The fine-structure constant is a seemingly random number with no units or dimensions, which has cropped up in so many places in physics, and seems to control one of the most fundamental interactions in the universe.
had a constant, called G, that represents the fundamental strength of the gravitational interaction. The speed of light, c, tells us about the relationship between electric and magnetic fields. The spring constant, k, tells us how stiff a particular spring is. And so on.
But that's not true for the fine-structure constant. You can have whatever unit system you want and whatever method of organizing the universe as you wish, and that number will be precisely the same. Change that number, change the universe. If the fine-structure constant had a different value, then atoms would have different sizes, chemistry would completely change and nuclear reactions would be altered. Life as we know it would be outright impossible if the fine-structure constant had even a slightly different value.
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