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One of the unsolved problems of physics relates to why the physical constants have the values they have. Did they have to be this way for everything to work out right, or are some of them just random chance?

One specific version of this problem concerns a number called alpha. Alpha is the square of the charge of the electron, divided by the product of the speed of light and Planck's constant. All the units of these terms cancel out, leaving a dimensionless constant with a value slightly more than 137. Why not exactly 137? Why not some other number entirely? Nobody knows.