I have been thinking about this problem for a few days and it's been keeping me up; I must be missing something, I just don't know what. I would appreciate any one shedding some light on this: Assume an inertial frame of reference and all external fields are negligible. 1. Say you have two equally charged particles traveling next to one another at a constant velocity. The velocity is tuned such that the repulsive force due to the electric field exactly balances the attractive force due to the magnetic field (created because the charges are moving). These particles should continue to travel parallel to one another. 2. Now say you have the same situation as in (1) but the particles start with zero velocity. The particles will immediately fly apart due the repulsive force of the electric fields. There will be no magnetic field (to begin with) because the charges are not moving. 3. Finally we can convert situation (1) into situation (2) by simply changing the frame of reference to that of the moving particles. For example surround the moving particles with a box that is traveling at the same velocity. To an observer inside the box the particles will appear to be stationary. What will happen to the particles in (1) when they are observed in (3)? A. Will they continue to appear to stand still due to the balanced forces, even though there should be no magnetic field generated by stationary charges? B. Will they suddenly fly apart because there is no magnetic field just because they now appear to be stationary to this observer? C. Something else? Given the choice, I would have to go with (A), but if that were true, that means that you should be able to measure “absolute velocity” by tuning the charge values until two identical particles at rest appeared to stop repelling each other. This can’t be right. According to Special Relativity (as I understand it), "The laws of physics are the same in any inertial frame, regardless of position or velocity". Since this is not the case in this situation, it appears to be a paradox, what am I missing? It’s probably some thing trivial isn’t it :-). Thanks for any help in understanding.