Quick answer
Cooper does not travel backward in time in the usual sense. Inside the tesseract, he can send information through gravity to Murph at different moments in her room. The future humans who built the tesseract give him that limited access because Murph, not Cooper, is the person who can complete the work on Earth.
Why the bookshelf matters
The bookshelf is the film’s way of showing gravity as a bridge across time. Cooper cannot speak directly to Murph, but he can move the watch hand and earlier books. The scene turns the apparent ghost from the beginning of the film into Cooper himself, acting with information he only learns much later.
What Murph solves
Murph receives the quantum data from the black hole through the watch. The point is not that she receives a finished answer; she has the knowledge and scientific skill to make the breakthrough usable. The ending gives her agency rather than making Cooper the lone saviour.
Why Cooper leaves Murph
When Cooper reaches the space station, Murph is old and surrounded by her family. She tells him not to stay for her final days. The emotional logic is that their reunion has happened, but Amelia Brand is alone on another mission and still needs help.
What to watch next
For another science-fiction story built around communication and time, explore Arrival. For a different kind of space-survival pressure, The Martian and Gravity offer useful next stops.
