Temporal anomalies discussions inspire questions, and the e-mail bag and comments sections have been filling, so it's time to answer.  Somewhere around the fourth installment of our series on Primer, Tim E. Sham, author of The Primer Universe, sent an e-mail raising what he perceived as a significant question about the film, what he referred to as "the disappearing Abe", or "the Houdini Abe".  In response to inquiry, he explained, "The Houdini Abe is the Abe that enters the U-Haul at 3 pm while Abe and Aaron watch with the binoculars. Essentially, he is said to 'disappear' from the timeline."

There actually is no problem with this "Houdini Abe"; his existence and disappearance as a temporal duplicate are completely necessary under the replacement theory of time, the theory which best explains most time travel stories, and also completely necessary under other theories of time.

Under replacement theory, Abe lived through the day and at the end of the day took his knowledge of the stock market closings and his air tank and traveled back to that morning.  As he emerges from the time machine, it has just been started because he, Abe, was there fifteen minutes before to set the timer.  The Abe who just started the time machine hopped into the car and headed for the hotel, and the Abe who just emerged from the time machine calls a cab and heads downtown, first to buy his stocks and then to find Aaron and tell him what he has discovered.  All day there are two Abes in the world, one with Aaron and the other at the hotel.  The one at the hotel leaves in time to get his oxygen tank and enter the time machine.  He emerges in the morning, and becomes the "second" Abe.  It is essential to the time travel story that he do so, or he cannot exist as the second Abe.

This is much the same for the fixed time theory:  if time cannot be changed, then we must assume that Abe traveling to the past has always happened, and that while Abe was hiding in the hotel he was also downtown talking to Aaron.  In this case there was no "original" version of history that Abe altered by traveling to the past, but simply two Abes in the world all day, one of whom leaves to become the other for what is for him the second run.  He could not not do so.

Parallel dimension theory gives us a slightly different outcome in theory, but one that is the same in perception.  In this case, when Abe left the future, he arrived in the past of another universe in which there was already another Abe, one who was exactly like him in every particular that morning and who was planning to do exactly what he did.  Late that afternoon that Abe climbs into the time machine, which moves him in his turn to another dimension, where there is another Abe planning to do the same thing.  In whatever we consider the prime universe, Abe climbed into a box and vanished from the world forever; but he created a cascading effect in which in every other universe an Abe arrives in the morning (from another universe) and another departs in the evening (to another universe), and so that other Abe is not a problem.  It is more complicated in divergent dimension theory, because the Abe who leaves from the second universe ought to create a universe which diverges from the one from which he came, and in that universe there is already an Abe arriving from the future when he does; however, the first time traveler would not have this experience.

Although there may be other theories of time travel, these are the ones commonly referenced in time travel discussions.  It would be much more difficult if there were not a second Abe who entered the storage unit and vanished forever.

When the fifth article in our Primer discussion published, "TW" asked what Aaron intended to do with the large box he was building at the end of the film.

It is on one level a moot question.  Overnight around the fourth day Abe and Aaron travel to the past, Thomas Granger appears from maybe three days in the future.  His involvement causes an infinity loop, the end of future history, because he prevents the events which lead him to make that trip.  Thus we can stretch time, from the moment the failsafe starts to the moment Granger departs, maybe eight or nine days.  Aaron and Abe returned to the first of those days and spent that night at the party.  They stand in the airport the day after that party, the day that Abe does not explain the workings of the machine to Aaron because his doppelganger has sabotaged his machine.  That creates a second infinity loop overlapping the first; history is caught in a loop not longer than four days, one of which is in the past as Aaron leaves.  If he reaches this foreign location, raises funds, equipment, and workers, and has a box running in two days, he might enter it minutes before time ends and return one day to minutes after the machine started.  He cannot do much, so it's not particularly significant what he hopes to do.

Is Aaron working on a "more powerful" device to send him further into the past?  Everything we know says that these machines cannot transport anyone to a point prior to their activation.  They do not travel through time, but create a temporal connection between two points.  A bigger machine has room to transport more, but there are not very many uses for it.  A large machine could temporarily duplicate more people.  If at five in the afternoon a hundred soldiers came from the battlefield and traveled back eight restful hours to morning, then marched onto that battlefield, there would be two hundred soldiers there.  Could you duplicate enough men to make a difference?  Could you plan for that?.  Under replacement theory you would have to ensure that the right men entered that evening to emerge that morning.

Is it really a time travel device?  It could be carrying passengers to another dimension, which would make an interesting escape hatch for anyone fleeing from whatever might not be in that other universe.  This, too, is problematic.  Something would have to have happened while the machine was running which could be prevented if someone could duplicate himself in the past.  It also means that there would be two of him in that other dimension.  If he prevented the problem, his double would have no reason to leave.

Aaron might not be interested at all in the machine's temporal effects.  Its output power exceeds its input power by about 6.25%; you could input a gigawatt and get back an extra sixty-two megawatts at no cost.  Twelve in series would double power output, cutting costs of electrical generation in half.  A judiciously designed system could become a perpetual power machine, the extra electricity tapped and the original power fed back to produce the same increase again.  An engineer could easily get funding for this, if he has a low-level prototype that demonstrates the increased output.  Aaron might be planning to profit from the more mundane aspect of his invention.

It is not completely clear what Aaron is building, but it does seem likely that it is another box. At one point he said that they should build one large enough for multiple occupants.  He might not realize that his time is limited.

All of this is speculative; the film does not offer an answer.  It's anyone's guess what he thinks he is going to do with it.  He will be out of time before he does it.

Several people have suggested that Primer works under some version of multiple dimension theory.  Arguably multiple dimension theory is not time travel, but if we are asking whether Abe and Aaron travel to other dimensions thinking it time travel, that's moot.  Is it possible for these events to occur under multiple dimension theory?

There are several theories of time involving multiple dimensions, at least two of parallel dimension theory and some distinct concepts of divergent dimensions.  It is this latter that is usually presented as explaining Primer.  Yet it is the more problematic.

We discussed what someone dubbed the disappearing Abe, that doppelganger who enters the storage facility while his duplicate is explaining everything to Aaron.  On nearly any theory of time he must exist, and since Abe has not interfered with him, he should make the same trip the first Abe made.

Given divergent dimension theory, Abe traveled to that morning and created a new dimension, which we are now seeing.  In his own universe, he entered the box and never emerged; he exited in another universe.  That there is a mysterious disappearance in that world possibly involving a criminal investigation is immaterial to this Abe, who doesn't know that.  He emerged, unaware that he had created a new dimension.

Now as his counterpart heads to the past, he, too, will create a new dimension, based on whatever the situation was at the exact moment in his own past of his arrival, the past of this universe.  Yet he will be arriving in the past at exactly the same time and place as the Abe who departed from the original universe.  Since the arrival of that other Abe is already part of the history of his world, when he gets there, that other Abe will also be arriving, and there will be two of them coming out of the time machine.  Further, unless they stop him, at the end of that day yet another Abe will get into the box and create a new universe, in which three Abes will climb out of that box that morning.

The only way to prevent this, given divergent dimension theory, is to prevent the Abe from this universe from getting into that box; but if we do, he remains in this universe alongside his duplicate (or more likely duplicates--Abe will not realize what has happened until there are at least two of him emerging from the box) for the rest of their lives.  (This seems to be the claim in Tim Sham's The Primer Universe, in which he says that the only way to prevent yourself from being duplicated is to turn off the box when you exit.)

It might be argued that the story we see is possible, given that it follows a very specific one of the vast number of variant Abes being created.  What happens in the next universe is of no consequence.  Yet if we turn our attention to the watch experiments, that that answer will not hold.

When a running stopwatch is put into the box activated for one minute, it emerges from the box having measured thirteen hundred forty-seven minutes.  The explanation given is that it has traveled between past and future that many times; this explanation must be close, since on this basis Abe determines he has a time machine.  That means, though, that this watch traveled to the past six hundred seventy-three times, returning to the future end between them, creating six hundred seventy-three universes.  Since in the original universe it was there in the past (reading zero), then in the second it must have encountered itself already there, and in the third it encountered itself encountering itself.  By the time the box is opened there must be six hundred seventy-four watches in the box.  In this case, we cannot claim that this happens not to be the watch that made all those trips, because the time on the watch itself demonstrates that it is.  If this watch has created six hundred seventy-three diverging dimensions, it created that many watches, each different by two minutes on their counters.

Some will argue that the new universe diverges not from the present history but from the original history.  However, since the watch was in the box before it was activated, there still must be at least two watches in the box--the one that was there originally plus the one that traveled through time to get here.  The absence of a duplicate watch is fatal to a divergent dimension explanation of the film.

Perhaps, then, pure parallel dimension theory explains this film.&

We addressed whether Primer might work under divergent dimension theory, and found difficulties.  Might it be possible, however, that the film works under pure parallel dimension theory?  Are Aaron and Abe traveling to different universes which already exist?

Again we have the problem that if this is the case, there will be universes from which they vanish, never to be seen again.  Each of them makes a solo trip near the beginning of their travels, and that puts them out of synch with each other.  This is not insignificant.  It means that from universe 1, Abe goes to universe 2, and Aaron in universe 1 never knows what happened to him; but then after Abe explains time travel to Aaron in universe 2, Aaron makes his secret trip back to the beginning, and so he leaves universe 2 for universe 3 and the next day Aaron cannot find him ever again.

However, the problem created by the shotgun party is insurmountable for this theory.

It was previously mentioned about parallel dimension theory that making the number of universes infinite does not solve problems, it only makes them more difficult to discuss.  Thus let us suppose that there are only ten universes for illustration; it should be apparent that the number of universes becomes irrelevant.  Skipping to the moment that Abe decides to be the hero, he and Aaron leave from universe one to visit the party in universe two; they also prevent their counterparts here from doing the same thing, so no one appears in universe three, and that pair go to universe four and stop their counterparts--in any case, there are two pairs in all even numbered universes and none in the odd ones.

However, Aaron says they repeated this multiple times.  That means that the spare pair in universe two went to universe three, where the boyfriend was waving a shotgun; and then they went to universe four--but wait, the pair from universe three are already at that party, and they are now at universe six where the pair from universe five are trying to intervene, who are now in universe eight confronted by the pair from seven, and so on.  Then if the boys make another trip to universe five, the pair from universe three is also there.

What parallel dimension theory is supposed to do is make it possible to change the past without changing anything that happened; but once the universes are so linked, travelers from different universes begin to interfere with each other, and so history changes anyway.  In this case, it is not possible for Abe and Aaron to have gone to that party more than twice and not encountered themselves as time travelers; yet they do not do so.  Thus parallel dimension theory does not resolve the problem at the party, and cannot make a coherent story of the movie.

If you are using some form of multiple dimension theory, either the universes already exist or your actions are creating them.  If the latter, you face the problem of duplicating yourself with each trip; if the former, the actions of your doppelgangers in all other dimensions must be included in considering the outcomes.

We should also consider whether the film works under fixed time theory.

Neither parallel dimension theory nor divergent dimension theory can support the events in Primer.  The question might reasonably be asked, though, whether the story works under fixed time.

Perhaps the first clue that the film is not following fixed time theory is the incident with the cell phone.  It could not happen as it does under fixed time.  To refresh, when Abe and Aaron are in the hotel their first time through the day, Aaron's cell phone rings, and after some discussion they answer it.  Then on the second time through the day the same call reaches Aaron downtown, and again after some discussion Aaron does not answer it.  Someone has suggested that it was answered by the other Aaron, at the hotel, so nothing was disrupted; but that answer will not stand.

First, Abe is right:  cell phones do not work that way.  Only one of the two phones is ringing, so if the phone is ringing downtown it is not also ringing at the hotel, and could not be answered from the hotel even if that Aaron somehow tried to do so.  Once the network finds the "right" phone it stops looking, and on the second pass through history the "right" phone was found downtown.

Even, though, if Abe were wrong, the filmmakers perhaps rather skillfully tell us in the downtown scene that the phone was not answered at the hotel.  At the hotel, Aaron answers his phone in the middle of the fourth ring; the downtown phone is clearly heard to ring at least five full times.  Had it been picked up at the same moment at the hotel, it would not have completed that fifth ring downtown.  The answers to questions about time travel stories are often in the minutia, and this is an excellent example of that, as the difference of an extra one and a half rings means that the phone was not answered.

(In this, it might also be noted that the phone downtown will show a call received and a call missed from the same caller at the same moment, but the call at the hotel will never show both calls in its call record whatever happens next.  Aaron's phone downtown will have to be replaced in the replay of history with the other phone, so we are not viewing the final form of history there.)

As the story comes to its close there is far clearer evidence that time is not fixed:  the pair intentionally change aspects of history beginning with the shotgun party, and accidentally change other aspects including the fate of Thomas Granger.  That Aaron can discuss what happened in previous versions of history (he knows what happened at the party the time he was the hero) demonstrates that history has been changed, and fixed time makes it an absolute that it simply cannot be.  Thus fixed time is excluded as a possible theory of time for Primer.

It seems likely that the characters at least think they are working with divergent or parallel dimension theory, because when they decide to seek out Joseph Platts and then escape punishment by altering history, they assume it will be all right because later that day their alternate selves will use the time machines to go back to that morning, which probably would be all right if the machines are moving them to divergent or parallel worlds--but other events in the film (as previously considered) are impossible for these theories.  However, not all the results are consistent with replacement theory, either, which leads to the problem that it does not appear that the writers had a consistent theory of time in mind when they created the story.