Comments to Lucretius: "I appreciate your edits and comments on the Fine-structure constant. About your latest addition,
'The fine structure constant so intrigued the physicist Wolfgang Pauli that he even collaborated with the psychologist Carl Jung in an extraordinary quest to understand its significance.[24]'
You might be interested to know that the formula discussed in the reference was previously found by Stanbury, and is slightly modified by Sherbon with a "coherent" physical model to support it."
Sherbon, Michael A. "Constants of Nature from the Dynamics of Time" SSRN Classics: Journal of Philosophical & Scientific Texts (November 6, 2008) Available at SSRN: abstract=1296854.
Citations:
Várlaki, P. & Rudas, I.J. "Twin Concept of Fine Structure Constant as the ‘Self Number-Archetype’ in Perspective of the Pauli-Jung Correspondence; Part I: Observation, Identification and Interpretation," Acta Polytechnica Hungarica, 6, 2, 77-108 (2009).
Várlaki, P., Fullér, R. & Rudas, I. "Fine Structure Constant - A Possibilistic Approach," in Rudas, I. Fodor, J. & Kacprzyk, J. eds. Towards Intelligent Engineering and Information Technology, Hungary: Springer-Verlag, 2009, pp.665-679.
Neumann, G. "Deciphering the Cosmic Number: The Strange Friendship of Wolfgang Pauli and Carl Jung by Arthur I. Miller," The Mathematical Intelligencer, 33, 1, 105-107 (2011).
Also relevant:
1/α ≈ 157 − 337ρ/7 ≈ 137.035 999 168, having three prime numbers with the prime constant ρ ≈ 0.414 682 509 851 111.
Sherbon, M.A. "Wolfgang Pauli and the Fine-Structure Constant," Journal of Science, Vol. 2, No. 3, pp.148-154 (2012) SSRN: abstract=2147980.
Latest experimental-QED determination of the fine structure constant:
Aoyama, T., Hayakawa, M., Kinoshita, T. & Nio, M. "Tenth-Order QED Contribution to the Electron g-2 and an Improved Value of the Fine Structure Constant," Physical Review Letters, 109, 111807 (2012) arXiv:1205.5368v2. "This Letter presents the complete QED contribution to the electron g-2 up to the tenth order. With the help of the automatic code generator, we evaluate all 12 672 diagrams of the tenth-order diagrams and obtain ... The improved value of the fine-structure constant 1/α = 137.035 999 173 (35) [0.25 ppb] is also derived from the theory and measurement of ae."