Sideways time was not new with this movie, nor has it been ignored since.  My earliest peek at it was in an old John Pertwee Doctor Who episode, in which the Doctor slides into what is frequently misnomered a "parallel world".  "An infinite number of choices, an infinite number of parallel worlds" is how he describes it (and wrong on two counts:  a very great but finite number of choices, a very great but finite number of divergent worlds--but it was a mistake which took genius to make).  The same approach to sideways time has become the basis for the wonderful fantasy Sliders, and has been incorporated into the concepts of the recent Multiverser game system.  In each of these contexts, the idea that divergent timelines exist based on events which could have been different is basic.  However, Back to the Future treats such divergent timelines differently--and I think in a way which makes better sense in many ways.  The divergent timelines in Back to the Future are presented as alternate possible worlds, not actually existing:  only one timeline truly exists, and if the past is altered, the known future ceases to exist, replaced by the new future which is built from that past.

I will mention that I find this position much more satisfying in both a subjective and an objective way.  Objectively, I find it absurd to imagine that each choice, each event, each occurrence, splits the world into two co-existing alternate histories.  By this view, either the universe is splitting into billions of divergent universes every second (after all, how many other things could you alone be doing right now?), or determinism is far more pervasive than any of us could imagine, such that even if you hesitate to push the mouse button, you have no alternative but to push it at the precise picosecond at which you will do so.  Subjectively, I do not like the prospect of imagining that for every moral or ethical decision I make correctly, there is another universe in which another me is making the opposite choice--and if so, how is that person really me, if he does not share my basic morals and ethics?  Although the existence of such worlds in sideways time--worlds in which the same people and places exist, and it is the same day and time, but the history is different somehow--is very appealing from the viewpoint of the storyteller, it is not so appealing as an explanation of reality.  (I would further mention that, as a theological position, I find the idea of dividing anyone into billions of divergent selves each with his own moral and ethical self-identity, his own spirit and soul, almost entirely indefensible.)

But we're going to run into trouble on this story long before reaching the point at which the theory of divergent timelines is important.

  The story launches from the end of Part I, as Doctor Emmett L. Brown sweeps into the presence of Marty and Jennifer, stuffing garbage into his recently-installed mini-fusion generator (looks like a tokomak design to me), and announcing that they must come back to the future with him, to help their children--an ending which suggested a sequel was coming.  But if we expected this film to be about the future, we were mistaken.  Marty and Doc must go to the future in order to set up the next twist in time, but they must again return to the past to repair it.  Looking at the movie carefully, we find not fewer than five trips from some point in the future into some point in the past.

It should be observed here that time travel into the future, by itself, creates no temporal problems.  The character who vanishes from the timeline by his own initiative, and reappears at some later time, has no more affect on the timeline than the one who moves away and comes back later, or takes an extended nap and then wakes up.  The only situations in which travel forward creates a problem are when that forward travel is induced by events in the future, or when that forward travel is tied to a return trip.  Temporal anomalies occur when events in one time change, but the causes of those changes lie in the future relative to those events.  That is, if something yet to happen causes a change in something which has happened, a temporal anomaly occurs.

It is clear from the early conversations in this movie that Doctor Emmett Brown has made several trips through time.  He went forward beyond the date to which he is taking Marty, and worked his way backward, picking up a newspaper at one point, arriving at the date on which Marty's son becomes involved in a crime, and observing the boy's movements, with a view to changing those events.  These "temporal hiccoughs" will have created a series of inoffensive N-jumps, as he by his presence changes insignificant details in the time line, creating C-D timelines which differ from the A-B timelines of the same period merely by his presence.  However, he forms a plan which can only result in failure or an infinity loop.

Returning to 1985 as the movie begins, he takes Marty and Jennifer (and his dog Einstein) back to 2015.  For Marty and Jennifer, this is a leap forward in time; however, for Doc Brown, it is a leap back from the points in the future in which he has collected information upon which he is about to act.  He has visited the future--we cannot say exactly what date; we will suppose that he went to November of this same year, since he left from November of 1985 to go thirty years forward.  This is a couple of weeks after October 21 of 2015, the date he has identified as the point at which the trouble starts.  He may have traveled beyond that, and those travels may complicate the temporal pattern significantly; however, for our purposes we may assume that he first got his information on November 12, 2015 (a date of no consequence to the matter, except that we need one).  On that date, Doc Brown first discovered the problem with Marty's son.  He returned to several dates between November 12 and October 21 (causing those hiccoughs), picks up the paper on October 22, and then tracks Marty Junior's movements on October 21 so that he may intercept him at the critical moment.  He picks up Marty because the young McFly can do a believable impression of his own son, and returns to carry out his plan.  Under the information we're given, Marty does abort the crime, and keep his son out of jail.

We look at the newspaper--like the photograph of the first movie, this is a plot device; however, it is slightly more believable:  whether or not Marty McFly Jr. commits the crime on October 22, the newspaper will be printed.  We would only question why Doc Brown would have bothered to keep it.  But although the newspaper serves as a valuable plot device, it also dramatically underscores the temporal problem which has been created at this point.

Doc Brown went into the future, and discovered the "future history" of certain events.  He returned to the time of those events (and his trip to the past behind that is incidental, although it sets up its own anomaly which we shall examine in a moment) and, relying on information from the future, changed that future.  We see that the future is changed, because the newspaper changes; we know that everyone alive the next day will remember the events of this day as including the damage to the courthouse, not the arrest of the younger McFly.  However, now the information upon which Doc Brown has made his plans has changed, and he will have no reason to do what he has just done.

I want to make it clear that it matters little whether time works the way proposed in these articles, or the way suggested by Doc Brown in the films.  I will explain the problem under both theories.

Under our theory, time advanced to the moment Doc Brown discovered the disaster he wished to avert--November 12, 2015, point B, for our purposes.  Then, because he intervenes, time snaps back from that moment to October 21, 2015, point C.  Creating the C-D timeline, Doc now erases the events from history--the very history upon which he relied to discover the import of those events.  In this timeline, Doc will arrive November 12, 2015, point D, and learn nothing significant about Marty's children.  Thus he will have no motive for his abrupt return to take Marty back to stop those events; and without his intervention, those events will happen, creating the history for him to discover and attempt to erase.  This is the infinity loop.

Doc Brown's theory strongly suggests that there is only one real timeline; alternate futures cease to exist and are replaced by new futures when events change them.  For this reason, the picture and the newspaper change before their eyes:  the original future history has ceased to exist entirely, and been replaced with the new future history.  Unfortunately, if this is so, then not only is it not possible for Doc to have discovered the now non-existent information, but even the Doc present in October 2015 will not remember the information which he previously learned in November 2015, because that information no longer exists, and he never knew it, and could not have acted upon it.  I realize that this is absurd (the primary reason why it is not part of my theory), but do not want to put too fine a point on it:  the movie does not fully explain its own theories of time, and we would be remiss to presume too full an understanding.  This is only the best reconstruction I can make of the matter; and either way, once Doc has caused the change which erases the events, he can no longer act upon those events.  Time has come to an end, and our story is over.

But we will continue the analysis as if there were a way out of this problem (indeed, there might be, if at some point on the CD timeline between October 21 and November 12, something else happens to make Doc Brown aware that he must intervene to cause history to occur as it has, or to otherwise disrupt the timeline).

We have mentioned that Doc returned to 1985 to pick up Marty, creating another N-jump.  You might think that Doc did nothing at that point to create an anomaly; after all, it would be no different if Doc were to spend a few hours in Boston, come back for a moment, and then return to Boston.  However, in his return trip he has passively brought back and conveyed information about the future:  the time machine has been redesigned so as to be able to fly, and Biff Tannen has seen it do this, and seen it disappear.  Since much of the added technology comes from the future, it is necessary that time advanced to at least 2015 without Biff Tannen seeing this, and then reverted to the alternate timeline (the C-D segment of this thirty year anomaly) in which he has that information.  This larger anomaly most likely would have been another infinity loop, since Doc's motivation for returning to the past was to retrieve Marty to change a future which he in fact changed, so at the end of this segment, he also has no reason to retrieve Marty.  It is from the C-D segment of this anomaly that the next is launched, as Biff steals the time machine.

There is a deeper problem in all this that complicates this anomaly immensely.  Doc has again undone history in a major way.  In removing Marty and Jennifer from 1985, he has prevented them from marrying and starting their family.  Although he quite reasonably found them there when he first arrived, when he returns with them in tow, their grown selves are not there, and there are no children, no reason for him to have brought them.  This further complicates things, as it means he will not have read about the young McFly getting in trouble, and so will not have gone back to get Marty.  That means that he will read about it, and will go back--an infinity loop may be created here.  But there's going to be another anomaly within this, because if Doc brings Marty to the future and finds nothing for him to do, he will then return Marty to 1985, restoring the timeline he knew (with minor variations) such that now he needs Marty to save his son--as you can see, a very convoluted infinity loop within the infinity loop.  But the film ignores the impossibility and moves forward, so we will have to do so as well.

Because Jennifer is picked up by the police and "returned home", there are some additional adventures created.  However, Doc's concern that something horrible might happen if Jennifer meets herself (or if Marty meets himself) is patently absurd.  Merely meeting yourself is not a problem.  For the person from the past who meets the future self, it might be a surprise, but, like Biff, there is every chance he won't recognize himself, and even if he does that is not necessarily a complication (unless, as Doctor Who somewhere suggests, temporal displacement involves changing some type of energy level such that physical contact between the two selves will cause a discharge--highly unlikely in our opinion).  For the person from the future, seeing the past self will only remind him that he once saw his future self.  If they meet in the past, the N-jump has already occurred, and time is already different; if they meet in the future, we are certainly on the timeline of the self who came to the future previously and returned to the past (because if not, the future self would not be there).  The only danger inherent in such a meeting is that the younger self may learn something which will change his life in a way which will change the older self such that the younger self cannot learn this.  (And it may be that Doc's concern is overblown for Marty's benefit:  he does not really believe that Jennifer merely seeing herself will destroy the time-space continuum as he says, but is concerned that if in seeing her 48-year-old self, her 18-year-old self will decide not to marry Marty, throwing the future into an infinity loop.)

In the midst of this, Jennifer learns a great many things which could become information by which an infinity loop is created; however, that information is not relevant to the events of this movie.  We will return to it when we examine Part 3.  Of far greater import, while Marty and Doc are retrieving Jennifer, Biff steals the time machine.

You will recall from our discussion of the Terminator films that at the moment anyone goes back in time, the timeline from which they have left ceases, goes not one picosecond beyond the instant the reverse time trip begins.  No history continues from that point; the A-B timeline has ended, and the C-D timeline replaces it, so any future the universe may have must follow from an altered timeline.  Thus Marty and Doc cannot return to the time machine, unless we can suppose that under the altered timeline events will bring them to a moment so similar to this one that all of the essential facts are unchanged.  However, we know several of the essential facts, and are forced to conclude that we have another temporal disaster.

We learn much about the newly created timeline from the next trip--the impossible trip--back to 1985.  It appears that Biff did give himself the sports almanac, and that relying upon it he makes himself a rich man.  He murders George McFly in 1973-after Marty is born (at least we don't have that disaster), but early enough to change Marty's life completely.  Marty has spent most of his life in far off boarding schools, and probably does not even know Jennifer, let alone Doc.  Meanwhile, Doc has been committed--the date is unclear, but it is clearly earlier than 1985, and thus before the creation of the time machine.  Thus, Doc will not create the time machine, nor will he bring Marty into the future to save his kids, and so the aged Biff cannot take the time machine from them to the past.  But wait!  The future may be saved if Biff realizes that he must take the book to himself, and so invests in developing the time machine from the papers of the institutionalized Doctor Brown.  Alas, he has no way of knowing that Doctor Brown was working on a time machine, and will not give those notes a second thought; and even if it happens that someone else develops time travel soon enough, and Biff is in a position to exploit it, his statement to Marty indicates that his older self never explained who he was, and his younger self has no clue that it was him.  The triggering event--passing the book from the future to the past--sets off a chain which makes itself impossible, and we have another infinity loop.  Once again all of time comes to an end, perpetually repeating two alternate sixty-year timelines.

Although this time I see no possibility of resolving time, I will continue to trace the timelines in this movie.  Somehow, Doc and Marty return to 1985, discover the problem, and research it in detail.  Although this return trip should create an anomaly, because the point in the future from which they are alleged to have returned does not exist, the nature of this anomaly cannot be defined.  However, there are a few temporal inconsistencies which the movie overlooks, which we will examine.

Doc drops Jennifer home and Marty off at "his" house, and returns to the lab.  But Marty discovers that he no longer lives there--that his entire neighborhood has been destroyed--and Doc discovers that he has been locked in an asylum.  Eventually, Marty learns that his father died, his mother married the wealthy Biff, and he was sent to boarding school.  Now we must ask the question:  where are Doc and Marty?  The Doc and Marty of this world never went into the future; therefore, Emmett Brown is a mental patient somewhere, and Marty McFly is attending school in Europe.  The two we see are temporal duplicates from an alternate universe sideways in time.  But under Doc's theory, there are no alternate universes in sideways time; there is only one existent timeline, and if it changes, all others vanish.  So if Doc is correct, then he and Marty--and Jennifer and Einstein--cannot be here; or else, upon their arrival, their divergent selves must cease to exist so that they may continue.  Neither of these solutions are satisfying.  To avoid the awkwardness of these alternatives, we must adopt the theory of sideways time--popularized most recently in Sliders, and explained somewhat in Multiverser--that alternate universes do exist, created by divergence from a common history.  Thus, Marty and Doc may still have (and recall) the histories of their own past, and may be here, while at the same time there is a divergent Marty and a divergent Doc (often misnomered "parallel selves"), the one in Europe and the other institutionalized.  But if this is so, then there will also be a divergent Jennifer and Einstein--and even if not, even if time has been so altered that neither of them were ever born (entirely possible, even likely given the disruption in this area), they are leaving their friends in that timeline, and returning to the past to eliminate it.  Doc suggests that time will change around them, bringing them back to the original future history.  However, were this so, then it would also shift the divergent Doc and Marty to the "original" history, and there would be two of each of them when these two return.  No, Jennifer and Einstein will be lost, trapped in a divergent universe without any way of returning home--and Doc and Marty, in a linear history time machine, will have no way of retrieving them.  In fact, when under the single real history theory of Doctor Brown history is altered, Jennifer and Einstein will vanish with the alternate universe, victims of a time travel accident.

If there were a way for Doc and Marty to have gotten to this alternate 1985, there would be nothing to prevent them from going back to 1955.  They embark on a fool's errand:  they seek to change the present by changing the past and, as we discussed with Terminator, there are only three possible outcomes of this:  first, you can fail to make the necessary change, so that the past is intact and you still desire to change it, causing an N-jump; second, you can make the change, eliminating your reason for doing so, and so undoing the change, creating an infinity loop; third--the almost impossible result--you can make the change and create a different reason for yourself to know to come back in time to make the change, creating a sawtooth snap which will hopefully terminate in an N-jump (but might still result in an infinity loop).  Marty and Doc return to 1955 with the intent to alter history; furthermore, they are basing their efforts once again on information which they are about attempt to erase.  A disaster stands before us.

Note that the history they intend to create is not the original, but another divergence which is closer to the original than the current history.  They are in the C-D segment of the anomaly created by Biff (itself an offshoot of the N-jump created in the first film), and are attempting to make a portion of that into the A-B segment of a new anomaly whose C-D segment will lead to a future essentially similar to the A-B segment of the other anomaly.

The adventures which follow are exciting and fun (my video store has these films in the comedy section), and of little concern to us in detail.  Doc's concern about encountering their selves is overblown, although it is true that if they recognize themselves they will know more about the future than they otherwise did (such as that they survived and returned to the past for some reason).  Also, if Marty's presence here in this sequence disrupts the events of his prior visit such that the other he can't return to the future, he creates an infinity loop (since he cannot then prevent himself from doing so), so it is necessary for him to prevent Biff's thugs from attacking his temporal duplicate.  After much finagling, he manages to destroy the book, creating the new C-D timeline, in which history is restored to that which he prefers, that of the more affluent family headed by the successful author.  Unfortunately, this restoration undoes the reason for Marty's return to 1955 (the second return), and another infinity loop results--once again, time comes to an end.

In the end, the time machine is struck by lightning, and vanishes into the past with its inventor.  Doc Brown is sharp, and has a letter delivered to Marty while the lad is still standing in the rain, introducing the beginning of Part 3.