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Unified Field Theory and the Configuration of Particles

Zhiliang Cao*, Henry Gu Cao

Shanghai Jiaotong University

Abstract: The Standard Model of particle physics is a theory concerning electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of known subatomic particles. The current formulation was finalized based on the existence of quarks. Because of its success in explaining a wide variety of experimental results, the Standard Model is sometimes regarded as a "theory of almost everything". Mathematically, the standard model is a quantized Yang-Mills theory. Therefore, the Standard Model falls short of being a complete theory of fundamental fields. It neither explains force hierarchy nor predicts the structure of the universe. Fortunately, Unified Field Theory (UFT) explains fundamental forces and structures of sub-atomic particles and grand universe. One of the important applications of the Unified Field Theory is that the mass of each sub-atomic particle has a formula. These formulas are structural formulas which can calculate mass of the particles. The mass of a particle decides its structure and characteristics.

Keywords: particle physics, Unified Field Theory, quantum chromodynamics, Standard Model

Received November 15, 2013; Revised November 24, 2013; Accepted November 27, 2013

Citation: Zhiliang Cao, Henry Gu Cao, Unified Field Theory and the Configuration of Particles. International Journal of Physics, 1 (6). 151-161. January 2013. doi:10.12691/ijp-1-6-4

1. Introduction

Unified Field Theory (e.g. [1,2,3]) provides particles’ configurations, a capability that no existing theory has. This paper compares UFT and Standard Model (e.g. [4,5,38]) as the first step to present UFT as a better theory.

The Standard Model has following assumptions:

1. There are six quarks that have either 1⁄3 or 2⁄3 times the elementary charge.

2. The relatively constant coupling force of Strong Interactions between quarks and gluons because all carry a type of charge called "color charge." Color charge is analogous to electromagnetic charge, but it comes in three types rather than one, and it results in a different type of force, with different rules of behavior. These rules are detailed in the theory of quantum chromodynamics (QCD), which is the theory of quark-gluon interactions.

3. The weak force is 10³² times stronger than gravity.

This paper will begin with the paradox of the Standard Model. It also addresses the force hierarchy problem of the current particle physics theories as well as fundamental questions unanswered by the existing theories. Then the paper will reexamine the existence of quarks and the theory of QCD (Figure 1). The paper also provides structural mass formulas for each particle.

2. Paradox of Standard Model

2.1. Paradox of Inseparable Quarks

Figure 1. QCD Proton Model

The up quark or u quark has an electric charge of +2/3 e. The down quark or d quark has an electric charge of -1/3 e. Unfortunately, there has been no particle with 1/3 or 2/3 of unit charge observed, meaning that no free quark has ever been observed. Therefore, the claim that “There are six quarks that have either 1⁄3 or 2⁄3 times the elementary charge” has never been experimentally confirmed. To make it plausible, the Quark Theory assumes the following QCD behaviors:

1. The force between quarks does not diminish as they are separated. Because of this, it would take an infinite amount of energy to separate two quarks; they are forever bound into hadrons such as the proton and the neutron.

2. In very high-energy reactions, quarks and gluons interact very weakly.

Figure 2. Quarks’ Bonding Coil

The resistance force created from coil (Figure 2) is proportional to the distortion of coil as a result of Hooke’s Law.

There are two possible cases relating to the distortion of quarks and gluons:

1. In close distance: If the quarks and gluons interact weakly in very high-energy reaction, then quarks should be separated out during the interaction. The high energy introduced momentum can break weak bonding (interaction) forces.

2. In relatively far distance: If the quarks and gluons have stronger bonding forces than Strong forces, then quarks and gluons in one proton will be able to interact with quarks and gluons in another proton. Therefore, proton-proton interaction should have a stronger force.

The inseparable quarks’ claim conflicts with the following observations:

1. In very high-energy reactions, quarks and gluons interact very weakly.

2. The coupling force of Strong Interactions between quarks and gluon is relatively constant.

2.2. Paradox of Bonding Forces

Figure 3. Particle Force Carriers

In Standard Model’s QCD theory, the Strong Forces are carried via gluon. When two particles interact, one particle throw a force carrier particle at the second particle. Based on Conservation of Momentum, both particles will move further away from each other to conserve their momentum. In QCD theory, the particles will get closer. The mechanism of exchanging force carrier particles between two particles is controversial since the particle does not follow the Conservation of Momentum. Therefore, the Standard Model in principle violates the Conservation of Momentum.

2.3. Force Hierarchy

Strong force is at the top of the force hierarchy (e.g. [39-50]), followed by electromagnetic force, weak force, and gravity, which is the weakest force.

2.3.1. Force Carriers

In current particle physics, forces between particles arise from the exchange of other particles. These force carrier particles are bundles of energy (quanta) of a particular kind of field as follows:

The electromagnetic force can be described by the exchange of virtual photons.

The nuclear force binding protons and neutrons can be described by an effective field of which mesons are the excitations.

At sufficiently large energies, the strong interaction between quarks can be described by the exchange of virtual gluons.

Beta decay is an example of an interaction due to the exchange of a W boson, but not an example of a force.

Gravitation may be due to the exchange of virtual gravitons.

The following conclusions can be made:

1. The idea of force carrier particles (Figure 3) is controversial.

2. “Virtual photons”, “gravitons” and “virtual gluons” are not plausible particles. The use of these unknown particles for the sake of theory is clearly inaccurate.

3. Even with the help of the force carriers, the force hierarchy is not explained properly.

3. UFT vs. Standard Model

The purpose of a theory is to explain some aspects of the world. Thus many kinds of explanations are rightly called theories.

The characteristics of good theories are:

1. Easy to obtain confirmations, or verifications;

2. Not refutable by any conceivable event is non-scientific;

3. Assert that things operate in one way and rule out other possibilities;

4. Less testability leads to less risk, therefore, a good theory is less testable.

5. Have a clearly defined scope.

6. The logical induction is certain.

3.1. Standard Model is Questionable

The Standard Model does not meet any of the above characteristics.

1. Standard Model can not exist without Quarks, but Quarks have never been observed directly;

2. Imagine a scenario where person A and person B are standing on ice, with person A holding ball C. When person A throws ball C at person B, ball C should bring person B closer to person A according to QCD theory. In reality, the two people will move away from each other. This simple scenario falsifies the force carrier theory of Standard Model.

3. The conservation of Charge Parity (CP) is an important law in Standard Model, but many various experiments have observed violations in Charge Parity.

4. The theory contains many questionable theories that can be easily challenged.

5. Wolfgang Pauli’s exclusive law is applicable only in the scope of the electron particle wave in an atom, but the law is not applicable for strong and weak interactions inside a subatomic particle.

6. Standard Model relies on untenable theories such as Quarks, force carriers, and quantum field theories. Its logical induction undertakes many unreasonable assumptions. Therefore, its logical induction is uncertain.

3.2. UFT Particle Theory is a Good Theory

UFT theory meets all the characteristics of a good theory.

1. It can be easily confirmed using mass formula that is applicable for any random particle. Any known particle has a proper mass formula that follows Unified Field Theory. Therefore the possible mass for particles are in a limited value set.

2. UFT follows simple rules, such as the Fibonacci sequence, addition, multiplication, and division. It can not be refuted by any non-scientific event.

3. The explanation rules out any arbitrary mass value for a particle. The mass value determines the properties of a particle due to the certainties of wave resonance.

4. The particles are built with simple unit charge waves. The existence of the wave can be confirmed by the stability of the electron. No other tests are needed.

5. UFT uses the Torque (e.g. [3]) model as the foundation for other building blocks, such as fundamental forces, unit charge, photon, Planck length and size of Universal Grid (e.g. [3]).

6. UFT is built on a simple relationship between space-time-energy (e.g. [3]) and their only possible 3D Torque model. The inductions of the theory are mathematically certain.

UFT provides predictions of unknown particles for the future research works.

4. Unified Field Theory and Particles

4.1. Fundamental Particles

The particle is formed as result of the proper energy distortion wave resonance:

Figure 4. Resonance Transmissibility

Any known slow particle is constructed by a basic structure with the unit charge (electron) mass as its unit.

The sub-atomic particles are composed of fundamental waves, since UTF has no concept of a fundamental particle. The fundamental waves are:

The simplified mass formula is a summation of the above formula. While the generic mass formula is:

Where,

fi is Torque wave distortion measure by electron mass unit in a unit of space.

Si is the individual wave of the basic wave structures.

For a basic structure, the energy formula can be:

Or,

A particle has many basic components. The total energy can be expressed as,

Where,

Ei (i=1, 2, …, N) is energy of basic component

Ex,y(x, y = 1, 2, …, N) is interaction energy between two basic components.

The interactions inside a particle can be either strong or weak.

The strong interaction’s unit is:

When interacting on the shell, the weak interaction’s unit is:

When waves resonate with one another, the weak interaction unit is:

When waves are dissonant with one another, the compensate wave interaction unit is:

Leptons have complex wave fractional series that do not have simple formulas.

The waves’ bonding energy is similar to the structure of a rope (Figure 5).

The fibers form threads, threads form thicker threads, thick threads form thin ropes, thin ropes form ropes, ropes form thick ropes and etc.

When threads form thin ropes, the twisting directions of threads and thin ropes are opposite. The waves in a particle structure have different charges as well. In a basic wave structure, the parent wave and child wave have different charges, and the total charge can only be one: minus one or zero. The complex particle itself can possess a charge count bigger than one.

Figure 5. Bonding Rope of the particle waves

4.2. The Theoretical Basis of Mass Formula

The electron has one Torque Grid distortion on its shell. It becomes the base of the other particles. Particle structures can be mathematically derived with mass formulas.

Any wave in the particle has a single unit charge so that it can be in resonance with the electron distortion. The total charge of the particle is the summation of the waves’ charges.

4.3. Wave Axes and 3D Shapes

Each major wave structure goes through the center of the particle. These structures are axes of the overall 3D structure of the particle.

4.3.1. Three Axes

Figure 6. Three Axes Octahedron shape

4.3.2. Four Axes

Figure 7. Four Axes Cube

5. Proton

Assume:

The structural formula for proton (e.g. [51-77]) is

The mass of a proton is:

The mass of an electron is:

If we use the electron as a unit, the mass of the proton is:

5.1. Configuration of the Proton

The mass formula explains the Proton’s mass. The additional mass 0.15267 provides hints of configuration of proton.

The structure 2A² strong interaction:

The weak interaction between (2*3) and eight faces (Figure 6) of A and 2A²:

Wave 2*3 does not have factor 5 in A (2*3*5). Since wave 2*3 is moving around. It interacts only half of the factor 5. The resonance weak interaction wave is:

The number matches exactly to the known Proton interactive mass 0.15267:

Figure 8. Proton Octahedron shape

6. Neutron

The structural formula for neutron (e.g. [78-113]) is

Using electron mass as unit, the mass of a proton is:

6.1. Configuration of Neutron

The Neutron is a complex particle with the Proton as its base particle plus 2.5 mass waves.

The 2.5 wave has a strong interaction with two A² structure with bonding energy of:

The weak interaction of 2.5 with ten ends of axes A, 2A², 3, and 3:

Weak interaction between 2.5 and 2*3*5 related to opposite charge:

The number matches exactly with the known Neutron mass.

7. Unstable Particles

7.1. Hadrons

7.1.1. Rho

The structural formula for Rho (e.g.[114,115,116]) is:

There are three axes (Figure 6):

Using electron mass as unit, the mass of a Rho is:

Strong interactions:

A² has higher energy and less stable. It tends to annihilate first in the decaying process.

7.1.2. Charged Pion

The structural formula is (with three Axes):

Using electron mass as unit, the mass of a Pion is:

Strong interaction between B² and (4*4 + 1), estimated factor is 4+1/16 = 4.0625:

(4*4 + 1) gets destroyed first during the decaying process:

7.1.3. Neutral Pion

The structural formula is

Using electron mass as its unit, the mass of a Pion is:

Strong interaction between B² and (2*2) + (2*2):

Weak interaction:

Structure 2*2 can either annihilate along with the other structure, or, it can be decayed to:

7.2. Leptons

7.2.1. Muon

The structural formula for muon (e.g. [117-129]) is

There are some special Lepton waves:

Plus weak interaction:

Figure 9. Muon Cube shape

7.2.2. Tauon

The structural formula for Tauon (e.g. [129-136]) is

There are some special Tauon waves:

Plus weak interaction on seven faces:

Figure 10. Tauon Pentagonal prism

7.3. Bosons

7.3.1. Higgs Boson

The structural formula for Higgs Boson is

Higgs Boson has no special significance other than having a (3*6*9)*(3*6*9) strong interactive wave.

7.3.2. W Boson

The structural formula for W Boson is

W Boson has a (3*6*9)*(3*6*9) strong interactive wave and negative bonding energy of (-30) for the (3*6*9)*(3*6*9) wave structure.

7.3.3. Z Boson

The structural formula for W Boson is

W Boson has no a (3*6*9)*(3*6*9) strong interactive wave and a (2*6*8)*(2*6*8) strong interactive wave structure. It has neither A nor B structure.

8. Celon

There are two known particles travelling at the speed of light: photon and neutrino (e.g. [137-177]). A photon’s wave length equals the wavelength of the “particle wave”. A neutrino’s wave length unit is 1/137 of electron’s size.

Particle type Celon is named after the Latin word Celeritas, meaning swiftness; both photon and neutrino travels at the speed of light, and they are categorized as Celons.

8.1. Photon

Figure 11. Photon movements

Figure 12. Photon Torque distortions

A photon (Figure 11) has a circular torque distortion (Figure 12) propelling itself forward in one direction along the torque line. Since the particle keeps moving, the photon both stretches and twists. The stretching is synchronized with the energy distortion on the grids. The center point has one Grid size distortion while energy distortion of its wavelength is one grid distortion as well.

8.2. Neutrino

A neutrino has a high energy spinning motion with weak interact range as its wavelength. The existence of the particle relays on the oscillation of the wave:

There is no physical Torque Grid. The subtle relationship among time, space, energy, and force is the reason behind the formation of Torque Grid. The above oscillation creates first level sub-grid structure that is 1/137 of the Torque Grid. The smaller size has 137 times the stiffness. The same unit charge force produces one sub-grid size distortion on the shell of the sub-grid. The sub-grid can be further divided by a factor of 137 into second level sub-grid. This process can be repeated an unknown number of repetitions.

The unit energy of a Torque grid (zero level) structure is 1. The unit energy of a first level sub-grid structure is 1/(137*137). The unit energy of a second level sub-grid structure is 1/(137*137*137*137).

The Unified Field Theory provides imperfect explanations of neutrino mass. Nevertheless, the mass formula can be used to predict neutrino from the new T2 lepton.

8.2.1. Electron Neutrino

When a neutron decays to a proton and electron, it release an electron neutrino:

Or,

Some of the oscillation waves are in the original wave form and released as neutrinos. In this case, there are more than one neutrinos. There is no anti-neutrino in existence in Unified Field Theory.

The observed energy of ve⁻ can be from 0 to 2.2 eV (0.0000011 e).

8.2.2. Muon Neutrino

The structure of muon is:

Neutrinos will be formed via 0.5 + 0.5/3 + 0.5/(2*3) + 0.5/((2+3)*2*3) + 0.5/((2+3+6)* ((2+3)*2*3)) + 0.5/((2+3+6+30)*330).

If 0.5 forms other energy, then, neutrino energy will be:

Or,

The observed energy of Muon neutrino can be from 0 to 170 KeV (0.34 e).

8.2.3. Tauon Neutrino

The structure of tauon is:

1 of the above electron units of the quantity of 19 will become (e⁻ + vt⁻). The energy of Tau neutrino is from 19+19 = 38.

When the neutrino mass is 30.362 e:

The observed energy of Tauon neutrino can be from 0 to 15.5 MeV.

8.2.4. Neutrino Flavors

Neutrinos are formed via different process and therefore, they have different structures known as flavors. There is no limit to the energy of a neutrino.

9. Predictions

9.1. New Leptons

The structure of T2 is:

Neutrino: 36+2*0.1495 = 36.3, or: 18.55 MeV

The structure of T3 is (may be harder to identify):

9.2. New Bosons

It may not be practical to discover new Bosons. We list the possible structure of new particles so that future experiments can verify the Unified Field Theory.

The structural formula for I Boson is

The structural formula for J Boson is

9.3. New Hadron

The structural formula for this new Hadron is:

10. Conclusions

A particle configuration has the following rules:

1. The particles are formed by charged energy waves with the electron mass as their unit.

2. The multiplication Fibonacci series forms energy ropes that are the basic structure of the particle.

3. Strong interactions and weak interactions add additional energy to the particles’ mass.

4. Leptons rely on their wave series to gain their stabilities, since they lack Strong interactions.

5. Each major wave structure forms an axis in the particle. The shape of a particle is decided by these axes.

6. Neutrinos’ movement in the space is similar to that of the photon. Neutrinos and Photons are categorized as Celons.

7. Unified Field Theory predicts the existence of new particles, such as new Leptons and new Bosons. Most practically verifiable particles are new Lepton T2 with mass of 3138.120811187736 MeV and a new Hadron with mass of 3320 MeV. The experiment findings will provide proof of Unified Field Theory.

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