Energy values for neutron and proton components from Table 2 and Table 3 are arranged into columns in Table 4. The simulated mass of the neutron and proton are marked in red below (Table 5 compares simulated mass with PDG and NIST data). The models include initial neutron expansion kinetic energy 10.15 MeV and potential energy 10.15 MeV. The energy 10.15 MeV/nucleon is also fundamental to atomic fusion. The neutron decays to a proton, electron, and anti-electron neutrino and its mass and fields are listed along with the decay products toward the bottom right side of Table 4.

Table 4. Neutron and proton mass simulations.

Table 5. Comparison of models with PDG [3] and NIST [4] data.

ModelFundamentals

The models are based on probability one and zero energy.

Energy = 0 condition (3)

Table 2 and Table3 information N and energy E values have specific meanings for each of four positions in Table 6. Table 7 shows an energy balance for each quark. (E₁ + E₂ + difference ke) = (E₃ + E₄). This can be considered zero energy based on separation.

Table 6. Meaning of energy positions for one quark.

Table 7. Quark mass plus kinetic energy and field energy.

Probability = 1 condition (4)

Table 6 positions also represent probability = 1.

Equation (5) is one of the four groups of N values in Table 2 that multiply to p = 1. Overall, P = p ∗ p ∗ p ∗ p = 1 indicates that Table 2 and 3 Standard Model quarks components obey probability = 1. Energy components emerge from P = 1 and E = 0 as mass plus kinetic energy and field energy. The neutron and proton are manifestations of information transitions from N = 90 with H, Z and W+/− intermediaries. This satisfies one of the criteria for a unified theory. The N value for the quark strong field is N = 2 higher than quark mass N (for each of 3 quarks). Whole numbers, the fraction 1 3 + ln ( 3 e ) = 1 3 + 0.0986 = 0.432 appear extensively.

Time and space are defined by a circle. Energy = h* frequency, also written as Et/H = 1. With C = r/t = 2.998e8 m/sec, it is also written r = h C / E where h = Planck’s reduced constant H 2 π = 6.582 E − 22   MeV ⋅ sec (Figure 1).

Figure 1. Space model.

E = gravitational field energy components from Table 3 = 0.69 + 0.69 + 0.69 + 0.740 = 2.801 MeV (6)

Mass and kinetic energy field values in Table 8 are from the proton mass model in Table 4. Published values for comparison are available [12]-[16].

Table 8.Neutron and proton model values for forces.

3.2.1. Strong Force

Combined Table 8 strong field

3.2.2. Electromagnetic Force

From Table 4, the electromagnetic force is the result of N = 3* 0.0986 = 0.296 being separated from the N = 10.432 − 0.296 = 10.136. This becomes the electron (N = 10.136 and energy = 0.511 MeV). The electromagnetic energy of the field E = e 0 ∗ exp ( 0.296 ) = 27.217 e − 6   MeV . This is the published value for the electromagnetic field [3]. During decay, the electromagnetic energy is separated into 0 = 2.72e−5 − 2.72e−5. This is the basis of opposite charges.

The permittivity constant e' (e prime) governs electromagnetism (including charge and the electrical field). Calculation of e' is below but shielding effects from the complicated electron orbitals are not included.

This compares favorably with PDG [3] published value 8.854e−12 N/m².

3.2.3. Residual Strong Interaction (AKA the Weak Force)

Energy with value 2*−10.15 = −20.30 MeV is missing in each proton and neutron simulated in Table 4. Three quarks form a bundle with kinetic energy 10.15 MeV orbiting in field energy 20.30 MeV. This embeds the mass 928.12 MeV in a 20.30 MeV field with 10.15 MeV of kinetic energy and determines a radius of 1.43e−15 meters (the radius of the atomic nucleus). This is not new to physics, but the origin of energy 10.15 MEV/nucleon is new.

3.2.4. Gravity

The Planck scale is currently associated with the gravitational constant. Literature reviewed below [16] reviews the Planck scale.

There is a mass on the left side of Table 4 related to the Planck scale Compton mass.

But we use G at the scale of protons. With r = 7.01448e−14 = hC/2.8011, the equation 21 hC equality can be be substituted into Equation (18).

Equation (22) is equivalent to equation 18 but based on proton scale masses and Table 4 values. The value 2.801/exp(90) weakens the gravitational field and force. More can be learned about the effect of exp(90) on gravity by studying orbits.

The column labelled cell radius is defined by Equation (7) that gives the circle r = hC/2.801 This radius varies with kinetic energy (ke). The derivation below is based on G remaining constant.

The column labelled Orbital R and conventional R = GM/V² agree down through Table 9. The equation below yields R with cell radius r multiplied by exp(90) and a mass ratio.

Table 9. Effect or exp(90) on orbits.

Fnew = (2.801/EXP(90)*ke/r)/(Mcen/2.49E+51)/10.15*938.27/130*1.602e−13.

The force of gravity is calculated two ways and compared with the inertial force, F_i. The new force equation is on the right. It agrees with F = GMm/R² for all orbits.

This equation can be understood as follows. Force is proportional to gravitational field E = 2.801/exp(90) MeV, increases with inertial kinetic energy ke and further increases with small cell radius r. The multiplier (central mass M/mass of universe) is the same multiplier used to determine orbital radius R from cell radius r. E/exp(90) weakens the gravitational field and force.

In topic 3.3 entitled “Expansion models”, kinetic energy/proton = 10.15 MeV from Table 4. This is the initial kinetic energy/proton for expansion and the velocity of each proton on radius small r is below lightspeed. There is potential tension between radius r that describes space expanding at C in the straight-line expansion model and r*exp(90) that describes gravity below C.

This is resolved with force equalities based on values that compares orbits for extreme conditions. Table 9 line 5 is for a central mass equal to the universe and line 7 is for a central mass of one proton. In line 5 cell size r = 7.045e−14 m for 10.15 MeV ke but based on exp(180) protons, the orbital radius R = 8.59e25 m. If a proton orbits another proton at radius 7.045e−14 meters, ke/proton = 10.15/exp(90) MeV.

The force on the orbiting proton in line 6 is calculated four ways:

The value 10.15 MeV/proton in Line 5 of Table 9 agrees with kinetic energy being converted to potential energy during expansion in Table 10.

3.2.5. Comparison of Gravity with the Other Forces

One of the un-resolved questions in physics [Wiki] is the difference between gravity and the three fields in Quantum Field Theory (QFT). According to Table 3 gravitation field energy = 2.801 MeV. The main difference between gravity and the other forces is that orbital radius R is large and force is low because 2.801/exp(90) MeV/proton. The bottom line of Table 8 shows that field energy causes curvature for all four forces with the equation r = hC/E and F = E/r is universal.

General relativity is the curvature of space. “Mass tells space how to curve and curvature tells mass how to move”. Table 9 equations indicate that a cell of radius small r is curved by

Curvature is caused by field energy r = hC/(2.801/exp(90)). It is enlarged by M_central and low kinetic energy.

This represents a step toward the goal of uniting gravity with the other forces. Gravity has gravitational field energy like the other three Quantum Field Theory field energies, and it appears that the energy experiences a quantum shift from 2.801 to 2.801/exp(90).

Physicists say that physics breaks down at a “big bang” singularity. Many believe that there was an early brief period of expansion called inflation. It was proposed to keep different areas uniform that are more than C away from one another. But new maps show huge voids and non-uniformities. The Lambda Cold Dark Matter (LCDM) expansion model was used by WMAP and PLANCK missions [17]-[22]. It is based on the Friedmann equation which expands space as r' = r(time'/time)^2/3.

3.3.1. A Probabilistic Argument for the Initial Number of Neutrons in Nature

Overall, the N values of the left-hand side neutron components of Table 2 equal 90. Written as a probability p = 1/exp(90). The equal but opposite left-hand side components are also p = 1/exp(90). They occur at the same time, multiplying the probability to 1/exp(180). To re-establish P = 1, there must be a vast number of particles. Specifically,

3.3.2. Straight-Line Expansion Model

In three dimensions, exp(180/3) scales equation 7 small r to large R = r*exp(60) meters. Each small circle (sphere) is expanding. A neutron with kinetic energy of 10.15 MeV is positioned on small circle radius r and travels around the circle with initial velocity 0.145*C.

The straight-line model [23][24] simulates time across the expansion radius in increments of time = 1.47e−21/(2pi)) = 2.35e−22 seconds. Large R expands outward at lightspeed since C = R/T = 2pi*R/(2pi*T). After neutron duplication an exponential (exp(N)) relationship is useful with

Table 10. Straight-line expansion.

The column on the left of Table 10 contains values for the beginning of expansion. The beginning is high temperature and nucleons are primarily neutrons that decay to protons plus 1.293 MeV. The initial gravitation force resisting expansion derived in Table 8 (3.76e−38 N) decreases as expansion occurs and potential energy increases according to integral F*dr. Potential energy increase.

The column of the right side of Table 10 contains current values. The model is zero net energy with KE + PE = 20.3 MeV.

This produces expansion that is compared with the LCDM model in Figure 2.

The current radius is determined by the Cephid variables [20] Hubble constant, H0 = 2.375e−18/sec (equal = 1/4.21e17 sec).

WMAP and PLANCK [18][19][22] mission analysis was based on the Lambda Cold Dark Matter (LCDM) expansion model. Figure 2 compares the two expansion models (Table 11).

Figure 2.Comparison of expansion models.

Table 11. Energy history/proton.

1) The straight-line expansion model are close to the WMAP [19] values for age (13.4 billion years) and radius (1.26e26 meters).

2) The concept of critical density is not supported in straight-line expansion. Velocity of a proton on the radius of the small circle model (Figure 1) is tangential to the surface, not perpendicular like LCDM cosmology. Thermodynamic pressure causes expansion in the straight-line model [25].

3) The straight-line expansion model can be applied to troubling observations. James Webb telescope observations shows fully formed galaxies well before they are predicted. Early black holes and red spots have been observed. The author studied and documented details of straight-line expansion [26]-[29]. It is possible that matter is pushed into Zel’dovich pancakes [30] by early perturbations in normal matter and is now observed as the cosmic web. A particle without kinetic energy is shown on the left side of Table 3 that aids black holes formation [28]. It is a neutron without kinetic energy (130.163 MeV) that according to the Jeans criteria cannot resist accumulation. This mass is also found in gravitational theory above in equation 19. Early formation of galaxies is promoted by relatively high densities [29] in the straight-line model.

4) WMAP documents presented cosmology parameters for their belief that an acoustic wave was responsible for the Cosmic Microwave Background (CMB) spot they measured as 0.0104 radians [18]. This spot in the straight-line model is the size of the galaxy clusters in the cosmic web [30].

5) The straight-line model is energy based. Initial KE = 10.15 MeV/proton. Expansion reduces kinetic energy triggering primordial nucleosynthesis at KE = 0.111 MeV adding fusion energy 7.07 * 0.29 = 2.03 MeV/proton.

Table 4 contains values that allow binding energy to be accurately predicted. The familiar E = const*exp(N) equation is applicable with a different pre-exponential. Binding energy was simulated with this probability-based approach [17]. Binding energy release is the weighted contribution from the protons and neutrons.

Li7 has 3 protons and 4 neutrons.

B E = 10.15 ∗ exp ( − 2 3 ) ∗ 3 + 10.15 ∗ exp ( − 2 4 ) ∗ 4 7 = 5.75   MeV minus retained energy = 0.087 = 5.664 MeV (NIST [4] = 5.664 MeV).

The protons retain energy due to electrostatic repulsion. The binding energy curve for all Atomic numbers is in Figure 3 with the asymptote 10.15 MeV [17].

Figure 3. Binding energy for neutron and proton.

The decay of a neutron to a proton is shown in the Table 2 and Table 3 models. The decay energy balance from a neutron to a proton is: 939.465 − 0.740 − 0.622 = 938.272 MeV.

The value 0.622 - 0.111 where 0.511 MeV is the electron and 0.111 is kinetic energy.

KE = 0.111 MeV is found in two important processes. During early expansion, kinetic energy/proton decreases from the initial value 10.15 MeV. When it reaches 0.111 MeV, primordial nucleosynthesis [18]-[20] is triggered, and free neutrons readily combine into He4. The second process that involves this value is fusion in stars [21]. Barrier energy 0.111 MeV must be provided before fusion can occur.

The author studied mesons, baryons, baryon resonance, their decay times, and properties [5][6]. Fitting data with fundamental particle values gave a tentative understanding of these transient particles. They are combinations of proton model components and kinetic energy that decay rapidly.

Decay time is related to a particle with kinetic energy circling once and then starting its decay if its wave function is unbalanced (Breit-Wigner theory [Wiki]). Mass m is the mass of the meson or baryon.

But there are several exceptions, for example the muon, pion, neutron and proton. Study [6] shows that circle time is modified by N, which slows the decay. Data for the bare neutron lifetime = 879.6 seconds [Wiki] and N = 13.431*3 + 17.431 = 57.73 slows the decay by exp(57.73).

With the equation E = 2.02e−5*exp(N), the proton model indicates that there are two levels to nature 1) an energy level and 2) a correlated information level. Each particle in our body contains information. Nature is mathematical and one can speculate that life uses the information level [31]. The ratio p/P compares an observation to a known reference. Our brains could have probability-based memory, perceptions, and thoughts like letters in the alphabet that represent learned words.

There is a difference between N for energy and S for thermodynamics. N is a fixed information value (code) and interacts in discrete quantities like quantum mechanics. There is a similarity between N and DNA information codes that keep the body and brain intact even though underlying chemical processes obey thermodynamic S. We know that the DNA code evolved but we do not know the origin of the pattern of N values in Table 2 and Table 3.