User:Korablino/Fine structure constant α derived from π and natural logarithm base e
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Fine structure constant α derived from π and natural logarithm base e
Mikhail Vlasov <redact>
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. [1])
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) [2]. 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]
References[edit]
- ^ Duff, Michael J., M-Theory (the Theory Formerly Known as Strings), International Journal of Modern Physics A, 11 (1996) 5623–5642, online at Cornell University's arXiv ePrint server
- ^ http://en.wikipedia.org/wiki/Fine_structure
External links[edit]