Back to the future is my favourite movie, I don’t know how many times I have watched it and I try to solve some time travel paradox involved in the movie. In my last effort to solve them I have built a diagram with the different realities created, the time travels and the time lines of the 3 movies together. I have followed some rules:
1. Every time travel will create an alternate reality in the destination time
2. Every time travel should move in the same timeline, either forward or backward.
3. The time travels are labeled with the names of the characters that traveled.
4. the red lines shows and alternate reality due to the arriving of a extratemporal character to the relative present. Alternate because the normal would be if time travels were not possible.
under those conditions we can summarize the movie as follows:
A first time travel was made by Einsteins (Doc’s dog) the time line 1 minute ahead of present was created (1985′), with almost no influence in the events, i.e. probably in the original time line the Doc would be also killed by the terrorist. The Einstein from the past didn’t have any information either any way to avoid this happening. After the Doc is killed, Marty escaping from the terrorist travels 30 years to the past, where he changed a lot the previous successes of his life, knowing his young parents. Thanks to the picture of this brother and sister, and with the help of the 1955 Doc and the information of the storm he managed to come back to a 1985» in this new 1985 his family is different, His father is a writer, he has a nice car, etc. and Biff is their employed. A change due to the encourage that his new father got when he hit biff in his face. Somehow they recognize him as his brother and son, I wonder how was the day before he came back to the 1985», where was Marty?, and after he came back, where did that other Marty go? so the answer to this is that in that timeline Marty also met Doc, and travel to the past. The doc is wise enough to don’t affect his career and be the same scientist as he was in the original timeline. Also he knew how to keep the track of the time so he will meet Marty and make him travel to the past and keep the universe safe from a time paradox which could cause a chain reaction that would unravel the very fabric of the space-time continuum, and destroy the entire universe!. he just changed by taking precaution of the murderers., thanks to a letter that Marty left him in the 1955′.
After this, the Doc of 1985» made several travels, according to his suitcase full of bills from different times, and from somewhere in the future, after the events of 2015» he come back to 1985». Again we have to trust in the very careful behaviour of the Doc in his travels to the past to be able to come back to a 2015» and a 1985» that matches with the reality where Marty is. The Doc then, takes Marty and Jennifer from a 1985»’ just created with very or no influence to a 2015» where the son of Marty went to jail creating a new 2015»’ to avoid that. However Biff overhearing the conversation between Marty and the Doc about the risks of the information in the Sports Almanac bought by Marty and related the DeLorean to the one he saw in 1985» follows them and steal the time machine to travel to 1955′, where Marty is struggling to come back to 1985′ and gives himself the sport almanac changing the whole curse of the timeline, now 1955». Biff came back to 2015»’ and leaves the time machine in the place from where it was stolen. Heres is one of the first paradox, Biff coming back from a new 1955» should reach a different 2015»’ where he should be rich and wealthy, no tot he same 2015»’ where Marty and the Doc are rescuing Jennifer from the 2015»’ McFly house. Jennifer and Marty know about the tragic accident that occurred to Marty in that timeline in the 1985»’. However after coming back to 1985»’ they appear instead in 1985iv the timeline generated from 1955» after 2015»’Biffs trip. in 1985iv Biff is a rich man due to his bets in sports, George McFly was killed years before in 1973. The city is violent and unsafe. The Doc aware of what happened took Marty back to 1955» creating a new 1955»’ where they take the almanac from biff restoring the reality they wanted, but the night of the storm when they planned to come back to a «restored» 1985 the flying DeLorean is struck by a light and sent back to 1885, for convenience, creating a 1885iv, minutes after it a postman delivers a 70 years old letter sent by the doc alive in 1885 and Marty looks again for the 1955 Doc, now the 1955»’Doc. Here is the 2nd Paradox, in the timeline where Marty is (1955»’), there is no Doc in 1885 who could have sent a letter. It could have happened in a hypothetical 1955iv, some how Marty went through a wormhole during the storm and appear in another reality to receive the letter.
Now, Marty with the 1955iv Doc look for the DeLorean hidden since 1885 in a cave and also discover that the 1885iv Doc was killed. Marty decided to go back to 1885iv, creating an 1885v where he avoids the Docs killing and agreed with him to come back to 1985. The day of the time travel, the Doc already in love with Claire, helped Marty to go back to 1985, now 1985v where the time machine is destroyed by a train. Again we supposed the history went smooth so it will exist a McFly family, a Jennifer, etc. the new 1985v is very similar, to the 1985»’, Marty avoids his car accident changing the story of the known 2015» and 2015», in other words there was no need to avoid Mcfly’s son arrest it was probably enough to avoid the car accident. The doc some years after in the 19th century decides to visit Marty arriving to 1985v in company of Claire and their 2 sons Julius and Verne, also Einstein is with them. He has built a new time machine from a locomotive, and the last dialog suggest that after traveling in the future they decided to settle down somewhen in the past.
After this explanation the most influence character in the series is the Doc, great scott! in his several time travels he managed to keep the equilibrium of the universe and the realities, even cheating a bit in 1885»’. As he explained the future is not written but it certainly is determined by present and past events, at the end Marty and Jennifer’s future is unknown but promising, Marty probably following a career as guitarist and head of a happy family.
Nonetheless, I still enjoy a lot watching these films, if any of you has a better explanation of the successes here explained is very welcome. to share them!
Oliver's Mind 
I think there is amistake in the ocunting of the 1885 relaities, you said the lightning strike sned DeLorean to 1885 creating, immediately 1885iv, where are 1885i ii and iii?
I kinda agree with the premise that a reality is created on each travel. But when? and the starting point or at the end? I think it is better to define it with Einstein travel. The new reality is not created when Einstein leaves shortly before 1.19am but when he finishes his travel a minute later, when he, ven Einstein, has the ability to alter the reality Marty and Doc are.
Now, I think the paradox you say Doc avoid by carefully keeping track of time from 1955′ until the moment Marty came back from 1955′ and creates 1985» is inevitable, at least under your premises. If Doc sent Marrty in a suggested time travel we have no information or clues, whenever MArty went, there theree was a new reality we can´t keep track of but that can affect the plot. Wecan assume there was no to a past point, no changes unexplained seem to be there (I thinkit is time to see it again), and the future could be good. However, which pradox? two Marties in the same reality? Biff even met him in 1955 and, apparently, the universe didn´t collapse.
Also, all travels Doc did, create new realities,we need to assume, he astonoshing care manage to keep the universe from destroying. As we need to assume he came back from 2015′, why you say 2015», I think you got lost inyour counting. If Einstein created a 1985′, there was a 1985. But we have a much fascinating problem. Which 2015 Doc came back, I mean, which storyline led to that 2015? I explain a bit. We all know that 1985» is theend point, at least in our own timeline, of the story between 1955′ and its own 1985, which we has noname for.
Well, thenex time I´ll write more.
What if we change the premises?
I think the premise of a reality being created each time there is a time travel is not that stable. Leads to some paradoxes.
We can adopt and try a premise based on multiverses. Hawking states that all realities are ocurring at the same time, I remember he writing about a universe in which Belice wins all medals in the olimpic games, however lower the probability, it is still possible. Our live is just a dice roll that constantly eliminates all the realities that are not ocurring to us.
So, we can state each timetravel is a switch in the probability of the reality, say a hacked dice. Each time a time travel is performed you arrive immediately a new reality, a reality in which the traveler arrive. Everything is the same but the fact there is a time traveler. We can think of a realities range and right beside 1955 reality, there is one with Marty arriving. Even a greatest rol for Dr Brown. I just think about a am/FM receiver. just beside your favorite station there is the same sation with a slight hiss.
Given that, the problem on the films arose because there was no control on the probabilities of the realities, Dr Brown tried hard to keep em mostly in control, but, When biff got rich and Hill Valley an inferno, there could be a probability´s probability change. I mean, of course there is a chance to arrive at one reality in the range.. Biffs actions change the order of that realities range, like if someone move the order of the radio stations.