User:Korablino/Fine structure constant α derived from π and natural logarithm base e

Fine structure constant α derived from π and natural logarithm base e

Mikhail Vlasov

Fine structure constant α is linked with constant π, natural logarithm base e and natural number 138 by next equation :

'''α = sinc(1-(1/π)×tanh(π/138)),                       [1] where sinc(x) = (sin(πx))/πx,            normalized sinc function tanh(x)=(e^x-e^(-x))/(e^x+e^(-x)), hyperbolic tangent function 138 = 2*3*23,                      represents electric field quanta - number of electric field states where multiplicand 2  represents positive and negative electric charge, multiplicand 3  represents number of electric charge values 1/3, 2/3, 1, multiplicand 23 is hypothetically (Mikhail Vlasov) related to the strings of the M-theory (Duff,Michael J. ) which are 1-dimensional slices of a 2-dimensional membrane vibrating in 11-dimensional space. As illustration, product (1+x)^11×(1+x)^11 contains 23 additives.

The equation [1] exhibits a discrepancy less than 2×10^(-8) in respect to the 2006 CODATA value for the fine structure constant. The discrepancy is attributed mostly to calculation tools. The approximation error is still worse than that of James Gilson’s 3×10^(-11). Nevertheless, equation [1] contains explainable natural number 138 unlike prime numbers 137 and 29 used in Gilson’s equation.

Other equivalent forms of the equation [1] for the fine structure constant reciprocal are

α^(-1) = (π-tanh(π/138))/sin(π-tanh(π/138))                 [2]

α^(-1) = (π-tanh(π/138))/sin(tanh(π/138)) ≅ 137.0357±0.0003        [3]