In about 1942, Albert Einstein was concerned about Adoph Hitler's explorations in nuclear energy, and wrote a letter to President Franklin Roosevelt urging him to finance an American program aimed at developing an atomic bomb; that led to the Manhattan Project, which we know is our history.  The movie then suggests that shortly thereafter Einstein heard rumors that Hitler was exploring time travel, and he wrote a second letter to FDR urging the creation of a similar American program.  That program was the Indiana Project, which actually was in Portland, Indiana.

Edward Charles Page was a brilliant physics student who grew up in Massachusetts and graduated from MIT in 1942.  He was already married to Ann and had a son named Richard, and he was snatched up by the program that year.

No progress had been made by the end of the war, and post-war budget cuts reduced the staff and research efforts, but Charles stayed with the project and in 1946 was head researcher.

Ann gets sick, and Charles, immersed in the research, does not realize just how sick she is.  In 1949 she dies of polio.  Charles is now raising Richard on his own, but he becomes obsessed with traveling to the past to save his wife.

Son Richard goes to MIT in 1960.  Because his father was obsessed with time travel research, the two were never close, and the son takes a job with the school in Massachusetts while the father continues working in Indiana.

In 1975, the Indiana Project is finally shut down without having shown results, and shortly thereafter father Edward has a fatal heart attack at 59 years old.  Going through his parent's possessions, Richard finds his father's journal, realizes that the man was close to discovering the secret of time travel, and spends the next decade trying to prove it.

On November 6, 1985, Edward writes that he has created and used a functional time machine.  He does not write how it works.  The central component is an Atari game system console.

Richard reportedly ran his first test by traveling one minute into the future.  He then immediately travels one minute into the past, arriving just after his departure.  He then waits a minute, sees himself arrive, and tells himself to travel back a minute.

Under replacement theory, this is an anomaly that probably works.  In the original history, the AB timeline, Richard removes himself from the timeline for one minute.  He then recreates the new history by going back and so being present in most of that minute.  He then encounters himself, but the self who has lived through the minute tells the self just arriving from the past to go back a minute.  There is a timing issue, but it's not unreasonable to believe that the second self would make the same trip at the same time, and arriving in the past would wait the same minute and direct the next iteration to make the same trip.  The only point of contention is that no one would remember traveling to the future and not meeting a version of himself that directed him to travel to the past, because that history has been erased.

However, there is a question of how this trip impacts our understanding of later trips, which we will eventually address.

Having accomplished one minute forward and one minute back, Richard decides to go longer, and sends himself back one day.  Since it is a time machine only, he winds up in his basement and realizes that the time machine has not yet been finished, so he can't return to the future; he winds up hiding in a closet until after his departure the next day, and recognizes from this that he must make the time machine portable, something that will travel to the past with him.  He thus makes a backpack version, something like those used in See You Yesterday, and continues his experiments.

Richard lost his mother Ann when he was about seven, and he decides that the best thing he can do for himself and for his father is to prevent her from dying of Polio in 1949.  The simple way to do that, he concludes, is to inoculate her against the disease as an infant, so he obtains the vaccine, locates her childhood home, and travels back to the 1920s where he injects her, and returns to the future.

We gradually learn the several consequences of this.  The first is that Richard now has a brother, Aden.  The second is that Ann died giving birth to Aden.  The third, which we learn much later, is that Ann is plagued with nightmares of some strange man repeatedly stabbing her with a needle.

Because his mother died in childbirth, Aden became a medical doctor to help keep people alive.  That leads to the second repair.

We are told that Richard was inexplicably comatose for three days in 1985.  Aden takes care of him, but never determines the cause.  Richard recovers completely, just as inexplicably, and returns to work.

In December of 1987 he persuades Aden to travel back to the moment of his own birth so he can be there to deliver himself and so save their mother's life.  We are told that Aden then becomes the first time traveler.

This would presumably exclude those two original experiments; Richard would have tested the machine when he created it, and so recognized the need for the backpack version.  However, it does follow Niven's rules here:  having changed the past by saving his mother from death by polio, Richard has no need to make the same trip, because his mother lived, and because he having changed the past it remains changed.  He does not need to take the polio vaccine to the 1920s because he is already there and brought it with him.  The version of himself who did so and returned to the present no longer exists, replaced by the version who grew up with a brother and was comatose for three days.  Under the rules we posited, it apparently works.

It would not work under replacement theory.  We have an AB timeline in which Ann died of polio in 1949, and in 1985 Richard traveled back to the 1920s to inoculate her against the disease and so she lived.  Because of that, in 1985 Richard has no knowledge that his mother was ever in danger from polio, and he makes no trip to the past; he thus does not arrive in the past with the vaccine, and Ann dies of polio in 1949.  That restores the history of the AB timeline which leads to Richard making the trip, which apparently undoes itself, which ends time in an infinity loop.

However, although it appears to work under its own rules, it calls into question those first experiments.  Richard had leapt ahead one minute, removing himself from history for one minute, and we know that in that first arrival he did not find himself in the lab.  He then leapt back to replace himself, and having arrived in the past he awaited his own arrival, and told himself to travel back one minute.  Wait, though--if it would not be necessary for him to travel back to inoculate his mother because he is already in the past with the vaccine, then if another version of himself had traveled back with the vaccine, would there not have been two of him?  And if that would be so, then it applies to those original experiments, that the one who traveled forward a minute and met himself and so traveled back a minute would find that he had already done so, and there would be two of him--a number increasing with each iteration of the journey.  The same thing would happen with the one day trip to the past, that each day there would be one more version of himself trying to hide in the basement for twenty-four hours.

It will not do to say that if you make a trip you already made you replace yourself.  It is evident that Richard gave his mother the injectable Salk vaccine; it is also evident that this was the cause of her later nightmares.  What if, knowing that he was the cause of her nightmares, he instead took back the Sabin oral polio vaccine?  Does he meet himself in the past, having both vaccines?  Note that if he instead decided that his brother Aden, the medical doctor, should vaccinate her with the Sabin dose, Aden would almost certainly meet in the past a version of his brother Richard who is completely unaware that he ever had a brother.  Why should it be different if a different version of Richard makes that trip with a different intention?  And if that is so, why should it be different if a different version of Richard (one who has a brother) makes that trip with the same intention?

Given that, it must be that when Richard made that first test experiment, he duplicated himself.  The rules as we extrapolated them do not work for the first two experiments.  It also means that the possibility of travel to the past cannot be tested, because the one who makes the trip does not remember having done so and no one else is aware that history was altered in any way.

However, Aden does save his mother's life.  In 1987, though, in the new history Aden is suddenly comatose for three days.  For some reason none of them understand, Richard so fully expects his brother to recover after three days that he comes to the hospital just in time to greet him as he awakens.  Aden is now a physicist teaching at MIT and working with Richard on the time machine.

It seems, though, that Ann just can't be saved, as having avoided polio and survived childbirth she then dies in an automotive accident in 1953.  The boys prevent that, but then she commits suicide in 1955, driving them to perfect their time machine and somehow save her.  Her depression, confided to a friend, included that she did not understand why she did not die in the crash, and that she has recurring nightmares of being stabbed repeatedly with a needle.  She commits suicide in February of 1956.

The boys decide that they can't save their mother if they can't make her happy, and they can't make her happy as long as their father is obsessed with solving the time travel problem.  They make a fateful decision.

When their mother commits suicide in 1956, the boys try to figure out why.  They found her when they came home from school, when Richard was 14 and Aden 5.  We might think it was because they remembered thwarting her suicide attempt in 1955, but of course under the rules here they don't remember that.  It must be that this time the suicide was more of a shock, because they were the ones who found her.

They deduce that their mother was depressed because their father never spent time with her, which in turn was because he was obsessed with solving the problems of time travel.  The answer, they decide, is to solve those problems for him.  Packing up all their notes with their time machine, the pair travels back to 1944, the end of the war, and delivers it all to their father.

The film only hints that this is what happened at this point.  Rather, we are told that Richard delivers equations and a functioning prototype time machine.  Presumably there is a demonstration of some sort, not described.

The military wants to use the machine to travel back in time and assassinate Hitler before the war begins; Roosevelt says no.  Thus the Americans don't actually ever use the device for anything before the next thing happens:  Soviet infiltrators at the Indiana Project steal the machine and all the research, and blow up a significant part of the site.  The Russians now have the time machine, and the Americans do not.

Edward, of course, does not actually know how to build a time machine.  He didn't build it, he never had time to read all the notes and equations let alone learn them, and even the basic components of the system, found in the Atari game system from thirty years in the future, are beyond the technology of the day.  Pressured to build another, he fails to do so.  The FBI and CIA begin to suspect him of being a Soviet collaborator himself, and start watching him.  Meanwhile, the KGB, equally in the dark about this machine, is concerned that he might build another, and they begin monitoring his activities.  He resigns from the project and moves to upstate New York, where he takes a teaching job at a local college, but family and friends note that he seems paranoid, believing that someone is watching him.

Meanwhile, the government believes that the Soviets are tampering with time.  Russia repeatedly beats the United States to many military projects; Sputnick was a stolen U.S. design, and Yuri Gagarin is the first man on the moon.  There is a passing mention that President Nixon is assassinated in Dallas, Texas, which probably means Kennedy was never elected.

Aden is born on schedule, and the two boys delight in working with their father in his basement lab.  Both become physicists and graduate from MIT, and both take jobs on staff at the university.

Edward has continued trying to solve the time travel problems, and continues to believe, correctly, that he is being watched.  He begins trying to build the lost time machine, but doesn't tell Ann because he believes she is safer if she doesn't know.  It is now the mid 1970s, and his sons are working for MIT; but Edward can't solve the problems because he doesn't have the equipment.

He decides he needs to use the equipment at MIT, so he speaks to his sons.  He tells them that although the CIA and the KGB both believe he built a time machine, he never actually did; they built it, and brought it to him.  They believe he is becoming more delusional, and refuse to help.

Edward breaks into the MIT lab, but is caught and arrested.  In custody, he tells the police about the Indiana Project.  MIT agrees not to press charges on condition that Edward gets psychiatric help, but before Richard and Aden can get home to tell him this, Edward and Ann are dead.

The police ruled it a murder-suicide, but the sons don't believe it.  For one thing, although the gun which shot them both was next to Edward's hand, no prints were on it.  They believe it to have been an assassination, but no one ever investigated that possibility.

In about 1995, the boys decide to sell their parent's home, and while they are going through it one last time they find their father's journal under a floorboard.  In a previous timeline, when Richard found this journal it contained a photo of his mother, with the words "I will save you" written on the back in his father's hand.  This time it has a photo of Edward and Ann together, and the words on the back are "You will save us."  The brothers begin working on the time machine.

It becomes obvious that they are involved in something outside their regular MIT duties.  In March of 1995 they cause a blackout at MIT.

This catches the attention of the CIA, which of course knows that their father had a time machine in the 1950s which the Russians stole and have been using to give themselves the lead in all things.  They detain the boys, and in essence tell them that they are to invent the time machine and deliver it to the CIA for use against the Russians.

It takes them over a year to do so, but in November of 1996 they have completed a working prototype time machine.

Before they finished building their machine, the boys agreed that they were not going to give it to the CIA.  Instead, they adopt a highly audacious plan.  Richard, alone, travels back to 1942, to the Indiana Project well before it had accomplished anything, and destroys the facilities using explosives.  The project is shut down.

We are told that thereafter although Edward's research was promising he moved to New York to teach.  Richard became a physicist, but Aden, born on schedule, became a medical doctor.  Edward died peacefully at age 77.

Richard was reportedly found comatose after a presumed stroke in 1996 following a failed experiment of an unspecified nature.

Time travel was never invented.

Several things are evident at this point, but there are other points that need to be recognized.

Under the version of replacement theory espoused by this website, the movie fails repeatedly.  Every time an arrival in the past undoes a departure from the future--which is true of every trip in the film--it should, by our reasoning, undo the arrival in the past restoring the departure and creating an infinity loop.  However, at the outset we noted that the film appeared to follow specific rules such that once a time traveler had arrived in the past his actions were part of history and his departure was irrelevant.  It would actually be more complicated were the time traveler to repeat the same trip, because that should logically duplicate his presence in the past under those rules.

It is apparent, too, that the movie itself could never have been made.  Any filmmaker attempting to tell the story about time travel would have to do so from the only version of history he knows, the one in which he lives.  The film in which the events change, even when presented so subtly as this film does it, could not have been made.  It is a fun conceit that makes the movie we watch possible, but no one could ever know all the details it includes.  Every history it mentions has been forgotten by everyone alive.

It is evident that the point of the final trip to the past that destroys the Indiana Project is supposed to be that it prevents Edward Page from becoming obsessed with time travel and prevents his sons from delivering the machine to him in 1944.  Under the rules, Richard and Aden should arrive in 1944 with the time machine, but find that there is no project to which to deliver it and their family has moved to New York.  Thus neither the Americans nor the Russians would ever receive or be aware of the time machine, and the Page family could live a normal life.

From this, we are to think that all of history is restored to its original form without any temporal interference.

However, the rules won't allow this.

It is the case that the Soviets never steal the time machine, and therefore never depart from any point in the future to bring stolen American technology to Russian scientists in the past.  However, it has already been established that under the rules the undoing of a departure from the future does not undo an arrival in the past.  Thus even though the Russians have no time machine and no motivation to attempt to steal American technology to send to the past, periodically time travelers will arrive bringing stolen American technology to Russian authorities, who will deploy these.  Yuri Gagarin will be the first man on the moon.  Under the rules posited for this, world history and the balance of power has been severely altered.  The elimination of the time machine does not restore history, precisely because erased departures do not undo arrivals.

As an aside, within the film once Aden is born, he is born on schedule in every subsequent history regardless of changes in the lives of Edward and Ann, including whether they live in Indiana or New York.  As we learned in About Time, this is improbable in the extreme; even slight changes in the lives of a couple seriously impact the genetics of offspring.  At some point Richard ought to have been working with his sister, or some otherwise different sibling, or possibly have had another sibling.  It is one of those improbabilities that are incredible, and the more so because it keeps repeating.

Thus not only is the movie impossible from the perspective that it could not have been made even had all that happened, it also proves ultimately to be impossible under its own rules.  It is still an enjoyable and subtly if darkly humorous movie, and a decent stab at a time travel story, but its ending is not possible.