Another example is the difference in mass between the proton and the neutron, which turns out to be perfect. A difference other than .2% would have resulted only in neutrons, and therefore no protons and no atoms.
Continuing, the amount of matter compared to anti-matter in the first fraction of a second after the Big Bang was such that in spite of massive annihilations the universe ended up matter and not antimatter.
A very good example of a coincidence that is too good to be true, and therefore a candidate for future physics principles, is the fine-structure constant. It has many meanings or definitions; it is known to incredible accuracy; but it remains an enigma to physicists.
According to the highly regarded Richard Feynman, "Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man."
Physically it shows up many places, for example it characterizes the strength of the electromagnetic interaction. It is also the square of the ratio of the electron charge to the Planck charge, which is physics lingo for the size of the smallest quantum.
It is further of interest because its expression contains several other fundamental constants, such as the electrons charge, the Planck constant, the speed of light and the electric constant. The universe is very sensitive to its value, since as little as a 4% change would stifle the stellar fusion that produces carbon.
You can be certain of one thing. The first person to develop a theory that yields the fine-structure constant will definitely get the Nobel Prize.
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