^
I would say that if both ships transgress the 1/2 c speed, they would simply "vanish", for the other. Not in a flash, just becoming invisible.
(Of course, "seeing" each other would be impossible, at the range they had both travelled until raching this speed – given our recent "exploits" in starship drives
)
How fast are galaxies travelling ? In relation to others ? How fast do they turn ?
