The Terminator movies provide another example of how time travel stories can become confusing. At the beginning of Terminator 2: Judgment Day we learn that Judgement Day (when Skynet launches the nuclear missiles and causes the nuclear holocaust) is on August 29, 1997. Then the war between humans and machines begins.
In The Terminator, a T-800 terminator is sent back in time to 1984 to kill Sarah Connor so that her son John Connor, the leader of the human resistance, cannot be born. She manages to crush it in a hydraulic press. In Terminator 2: Judgment Day a T-1000 terminator is sent back to 1995 to kill John. Another T-800, which the human resistance had captured and reprogrammed, helps Sarah and John fight the T-1000. They learn that a chip was salvaged from the destroyed T-800 and that it become the basis on which Miles Dyson would develop the neural net processor chip which would then be used to create Skynet.
After hearing what his work would cause, Dyson takes Sarah Connor, John Connor, and the reprogrammed T-800 to Cyberdyne so that they can destroy his work and the salvaged components to prevent anyone from developing the technology. The T-800 helps them defeat the T-1000 and then allows itself to be destroyed so that its chip cannot be salvaged. Sarah and John think Judgement Day has been averted, but in Terminator 3: Rise of the Machines John learns that they only postponed it to July 25, 2004 and that Judgement Day is inevitable.
After I first saw Terminator 2: Judgment Day I remember thinking about the problems with consistency. In the original timeline (call it timeline-1), humans create Skynet (seemingly without help from the future). It turns against its creators, triggers Judgement Day, and begins the war between humans and machines. Skynet sends the T-800 into the past to kill Sarah. The T-800 fails and leaves a chip for humans to discover. This begins timeline-2 in which humans develop Skynet with the help of future technology, resulting in a postponed Judgement Day.
This creates a causal paradox. Humans first develop the neural net processor without help from the future (timeline-1). When the first T-800 is destroyed, it triggers timeline-2 in which humans develop the chip with help from the future. This means timeline-1 no longer exists, and yet timeline-2 would not exist without it. (For reasons explained here, I am assuming that changes in the timeline do not create a parallel, coexisting timeline in which the changes exists while the original timeline continues to exist.)
One could settle this by proposing the existence of an overarching timeline which includes all events and all changes to those events. Think of it as something similar to a person sitting in a theater while watching a movie involving time travel. He watches the characters travel forward and backward through time, changing history, and experiencing those changes. For the characters who never time travel, the changed timeline is all they know. For the viewer, every version of history is part of the same whole. Elements of any timeline which cease to exist in the movie’s world will still exist as a part of the total story from the viewer’s perspective. His perspective incorporates every version of the movie’s history without changing his all-encompassing history. The viewer’s watch also continues to move forward in a linear direction without changing.
This would allow the timeline of the story to change without creating paradoxes (at least from the viewer’s perspective), but it would prevent the author of any such story from including any concept of special relativity in his explanation of time. Relativity depends on time being relative from every perspective. There can be no privileged reference frame, but the viewer in the theater does have a privileged reference within which time is not relative. Therefore it seems that this paradox does have a possible solution, but it limits which scientific theories the author can include.
By now you may be wondering why any of this matters in real life. It doesn’t. Not one bit. I do not believe in time travel. I just enjoy science fiction stories, and I enjoy pondering the implications of such stories. This is also one more example of how time travel stories create logical problems and how thinking about time travel can make your head hurt.
By the way, if anyone reading this knows of any time travel story with no paradoxes, then please post it in a comment. I would enjoy reading it.