It should be stated up front that The Time Traveler’s Wife works brilliantly well as a fixed time theory story. Nothing ever changes; the main character even comments more than once that he has attempted to change events and failed to do so. If you can accept a few minor predestination paradoxes (events whose causes are their own effects, the uncaused cause that is so problematic in some stories), the film tells a coherent story in which all causes and effects fall into one history.
It helps immensely that the time traveler has no control over his abilities. Even after his daughter suggests that she sometimes forestalls her own disappearance by singing, he, whose mother was an operatic vocalist who died horribly when he was six, never could bring himself to sing and so never could prevent his own trips. It is thought to be a genetic defect, and the fact that his one child also has it suggests that it is. There is some suggestion that it might be induced by stress or by alcohol, and some that it might be controlled by drugs, but this is all inconclusive, and we are left with the fact that he travels in time when he does, completely outside of his own ability to cause or prevent it.
The predestination paradoxes are informational. He explains to his younger self what happened when he had just experienced time travel for the first time. He gives his future wife the name of the geneticist who is working on his cure, who later gives it to him, resulting in him tracking down the doctor and persuading him to take the case. He also gets his daughter’s name before she is named by traveling to the future and meeting her.
Another challenge in the film is determining which version of him we are seeing. It is humorous when he vanishes while dressing for the wedding but then, somewhat older and with greying hair, shows up in time to throw on the tux and stand in for himself. It is more complicated when she rescues a younger him in a parking lot late at night. There are also scenes we never see–when they are shopping for a home, he very quickly determines that the first two are not right by looking out a window for something he sees at the third, as if he already knows something about the house in which they will live in the future.
We could end the discussion at this point, declare that it is indeed an excellent fixed time film and that the predestination paradoxes are the tropes of such a story and of no special consequence. However, there are several reasons to challenge the fixed time concept entirely (not the least of which is the predestination paradox itself, but also its handling of the grandfather paradox). Thus our analysis will ask how the film works under replacement theory. There are several challenges to this, the most significant being that we often see one side of a time journey–the departure only, or the arrival only–and although we are given a few dates and a few durations, there are also suggestions that he has made many more trips than the film shows, and constructing even an accurate incomplete overview will require several “best guesses”. However, it is a movie worth watching despite its complications, and worth examining despite its seeming simplicity.