What is meant by "current" in this context? This is a quote from Optics by Hecht:

A stationary charge has a constant E-field, no B-field, and
  hence produces no radiation—where would the energy come
  from if it did? A uniformly moving charge has both an E- and
  a B-field, but it does not radiate. If you traveled along with the
  charge, the current would thereupon vanish, hence B would
  vanish, and we would be back at the previous case, uniform
  motion being relative. That's reasonable, since it would make
  no sense at all if the charge stopped radiating just because you
  started walking along next to it. That leaves nonuniformly
  moving charges, which assuredly do radiate. In the photon 
  picture this is underscored by the conviction that the fundamental

And from the Wikipedia page on electromagnetic waves:

An electromagnetic field very far from currents and charges (sources) is called electromagnetic radiation (EMR) since it radiates from the charges and currents in the source...

I've always thought of a current as a flow of electrons through a conductor, but here it seems to mean something independent of a medium through which electrons can flow. So what is current in this context?
Thanks!
 A: Current is defined by the movement of charges from one point to another, and the concept is independent of a medium, or the charges being electrons. In this context the current is constituted by the uniformly moving charge. And that is why an uniformly moving charge doesn't create any radiation, as what happens to be a current in one frame is stationary charge in a frame travelling alongside it with same velocity.
However the same doesn't hold true for an accelerating charge. Thats easy to see, for in no inertial frame there won't be a stationary charge. However this reason doesn't suffice, and you would need to solve the Maxwell's equations for a complete treatment of the problem.
A: Current is the motion of charged particles, not necessarily electrons and not necessarily in a conductor. For instance the motion of ions in a solution creates current, or holes in a solid.
Currents and charges are the sources of Maxwell's equations. These sources create the electric and magnetic fields. When the sources behave in certain ways (like accelerating charges and time varying current in sine waves for instance) they will create EM radiation like in your 2nd quote while if they behave in other ways (like non moving charges or static currents), no radiation will be emitted, just like in your first quote.
