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

[Ilja Schmelzer]

2020-04-24 12:16 GMT+06:30, Arend Lammertink <lamare at gmail.com>:
> On Fri, Apr 24, 2020 at 6:42 AM Ilja Schmelzer <ilja.schmelzer at gmail.com>
>> The very idea to prove mathematically that the Maxwell equations are
>> incorrect makes no sense.
>>
>
> I agree that the very idea to prove that the Maxwell equations are
> _mathematically_ incorrect makes no sense, I'll give you that.
>
> The point is that Maxwell's equations are totally out of whack with
> the vector Laplace equation. How much sense does that make?

Also not much.  These are quite elementary mathematics, so either
the result is completely irrelevant or you made some elementary error.

> Especially given that Maxwell's equations eventually lead to both
> relativity as well as gauge theory and QFT, two mutually exclusive
> theories that cannot both be correct.

If you have in mind special relativity, the only conflict with QFT appears
if you insist on the Minkowski spacetime interpretation. With the Lorentz
ether interpretation you cannot prove the Bell inequalities (quantum causal
influences could go FTL in the hidden preferred frame) so that no
conflict occurs.

> Hasn't the "gauge freedom", which forms the basis for gauge theory,
> crept into the model exactly because Maxwell's equations are totally
> out of whack with the vector Laplace equation?

Whatever language you use to describe this ("crept into", "out of whack")
it does not change the well-known and established facts about the
Maxwell equations, in particular their gauge invariance.

> How much sense does it make to have a model which has been developed
> within the aetheric paradigm that has "gauge freedom"?

Gauge freedom simply means that some configurations of the field
cannot be distinguished by measurements.  This is completely unproblematic
except for empiricism/positivism, where unobservable things cannot exist.

But there is no reason to care about these outdated philosophies of science.
In Popper's critical rationalism restricted human abilities of
observation are not
a problem at all.

In my approach to ether theory in modern physics gauge fields play a central
role too.  See https://ilja-schmelzer.de/matter