Is there a contradiction in Ampere's force and motion?

[Artlav]

I've been thinking about Ampere's force attraction between two parallel currents, and one case got me confused.

Imagine two streams of similarly charged particles traveling alongside in a vaccuum, which is by definition an electric current. For the small time they would flow along until repelled, there should be two forces acting on them - repulsion from charge and attraction from ampere force, right?

Now, if the observer is to move along the current, so as to make the particles stand still relative to him, he should measure no ampere force, and thus they would have to repel faster than in first case.

There we get a contradiction.

What have i missed?
-Does a moving charge in a vacuum constitute a current?
-Does Biot–Savart law only work if there is a wire of some sort, and no magnetic field created otherwise?
-Something about relativity?
-Something else entirely?

 

[jtbell]

-Something about relativity?

Bingo!

The components of the electric and magnetic fields are also components of the electromagnetic field tensor. When you switch from one inertial reference frame to another, this tensor transforms under the Lorentz transformation in such a way that the net physically measureable effect is the same in both frames, after taking into account length contraction, time dilation, etc.