### 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 object. The Compton wavelength of a particle x is obtained by

*λx = h/m _{x}c *

and the Compton frequency by

*fx = m _{x}c/h *

where mx is the mass of particle and h is the Planck constant. Everything else being constant, mass is directly proportionate to frequency.

Previously, I assumed that particles in their wavelike motion enter and exit singularity relative to their frequency. We may assume that from here, kinetic and potential energy alternate and cause the wave motion to continue as long as they are not disturbed. Obviously, as long as the Compton wavelength of a particle does not change, its character stays the same, but if the Compton wavelength changes, we are dealing with a new particle. Changing the Compton frequency is possible in high energy accelerators. In accelerators, the new particles are constantly formed and interchanged with each other. Inversely, we can postulate that the wave chosen depends on the amount of energy (kinetic energy) that is delivered in by a specific particle. Combining it with the assumption of pre-existingplane waves, we may conclude:

**Assumption MG1**. Fundamental particles associate only with waves that are harmonic to their Compton frequency.

### Fundamental Constants

Previously, I mentioned that this section is the centrepiece of this model. Here I offer explanations for the nature of the Planck constant, the hierarchy problem, and masses of fundamental particles.

First, let us discuss fundamental constants. There are some numbers that are frequently 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 originate from the 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 the Planck constant (denoted as h) with the value of

h = 6.626 0693 × 10^{-34} J s.

There are others, such as the gravitational constant, the Boltzmann constant, Dirac’s constant (h/2π), and the Coulomb force constant. Masses of fundamental particles are also considered constant. Their values never change and besides we do not know where their values come from. Unlike the CIPA model, in this model, zero point energy is not intrinsic. If it was, 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 assume a portion of ZPE energy accompanies the particles, which are travelling along the wave. I will take the lead from CIPA researchers and 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” (Haische 1994).

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 the frequency of objects? Let’s review it. For the wavelength of a particle, we may write,

*λ _{x} = h/m_{x} c *

Where λ is the wavelength of the object, h is the Planck constant, c is the speed of light, and m_{x} is the rest mass of the particle. Then,

*λ _{x} = c/f_{x}, *

we may write :

*c /f _{x} = h/m_{x} c *

*f _{x} = m_{x} c^{2}/h *

**(1)**

*,*

and since E = m_{x} c^{2} we may write,

*f _{x} = E/h, or *

*E = fx h*

This is Planck's relation.

In equation (1), we conclude that the frequency of any object is proportionately related to its rest mass. Having the wave-particle 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. We call this energy from singularity Es. Therefore, Es is the energy delivered during each wavelength.

*E _{k} = E_{s} × f*

**(2)**

where E_{k} is the total kinetic energy of the particle and E_{s} is the unit of kinetic energy delivered in each wavelength. Obviously, objects with higher frequencies deliver more energy and thus are more massive. To calculate E_{s} of different particles, we used the Einstein equation Ek = m_{0}c^{2}, where m_{0} is the rest mass of the particle and c is light speed. Then we write the total energy as the product of the Compton frequency of the particle and E_{s}:

E_{k} = E_{s} × fcom

Thus, the energy derived from singularity during each wavelength is calculated as follows:

E_{s} = fcom /E_{k }

As examples, we will calculate the energy borrowed from singularity (Es) during each wavelength for electron and muon using the above equation. Values for the Compton frequency and the mass of the particles used in these calculations are obtained by experiments in the Fermi lab and elsewhere.

E_{e} = m_{0} c^{2} = (9.109826 x10^{-31})(9x10^{16}) = 81.988434x10^{-15 }

E_{e} = E_{s}x f_{com }

f_{com} = c/λcom = (3x 10^{8})/(2.426310215 x10^{-12}) = 1.236445357x10 ^{20 }

Es= Ee /f_{com}= (81.988434x10^{-15})/(1.236445357x10 ^{20}) = 66.30979164 x10^{-35 }

The result is consistent with the value of the Planck constant with a small margin of error. This is re-inventing the wheel but giving it a new “spin.”

**Assumption MG2**. We may conclude that the Planck constant is the amount of energy delivered by particles to space-time in each period.