Title: Part II Theory of Everything: pair production

Wanchung Hu

PostDoc Fellow

Taipei, Taiwan ROC

Correspondence to: lukluk73_2006@yahoo.com.tw

Abstract

In setting up theory of everything, we cannot neglect the importance of pair production. In gamma ray photon-photon pair production, two beams of gamma ray (511kev) can form positron and electron pairs which are made of charge and mass. In gamma ray photon-nucleus pair production, one beam of gamma ray(1022kev) can form positron and electron pairs. During pair production, the energy should be conserved. Thus, total rest mass energy of electron and positron are also 1022kev(E=hf=2mc^2). However, electromagnetic radiation has additional energy density depending on wave amplitude (Energy density=eE^2) which is neglected in the calculation during pair production. Here, I propose that the EM wave energy density depending on amplitude is transforming to electrostatic energy to form charges during pair production. The equation is E^2=1/2(Kq/r^2)^2. Thus, mass is made of wave frequency and charge is made of wave amplitude during pair production. In the second part of this article, I will try to solve the mystery of 137. In my deduction, I will show that the ratio of 1/137 is the ratio of electrostatic energy and rest mass energy of a particle. In addition, I will deduct that particle size is depending on mass, lightspeed, and planck constant(r=h’/mc). These theories contribute the setting-up of theory of everything.

Main text

It is well known that gamma ray can be transformed to electron and positron pairs during head-on collision with the other gamma ray or atom nucleus. During the process, energy should be conserved. Each electron or positron has the same rest mass energy: 511kev, so the total rest mass energy is 1022kev. Thus, the initial one beam gamma ray should be 1022 kev. Or, each gamma ray beam for head-on collision should be 511kev. In order to fulfill the conservation of energy, the equation is:

E=hf=2mc^2(E=energy,h=planck constant,f=wave frequency,m=rest mass of electron,c=lightspeed)

The above equation matches the experimental observation. However, it is important to point out something is missing during the energy transformation. Each photon has not only frequency but also amplitude which constitutes the EM wave density eE^2. In addition, charged particles have their electrostatic energy. Thus, it is reasonable to postulate that EM wave density eE^2 is transformed to charge electrostatic energy. Only by doing that, total energy is conserved during pair production. Thus, the initial EM wave energy density should be the same as charge energy density after pair production.

The initial total EM wave density is S=eE^2 including both magnetic and electric field components. (S=energy density(energy per unit volume, e=electric permeability constant, E=electric field)

It is worth noting that energy density(J/m^3) is equal to force per unit area (N/m^2) which is used to derive the equation later.

If we assume that electron is a solid ball with its charges equally distributes in the solid ball, then the electrostatic energy of electron is:

E=(3/5)KQ^2/r (E=energy, k=Coulomb constant, Q=total charge, r=electron radius)

Thus, the initial energy density is equal to aftermath energy density:

S=eE^2=[(3/5)KQ^2/r]/[(4/3)pi*r^3]

Thus, we can get E^2=(9/5)(KQ/r^2)^2

However, electron is a small conductive sphere. Its charges should be equally distributed on the surface of sphere. Thus, it is more reasonable to assume the electron should be like a hollow ball. Thus, the electrostatic energy of electron should be:

E=(1/2)KQ^2/r

The force for unit charge on the sphere surface is:

F=(1/2)KQ^2/r^2

Since energy density is equal to the force per unit area, the energy density of the hollow electron sphere should be:

S=[(1/2)KQ^2/r^2]/(4pi*r^2)

Thus, the initial energy density is equal to aftermath energy density:

S=eE^2=[(1/2)KQ^2/r^2]/(4pi*r^2)

Thus,

E^2=(1/2)(KQ/r^2)^2

Thus, we can predict that the wave amplitude for generating proton-antiproton or neutron-antineutron should be different. Although proton and neutron have the same mass, the wave frequency for generating proton-antiproton or neutron-antineutron should be the same. However, proton-antiproton requires more energy to be synthesized.

Here, I have an interesting finding. There seems to be a correlation between plank constant, gravity constant, and Coulomb constant.

The reduced planck constant is 1.05*10^-34

The magnetic permeability is 10^-7

The gravity permeability (2G/c^2) is 1.48*10^-27

Thus, we multiples 10^-7 with 1.48*10^-17. Then, we multiplies the above result with (1/2)^0.5, and we get the perfect reduced planck constant 1.05*10^-34. It is very interesting!

In the second part of article, I would like to deduct particle size during pair production. I will show that particle size is depending on its mass, lightspeed, and planck constant.

In my last manuscript, we know that particles like electrons are spinning in lightspeed. Thus,

C=r*W (C=lightspeed, r=particle radius, W=angular velocity of spin)

In addition, there is relation between spin angular frequency with wave frequency.

W=2pi*f (f=wave frequency)

During pair production, hf=2mc^2. Thus,

W=(4pi*mc^2)/h and C=r*W. Thus,

r=(1/2)(h’/mc)

So, there is relation between Compton wavelength (h/mc) and particle size. My deduction is well correlated with experimental observation. A theory suggested that Higgs mechanism gives all particle mass, and I think that theory is incorrect. I think all masses are transformed from wave frequency during photon-photon pair production. In the early universe, the space-time dimention is quite small, so there are much higher chance for photon-photon pair production to generate particles with masses and charges.

Finally, I will try to solve the mystery of number 137. 137 is suggested a coupling constant for electromagnetic interaction. However, it is poorly understood why it should be 137. Here is the fine structure constant:

Alpha=KQ^2/h’c=1/137

Since the particle radius for electron or proton is r=(1/2)(h’/mc). Thus, the fine structure constant is changed to be:

Alpha=[(1/2)(KQ^2/r)/mc^2]=1/137

Thus, we can see that alpha is a ratio between electron/proton hollow sphere’s electrostatic energy and their rest mass energy mc^2. Thus, it is why 1/137 is the coupling constant of electromagnetic interaction.

In summery, I sincerely hope my work will contribute the setting-up of theory of everything. Please give me some comments of my manuscript. Thank you very much.