This question is related Significance of electrical fields of infinite objects but is not a duplicate, imo.
My question is based on reading Frank Close's book "The Infinity Puzzle", which on page 42 deals with the problems facing the initial attempts at renormalisation of QED.
Irrespective of the scale we use, if any charge is infinite, why is it not infinite at all scales?
Obviously I'm missing something here, as when we measure the electric charge of the electron, we obtain a finite value, but is it possible to give a short explanation (that I can pass on to my high school pupils) as to how an infinity occurs at some scales, but not at others?
If the electric charge is infinite, then should this property not supersede all notions of scale?
This must be a common question, if I find a duplicate I will remove this question. Also, I'm very leery of analogies, so if the answer lies in a mathemathical form, a pointer to the resource/paper would be greatly appreciated.
EDIT: This was a badly thought out question, but just in case it is of value to someone else (and the comments are deleted), I have included them below
Electric charge is not infinite at any scale. The spurious infinities found in perturbation theory are due to a poor choice of variables (and lack of care when dealing with distributions). There are no infinities in physics. – AccidentalFourierTransform 32
Reading the chapter more carefully in the light of your comment, yes he never claims what I state....I might be getting the infinity idea from the (many, many) possible distributions of momentum between real and virtual particles......thanks for your comment, I am obviously mixing up concepts