The idea is that the electron sends a random virtual photon to a random direction, which "smears" its probability distribution close to the proton.
The classic vertex correction is not random. That is a big difference from Welton. Why would the classical correction produce the same result? Does the classical correction displace the electron in such a way that δr² is roughly the same as for Welton?
The mass reduction fraction is:
M(r) = 1 / (4 π ε₀)¹⋅⁵ * e³ / (mₑ¹⋅⁵ c³)
* sqrt(2) / r¹⋅⁵.
Let the electron move some distance Δr toward the proton. If it moves 1% faster, it will in the same time move 1.01 Δr. If the electron comes from a large distance close to the proton, we obtain the correction simply by integrating:
∞
∫ -1 / r¹⋅⁵ dr * constant
r
= 2 / sqrt(r) * constant.
A reasonable assumption is that we should calculate the displacement when
r = λₑ = h / (mₑ c).
But the exponents for e and ε₀ will differ from the Welton formula. This is not going to work. The problem is that Welton's displacement is random, while the classical displacement is systematic?
*** WORK IN PROGRESS ***
