[Physics] Mathematical proof Maxwell's equations are incorrect?

[Arend Lammertink]

On Fri, Apr 24, 2020 at 6:04 PM Arend Lammertink <lamare at gmail.com> wrote:
>

> > > Could it be that because of the vector identity ∇⋅𝐁= 0 that "some
> > > configurations of the field", namely the addition of curl-free
> > > components to the field, by definition results in the zero vector?
> >
> > Again, you have to explain what you mean, given that addition is
> > an operation, but a configuration is not.
>
> Elsewhere, I made this argument:
>
> Gauge theory is built on the principle that you can add curl-free
> components to the vector potential field [A] and divergence free
> components to the scalar potential field Φ. Vector theory learns that
> doing so results in the null vector for the resulting force.
> Therefore, we can conclude that gauge theory yields no force and
> therefore no physical effect at all. It should thus be rejected and
> therefore QFT should be revised.
>
> It's the same vector identities that enable us to write:
>
>  ∇×𝗘= 0
>  ∇⋅𝐁= 0
>
> that lead to the conclusion that neither the addition of a curl-free
> component to the vector potential field [A] nor the addition of a
> divergence-free component to the scalar potential field Φ result in
> anything other than zero in the respective force fields 𝗘 and 𝐁.
>

Oops, that's nonsense, i.e. the identities mentioned.

Obviously, the curl of a curl-free component is zero, as is the
gradient of a divergence-free component.