Then I read The Road to Reality by Roger Penrose and in the chapter on renormalisation it mentions just “by the way“ that the problem goes away if you assume the universe has a minimum scale, or something like that.
Why isn’t this common knowledge? Why isn’t this one of the first things that gets told when talking about renormalisation?
Why is the default assumption that the universe is continuous? Doesn’t seem like we have a good reason for it, other than the fact that we use integration as a tool and that assumes continuity by default. Does it make mathematical analysis easier all-in-all? Why not just pick the Planck length as a reasonable assumption for the quantisation of space? Might not be correct but probably a more reasonable guess than assuming that it’s continuous?