There is one aspect of time travel that I feel has not been addressed. Whenever time travel and the like takes place, there is an underlying assumption that the actions will always be the same unless affected by alterations. For example, one might try to kill a man so that he will not destroy the world. This assumes that, if his actions are not altered, the man will repeat his mistakes. As a result, most of the stories have a simple cause and effect in that specific actions will have specific results. There may be butterflies, but, there is still the assumption that unless the actions vary, the effect on the timeline will always be the same accordingly to the specific changes.
The problem with this is that even with a controlled setting, one cannot predict that one will react the same way to a situation. There have been scenarios in which new events influence the character's decision, but this does not give the character the independence to make his own choices independent of setting. Until the character acts, his future is open to chance. There would be a chance that, should time repeat itself, the previously mentioned man, despite no changes, may decide not to destroy the world for no better reason but his own will. This also would affect the notion of time loops, as a person may destroy the loop by reacting differently to the infinitely-occurring catalyst.
I admit that my idea is sketchy in some areas, but I feel that the concept should be explored further. Hopefully I will one day write a story based on this notion, perhaps of a man who finally breaks an infinite time loop by choosing, on pure whim, to rescue a girl instead of ignoring her.
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