The Static Timeline Theory
This can be a answer to the Grandfather Paradox
The grandfather paradox asks a simple question: if you go back in time and stop your grandfather from having children, how can you ever be born? The Static Timeline Theory answers that the question rests on a wrong picture of time.
The past is a finished film. Every moment that has ever happened is a frame on a reel, fixed in place. Nothing you do later can erase or rewrite those frames.
Time travel is pressing play. When you travel back, you don't edit the reel. You start playing it from that frame. While you're there, time moves normally and your actions are real. It's like pausing a recorded football match and taking control of the players: from that point the game runs live, but only while you're playing.
Returning to the present stops the playback. The moment you leave, that stretch of the past freezes at the exact frame where you left. Everything after it was never replayed, so the present you return to is untouched.
Two examples
The cup. In the original timeline, a cup sits on the left side of a desk at 9:00 AM. You travel back to 9:00 and move it to the right. For as long as you stay, the cup is on the right. When you leave at 9:30, that half hour freezes. The frames after it still show the cup on the left, so the present is exactly as you left it.
The grandfather. You travel to 1960 and stop your grandfather from meeting your grandmother. For the days you're there, that timeline plays out without him. When you return, those days freeze, and every frame after them, including your parents, your birth, and your life, remains exactly as it was. No paradox, because you never rewrote the frames that made you.
The core idea: your actions are real while you're in the past, but they never ripple forward, because the future frames were never replayed.