While that wouldn't work for heaps of reasons, I like your idea. I guess the issue would be discerning 'when' such a thing happened, and finding the right item to look back at, which would be a difficult challenge...
It has been suggested that black holes could provide this mirror, but it requires resolving not just something the size of Earth, but something much smaller, at a distance of 30 million light years +. Unfortunately you actually start hitting up against the limits of spacetime's resolution itself fairly quickly. But at least in principle, it is possible that some lucky photon has bounced off a dinosaur, and has traveled all the way out there, and all the way back to Earth, just now, that if you knew where to look in the sky, perhaps such a photon might even enter your eye now. Or perhaps there is some human out there who really has "seen" the dinosaurs. But you'd never really know.
Beyond speculation, I'm not aware of anything showing spacetime to be discrete.
> Beyond speculation, I'm not aware of anything showing spacetime to be discrete.
It is a prediction of loop quantum gravity [1]:
In 1988, Carlo Rovelli, Lee Smolin, and Abhay Ashtekar introduced a theory of quantum gravity called loop quantum gravity. In 1995, Rovelli and Smolin obtained a basis of states of quantum gravity, labelled by Penrose's spin networks, and using this basis they were able to show that the theory predicts that area and volume are quantized. This result indicates the existence of a discrete structure of space at very small scale.
[1] https://en.wikipedia.org/wiki/Carlo_Rovelli#Loop_quantum_gra...
And this in turn is one of the big reasons why FTL is probably impossible: It is in essence time travel.