Consider a uniformly moving charged particle (moving along the x-axis say). Consider an observer a light minute away from the origin, on the y-axis. Now, when the particle crosses the origin, the observer measures that the electric field points towards the origin. Why is this? This seems really weird to me. Why isn't it the case that the observer instead measures the electric field as if the particle is where it was a minute before crossing the origin? Would it be the case then, that an observer capable of seeing the particle (perhaps say instead that it was replaced with a large sphere), would then see the electric field eminating from a point ahead of the sphere?