Normalization Methods in Algorithms for Empirical Equations in Terms of the Cosmic Microwave Background Temperature

Abstract

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 ( T c ) and gravitational constant ( G ) were calculated to be 2.726312 K and 6.673778 × 10 − 11 m 3 ∙kg − 1 ∙s − 2 , respectively. Every equation can be explained numerically in terms of the Compton length of an electron ( λ e ), the Compton length of a proton ( λ p ) and α . After several trials, we describe the algorithms used to explain these equations. Thus, no dimension mismatch problems were observed. In this report, we describe the normalization methods in our algorithms used to explain these equations in detail. Our redefinition method is a part of the normalization in the algorithms. Furthermore, the definitions of the gravitational constant are discussed.