I thank you very much for taking the time to explain this to me. I generally only learn things when the come in a form that interests me (f.e. is there design or not). Math did only find a way in my head when I got interested in economics.
What was the violation of the rule? That antimatter decays slower or something like that?
Something like that. It's hard to describe easily, but in the case of the neutral kaon, it was found that it lived longer than expected. The crucial experiment was done by
Fitch and Cronin.
Is there a theoretical explanation why this violation exist?
There is. It depends on the fact that there are 6 flavors of quark: 3 'families' of two quarks each.
up and down
charm and strange
top and bottom
The names are just convenient labels, although the strange quark was named because it was something of another surprise.
When a strange quark decays, it might be the case that it always turns into a down. And every charm quark always decays into a top. But that's not the case. The three families 'mix together' when they decay with different probabilities. If you assemble all the probabilities of one family decaying into another, that builds up a 3x3 matrix of possibilities, the
Kobayashi-Maskawa Matrix.
If the 3x3 matrix has all real values, then CP is conserved.
But if there are complex values, then CP is violated (since this is quantum mechanics, complex numbers enter into the picture).
So this is the theoretical basis for CP violation. It might be the case that the actual numbers are all real and CP is not violated, but when we measure them experimentally, we find that some of them are indeed imaginary, so experimentally, we determine that CP is violated. CP violation is *allowed* by theory, but it takes the experiment to verify whether it actually is or not.