The fine-structure constant is dimensionless, so it appears to denote a relationship between similar things. The obvious places to look would be in relative sizes of spheres and circles. However, to this date, no-one has been able to find a geometric relationship that would yield this number.
One possibility for this may be that things are not completely circular at the subatomic level. The constant may indicate an imperfection. Perhaps the same imperfection that yields gravity and the difference in size between the proton and the electron.
Things may be ellipsoids rather than spheres at the subatomic level. This is after all the way things are at the macro level, so why not also at the subatomic?
Whatever it is, one thing is certain. Whoever finds a simple geometric explanation for the fine-structure constant should be first in line for a Nobel Price in physics.
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