The equations of maxwell are:
1. div E= q/e0
2. div B= 0
3. curl E= dB/dt
4. curl B= u0*(J + e0*dE/dt)
These are differential equations that describe fields.
The fields have 3 dimensions each.
You can test these with experiments.
This video explains well how we can understand this:
Divergence and curl: The language of Maxwell's equations, fluid flow, and more
Because the differential equations form a cycle, we get a resonating system.
In this case these equations describe electromagnetic waves (=light).
If you look at the video above, you can see that maxwell equations are very similar
to fluid equations, but are also very different.
I think that maxwell tried to model a static aether with his equations.
It is there where I think we find inconsistencies.
It is hard to understand what a single charged particle does and how things react on a distance.
That is because the equations are abstractions..
Abstractions hide things. In this case single particles/objects and their dynamics.
With coulomb's law we get the force for single objects/ particles:
F= k* q1*q2 / r^2
where k= 1/(4*PI*e0*e1)
This is only for a static situation, but still works well
in our atomic models.
When moving we get Lorentzforce too
F= q*(E + v*B)
where E= electrical field and B= magnetic field.
These equations related to single charged particles are
equivalent with the above maxwell equations.
We can easily see that magnetic field and resulting force are the result of
charges moving relative to each other.
Both Einstein and Weber tried to put that into equations.
Einstein wanted to maintain the maxwell equations fully, and so derived special relativity.
In special relativity, each speed is related to a timeframes, which changes when the object
changes speed. The timeframe defines the speed of time and the stretches space in the frame
into the direction of movement. this also decouples light from existence, as light moves
with the speed of light and has no time or space.
To do this he added a time dimension, but in practice you also need dimensions to
express the lengthcontraction. So in practice you need both the vectors of
position and speed before you can do any calculation (6 variables).
Because most examples are in 1 dimension, this problem is usually ignored.
In general relativity there are even 16 variables related to space and time (=level 4 Tensor).
I do not understand Weber fully, but
Weber seems to try to replace the speed with some kind of relative speed immediately.
Then derives all equations from that concept.
But let's look at the Coulomb and Lorentz equations first.
I assume first that all electromagnetic fields distribute with the speed of light.
That is what we see in radios.
So if a particle/object moves, we can assume that its electric field distributes with the speed of light.
With 2 static particles/objects we get the coulomb force.
Q1


Q2
Now let's assume that 2 particles/objects move in parallel on distance R with speed V.
?Q1>


?Q2>
What will be the force between them?
Due to the speed of light, there will be a slight delay between the sending and receiving of the
electric force.
The electric force will come from behind partially, instead of sideways.
We can not have that happen, as this would cause 2 equal charged particles to run
off into infinity. It is like free energy.
So instead we must have a force that is only sideways.
This can be simply a property of the electric field: when it moves, it only gives force in a certain direction.
The field also needs a longer path from one charge to the other.
This also needs correction.
The new path distance r= sqrt( R*R + v*v/c*c)
This gives a force difference of: Fdiff= Q*Q/r*r  Q*Q/R*R
Fdiff= Q*Q/(R*R+..)  (Q*Q+v*c*v*c*Q*Q)/(R*R+..) (simplified)
Which with low speeds becomes:
Fdiff= Fmagnetic
So I can derive the Lorentz magnetic force with just assuming a delay cause by the speed of light,
and using Coulomb's equation.
If the speed v is very close to the speed of light, the force will disappear, as if the
electric field is no longer there. I think this is what we see in beams of electrons too.
Now let's look at how Veritasium explain's magnetism with Special Relativity.
How Special Relativity Makes Magnets Work
Here he explains how the lengthcontraction causes magnetism.
But why did Einstein not consider the delay that is caused by the speed of light?
Well, it would break with his idea of relative time and such.
In the video, why is there no force when only the electrons are moving?
(Youtube sadly blocked the video I looked for in the search)
According to SR, the electrons should now be closer together and cause attraction,
but it does not.
Do the electrons spread differently when moving to compensate for it?
If I follow my own theory, it seems they do.
And what happens when movement changes?
Let's assume that one object is stopped by block. Like an electron that hits a gold atom.
With the speed of light this change in speed is distributed to the other particle with a delay.
Now the force and field is suddenly more behind the particle/object that is still moving.
The field is also not correcting any more for the movement.
This means that the field will now push the moving object forward.
This is exactly like induction.
Now I used the simple logic of a delay caused by the speed of light.
Something that seems to be ignored by both Maxwell and Einstein.
Which makes it hard for me now to accept Einstein, as his solution is
far more complicated and does not seem logical at all.
There are many different ways to solve the problems.
Even my very simple solution works.
It would be interesting to find where the differences are,
and test different aspects of it.