If the proton radius is truly fundamental, S and P states of hydrogen should show the same kind of shifts for hydrogen that has the muon instead of the electron. A very interesting experiment measures the diameter of the proton by means of the spectroscopy of the muon form of hydrogen and finds a much different shift in the frequency of muon hydrogen lines due to the finite diameter of the proton. The electron in the hydrogen S ground state has a certain probability of being at the proton surface but not inside the proton diameter and so the S state frequency shifts very slightly as a result. The electron in a P excited state on the other hand has no probability for being at the proton center and a very low probability of being at the proton surface as well.
The muon form of hydrogen is a hydrogen with a muon instead of an electron in orbit around the proton. The muon charge is the same as the electron, but the muon mass is 207 times that of hydrogen but decays very quickly with a lifetime of 2 microseconds. Even with a short lifetime, the quantum correction should yield the same proton radius for both electron as well as muon hydrogen. Instead, the proton radius is much different for muonic hydrogen as the figure shows.
There are other calculations that show the proton radius, but neither of them seems very realistic since they do not depend on the progressive perturbation of approximations that help define reality.
Each of the electron and muonic spectroscopy results are valid by mainsteam science and are determined within mutually exclusive uncertainties. There is therefore not a single proton radius and neither explanation is more valid than the other.
Thus, there is a dilemma. What is the real proton radius...0.8758 or 0.84087 fm? Both measurements of atomic hydrogen and muonic hydrogen appear to have sufficient precision to preclude each other.
One alternative explanation is in aethertime, where energy states also depend on lifetimes. In aethertime, incorporation of the muon lifetime shifts the observed of the muonic hydrogen to now agree with that of atomic hydrogen. The shift is
While in mainstream science, the lifetime of a muon state does not affect its energy, in aethertime, the lifetime of a state does indeed affect its energy if only very slightly.
Note that Gary Simpson has reported a quaternion calculation that shows a similar radius to muonic hydrogen, but far different from atomic hydrogen as the figure shows. Since no error measure was cited, it is not clear what this calculation means.
Note that Haramein has used microscopic black holes to predict the charge radius of the proton that agrees with the muon result, but there is no correct result and both results of electron and muon hydrogen are equally valid. The charge radius of the proton and electron are the same and are very different from the "hard" 1/e radius of the proton. The electron, you see, has no radius other than its charge radius.