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

Abstract

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 ( 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 in terms of the Compton length of an electron ( λ e ), the Compton length of a proton ( λ p ) 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.