I just watched A Sound of Thunder, a USD 52 million movie shot in Prague in 2005. The movie, originally scheduled for 2002 but delayed because of the floods, has received horrible ratings (2.8 of 10 stars in average) and lost a lot of money but I found it pretty inspiring.
Of course, time travel cannot be logically self-consistent because there are lots of logical problems with the history that is not a single-valued function of time. But as an inspiration and arts, I still found it pretty cool.
A neurotic woman invents a time machine. Of course, such things have to be invented by a woman. A greedy guy creates a company organizing safari trips where they kill a dinosaur (by a freezing gun) right before the moment in which the dinosaur would die naturally. But they are not allowed to change the history in any way because such a change would also modify the future through the so-called time waves - pretty impressive visual scenes in which a soliton screws a lot of things in the city are included.
However, the government regulators are corrupt, as usually, so they turn off the biofilter during the missions. Later, it turns out that one of the trips has seriously altered the history. More concretely, a participant stepped on a butterfly. The whole evolution of life was different than it is on the original branch of the multi-valued function of spacetime. Consequently, a lot of bizarre animals that have evolved in the alternative Universe are jumping on the scientists - and sometimes the scientists become fish themselves - as they move from one branch of the spacetime to another.
I can't really explain you details how it works because I don't fully understand these details and what I don't understand is pretty hard for me to remember.
Meanwhile, their main branch of the spacetime is completely screwed, too. People are hungry and irrirated. Eventually many important characters decide that it is essential to stop the greedy CEO from organizing the safari trips. So they return 65,000,001 years into the past. Unfortunately, at some moment, they can't find any functional throat of the wormhole for the time travel. So they locate a particle accelerator instead. ;-) It can fulfil the same task even though it is less stable.
Eventually, two copies of the main hero are able to appear in the critical scene with the butterfly. One of them, the one who didn't appear on the picture in the previous branch of the shooting scene, saves the butterfly and also gives his clone and his female colleague a visual proof that something goes seriously wrong. The new copy of the hero - the savior - disappears in 20 seconds and returns to the particle accelerator that is just undergoing a spectacular time wave.
The remaining scientists shoot the evidence of two anomalous copies of the main hero on the holodisk. (The other, "third" copies from the other expeditions are not there, because of subtle and unexplained rules of interactions between the branches of the spacetime.) Once they return, they pretend that the holodisks were lost. But in fact, the main heroes secretly watch it and show it to the neurotic woman who invented the time machine.
The lethal modifications to the history are undone so perfectly (and banned) that no one can remember that anything wrong with their spacetime and evolution of life has ever occurred. ;-)
When I write this description, it sounds, of course, almost completely absurd and it is impossible to avoid laughter but I like their creativity and the diverse ways how physics concepts have been incorporated into the movie. And some of the criticisms that I have read are simply lame. For example, the movie correctly says that the uncertainty principle implies that no ("ordinary") event in the real world is completely certain.
I think it is a correct conclusion but some people would only accept the original textbook inequality involving the position and the momentum which is very narrow-minded and shows that the critic doesn't really understand the universal character of the uncertainty principle. For example, it is true that the uncertainty principle implies that there can't exist 100% reliable guns. The movie is saying the right thing.
Concerning time machines, all these movies clearly use two different types of time. One of them is the movie time, as observed by the audiences, and the other one is the historical time encoding what kind of animals are likely to occur and where you should draw the events into spacetime. These two times are not necessarily increasing functions of each other. More precisely, the historical time is a non-monotonic function of the movie time.
Somewhat bizarrely from a physics viewpoint but naturally from the literary viewpoint, causality mostly holds if events are ordered by the movie time: events that happen at the end of the movie are pretty much consequences of those that happen at the beginning of the movie (even though some of those at the beginning may be suppressed to make the movie more dramatic).
The causality according to the historical time ordering is, of course, completely violated; that's the very point of having a time machine. And new branches of spacetime may be created by the movie characters as a function of the movie time and according to their free will. Nevertheless, locally, in short enough portions of the movie, the movie time and the historical time must coincide. It is not a fully self-consistent set of rules but it is sufficiently self-consistent from a viewpoint of sloppy movie directors. ;-)
I also liked how they talked about the pioneers such as Christopher Columbus, Neil Armstrong, and Charles Brubaker, the first man on Mars. ;-)