If the lens curved light back toward us, could we see earth several million years ago?
replies(4):
To see earth, the lensing would been to be focused on where Earth was 2x ago. Still possible in theory, and you might even argue just as likely as a fully reflecting curve. But you'd not call it "back towards us". It would need to be "curved to where earth was".
The idea being that a spacecraft traveling at 99% of light speed can't ordinarily catch up with light reflected by Earth. But if the light curves, and the spacecraft can travel directly towards where the light will end up (spacecraft traveling "as the crow flies"), it might be possible to catch up.
Same way I might be able to catch up with Usain Bolt at a track event if he's forced to run on the track, and I'm allowed to run across the turf in the middle.