**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 *M*^{2} = *M*^{2} is "broken" by making the
substitution *M* → *M* − *y* on its left side, and the
substitution *M*^{n} → *M*^{n} − *x*^{p} on
its right side, where *p* equals the order of the identity; these substitutions convert the above identity into
the equation (*M* − *y*)^{2} = *M*^{2} − *x*^{2}. These same
substitutions are also applied to the only slightly more complicated
identity (*M* / *N*)^{3} + *M*^{2} = (*M* / *N*)^{3} + *M*^{2} to
produce this second
equation (*M* − *y*)^{3} / *N*^{3} + (*M* − *y*)^{2} =
(*M*^{3} − *x*^{3}) / *N*^{3} + *M*^{2} − *x*^{3}.
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 (*M*^{3} − *x*^{3}) / *N*^{3} + *M*^{2} −
*x*^{3} = (10^{3} − 0.1^{3}) / 3^{3} + 10^{2} − 0.1^{3} = 137.036,
which incorporates a value close to the experimental fine structure constant inverse.

**Comments:** 4 Pages.

**Download:** **PDF**

[v1] 8 Feb 2011

[v2] 14 May 2011

[v3] 14 Oct 2011

[v4] 2012-02-29 14:27:18

**Unique-IP document downloads:** 148 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful. *