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It'd be a Stable Time Loop, because eventually the grandson would have to travel back to become the grandpa again, else you have a paradox.
Wasn't something similar the actual plot to that episode of Doctor Who? The one that introduced us to the Weeping Angels?
Keeper of The Celestial FlameIt's a Predestination Paradox. Simply put, the information in the loop has no origin outside of the loop itself. The loop has no way of starting in the first place, but it's still a Stable Time Loop because if you ignore that fact, the loop is self-sustaining.
Edited by Fighteer "It's Occam's Shuriken! If the answer is elusive, never rule out ninjas!"

So what happens when you combine The Slow Path with My Own Grampa? (Like, you get sent into the past, become your own grandpa, pass on your knowledge to your grandson/yourself, die from old age, and then your grandson/yourself rejoins your group, and everything continues like normal.
I think this is too specific for a trope, but if someone has an example of this happening, I think that would be fun (maybe a webcomic or something.)
Edited by TheKing42