John Carlos Baez on Nostr: - the old work was sloppy, and that's part of what made our heads spin. The new work ...

- the old work was sloppy, and that's part of what made our heads spin. The new work - like the paper I pointed to, but also stuff by Kijowski - is more careful about taking the limit as the particle radius goes to zero. I don't fully understand it, and I'm not sure they've gotten to the bottom of everything, but they are now proving theorems.

I'll quote some:

"Since the motion of a finite-size body will depend on its detailed composition as well as on the details of its internal states of motion, we must consider a limit where the body is shrunk down to zero size in order to have a chance at obtaining a simple, universal description of its motion. As mentioned above, normally such a limit is taken at fixed charge and mass, thereby reproducing the same difficulties as arise if one attempts to work directly with point particles. The main new idea in the present work is to consider a mathematically precise limit—based on suitable one-parameter families of exact solutions to the Maxwell and matter equations—that will enable us to avoid these difficulties and thereby to derive self-force effects in a mathematically rigorous manner. Following the basic ideas of [9] (which were formulated in the context of general relativity), we consider a modified point particle limit, wherein not only the size of the body goes to zero, but its charge and mass also go to zero. More precisely, we will consider a limit where, asymptotically, only the overall scale of the body changes, so, in particular, all quantities scale by their naive dimension. In this
limit, the body itself completely “disappears”, and its electromagnetic self-energy goes to zero."

(1/2)