According to Einstein's relativistic interpretation magnetic field caused by charges moving inside a wire is caused only by the relative speed between charges and the observer. So, if electrons are moving inside a wire and observer is stationary, than observer will measure a magnetic field.
Now, electrons are moving relatively slowly inside a wire. Just few inches per second, or even less.
What would happen if somebody moved the instrument measuring the magnetic field at a same speed as the movements of electrons inside a wire and in the same direction?
Would that moving instrument measure no magnetic field at all?