If we consider two static charges in the space we know that they will experience a repulsion force according to Coulomb.
If the two particles are moving along the same direction at a fixed speed (like in a particle accelerator) the charges will start to produce a magnetic field that will attract each other. When the speed is relativistic enough, the two forces are almost compensated.
This is true in the frame of the lab, but what happens in the frame of the particles?
Two particles traveling at a fixed speed one next to the other do not see any magnetic field, only the electric, so how they justify the fact that the force disappear? In their frame the force is still present and they will not see it disappearing, but they will simply experience the usual Coulombian force. But when we do the change of coordinates between the laboratory frame and the particles frame the time will change according to the Lorentz transformations and it will slow down, slowing down also the effect of the electric force.
It is amazing that the time slows down at the same rate required by the magnetic field to compensate the electric field in the laboratory frame.
In other words we could say that the magnetic field is the expression of the time dilatation applied to the electric field. What do you think?
