Compactly Approximating The Fine Structure Constant

The website vixra.org is a completely non-selective pre-print service for amateur physicists, most of which, to be perfectly honest, is crackpot material. A recent paper there, however, caught my eye because its claim is unambitious, unambiguously proven, and cute.

The author of the one page paper simply proposes a simple formula to approximate one divided by the Fine Structure Constant that matches its true value to two parts per billion precision (in fact, the actual precision is four parts per billion).

In standard deviations of statistical uncertainty of the experimental value, it isn't really even close - it is sixteen sigma from the measured value. The experimentally measured value of the Fine Structure Constant, according to the Particle Data Group, is actually:

1/137.035 999 084(21).

But, it is still a lot better than the three or six significant digit approximations often used in practice when greater precision isn't necessary.

The author, Roger N. Weller, doesn't claim that it has any theoretical foundation. 

It is simply a cute and compact way to approximate this physical constant to a 4 parts per billion precision (the claim is two parts per billion, but the measured value is out of date), mostly utilizing the base ten numbers 1, 2, 7 and 9 and various combinations.

I dedicate this post to the late Marni Dee Sheppeard, a theoretical physicists and Internet friend of mine, whose relic blog I link to, who would have really appreciated this formula. Some of her PhD informed theoretical physics work leaned heavily on combinations of 2, 7 and 9 in the the fundamental structure of Nature (see, e.g. here).