4The fact that commutation can fail makes a huge difference in the whole patch formalism. It
may be possible to create a formalism in which commutation always succeeds, with the result of
what would otherwise be a commutation that fails being something like a virtual particle (which can
violate conservation of energy), and it may be that such a formalism would allow strict
mathematical proofs (whereas those used in the current formalism are mostly only hand waving
“physicist” proofs). However, I’m not sure how you’d deal with a request to delete a file
that has not yet been created, for example. Obviously you’d need to create some kind of
antifile, which would annihilate with the file when that file finally got created, but I’m
not entirely sure how I’d go about doing this. So I’m sticking with my hand waving
formalism.