. If x denotes the mass of a particle, we may interpret the negative domain in the complex number diagram where the particle loses its mass.

Compton Wavelength
Webster's dictionary provides conventional definition for wave as “A disturbance or variation that transfers energy progressively from point to point in a medium.”
In 1924, Louis-Victor de Broglie postulated that all material objects have a wave-like motion. He postulated that any particle has an accompanying wave function. He also introduced Compton frequency, which is a kind of oscillation and circulation of the charge around a charged particle. Each object has its specific Compton Frequency.
He suggested the equation below to govern the relation between wavelength of a mass and its momentum p:
l = h/p, where h is the Planck constant.
Previously, we speculated that the key to understand quantum mechanics is hidden somewhere in Campton wavelength of particles. Wikipedia describes the Compton wavelength as:
“The Compton wavelength λ of a particle X is given by λX = h / m_Xc, where h is the Planck constant, m_X is the particle's mass and c is the speed of light. A particle generally behaves quantum mechanically when observed at distances shorter than its Compton wavelength.”
Every object has its own Compton wavelength. Only Compton wavelengths of small objects such as atoms are detectable. The wavelengths of larger objects are so small that cannot be detected. Underneath we are going to analyze the particle’s movement during its Compton wavelength. It furthers:
 “In particular, in the uncertainty relation for position and momentum,Δx Δp ≥ h. When the position uncertainty Δx is less than the Compton wavelength, the momentum uncertainty Δp is equal or greater than m_Xc. Since momentum carries energy, the uncertainty in energy is equal or greater than m_Xc², which is enough energy to create another particle of type X.”
Therefore, the article predicts particle creation along the wavelength. This is in line with the scenario that we will be discussing in this chapter. The article further continues;
“The Compton wavelength is therefore generally viewed as the cutoff below which quantum field theory, which can describe particle creation and annihilation, becomes important.”
In this model I will suggest creation and annihilation of particles along their Compton wavelength as well.
The Schrödinger equation for motion of particles (traveling wave) along x-axis at the time of t can be written as:

y (x,t) = A exp^{[ i ( kx-wt )]}   

Where A is amplitude of the wave, k is wave number and w  is angular velocity. We may expand the above equation as:

y (x,t) = A exp^{[ i ( kx-wt )]} = A cos  ^{( kx-wt )} +i Asin^{( kx-wt )} .

This function is a complex number with i Asin^{( kx-wt )} as its  imaginary part.
As we can see, on particle-wave function dimensions x and t are complexified (demonstrated in complex number version) by the imaginary number i. In order to describe the particle-wave function, physicists are not using the kaluza-klein dimension, or any of the extra dimensions in the string theory, instead they have to choose a virtual dimension out of our space-time to be able to explain the quantum wave function, an imaginary dimension. Yes, we can imagine the complex numbers in our mind. But wave function is happening all over the world in every moment, even if, our mind is not with it. Therefore, there should be another being out there to accept the image, to be able to accommodate the imaginary part of the complex numbers.

Wave Function in this Model
Mass, Energy-Information Phase Transition 
Although wave function was introduced as a model to represent the Heisenberg Uncertainty Principle, we can make the following argument for a β ray (composed of electron particles). Einstein’s Special Theory of Relativity says that nothing can travel at or above the speed of light in our space-time universe. The reason behind this is that in The Special Theory of Relativity, the relation between mass and its speed can be obtained from:

m = m₀/√ (1-v²/c²)

Acceleration boost augments the particle’s mass. At speed of light v²/c² becomes 1. In this case 0 will divide m⁰. So mass will increase to infinity.
 
m = m₀/ √ (1-v²/c²)
m = m₀/ √ (1- 1)
m = m₀/ 0 = ∞
Here, we face the infinity, the notion that most physicists detest. This is another road sign indicating that we need to strive for a deeper understanding of reality. We must not ignore these signs that have been avoided for fear of the unknown). Since infinity does not exist in space-time universe, besides we need an infinite amount of energy to move this infinite mass, this goes beyond explained physics. Known physics does not have any explanation for it.  John Earman writes:
“In 1960 Einstein found that, in a condition of static equilibrium, as the radius of the cluster approaches Shwarzchild radius. The particle would eventually have to move faster than light.”⁴
By definition, there is no (mass-like) medium in space-time. The notion of “Ether” has been rejected at the beginning of the twentieth century. The mystery of fields (electromagnetic fields, Gravitational fields, etc.) has yet to be explained.
Let us suppose that during the course of its wavelength the particle oscillates in third direction (z direction) while traveling along a spatial dimension (x-axis) with linear speed v. Please note that while oscillating the particle is traveling in another direction as well (along z-axis).

Diagram #1

The above diagram shows a polarized wave particle, which possesses mass and propagates along X-axis.
We take the propagation speed down the X-axis constant all along its wavelength. With this assumption, particle accelerates in its wave like motion along x-axis and its actual velocity increases according to the position of the particle along the curve. In other words, the actual speed will exceed the propagation speed as the particle leaves the peak and travels down the slope. The equations can be written as:
 
Dz/ Dx = tang. a
Dz= Dx tang. a
Dz/ Dt = tang. a Dx/ Dt
If
lim Dt®0 Dt Dz/ Dt = lim Dt®0  tang. a Dx/ Dt
in this situation we may write  Dt gets near 0, therefore
Vz = tang. a Vx

Please note that in the above diagram, the angles a and a' are equal because their sides are perpendicular to each other.
For the speed of particle in any point we can write:

V² = Vz² + Vx² = Vx²+ Vx² tang.² a = Vx² (1+tang.² a),

Therefore;
V = Vx √ (1+tang.²a) … (1)⁴⁰

Regardless of the propagation speed, as the particle approaches the x-axis there is a moment when its speed equals and exceeds the speed of light. For example at 89o angle the tangent value is 57.2900 and its value for 90^o is infinity. So there will be a time for any particle to reach the light speed as it travels towards the X-axis along its wavelength.At a =90^o particle speed is supposed to reach to infinity.

V = Vx √ (1+tang.²a)
V = Vx √ (1+ ∞)
V = ∞

Since infinity is not defined in space-time physics, we normally would say the speed equals maximum. But because this model contains the singularity in which infinite energy is allowed I choose to leave infinity in place.

Infinite Speed and Non-Local Zone
At the time when a = 90^o, Vx cannot have any amount other than zero in space-time.  So for our original assumption to hold (Vx to remain fixed all along the wavelength) we have to assume that the wave particle leaves the space and enters a zone with no dimension. With infinite speed (the assumed actual speed), the wave particle cannot remain in space-time. It has to leave and enter a non-local entity. We are led to this conclusion by the fact that the only place that an object can have infinite speed is a non-local zone.

 

 

How are we going to describe this format of wavelength? Where do we find a non-local zone for the particle to enter?
Mind you that the space-time in this model is discrete, and therefore the singularity is in the neighborhood and readily available to deportees of space-time. By our previous assumption singularity is non-local.
 We have also previously supposed that singularity cannot contain mass. Having the conservation of mass and energy law in mind, we can deduce that mass has been converted into energy while joining the singularity.
According to the Standard Model of particles, subatomic particles are zero-size and mass-less. Higg’s boson adds the property of mass to them while they are traveling in space-time (see Mass & Gravity chapter). Therefore, we may assume that the particles lose their mass while leaving the space-time.
To build a more objective argument let us study particles with a propagation speed of 1/20c.  If you are not up for the mathematics, you may rather skip this portion.
In equation #1, V = V x √ (1+tang ² a). For the particle to reach to speed of light, the magnitude of a, can be calculated as:
 
C = 1/20 c √ (1+ tang ² a),  and,
√ (1+ tang. ² a) = c / c/20,  therefore,
20 = √ (1+ tang. ² a)  then 400 = (1 + tang ² a)

Thus tang.²a = 399 Hence tang. a = 19.98, which approximately corresponds to tangent of 87^o.

Invariance around X-Axis
We redraw diagram #1 for this speed as:

Diagram # 2

 

Formula V = V x √ (1+tang² a) requires that as the a increases beyond 87^o the speed also increases. At a = 90^o the speed of the particle-wave reaches to infinity. The calculations below show that beyond c speed, the elements under examination do not change.
We formerly assumed that at speed of light mass has to convert to energy. The amount of mass itself calculated from
m = c²/E.  In addition, the momentum (p) of the wave-particle at this point is obtained from:

P = (E/c²)*V
 
As the wave-particle departs from 87^o and gets to 90^o (hits x-axis), tang.a will be infinity so speed will amount to infinity. If V= infinity, then:
 
P= (E/c²)*V= (E/c²)*V = (E/c²)* infinity = infinity

The momentum equals infinity and:

E total = √ (p ² c ² +m₀ ² c⁴) = infinity

It is apparent then that in our example from the 87^o to the 90^o zone the amount of energy remains infinite.

Mass at 90 ⁰
Let us look at mass at 90^o. For mass at 90^o angle, we may write,
m = m _o / √ (1-v² /c²) = m _o / √ (-1 (v² /c² -1)) = m _o /i²(v² /c² -1) = m _o /i² (infinity² /c² -1) = 0.

This denies the presence of mass in the 90^ozone.

Space around X-Axis
If momentum is infinite in 90^o, then space looses its meaning around the X-axis:

l =h / p = h / infinity = 0

And the wave number k turns to k=2 p/l= 2 p/0= infinity.
Dk = k- k_o,   Dk = ∞- k_o,   Dk = ∞
In addition, we can write the Heisenberg uncertainty formula as:
 
Dk *D x ≥ h/2p

Therefore Dk has an inverse relation with D x
Dx ≥ 1 /Dk
If Dk equals infinity, then Dx can shrink to zero, which means, there is no movement in space. We can interpret and speculate that wave-particle does not encounter space at a = 87^oto 90^o.
As an alternate approach, at the infinite energy point we might express the following:

y (E) = (E max) e^{i (kr^n - w t)} = (E max) e^{i (kr^n - w t)}
E = infinity = (E max), then, e^{i (kr^n - w t)} =1 Therefore i (kr^n - w t) = 0

Or, k r^n =wt, And since 2 p/l* r^n = 2 p/ T*t, Hence, r^n = t* l/T = 0. We conclude that there is no space in 90^o point. Then we can conclude that,

Assertion WP #2: space disappears intermittently during the course of the particle’s journey along its wavelength.

Time around X-axis
We can also write the Heisenberg Uncertainty Principle as:
 
Dt * DE ≥ h/2p
If D E = infinity then, D t = 0

Again, it shows that time remains put for wave-particle at a=87^oor 90^o. ⁴⁰

Assertion WP#3: Time stops intermittently for the objects during the course of their wave motion.

Tunneling along the wavelength
Quantum tunneling is well established and described. Cassimir effect and the Lamb shift are the manifestations of quantum tunneling (see quantum tunneling in quantum mechanics section). The above description for the wavelength suggests tunneling of the particle while travelling along its wavelength.

Second Half of the Wavelength
Then, the particle leaves the x-axis and moves towards the trough. Here, the changes in the z-component of the movement decelerates as does the linear speed until the particle surpasses 87^oagain and reaches a speed that it can have in space-time (less than c). This is the time for the particle to acquire mass again. The particle reappears when the wave reaches the possible speed in space-time. This can be an explanation for the experiments which show electron jumping in and out of the existence in our universe.

Bouncing Ball
The assumed function mimics the movement of a bouncing ball in a frictionless gravitational field. Let's look at bouncing ball scenario.
Gravitational force pulls the ball to the ground. When the ball hits the ground, the electromagnetic force of the atoms in the outer layer deflects the ball. As a result the ball bounces back.

In this model, for an object to have a wave like motion, the interface between proposed singularity and space-time must possess an attractive and deflecting force. The uncertainty principle predicts that in small scales the gravitational fields rise and fall. Mind you that, according to the General Relativity, the shape of space follows the changes in the gravity. If the space in ultra short scale is curved the object will follow the curved space in a wave like motion. 
On the other hand, the energy in singularity has to be unified and invariant. Note1

Special Theory of Relativity

 

 

 

 

 

 

 

 

 

According to the Special Relativity, objects move in a 4-dimensional space-time. A stationary person just moves through time dimension. Thus gets older fast. A person moving with speed of light only travels in space dimension. Therefore stays young forever. There is no passage of time for such a person. Other movers move within a combination of space and time according to their speed.
In addition, the combined speed of an object through space and its motion through time is precisely equal to the speed of light.
Going back to particle’s wave function in this model, we can sketch the diagram below to illustrate particle’s motion through the space and time.

 

Closer to the X-axis, the particle’s speed equals light speed. Therefore, its movement through time dimension is ceased.

Zero Point Energy
From here the stochastic electrodynamics will continues to explain the scenario. The theory is based on assuming that zero point energy (ZPE) is pervasive throughout the space. This energy is supposedly an integral part of the universe. The theory can explain many physical paradoxes just by adding the concept of ZPE to the ordinary classical physics. For example, it can explain numerous phenomena including inertia, gravity and the radiation paradox of the Bohr‘s atom based on fluctuating electromagnetic field associated with zero-point energy. According to stochastic Electrodynamics, the ZPE field creates a range of superimposed random waves of all frequencies and phases in all directions, with a power spectrum proportional to the cube of frequency.
Haisch, Rueda and Puthoff (HRP, 1994) in the paper “Inertia as a zero-point field Lorentz force” showed how inertia (the force needed to alter an objects movement) can be explained by interaction of particle with zero point fields. They assumed that:
“A fundamental particle (such as an electron) could be treated as a two-dimensional Planck oscillator driven by electric components (Ezp) of the ZPF to oscillate in the xy-plane. They then examined the effects of the magnetic components (Bzp) of the ZPF on the Planck oscillator under the condition of constant acceleration in the z-direction. The result was that the Lorentz force due to Bzp fluctuations proved to be proportional to the acceleration of the Planck oscillator, thus suggesting its interpretation as the reaction force due to inertia.”⁵⁴ I refer the reader to California Institute for Physics and Astrophysics web site for further information about Stochastic Electrodynamics.
Combining the above explanation with the presented model for wave-particle, one may find a good explanation for equivalence principle (Which implies that mass and gravity are equivalent with each other). Previously, I attributed zero point energy to singularity.

Heisenberg Uncertainty Principle defined
In classical physics we are able to exactly measure a pair of quantities like position and momentum of an object. On the contrary, in quantum mechanics if we pinpoint the exact location of a particle the measurement of its momentum is uncertain by infinity.  Heisenberg Uncertainty Principle tells us that we cannot be sure about the position and momentum of a particle at the same time.

For the uncertainty between momentum (p) and position (x) we can write Heisenberg equation as:

Dp Dx ≥ h /2 p

Where h is Planck Constant.

The diagram below shows the location and momentum relation in our model.

In 1922 Louis de Broglie postulated that any moving particle or object has an associated wave. The postulate is one of the principals of quantum mechanics. The classical physics deals with the linear motion of the objects and ignores the fact that every object also oscillates along the way.   In contrast, since quantum mechanics is dealing with the object within its wavelength, it faces with the puzzle of uncertainty principle. The model described can offer an explanation for the mystery of the uncertainty principle.
In this model, when a particle moves down the slope from the peak during its wave function, the changes in position along x-axis (Dx) are diminished. However, the changes of its speed and therefore its momentum (Dp) increase.

At the peak of spatial displacement, the particle has an instant of zero momentum and therefore zeros changes of momentum. As the particle travels down the slope, its momentum increases and the rate of increase multiplies as it closes to x-axis. Around the x-axis, the particle’s displacement is zero, and the changes in the momentum are maximal. We have assumed that around the X-axis the particle disappears. Therefore its location has the maximum uncertainty.
This is the realization of Heisenberg location/momentum Uncertainty Principle.
In Mass & Gravity chapter, the physical description of the Planck Constant (h) in this model is presented. According to our calculation, the Planck Constant can be taken as the kinetic energy That is delivered by the particle to space-time during each wavelength.  This Planck Constant description confirms the close match between Uncertainty Principle and particle-wave action in this model.

Energy-Time Uncertainty

According to the Heisenberg Uncertainty Principle, the relation between energy (E) of a particle and time (t) is obtained by:
DE Dt ≥ h /2p
Then, DE ≥ h /2p Dt

If as I have assumed, h is the kinetic energy delivered to space-time by the particle, Then this energy decreases as the particle climbs along the curve. The changes in the kinetic energy also is reduced at the first quarter of the wavelength in a bouncing ball model. On the other hand, we pin point time zero when the particle-wave crosses the X-axis and initiate its wavelength. Around this point, time changes are minimal. Whereas, the energy changes are maximal. Heisenberg equation indicates that when the changes in time is zero the changes in energy of the particle increases up to maximum. At the peak of the curve, Dt is maximal and changes in energy are minimal. See the above diagram.
Therefore this particle-wave model is in line with the Heisenberg Uncertainty principle for time and energy as well. This property exists because the particle in this model is not traveling in a homogenous motion; rather it is either decelerating or accelerating along its wavelength.

Number-phase Uncertainty

According to quantum field theory, the number of quanta of a field N and the phase f of the same field (its rhythm of oscillation) obeys the uncertainty principle as well.

D N D f ≥h /2p

The above equation suggests that number of quanta in a field is not fixed. that implies that periodically some of the quanta disappear from the field. This is in line with the above model where particles disappear along their wave function. It also suggests that energy of the field fluctuates. This is also in line with the above model where particles deliver fluctuating kinetic energy while traveling along their wavelengths.

There are many complimentarity relationships that follow Heisenberg Uncertainty Principle. It is interesting that in general, one of the pairs is a space-time element and the other one is a component of the proposed singularity. For example location at the first equation belongs to space-time whereas momentum belongs to informational domain. Similarly in the second equation, time is a space-time element and energy is originated in singularity. In the third equation, Quanta are matter and phase attributes to energy/information domain. Here we may assume that Uncertainty Principle belongs to grey interface between two entities. At the boundary, there is a trade between the components of space-time universe and the singularity. Any increase in one’s clarity is at the expense of the other one’s haziness

Max Born postulate

In 1926 Max Born suggested that:
“An electron wave must be interpreted from stand point of probability. Places where the magnitude of the wave is large are places where the electron most likely to be found. Places where the magnitude is small, are places where the electron less likely to be found.”1
The Born’s electron probability wave favors the presence of the electron near the peak of the translation wave. Here we can offer an explanation for the Max Born's suggestion. In our wave model, the speed of electron s reduced around the peak of translation wave,   therefore it is detectable in space-time. However, we can assume that as the actual velocity increases to reach the light speed (299,792,458 m/s) the probability to pin point it is reduced. At the speed of light electron as a mass disappears from space-time. Therefore, we cannot follow its trajectory.

Wave Function and Complex Numbers System
According to Lorentz equation the length of a particle decreases at higher speeds (length contraction). We may write Lorentz transformation equation for linear motion as:

L = L0√ (1-v²/c²)

In velocities greater than the speed of light (v>c) Lorentz transformation equation moves us to the imaginary domain because (1-v²/c²) turns into a negative number. L = √-n. ⁴⁰
Formerly the imaginary domain was related to the proposed singularity; hence I conclude that, any particle which exceeds the speed of light moves to singularity.
The above interpretation of wave function offers an explanation for using complex numbers to define wave function in the Schrodinger's equation mentioned above. While real number corresponds to the particle in space-time, imaginary number relates to the trace of particle in singularity. That is one way to describe wave function by complex numbers.

The above diagram shows were the objects meet the singularity during their wave function.

Water Waves

Water waves can be taken as an analogy for the above concept. As the water molecules rise from the surface we see them as wave. When they fall, they join the sea of water again. And then the cycle repeats itself. What we see are waves at the surface, but in reality, the waves are extension of the sea. They take a specific shape while in action. Please note that the identity of the molecules of water in subsequent wave is not necessarily similar to previous ones. This resembles the identity problem of particles, in quantum fluctuation. By definition, we cannot identify different electrons from each other. We just see the wave. 
The main factors, which are hidden here, are the energy field, which is moving the water molecules and the data, which regulates the movement and shapes of wave’s motions. The collective action of field (data and energy), which is not observable, and the water molecules, which are observable, form the visible waves. Just getting preoccupied with the shape of the waves and ignoring and normalize contributory factors from underlying sea is not a sound strategy.
We can mention the musculo-skeletal motion as explained in Holonomic Brain Theory as an analogy, as well. In this theory, the movement footprint is in spectral and non-local form. However, when the behavior is materialized it turns to body motions, which are local and observable. Mind you that mind is one of the main contributory factors in this model.

Dirac's Electron
The Dirac equation for electron can be written as:

Ψ = (a A , b A' )

This 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 bA'). These two particles have opposite charges and are continually converting into one another.

Roger Penrose, Road to Reality56

 

In Dirac’s electron wave model, the anti-particle in second portion of the phase, has an opposite charge and is called anti-particle. The anti-particle of electron is positron. The birth and rebirth of the Dirac’s electron is in line with this model. However, the instantaneous speed of Dirac particles is always constant and equal to the speed of light.  The variation in propagation speed comes from the zigzag motion of two components as they average out.  In this model, I have proposed that the speed along the propagation line is constant but the instantaneous speed of the particle changes between the propagation speed and the speed of light in a 2-dimensional wave plane.  The disappearance and rebirth of the particle comes by its entering and rising from the singularity.

Symmetry and Super-Symmetry Theory
       A system has symmetry if someone can change its components, reflect it in the mirror or rotate it and still we cannot notice any difference in it. 

For example, if we rotate a circle or a sphere there will be no noticeable difference in them. Therefore we say that they have perfect symmetry. An image in the mirror is symmetric to the original object. Physicists believe that the universe is symmetric in principle. For example the laws of physics are applied symmetrically throughout the universe. Doesn’t matter where you are in the universe the laws are the same.
Super symmetry is a kind of hypothetical symmetry where fermions and bosons can transform to each other. Fermions and bosons are different category of particles in standard Model of particle physics. Fermions like quarks possess mass and are basic constituents of matter. Bosons on the other hand, do not have mass and are force carriers. Photon is a boson. It does not have mass and carries electromagnetic radiation.
 The Super-symmetry concept was gradually developed by Russian and European physicists during 1970’s.  This kind of symmetry is a bet different from a perfect symmetry because transformed products are different from each other. Nevertheless it is considered symmetry. The Super-symmetry concept solves many paradoxes in theoretical physics like Hierarchy problem.
Any known massive fermion is supposed to have a super-symmetric bosonic partner. In addition any boson is presumed to have a super symmetric fermionic counterpart. The super-partner of fermions named by an s added to the related fermion. For example, the super partner of electron is selectron. The super-partner of a boson is named by tacking ino at the end of the related boson name. Therefore, the fermion counterpart of photon is called photino.
The problem is while all of the particles in Standard model are observed in accelerators, none of the super-partners are found yet. Some physicists came with this idea that may be super-partners are more energetic than the actual partner. Therefore the existing accelerators cannot detect them.
There are high hopes that The Large Hadron Collider that will resume working in few years can find this super-partners. All sounds fine, except that if LHC, which can find particles up to a few thousand Giga electron volt (much higher than expected energy for super-partners) cannot find them the super-symmetry solution will be ruled out. We rule it out, because we have not found reasonable size super-partners in space-time universe.
The above definition for the wave-particle function, which suggests transformation and interchange of a fermionic particle to a non-mass trace, is in line with super-symmetry theory. Except that the non-mass trace reside in singularity where we cannot detect it. It is presumed that transformation in super-symmetry takes place in super-space. Interestingly, extra super-space dimensions in super-symmetry do not have any size which mimics the proposed singularity. Moreover, unlike fermions that have to follow PPauli Exclusion Principlel, several non-mass bosons can occupy the same qquantum stateuand spot. Therefore, the non-mass super-partner of fermions in this model can reside in singularity where exclusivity is not honored.
Flavor problem is another difficulty with super-symmetry. Recall that in the Standard Model each category of particles is called a flavor. For example, electron, muon and tau are one flavor of particles.  Up, charm and top quarks form another flavor. Normally members of each flavor do not directly transform to each other. For example during decaying of muon to electron a muon neutrino and electron antineutrino are also produced that preserves the particle number. This is not true for super-partners. The bosonic super-partners get all mixed up. In super-symmetric theory, if for instance electron were paired with smoun, an interaction would be generated that are not seen in nature. 
Unseen super-partners in the colliders and merge of bosonic super-partner open the arena for new speculations.  Maybe we are looking in a wrong place for a wrong object. Physicists traditionally work and look within the objective and tangible arena. That is why to find the answers they speculate objective bodies like super-partners. They even assume that force fields are made from virtual particles.
May be objective arena is not enough to explain the universe. May be we have to look for non-tangible domain and elements to build new theories. It seems that the mainstream interpretation of Quantum Physics is pointing to such a domain.

Tachyon
This model also incorporates and explains the notion of tachyons. A tachyon is a hypothetical particle that travels at superluminal velocity. By definition, tachyon's mass squared is negative. That means to define it we have to use imaginary number (√-n). Alternatively, we may say its rest mass is imaginary. We may also re-word the previous sentence by saying; tachyons rest mass belongs to informational domain. Previously, I considered the singularity as information domain. I have also speculated that faster than light speed objects loose their real mass and enter the singularity.

Nature of Photons
Same speculation can be extended to photon itself. By definition, photon does not posses any mass. The speed of photon as light particle is constant and amounts to approximately 300.00km/s. As such, it has to reside in the boundaries of space-time. As mentioned in boundaries chapter at the vicinity of border-line matter gets pale and disappears. Therefore, since photon stays in the boundaries it does not possess mass.

Photon stays at the boundaries of space-time

 

Maybe that is why Pauli Exclusion Principle which indicates that two similar particles cannot occupy the same location in space, does not apply to photons. Since Photon stays at the boundaries but does not enter space-time, there is no competition for obtaining territory. There is no territory at all to fight for.

M Theory
The M Theory (the new and united version of string theories) explains the process of the appearing and disappearing particles by postulating that particles are absorbed and emitted by the p-brane.  The p-brane is a hypothetical space-time, which can have different dimensions. The advantage of the p-brain assumption is that it keeps us in our comfort zone while providing solutions for our paradoxes.  In the model presented in this chapter, the transformation is happening in an entity outside of the space-time.

Defiance of Heisenberg Uncertainty Principle  
My description of particle wave function is also in accord with recent experiments conducted by Shariar S. Afshar from Rowan University in New Jersey. 
Afshar defies the notion that nature never permits us to observe both the particle and wave aspects at the same time. The uncertainty principle conveys that a particle can be either a wave or a particle and never simultaneously both. In the above model, I have described the particle as a real entity which is moving in a wave like motion, capable of being detected in both versions simultaneously, at some occasions.
  
Singularity: An Active Entity
In order to uncover solutions for the paradoxes, singularity cannot be considered merely an inactive pool of energy and information. The particle wave is continuous.
Below zero is not nothingness. There exists a vast computational territory, territory of negative numbers. Interestingly, these numbers interact with positive numbers and affect them drastically. Contextuality in the Bell-Kochen-Specker theorem can be viewed as evidence for such activities. The theorem simply states that in quantum mechanics, the value of different non-compatible observables is also correlated with each other, even though they are not complimentary pairs (complimentarity characteristics like location/momentum and energy/time. See Quantum Mechanic chapter). For the values to be interrelated we need an active media which not only accommodates the values, but also intermingles them.
In wave motion, the particle reappears and carries the information back to space-time. Quantum tunnelling (when a particle passes through a barrier and only reappears in space-time when the barrier is out of the way) can be explained by assuming the presence of a particle in singularity. Remember that particles in the Standard Model (standard model of particles is a science which deals with subatomic particles) are zero-size.
If we have in depth and precise knowledge about the true nature of things, we will come to the conclusion that “God does not play dice with the universe”. We will come back to a deterministic world again.

Us as waves

The above model can be applied to wave-particles, such as alpha and beta rays or atoms and even objects that are much more massive. According to Louis de Broglie, any object has a wave. However, massive objects have much smaller wavelengths. In 1916 Walter Nernst also proposed that a complex body can only form and emerge from its component atoms if they become able to tune together their fluctuations. on the other words, they have to produce a common phase of oscillations to create a complex body. The produced complex wave can be regarded as the identity of the complex object⁷⁵. Cohesion of a system requires that each component resonate at the same phase. In other words, the whole assembly should have the same wave function. Similarly, quantum biologists believe that organisms have macroscopic wave function. The wave demonstrated can be a harmonic of a much smaller microscopic wave that according to de Broglie every object including live organism owns. In this view, the atomic components of a living organisms are just building blocks. The blue print is the wave that organizes the atoms in specific shape and function. It can be speculated that we as humans are also follow a wave function. The phase is the origin of self. This can explain how emotions are so overwhelming and spread all over the body (2).

Our livelihood is because of our fidgety
We are waves, resting is our absence

Rahi Moayeri, Iranian Poet

Can we further assume that we are also traveling to singularity back and forth many times per second? Then we find a realm where we all unite. This can be the origin of oneness that we sense. This can be the source of passionate feelings that we have for humanity and other beings.

The 16th century philosopher Mulla Sadra proposed a similar idea under the name of al-haraka al-jawhariyya.

Substantial Motion
Mulla Sadra (1571-1640) The Iranian philosopher, and perhaps the single most important and influential philosopher in the Muslim world maintained in his substantial motion (al-haraka al-jawhariyya) that:
“Substance only changes suddenly, from one instant to another, in generation and corruption.”⁶²
This is in line with the complex number assertion C#1, which postulates that matter appears and disappears periodically.
It is also in line with Assertion WP#2 in this chapter, where it suggests that mass joins singularity and appears again in space-time in each Compton wavelength.

Notes
1) Here, I am referring to Poynting vector of the zero-point fluctuations. Interested readers can look at the following website for further information:
http://en.wikipedia.org/wiki/Poynting_vector
2) The concept is well developed by Emilio Del Giudice from National Institute o Nuclear physics, Milan, Italy. The article appeared at the book Brain and Being⁷⁵ .

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