### Rest Mass in this Model

Einstein’s special relativity implies that a object’s mass in motion increases proportionate to its speed. The Lorentz equation for transforming mass in motion is as follows:

*m = m _{0}/√ (1-v^{2}/c^{2}) *

Where m is mass in motion, m_{0} 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? Let’s take the lead from the following statement, from Professor Wesson of the University of Waterloo

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. (Wesson n.d.)

In this model h is the total energy (Hamiltonian) of the particle delivered to space-time during each wavelength.if we extend the equation deB = h = p to inside the pilot wave, and if we take h as the particle’s total energy within each wavelength, then the particle’s variable kinetic energy is directly related to its variable momentum. In 1920, De Broglie proposed that every object has a wavelike motion. In accordance with De Broglie’s postulate, larger objects follow shorter wavelengths and have higher frequencies. Quantum mechanics, on the other hand, postulates that the smaller the scale, the more turbulence observed in the fabric of space. In previous sections, we assumed 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.

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

Ψ(x_{a}) = e^{-ip}a^{xa/h}

Where p is momentum. Adding 2πħ to the p_{a}x^{a} will not change its quantity. The equation has a time-like period of 2πħ/p_{0} and a space-like period of 2πħ/p_{1}. 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. 2πħ/p_{1} indicates that along x direction, momentum is also periodic. This means momentum appears and disappears during each period as well.

In addition, in view, wave function is a complex function and has an imaginary (out of space-time) component. Formerly, we also speculated that the mechanics of particles in this movement mimic a bouncing ball. The two forces acting on a bouncing ball are the attractive force of gravity and the repulsive force of electromagnetism 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 that ejects the particles and throw them into space-time. Accepted phenomena such as quantum fluctuation and accelerating expansion of the universe demand a repulsive force. They are believed to be due to ZPE and dark energy, respectively. Zero point energy is considered to be part of the boundary condition of the universe. Therefore, the assumption that a repulsive energy enters from boundaries is not out of line.

The rest mass is indistinguishable from the energy that particle carries. The Compton frequency (the frequency of an object in rest) is a multiple of the Planck constant h. There are similarities between Sakharov-Puthoff model and the above scenario. In the Sakharov-Puthoff model, the perturbation of particles in the presence of ZPE creates the mass and curvature of space. In the model at hand, the presence of matter (and its travel in and out of the proposed singularity) is needed for transferring ZP energy to space-time.

In the CIPA model, because the number of possible wave modes is enormous, the sum of tiny energy per mode times the huge spatial density of possible modes yields a very high energy density, which is contrary to observations. In our model, we confine energy delivery to particles themselves and not all possible waves. Therefore, the undetected high energy problem does not arise. This can only happen if ZPE exists outside space-time while just certain amount of energy is delivered by existing particles or fields into space-time.

### Pre-existing Waves

Alternatively, we may postulate that plane waves introduced in the QVIH may actually exist. The attractive and deflective force of zero point fluctuation may create randomly phased plane waves (ripple) in space-time.

Roger Penrose indicates that Einstein’s 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” (Penrose 1955).

We may further speculate that a particle according to its energy level gets involved with a harmonic wavelike curvature of space and continues its journey, just like a planet or any other object travelling 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. As we get to smaller wavelengths, we gradually get closer to the territory of hadrons, atoms, 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 nano-meter. This is 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, has a wavelike motion and enters and exits singularity in each period of our wave motion. Then this can explain some of the strange findings in trans-personal psychology experiments.

### Mass and Wave Function

In the wave-particle section, we presented a 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.