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

Abstract

Previously, we presented several empirical equations using the temperature of the cosmic microwave background (CMB), which were simple and mathematically connected. Next, we proposed an empirical equation for the fine-structure constant. Considering the compatibility among these empirical equations, the values of the CMB temperature ( T c ) and the gravitational constant ( G ) were calculated to be 2.726312 K and 6.673778 × 10 -11 m 3 ⋅ kg -1 ⋅ s -2 , respectively. Then, for the values of the factors 9/2 and π in our equations, we used 4.48852 and 3.13201, respectively. Using the redefinition of Avogadro’s number and the Faraday constant, we explained that these values can be adjusted back to 9/2 and π. However, our arguments have become quite complex. Thus, we now attempt to simplify these empirical equations. We show that every equation can be explained in terms of the Compton length of an electron ( λ e ), the Compton length of a proton ( λ p ) and α .