Authors: J. S. Markovitch
The fine structure constant is shown to arise naturally in the course of altering the symmetry of two algebraic identities. Specifically, the symmetry of the identity M2 = M2 is "broken" by making the substitution M → M − y on its left side, and the substitution Mn → Mn − xp on its right side, where p equals the order of the identity; these substitutions convert the above identity into the equation (M − y)2 = M2 − x2. These same substitutions are also applied to the only slightly more complicated identity (M / N)3 + M2 = (M / N)3 + M2 to produce this second equation (M − y)3 / N3 + (M − y)2 = (M3 − x3) / N3 + M2 − x3. These two equations are then shown to share a mathematical property relating to dy/dx, where, on the second equation's right side this property helps define the special case (M3 − x3) / N3 + M2 − x3 = (103 − 0.13) / 33 + 102 − 0.13 = 137.036, which incorporates a value close to the experimental fine structure constant inverse.
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