Highly Accurate Relations between the Fine Structure Constant and Particle Masses, with Application to Its Cosmological Measurement

Abstract

Highly accurate algebraic relations between the fine structure constant a and a wide range of particle masses are given, ranging from Δ a/a = (2.1 ± 0.1)×10 -7 to Δ a/a = (-2.7 ± 0.3 ± 0.6)×10 -8 , and with a very large standard deviation, ranging to Δ a/a = -5.5×10 -9 . The analysis is based on empirical relations that exist among some particle masses, and also on several theoretical assumptions, of which the most significant is that the electromagnetic contribution to the electron’s mass is finite, and given by f am eb , where f is a dimensionless parameter that is shown to be equal to 1.032409810 (63), and where m eb is the electron’s “bare mass.” The relations for a and f are homogeneous degree zero in the particle masses. The relations for f in terms of particle masses are found by trial and error. A quadratic equation is given relating a to f and m e / m p . This equation is used in the application to cosmological measurements of a , and , where it is shown that, to a few percent accuracy, δ a/a ≈ - δ μ/μ . This relation can serve to test the validity of measurements of a and μ .