The universe has a uniform electric field E pointed along the x axis. The universe also has a uniform magnetic field B pointed along the y axis. Now suppose you have a proton moving along the z axis with velocity v=E/B. The electric and magnetic forces will cancel and the proton will move strait along the z axis unaccelerated. To find the electromagnetic fields in the reference frame of the proton, you perform a Lorentz transformation and find that the fields are zero. So far so good; now transform the fields back into the original reference frame. They are zero now in all reference frames. What am I doing wrong? Edit. Oops. They're not zero; you end up with a magnetic field only. Ok, I can go to sleep now.