current travels through the actual cross section of a wire. it induces a field around the wire, but that has nothing to do with the actual current which IS traveling through the wire.
and on the comment about light frequencies we cant see, when you said things would be invisible, not really, everything would just be dark. if something absorbs all wavelengths of visible light it appears to be black.
the one exception to this would be black holes because there is an event horizon where not even light can escape, so to a "naked" eye it would look like a black circle. this is different from something absorbing visible light. in this case its actually "taking" the light from around it.