I've saw the Current in Wire special relativity magnetism question, but the answer did not convince me at all.
My doubt is crystal clear.
I know the electrons move in a very high velocity in all directions and often collide with each other (relaxation time lapse). This move is random and don't change wire linear density. I also know that the velocity of free electrons (drift speed) in the wire is quite slow, but it defines the current. No drift, no current.
Suppose a external positive charge moving in the same speed of electrons (v) to the right.
So it should be possible measure a electric (not magnetic) force on it, because the electron drift in the current direction is denser and are many free electrons that sum up this tiny effect.
If one changes the reference moving together electrons in the wire, I think that is concerning the drift speed and not the real average electron velocity in random directions.
In the stationary reference, except for drift, the average velocity of both electrons and protons approaches 0.
When the reference is changed relative to speed v to the right. First, we suppose that it's the average electron velocity. In that case, the electrons will no longer be stopped but at a mean velocity v to the left. The protons have exactly the same behavior, so both shrink their distances and the wire linear density remains the same.
So, it only makes sense to refer to stopped electrons if we were talking about the drift velocity that is zero when there is no current. The reasoning that walking along with the drift then makes sense. In the new reference, the protons now have a drift to the left and the eletrons be stopped in the referece that uses drift velocity to the right
However, in that case, the the total effect would be supposed to be low, according to some respondents, but it's the only one that make sense.
I'm confused.
In short, why is there no electric force (just magnetic force) acting in a moving charge on the stationary reference?
if drift velocity is enough to explain magnetism, why it does not generate shrink with electron drift in stationary reference and therefore the wire is not neutral anymore.
PS
For instance, this article says literally that magnetism comes from the drift velocity
By the way, it's remarkable that we can measure magnetic forces at all, since the average drift velocity in a household wire is only a snail's pace: v/c is typically only $10^{-13}$, so the Lorentz factor differs from 1 only by about one part in $10^{26}$. We can still measure this effect because the total charge of all the conduction electrons in a meter-long wire is tens of thousands of coulombs; two such charges separated by only a few millimeters would exert enormous electrostatic forces on each other.
