Solution for the Interpretation Problems Regarding Empirical Equations for Calculating the Cosmic Microwave Background Temperature

Abstract

We build upon previously proposed empirical equations involving the cosmic microwave background (CMB) temperature and extend the approach to include an empirical formulation for the fine-structure constant. To ensure consistency across these relationships, revised values for the CMB temperature ( T c ) and the gravitational constant ( G ) were obtained. The recalculated gravitational constant, 6.68917534 × 10 − 11 m 3 ·kg − 1 ·s − 2 , remains marginally greater than the accepted value of 6.6743 × 10 − 11 . A recalculated CMB temperature of 2.7256307 K matched the observed value of 2.72548 ± 0.00057 K. We subsequently tried to validate Equation (12) independent of the MKSA unit system. However, interpretation problems occurred in our proof. In this report, we propose a correct proof for Equation (12) with an explanation for the relationship between macroscopic units and microscopic units. Furthermore, using our algorithms, we can explain the relationships among the various units within and outside the MKSA unit system.