forgive my ignorance, but don't you have to assume uniform density in both cases? It seems to me the person in the earth elevator halfway down would feel more gravity toward the center of the earth because there's actually more mass due to the higher density. In a similar way, the proton would have higher mass toward the center because of the higher wave amplitude.
correct, it does assume uniform density, if it didnt, you could say the density was zero throughout the sphere except for a small spherical region, and it would be trivially false then
I was illustrating how in principle radii can be derived in a phenomenological sense.
I didn't read the actual papers by the experimenters of the proton radius determination, but it would probably require a modification of the Hamiltonian for the hydrogen atom, since usually one treats the nuclei as point particles.
