There aren’t any small or large protons, just protons nor is there any exotic hydrogen or exotic deuterium, they’re perfectly ordinary. Their properties are perfectly well described by the Standard Model and don’t provoke fluctuations of spacetime, that would require appealing to effects of quantum gravity.

Stam Nicolis You say "There are no small or large protons" I also tell you the same thing but on condition that you refer to the current theories of physics. But I think only a few people have understood that things have changed since 2010 with the emergence of Randolph Pohl's team experiments in muonic hydrogen and deuterium. My two articles that give my own explanation of this team's results are mentioned on RG.I explained that the team "artificially" reduced the proton radius 0.8758fm (accurate measurement before 2010) using muons and obtained finally 0.8409fm (from muon hydrogen) and 0.836fm (from muon deuterium). That's all they did. I find that their experiments since 2010 using muons have nothing to do with the subject of a more accurate measurement of the proton. The radius of the proton is already very precise before 2010 with its value of 0.8758fm. I gave the value 0.87564fm which is closely related to 0.8409fm and 0.836fm. Muonic hydrogen and deuterium perhaps have been existed in the early universe. Now, people should realize that this team's experiments since 2010 are not to determine a precise value for the proton radius, but to perform exotic phenomena in unified physics beyond the Standard Model incorporating quantum gravity.

The uncertainties of the measurement of the radius of the proton don’t imply that spacetime shows quantum fluctuations; they imply that the systematic and statistical errors of the calculation from lattice QCD have room for improvement-which is true.

The disagreement between the calculated value of the proton radius and the experimental measurement doesn’t imply that the contribution of unknown parricles is required, because the calculation within the Standard Model isn’t precise enough yet.

However it is certainly not the result of quantum fluctuations of spacetime, for the simple reason that they are negligible at these energies, in the absence of black holes.

Dear Jamil Kooli ,

In principle, to reduce anything back to quantum gravity - I think it's wrong. Quantum gravity, which must be based on graviton, can be considered secondary in reality by its nature. So the answer to your question is clear. The explanation is present in my graviton project:

https://www.researchgate.net/project/A-new-formulation-of-the-possible-nature-of-the-graviton

Regards,

Laszlo