undrendo on Nostr: There are several steps that look strange: - eqn (13): the notation "d/dτ" stands ...

There are several steps that look strange:

- eqn (13): the notation "d/dτ" stands for a covariant derivative "u⋅∇", but it isn't clear which connection they're using for the "∇", if it's the same described in the previous lines. But then how is the proper time τ modified, given that they modify the metric to include an electromagnetic potential?

- eqn (24): they define the norm ρ of the charge 4-current to be equal to "-A⋅u". Something feels wrong about the degrees of freedom here. In principle there can be other forces, which means that "A" and "u" can be independent; and we know that "ρ" is independent as well – you can put any charge in any electromagnetic field. This equation instead makes ρ dependent. But maybe I'm miscounting the degrees of freedom.

I think they should have proceeded in a less nonchalant way in their steps and explanations, though, given the potential novelty of this result.

Maybe John Carlos Baez (npub1nf4…nqe4) has some comments on this paper as well.