The first popular movie about time travel was Back to the Future. It has a pretty good grasp on the physics of time travel - for the 1980s, at least. There's no denying, though, that there is a glaring plot problem in the movie. Look at the following timeline:
Firstly, we see the normal flow of time in Timeline X, from Point A1, then to Point B1 and finally to point C1. At Point C1, Doc discovers time travel, and both Doc and Marty go back to Point B1 in their DeLorean.
The problem arises here. At Point B1, they change things. Marty interacts with his father George, and as a result, George gets the courage to stand up to Biff. Due to Marty interacting with George, the future has changed and they are now in a completely different timeline, Timeline Y.
Marty has disappeared from his original Timeline X, and appeared in Timeline Y, where Biff is a wimp and George is successful. This is a huge problem, since in Timeline Y, there should already be a Marty.
There are thus two Martys (Marties?) from different timelines which are existing in the same timeline together. Confusing, isn't it? Herein lies the problem in Back to the Future 1. See any fault in our logic, or have a suggestion? Comment below!