We introduce a quantum mechanical model of time travel which includes two figurative beam splitters in order to induce feedback to earlier times. This leads to a unique solution to the paradox where one could kill one's grandfather in that once the future has unfolded, it cannot change the past, and so the past becomes deterministic. On the other hand, looking forwards towards the future is completely probabilistic. This resolves the classical paradox in a philosophically satisfying manner.
By the way, Greenberger is the G in the famous GHZ paper on quantum theory - so he's definitely no amateur.
The paper uses the mathematical formalism of quantum mechanics, but it is very well-written, so it's easy to skip the equations and see what's going on.
As it turns out, the authors feel that time-travel paradoxes are resolved quantum-mechanically as follows: it might be possible to travel into the past, but you still couldn't change any facts about the future.
This of course, is the theme of numerous science fiction works. The first I personally encountered was the Twilight Zone episode "No Time Like the Past" where
Paul Driscoll uses a time machine to try and change three past events: the bombing of Hiroshima, Hitler's rise to power and the sinking of the Lusitania. He fails miserably at all of them, and decides to escape to the past. He picks Homeville, Indiana. After learning from a history book he's brought along that a fire, started by runaway horses, will burn down a school and injure several children. He sees the wagon with the horses, and in trying to convince the owner to unhitch them, he frightens the horses and they start the fire. Driscoll returns to the present, content to leave the past alone.
from Ritterson's Episode Guides: The Twilight Zone
I remember feeling very frustrated watching this as a child!
In Behold the Man Michael Moorcock's 1969 time travel story, the protagonist goes back to see what Jesus was really like. Jesus turns out to be an idiot and Mary is harlot. The protagonist is bitterly disappointed, but his time machine is broken so he's stuck in the past. However he ends up, really despite himself, saying and doing things that give rise to the Legend of Jesus. "Behold the Man", by the way, is Pilate's sarcasm (John 19,5) as he has Jesus paraded before the crowd.
Motherhood takes another beating in the opening pages of An Alien Heat, the first of a fabulously decadent time travel series, also by Michael Moorcock.
There's a very different way of resolving time travel paradoxes spectacularly unfolded in The Man Who Folded Himself by David Gerrold. If you go back in time to strangle your grandfather in his crib, instead of being thwarted (ala the Twilight Zone) or disappearing in a puff of smoke, the result is quite different. You're still there and you have a dead baby in your hands! History now stands as follows: the past is exactly the same as it was until you materialized in your grandfather's nursery. But events now unfold "normally" with you in the room with the dead baby. This is somewhat reminiscent of the "Many Worlds" interpretation of quantum mechanics due to Hugh Everett. A time travel to the past causes history to fork into a new branch, but unfortunately, you the time traveler have no access to the original branch. If you immediately time-traveled "back" to 2005 you'll find that you were never born and that all other influences your grandfather had on his future never happened.
An earlier version of this same approach to time travel paradoxes occurs in Robert Heinlein's "A Door into Summer". As far as I can tell, this is a actually a logically consistent way to avoid all paradoxes. The physics is a different matter.
I loved the time travel machine from George Pal's 1960 film of H.G. Well's The Time Machine
