This is not a duplicate, I am not asking whether the proton is a stable particle, or why it is. I am asking about the definition of stability/decay whether it is boolean or not.
I have read this question:
where John Rennie says:
There isn't a potential barrier in beta decay, whether it's beta minus or beta plus decay. In both cases the decay is slow simply because the transition probability is so slow.
and where Emilio Pisanty says in a comment:
Stability is a boolean variable, in QM as well as anywhere. If the system is in an unstable state, then it's in an unstable state, period.
There must be a misunderstanding, because beta minus decay happens, because in QM, it is all about probabilities. In this case, it happens slowly. But the proton rich nucleus is unstable.
Now if the proton rich nucleus is unstable, and it is all about just probabilities as per QM, then everything, every quantum system (composite) is unstable. Period.
One would say that there cannot exist a single quantum system, that would be stable infinitely. Even a stable atom (or a stable proton) will decay eventually. Since even the protons inside it have an average lifetime of 2.1*10^29 years.
The free proton (a proton not bound to nucleons or electrons) is a stable particle that has not been observed to break down spontaneously to other particles. The spontaneous decay of free protons has never been observed, and protons are therefore considered stable particles according to the Standard Model. However, some grand unified theories (GUTs) of particle physics predict that proton decay should take place with lifetimes between 10^31 to 10^36 years and experimental searches have established lower bounds on the mean lifetime of a proton for various assumed decay products. Experiments at the Super-Kamiokande detector in Japan gave lower limits for proton mean lifetime of 6.6×10^33 years for decay to an antimuon and a neutral pion, and 8.2×1033 years for decay to a positron and a neutral pion. Another experiment at the Sudbury Neutrino Observatory in Canada searched for gamma rays resulting from residual nuclei resulting from the decay of a proton from oxygen-16. This experiment was designed to detect decay to any product, and established a lower limit to a proton lifetime of 2.1×10^29 years.
Now the contradictions is where one says that anything that is a composite particle will eventually decay, does have a mean lifetime (even free protons according to GUT but not SM), but stability is a boolean variable.
If stability is a boolean, and everything (composite) does have a mean lifetime, then basically the definition of stability is the same as the definition of elementary vs non-elementary particles.
But here comes the contradiction, there are even elementary particles that are not stable, and some are stable.
Like the electron, is defined as a stable particle, but has a mean lifetime of 6.6*10^26 years.
There are elementary particles that spontaneously decay into less massive particles. An example is the muon, with a mean lifetime of 2.2×10^−6 seconds, which decays into an electron, a muon neutrino and an electron antineutrino. The electron, on the other hand, is thought to be stable on theoretical grounds: the electron is the least massive particle with non-zero electric charge, so its decay would violate charge conservation. The experimental lower bound for the electron's mean lifetime is 6.6×10^28 years, at a 90% confidence level.
So the muon is unstable, because we have observed muons to decay, but the electron is stable, because we have never observed one to decay, but the electron does have a mean lifetime, 6.6*10^28 years.
Even as per the SM, the contradiction is there. Do we only say that stability is boolean, because we have never observed the electron and proton (free) to decay, but we give them a mean lifetime?
As per QM, it is all about probabilities, and nothing lasts forever. Even the stable particles ( electron and the proton) will have a mean lifetime.
Does QM probabilities win or does the SM stability (boolean) definition win?
Is stability a boolean, that is, are we defining stability as the particles that have never been observed to decay (electron and free proton), and are we defining unstable the particles that have been already observed to decay?
Or are we saying that QM is all about probabilities, and even the stable particles (electron, proton) do have a mean lifetime and will eventually decay?