Ratio of Gravitational Force to Electric Force from Empirical Equations in Terms of the Cosmic Microwave Background Temperature

Previously, we presented several empirical equations using the cosmic microwave background (CMB) temperature. Next, we propose an empirical equation for the fine-structure constant. Considering the compatibility among these empirical equations, the CMB temperature (Tc) and gravitational constant (G) were calculated to be 2.726312 K and 6.673778 × 10−11 m3∙kg−1∙s−2, respectively. Every equation could be explained in terms of the Compton length of an electron (λe), the Compton length of a proton (λp) and a. Furthermore, every equation could also be explained in terms of Avogadro’s number and the number of electrons in 1 C. However, the ratio of the gravitational force to the electric force cannot be uniquely determined when the unit of the Planck constant (Js) is changed. In this study, we showed that every equation can be described in terms of Planck constant. From the assumption of minimum mass, the ratio of gravitational force to electric force could be elucidated.

Correspondence Principle for Empirical Equations in Terms of the Cosmic Microwave Background Temperature with Solid-State Ionics

Previously, we presented several empirical equations using the cosmic microwave background (CMB) temperature that were mathematically connected. Next, we proposed an empirical equation for the fine-structure constant. Considering the compatibility among these empirical equations, the CMB temperature (Tc) and gravitational constant (G) were calculated to be 2.726312 K and 6.673778 × 10-11 m3·kg-1·s-2, respectively. Every equation can be explained in terms of the Compton length of an electron (λe), the Compton length of a proton (λp) and α. However, these equations are difficult to follow. Using the correspondence principle with the thermodynamic principles in solid-state ionics, we propose a canonical ensemble to explain these equations in this report. For this purpose, we show that every equation can be explained in terms of Avogadro’s number and the number of electrons in 1 C.

A Fine-Structure Constant Can Be Explained Using the Electrochemical Method

We proposed an empirical equation for a fine-structure constant: . Then, . where mp and me are the rest mass of a proton and the rest mass of an electron, respectively. In this report, using the electrochemical method, we proposed an equivalent circuit. Then, we proposed a refined version of our own old empirical equations about the electromagnetic force and gravity. Regarding the factors of 9/2 and π, we used 3.132011447 and 4.488519503, respectively. The calculated values of Tc and G are 2.726312 K and 6.673778 × 10-11 (m3⋅kg-1⋅s-2).

Explanation of the Necessity of the Empirical Equations That Relate the Gravitational Constant and the Temperature of the CMB

In previous papers, we proposed an empirical equation for the fine-structure constant. Using this equation, we proposed a refined version of our own former empirical equations about the electromagnetic force and gravity in terms of the temperature of the cosmic microwave background. The calculated values of the temperature of the cosmic microwave background (Tc) and the gravitational constant (G) were 2.726312 K and 6.673778 × 10-11 m3⋅kg-1⋅ s-2, respectively. Then, for the values of the factors 9/2 and π in our equations, we used 4.488519503 and 3.132011447, respectively. However, we could not provide a theoretical explanation for the necessity of these empirical equations. In this paper, using the redefinition method for the UNIT, we show the necessity for our empirical equations.

Bell’s Non-Locality Theorem Can Be Understood in Terms of Classical Thermodynamics

Bell’s non-locality theorem can be understood in terms of classical thermodynamics, which is already considered to be a complete field. However, inconsistencies in classical thermodynamics have been discovered in the area of solid-oxide fuel cells (SOFCs). The use of samarium-doped ceria electrolytes in SOFCs lowers the open-circuit voltage (OCV) to less than the Nernst voltage. This low OCV has been explained by Wagner’s equation, which is based on chemical equilibrium theory. However, Wagner’s equation is insufficient to explain the low OCV, which should be explained by fluctuation and dissipation theorems. Considering the separation of the Boltzmann distribution and Maxwell’s demon, only carrier species with sufficient energy to overcome the activation energy can contribute to current conduction, as determined by incorporating different constants into the definitions of the chemical and electrical potentials. Then, an energy loss equal to the activation energy will occur because of the interactions between ions and electrons. This energy loss means that an additional thermodynamic law based on an advanced model of Maxwell’s demon is needed. In this report, the zero-point energy can be explained by this additional ther-modynamic law, as can Bell’s non-locality theorem.

Erratum to “Empirical Equation for the Gravitational Constant with a Reasonable Temperature” [Journal of Modern Physics 11 (2020) 1180-1192]

The original online version of this article (Miyashita, T. (2020) Empirical Equation for the Gravitational Constant with a Reasonable Temperature. Journal of Modern Physics, 11, 1180-1192. https://dx.doi.org/10.4236/jmp.2020.118074) unfortunately contains the very important mistakes. The calculated temperature was 2.7195 K, which is similar to the temperature of the cosmic microwave background 2.7254 K.

Erratum to “Various Empirical Equations to Unify between the Gravitational Force and the Electromagnetic Force” [Journal of Modern Physics 12 (2021) 859-869]

The original online version of this article (Miyashita, T. (2021) Various Empirical Equations to Unify between the Gravitational Force and the Electromagnetic Force, Journal of Modern Physics, Vol. 12, 859-869. https://doi.org/10.4236/jmp.2021.127054) unfortunately contains the very important mistakes. The author discovered the possible problem in Equation (26) shown in Appendix. To fix the problem, the author wishes to change Equation (2) and make it more accurate.

Empirical Relation of the Fine-Structure Constant with the Transference Number Concept

The fine-structure constant of 1/137 is puzzling and has never been fully explained. When the interaction coefficient is 1/137, the transference number should be 136/137. With the transference number concept, we noticed that we must examine the constant of 1/136 instead of 1/137 to discover an empirical relationship in which the fine-structure constant is related to the mass ratio of electrons and quarks. Then, the physical meaning of this empirical relationship is discussed.

Empirical Equation for the Gravitational Constant with a Reasonable Temperature

Ted Jacobson discovered that gravity was related to thermodynamics. However, the calculated temperature using the Boltzmann area entropy is still not reasonable. We searched and discovered an empirical equation for the gravitational constant with a reasonable temperature. The calculated value was 3.20 K, which is similar to the temperature of the cosmic microwave background of 2.73 K. Then, we examined Yasuo Katayama’s theory. For this purpose, we introduced the modified Wagner’s equation, which is compatible with Jarzynski equality. Finally, using Ted Jacobson’s theory, we proposed our theory of gravity with the Gibbs volume entropy.

Various Empirical Equations to Unify between the Gravitational Force and the Electromagnetic Force

Previously, we proposed several empirical equations to describe the relationship between an electromagnetic force and the temperature of the cosmic microwave background (CMB).We attempted to justify why our empirical equations cannot be coincidental from the mathematical connections between our three equations. However, there are small errors in our empirical equations, which may lead to “indeed or not” arguments. After evaluating our equations, we discovered a method to improve the accuracy of the numerical calculations. For the value of the CMB, we used 2.72642 K instead of 2.72548 K. Regarding the factor of 9/2, we used 4.48870 instead of 4.5. Regarding the factor of π, we used 3.13189 instead of 3.14159. Then, the error becomes less than 10-5. This means that our equations cannot be coincidental. Furthermore, we attempt to provide hints on how to construct the background theory.

A Twenty-Year Follow-up Case Study of an Office Worker Who Returned to Work despite Serious Memory Disorder Caused by Herpes Encephalitis

This study followed a 52-year-old male patient, who had suffered from severe impairment in recent memory due to se- quelae of herpes encephalitis, for 20 years. He returned to his highly intellectual work and performed well despite his doctor’s prediction. While the patient showed consistently poor results on various neuropsychological memory tests, he demonstrated incredible performance at work. This case exemplifies an extreme case that declarative memory is formed with the support of semantic memory, procedural memory, and his strong interests. Additionally, it offers lessons that results on memory tests do not necessarily correspond to the actual level of competence. The focal sites were found on both sides of the medial temporal lobe, predominantly on the left side. The T2-weighted magnetic resonance images (MRI) obtained 9 years after the onset confirmed widespread damage to the left brain including parahippocampal gyrus, hippocampus, spindle gyrus, and amygdaloid complex, with microlesions extending from the right parahippocampal gyrus to its antero-interior rim. However, the damage to hippocampus was presumed to be minor.

Various Empirical Equations for the Electromagnetic Force in Terms of the Cosmic Microwave Background Temperature

Previously, we proposed an empirical equation describing the relationship between the gravitational force and the temperature of the cosmic microwave background (CMB). After evaluating our equation, we discovered many empirical equations describing the electromagnetic force in terms of the CMB, including equations for the Rydberg constant, the Bohr radius, the Compton wavelength, the classical electron radius, the Hartree energy, the Coulomb’s law with distance, and the ratio between the gravitational force and electric force. The background theory is not yet complete. However, we can justify why the discovered empirical equations should not be coincidence.

Empirical Equation for a Fine-Structure Constant with Very High Accuracy

We proposed several empirical equations about the electromagnetic force and gravity. The main three equations were connected mathematically. However, these equations have small errors of approximately 10-3. Therefore, we attempted to improve the accuracy. Regarding the factors of 9/2 and π, we used 4.48870 and 3.13189, respectively. Then, the errors become smaller than 10-5. However, we could not show any reasons for these compensations. We noticed the following equations. , . Then, we can explain the von Klitzing constant Rk=3.131777037×4.488855463×13.5×136.0113077. It is well known that the von Klitzing constant can be measured with very high accuracy. We examined this equation for the von Klitzing constant in detail. Then, we noticed that 136.0113 should be uniquely determined. The von Klitzing constant is highly related to the fine-structure constant. After the examination of the numerical connections, we can explain the value of 137.035999081 as a fine-structure constant with very high accuracy. Then, we attempt to explain this value from Wagner’s equation.