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4. A Note on the Fine Structure Constant

 
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A Note on the Fine Structure Constant (1970)
            The electromagnetic coupling constant (img) is the (velocity) amplitude for an electron to emit or absorb a photon. The square of this number is the fine structure constant.  It was first observed in the analysis of the emission of two different photons from a hydrogen atom where the photons had almost the same energy.  The difference in energy resulted from the electron having one direction of spin for one emission and another direction for the other.  Thus, the name “fine structure” was given.  The fine structure constant, img, is a dimensionless number with a value equal to the square of the electromagnetic coupling constant, 0.007297352533 (27), i.e., it has been measured with an accuracy of 5-parts in a billion.  It is the orbital speed in speed of light units of an electron in the lowest energy state of a hydrogen atom.  The orbital analysis gives the fine structure constant as

img

Where img is the charge of the electron, img Planck’s constant, and c is the speed of light.  The constant is also the ratio of the electrostatic force to the nuclear force.  It is this latter interpretation which we were able later (some 35 years after this paper was published) to completely explain the fine structure constant.  The constant is most often given by its reciprocal 

img

            During our research at McDonnell Douglas we were working with a kinetic particle low density “gas”.  The gas, of course, has a Maxwell-Boltzmann distribution of speeds.  Thus, the root mean square speed and the mean speed certainly have great significance to the theory we were developing.  We, of course, had no idea how they might be related to our theory other than we thought one of the speeds would be related to the speed of light.  I was the supervisor of our group and I reported to Dr. Robert M. Wood.  Dr. Wood had us working on a numerical scheme from interrelating the various constants of physics.  I began studying various combinations of the background root mean square speed img and the mean speed img.  During these studies I tried the combination and since img this gave

(img) = 0.085401882.

I was unaware of the electromagnetic coupling constant so I was not aware of the closeness of this number to it.  But I squared the number—took the reciprocal and I obtained

img = 1/137.1087334

We all knew the number 137.1087334 was close to reciprocal of the fine structure constant.  The difference was one part in a thousand.
            We knew this ratio img was related in a significant way to the kinetic particle theory we were developing.  Dr. Darell B. Harmon, Jr. almost immediately realized that the number we obtained had to be corrected for the center of mass system used in the electron orbit analysis and this gave us a value correct to one part in 100,000.  It was many years later that we discovered a possible mechanism causing the remaining 1 part in img error and this recently discovered mechanism might reduce the error to the measured error.  The three of us, Darell Harmon, Bob Wood, and I were excited about this discovery and we published this note.  I knew then that the universe absolutely had to be made up of kinetic particles.  There is no way that such meaningful parameters could be interrelated to give a number that was within 1 part in 100,000 of a measured parameter and not be of significance.  I believe if knowledgeable physicists reviewed our work in detail some of them would have thought we were on-the-right-track.