Although the film is popularly known by the long title Teenage Mutant Ninja Turtles III:  Turtles in Time, the tagline does not appear either on the DVD case or in the opening credits, and it is also popularly known by the short title TMNT3.  The copyright says 1992, so we will assume that the action in the "present" occurred that year.  Meanwhile, although there are at least four time trips, they (the ones we can confirm) were all made to 1603.  There is evidence of another trip, apparently from further in the future to further in the past, but the details of this are sketchy at best.

Everything revolves around a scepter that looks more like the top of a lamppost.  In 1992 it is an antique which news reporter and Turtles friend April O'Neil found in a junk shop and bought as a gift for Splinter, giant mutant rat who is their wise elderly sensei.  In 1602 it is an heirloom of the family of Lord Norinaga of Japan, which he regards as a secret weapon and something of a good luck charm.  Unfortunately it is some type of presumably magical time travel device, and Lord Norinaga's son Kenshin manages to activate it, starting the adventures.

This particular device requires "equal mass displacement", that is, any object that travels through time must replace and be replaced by a comparable object of the same mass.  This concept is stretched a bit.  While Kenshin seems slight for a man, the odds that he is exactly the same mass as April O'Neil, or that neither of them would gain or lose so much as a gram over the adventure, seems improbable; and given their muscular bulk and the presumed weights of their shells, it is hardly credible that the turtles do not weigh significantly more than the four warriors identified as "honor guard".  (Perhaps we would believe it if they had had the expected build of heavyweight Sumo wrestlers, but they barely pass as samurai.)  In any case, because Kenshin has activated the device by reading the inscription on it, it finds April O'Neil holding the device three hundred eighty-nine years in the future, and swaps each for the other.

The turtles then figure out what happened, and organize themselves to travel to the past.  We discover, if we're paying attention, that the device does not swap people from random points in time but only between points that are aligned with each other, and only at specific moments of alignment.  This gives them sixty hours to recover April, and limits their opportunities for return to twelve hour intervals, with the further stipulation that those who will replace them must be touching the scepter at the right time as well.  This, too, is a rather loose requirement--on the second trip, the four turtles switch with the four-man honor guard all of whom are mounted on horses and thus only one of whom is in direct contact with the scepter.  Yet it does matter.

They have what is seemingly a significant impact on Japanese history, which we will have to consider carefully in the series ahead, and then Kenshin and three members of the honor guard return to 1602, bringing April and three of the four turtles back to the present.  Michelangelo remains in the past, and the only member of the honor guard to be named in either the script or the credits, Benkei, remains in the future.  About a minute later, there is one more trip, as Benkei and Michelangelo switch places, restoring everyone to their correct time.

There is one other temporal complication.  Norinaga keeps a scroll with the scepter, which depicts and apparently tells the story of four kappa, or demons, who look exactly like our turtles, use the same weapons, and wear the same colored masks.  (It is one of the jokes of the series that the turtles wear masks so we know who they are.)  These turtle demons apparently appeared two hundred years before (if that is exact it means 1403) and thwarted the ambitions of Norinaga's ancestor; our turtles have not yet made such a trip and know nothing about it.  The odds seem very much against the idea that someone else appeared in the past, or that the artist's conception of whoever interfered then would so closely match the actual appearance of the Turtles, and thus the simplest explanation would seem to be that the Turtles in their future will make another trip further into the past.  This, too, is a complication.

To begin, however, we will have to attempt to construct an original history.

Before we attempt to reconstruct an original history, it should be noted that in some ways the entire story is much simpler if it is not real time travel, but parallel dimension travel.  These dimensions are not quite parallel.  The Turtles leave from one and arrive in another and Kenshin leaves from that other and arrives in the one, and all the travel we see is between those two dimensions; if, though, there was a Kenshin in the world from which the Turtles came, he never went anywhere, and if that world had Turtles of its own, they never went anywhere either.  Similarly, we can suppose that Turtles from yet another dimension, who had never traveled to 1603, traveled to 1403.  That simplifies matters, because it then ceases to be about time travel at all, and is in a very real sense not different from The Chronicles of Narnia or Through the Looking Glass and What Alice Found There.  It is an adventure in another universe to which a portal has been discovered.

Yet it does not simplify everything.  There is the problem of the artifact itself.  We see it as something made perhaps by an ancient Japanese magician which connects with itself across time.  Now suddenly it connects not across time but across dimensions that are at different points in time relative to each other.  To resolve our temporal problems fully there must be at least three of these existing in different dimensions, and they must be dimensions at some temporal distance from each other; yet the devices must be identical, and that suggests that they must have been made by the same person (even if a parallel self) at the same moment in history.  The problem arises that the first one will not work, because they will only work if there are two; and indeed, even if there were two created at nearly the same instant that were tested shortly after being made, the traveler would be unaware of having traveled to another dimension because it would be the same time and place when he arrived.  It cannot work.

That problem, though, plagues our device in a different way if we take it to be a time travel device that communicates with itself:  at the moment of its creation there is no future version of itself for it to contact, and so it will fail to work until it has existed long enough that it can be used to travel to its own past.  Whether the inventor will test it a second time having had it fail the first time is questionable; but then, he would also have to test it the second time having succeeded the first time, or he would undo his own success.

Perhaps, then, the device was not made by an ancient wizard, but is a gift from gods, created in some realm outside spacetime by beings who need not test it.  Perhaps no one knows what it does because it has never done anything at all before, or because whatever it did no one recognized or understood.  This is the first time it has worked, because this is the first time it is properly aligned with itself with persons on both ends ready to make the trip.  Certainly someone held it in 1403 and pronounced the words, but then nothing happened because there was not yet a future time from which someone could be summoned.  Kenshin perhaps held the staff in 1603 and got no response, because until history reached 1992 April was not at the other end.  What matters in temporal terms is that in 1992 April O'Neil held the staff at the properly aligned moment such that Kenshin could trade places with her when he activated it, and that gives us our first trip.

If it is a hop to a parallel dimension, then we have no time travel in any real sense; we have two similar worlds working to make each other different.  As we move forward to examine what the original history would have been without the time travel, we are creating the world in which the turtles never arrived, which would be the world from which they departed, whether that is the future or another universe relative to the events we call 1603.  Our interest is in time travel, so we will assume that time travel is involved.

Reconstructing an original unaltered history of this film is challenging.  We can easily identify "changes" in the sense that individuals traveling to the past performed specific actions which had specific results; what is not so simple is identifying what the original form of events might have been, that is, what would have happened absent those actions.

For example, we are shown a scroll on which images of the Turtles appear, and told that two hundred years earlier the same supposed demons arrived and defeated the diamyo's ancestor.  The Turtles we are following have not yet made that trip, and so there ought to be a history in which they arrive in 1603 in which they did not arrive in 1403.  That means that the scroll does not exist.  It means that Kenshin and Norinaga do not recognize the Turtles as the kappa in the pictures.  It also means that Norinaga's ancestor was not defeated by Turtles from the future in 1400--and therein we have the major problem.  Did that family win its war in the original history, and if so how does having lost it instead alter the situation in Japan two centuries later?

It is possible that we have our temporal trips out of sequence.  It is natural for us to assume that if the Turtles traveled to 1603 from 1992 and then traveled to 1400 from, say, 2000, they made the trip from 1992 first--and in a temporal sense of course they did.  However, it might be that in a sequential sense these trips are reversed.  Remember, if they travel from 2000 to 1400, they necessarily create a new timeline, a new and different history; it is possible that turtles departed from 2000 first, arriving in 1400 and then either dying in the past or leaving for the future, then as that future was being written April O'Neil left from 1992, leaping back to the 1603 of that history, in which the Turtles had already arrived in 1400 because they made that trip first.  If we can then resolve all four known trips to N-jumps our history can advance to 2000, and we then address what happens to the original anomaly as the Turtles who leave from this history already know that they were in the past in 1603, that there was reason to believe they had been there previously in 1400, that they won both times, and that the scepter was the instrument of their time travel.

That aspect is itself awkward.  If this reconstruction is correct (and we are not certain it is), then in the original history the turtles in the year 2000 have not seen the scepter before; something they will do in 1400 will cause the future of the scepter to alter such that it lands in their hands a few years earlier.  They will thus not know in 2000 of the original history that it is a time travel device.  Yet their replacements will have a considerably more thorough understanding of the device, having used it a few years earlier to rescue April.  (We have reason to believe that the device was involved in that other trip, because the scroll is kept with the scepter, which makes sense if the two are connected.)  That suggests that their original trip was accidental, but their replacement trip was intentional, which leads to other problems.  We escape this if we assume that the first trip was made by April; but then we are back to the first problem, that the absence of the Turtles in 1400 will change events in 1603 in ways we cannot determine.

Some will say that all of this is nonsense, because history is fixed, and the Turtles who are going to leave from 2000 have already arrived in 1400; they are fated to survive the events of 1603, return to 1992, and then make the other trip a few years in their future.  It must be admitted that there is no evidence in the film which prevents it from working under fixed time theory--if fixed time theory itself works.  We have here something of the billiard ball problem.  Since the Turtles handle the scepter in 1400 and again in 1603, the fact that they have it in 1992 and in 2000 is only true because of what they did when they were in the past.  Although it is hidden, this is a predestination paradox, an example of an uncaused cause, and thus an event which only happens if it happens.  Anything which only happens if it happens, which is its own necessary cause, cannot happen.

That's not to say that the film necessarily resolves under replacement theory; we still have to determine that.

Whatever we decide concerning the sequence of our trips, we still have an original timeline in which no Turtles arrive in either 1400 or 1603, and the Norinaga family has a very different history.

In the history of 1603 which we see, Norinaga's ancestor lost the war in 1400; yet the family retained its defensible home and its heirlooms.  While we want to know how the world would have been different had they won, it is puzzling to wonder what changed because they lost.  They might perhaps have fought against another noble house, and been forced to pay tribute to them; this, though, is more the pattern of middle eastern petty kingdoms, not of Japanese feudalism in which each daimyo holds his land at the pleasure of the Mikado as determined by the Shogun.  It is more likely that it was a peasant revolt, in which the Norinaga family attempted to quell an uprising.  That means that the war fought in 1400 was between Kenshin's ancestors and those of Mitzu, the young girl leading the present rebellion.  The fact that she believes the war will not be able to end, perhaps ever, unless she and Kenshin marry gives some credibility to this theory, as it suggests that the tension has existed for longer than her lifetime.

There is, however, an unwarranted assumption here.  We know that in the history we see, in 1400 the Turtles came from the future and fought against the Norinaga forces, and that the daimyo lost.  Our Lord Norinaga assumes, apparently because his histories tell him so, that his family would have won had it not been for the intervention of these kappa, these turtle-shaped demons who interfered.  That, though, might be no more than his own family arrogance.  It is entirely plausible that there was an original history in which peasants fought against the Norinaga household and won.  We have no reason to believe that the Turtles either were summoned from the future or were sent from the future because it was necessary to change the outcome of the war.  We could have an original history in which peasants defeated their daimyo, and then an altered history in which peasants assisted by Teenage Mutant Ninja Turtles from the future defeated their daimyo.  The critical difference would be that the daimyo's family would blame not so much the peasants as the Turtles, keeping a record of this seemingly supernatural interference for future generations.

That reduces the importance of the trip to 1400.  The scroll still matters to the psychology of the Norinaga leaders, but we are not looking at an original history in which a war was won and an altered history in which it was lost, and so given two centuries and the assumption that no one of consequence died in one timeline and not in the other, by 1603 most of what we find is as it would have been.

Of course, in the original 1603 we do not have visitors from the future, either; but again we have that peculiar question of what would have happened had there been no temporal tampering.  This time it is much more complicated, because we know who the players are and how they interacted, which means that the possibilities are a bit more interesting.

Our original history is a Romeo and Juliet variant.  Kenshin, in the role of Romeo, is son of the Daimyo, in love with Mitzu, in the role of Juliet, who is the leader of the rebels, and she with him.  Mitzu's family apparently has a leadership role among the peasants, and we surmise has long been at odds with the ruling Norinaga family rulership, giving us our Capulets and Montagues.  The part of Verona is played by seventeenth century feudal Japan, the role of the meddling priest played in later iterations by a telejournalist and four giant mutant turtles.

As we meet Kenshin's father, Lord Norinaga, he is about to execute his son for the stubborn youngster's flagrant disregard of his father's wishes, which clearly include defeating Mitzu's family by combat, not having his son doting on some peasant girl.  The execution is interrupted by Walker, a British trader profiteering on the political unrest here by offering to sell guns for silk and silver.  Kenshin enters the fortress, finds the sceptor, reads the words on it, and in the history we see vanishes to the future.  However, since that future cannot exist until a chain of events occurs leading to the moment when April O'Neil is also holding the sceptor and the universe is properly aligned to connect them, in the original history nothing happens--Kenshin remains in his father's fortress awaiting whatever judgment will come next.

Given that no one arrives from the future, we have two major variables that would alter history drastically, plus a third that might alter it significantly.  The first is whether Kenshin marries Mitzu, and the second whether Norinaga wins the war.  The third is the genetic problem we discussed in connection with Timeline (and more recently with Blackadder Back & Forth), that the deaths of specific individuals can change the genetic identities of entire populations in a few short generations.  We see only one person (Walker) die; we see one person (Yoshi) saved from a threat of death which might not have existed had the Turtles not arrived.  We cannot guess the carnage that was prevented by the time travelers.  It is difficult to believe that there was none, and important to recall that the Turtles were trained by a rat who learned his craft from a Japanese master, a master who might never have been born had one wrong person died (or not died) in 1603.

Among those is Kenshin.  His death has another impact, though:  if he marries Mitzu, it brings peace to the territory; otherwise, the war continues perhaps for another generation.  Yet it is more complicated, because if Norinaga executes his son there might not be another generation--the Norinaga clan ends with Kenshin, for whom there is no evidence of a brother, a surviving mother, nor even a sister to inherit.  We believe the war would continue without that marriage because Mitzu says so, but who will fight once Norinaga dies?  What is of greater concern is that the war will be devastating until it is over, and will change too many lives for the future to stabilize after that is changed.

Even if Kenshin survives, there is still a significant chance that the war will continue and that he and Mitzu will never marry.  She might be among the casualties, breaking the connection he has to his people and extending the war into his own generation.  They might both survive and never overcome Norinaga's objections.  They might both die.  In any case, we have the war we seek to prevent, and the history we cannot reproduce.

Perhaps it is not so, though.  Norinaga returns to find Kenshin, who is looking at the family treasures.  He decides to give the lad one more chance, allowing him to survive.  This time the heir manages to escape, find Mitzu, marry her, and return with his bride a fait accompli, averting the war entirely.  Walker returns to England, perhaps having sold weapons to the daimyo at a lower price; his spy Whit dies in Japan.  This might impact the genetic lines in England, but probably neither of them are ancestors of the religious dissenters who settled New England nor of the Irish O'Neil clan, so April might still exist.

Thus our best hope is that the time travelers did not alter anything that mattered, that Kenshin marries Mitzu and war is averted, and the only thing missing is the tales of turtle kappa tipping the battle.

It will become more complicated, though.

We now approach what we have decided to treat as the first trip to the past, in which April O'Neil replaces Kenshin in 1603.  In the film, her disappearance from the future prompts the turtles to examine the scepter, and so to pursue her into the past.  That cannot happen this time.  Before Michaelangelo can apply his technical know-how to the device, all of history from the moment of her arrival in the past to that of her departure from the future must be rewritten, and must stabilize into a form that supports itself (in which she was holding the sceptor sitting in their lair a moment earlier).  To clarify, at the moment April was holding the staff there was a history of the world in which, as we suppose, Kenshin married Mitzu and brought peace to the province.  When April leapt to the past, Kenshin was thrown to the future.  We must determine what happens in the universe in which April replaced Kenshin before we can consider what happens next in the future.

Here things look bleak.  It is now impossible for Mitzu to marry Kenshin, and no one will ever know what became of him even if April attempts to explain what she knows.  It also does not appear that April would escape her imprisonment without the help of the turtles.  Norinaga believes her to be a witch; Jackson denies that witches exist, but has no better explanation and is not going to get one from April no matter what he does.  No rescue will come, Kenshin will not return, and ultimately April O'Neil will die in 1603 while Lord Norinaga's son Kenshin will never be seen again.

The war will continue, and people on both sides will die.  Even if we assume that none of this impacts April O'Neil's ancestors in Ireland, it will change the population of Japan and may well undo the existence of Splinter and the Turtles.  That in turn would eliminate her interest in the sceptor (which she purchased for Splinter) and her reason for being in a lost section of the subway system holding it at the right moment.

At this point, though, our analysis hinges on probabilities, not certainties.  We can say that given the changes in the genetic diversity in feudal Japan, the odds are against Splinter's teacher ever being born or Splinter becoming his pet and being exposed to the mutagenic chemical which made him who he is and the Turtles who they are.  We cannot say it certainly could not have happened.  Thus we cannot say that it is impossible for the present as we know it to exist given those changes to the past.  It is possible for the scepter, which we cannot trace between its appearance in 1603 and its appearance in 1992, to be found by April in an antique store and thus acquired as an intended gift for Splinter, and that she would be holding it at the right moment in the right place for Kenshin's activation of the scepter to take her.  While things look bleak for Mitzu, for Norinaga, and for April, we might against all probability reach the correct present entirely by accident.

In that case, history can continue for a few more hours while Michelangelo divines the concept of equal mass displacement in time travel, and the Turtles prepare their rescue of April.

As a practical matter, it would have been much more sensible for Kenshin to use the scepter to return, then if it did not happen that April was restored to the future he would have to find her and have her use the scepter, while the turtles ensured that whoever was swept to the future was ready to return to the past when that happened.  That, though, would have been a lot less interesting as a Teenage Mutant Ninja Turtles movie.

Although it is improbable, we will accept it as possible that when April replaces Kenshin in the past, history stabilizes such that she is there in the future when she needs to be to make that trip.  We now hit the next event in our temporal anomalies, as Michelangelo determines how to operate the device, and the four Turtles leap to 1603 in an effort to rescue April.

At this point, nearly everything we see in the movie can happen, except for the ending.  The Turtles have reached the past, and will rescue April, be mistaken for demons, save Yoshi, and win the war.  Then they will attempt to return to their own time--and will fail to do so.  We once again have the problem that in traveling to the past they have changed history, and history must reach the future before there is a future from which anyone can travel (a problem addressed significantly in Timeline, and then addressed in more detail because of the recall devices).  Once you travel to the past, you can only return to the future created by what you have done in the past; and if something must happen in that future before you can be removed from the past, then you are effectively stuck in the past for the remainder of your life and however many additional years it takes to reach that future moment before you can depart.  We thus must consider what impact April and the turtles will have in the past, and whether it will make it impossible for them to exist as they must in the future.

The Turtles will not impact the gene pool; they will have no children, and no one is likely to forego or delay marriage to someone else in the hope of marrying one of them.  It is a bit different for April, who might be considered an eligible maiden; but she is already old for the time, and foreign, and suspected of being involved in magic, so it is at least possible that she will not change the past in this way.  More complicated, though, is that Kenshin and the honor guard are gone.  We have every reason to believe that Kenshin and Mitzu would have had children; we have more reason to believe that the honored soldiers who personally guard Lord Norinaga would have families.  Their absence from the past endangers the existence of Splinter's master, and so of the Turtles as we know them and of April's involvement.  Again, though, we are discussing probabilities.  It may be unlikely in the extreme that the necessary future will arise, but it is not impossible.  Viewed from the opposite end, we are told that a few days later in 1992 Kenshin activates the scepter and returns to 1603, and therefore those few days must exist, and therefore time must have stabilized, the events of history playing through sufficiently unaltered to put the right people in the right places at the right time for the trip to occur.  The Turtles and April died in the past; but they were not missing long from the future, because a few days after they departed from the future another anomaly rewrote history once again, removing them from the past.

Kenshin and his father's honor guard are in the future a couple days before his impatience drives him once again to activate the device which brought him to the future in the foolish but apparently correct hope that it would return him to his own time.  (He has no good reason to be certain it will not take him further into the future.)  He thus makes another change to history.

Although this was covered, it is important to understand the difference in experience between the travelers to the future and those traveling to the past.  For Kenshin and the honor guard, it was 1603, and then they leapt to 1992; three hundred eighty-nine years passed in an instant for them.  They were in 1992 for a few days, and then they returned to 1603.  For April and the Turtles, they were in 1992, and in an instant they leapt back to 1603, and they dealt with life as it came to them, and looked for a way to return to their own time but never found one.  They will be in the past for three hundred eight-nine years, plus or minus a few days, waiting for the moment to come when Kenshin activates the device to change the past.

Then when that happens, Kenshin and three members of the honor guard leave 1992 and leap back to 1603, while April, Leonardo, Donatello, and Raphael leap across three hundred eighty-nine years to reach what they consider "the present".

Michelangelo is not with them.  He did not reach the scepter in time in the past, and Benkei was not touching it in the future, so they did not trade places.  Thus Michelangelo now must wait three hundred eighty-nine years for the future to arrive in which he can trade places with Benkei.

Everything else is returning to our expectations.  If the gene pool could survive the loss of all five men removed from the past, it can probably survive the removal of just one; we can again reach the future.  After his initial failed attempt to reactivate the scepter, Mike probably toys with it from time to time trying to figure out how to fix what is not actually broken (and hopefully he does not break it in the process, because everything depends on it being functional when April gets it from the antique shop in 1992).  He, though, wanted to stay in the past; and Mitzu wanted him to leave because she wanted Kenshin back--whom she has.  So he will play with Yoshi and help his friends in 1603 until he dies, unable to return to his own time and separated from his brothers.

This may be the oddest part to understand.  It is not Benkei who activates the device--he is simply holding it and fleeing from the Turtles, whom he has never before seen.  It must therefore be Michelangelo who, having missed the trip when Kenshin activated it, activates it again.  As we have stated, it does not work, because the moment three hundred eighty-nine years in the future when Benkei can depart cannot exist until that time has elapsed and all of history supports the moment that Benkei is holding the scepter.  It is as if the signal sent to the future (as with the Timeline recall devices) travels with time to that moment from which it can respond to Mikey's action in the past.  Yet once that time has elapsed, it changes the past such that the first time Michelangelo attempts to activate the scepter (from his perspective) it works, and he is carried to the future.  All of the years he spent in the past are immediately erased, as Benkei returns to his place in history.  In this history, Michelangelo will never know that the device failed; he will have no memory of the life he now will never have lived.

Near the beginning of our analysis we discussed the problem involved in the fact that when the Turtles arrived in 1603 from 1992 they were told that they had already been there two hundred years previously.  The best explanation for this is that at some point in the future, which for convenience we named as 2000, they were going to travel to 1400, plus or minus a few years.  We also recognized that it was possible that that trip occured metaphysically before the trips covered in the movie, despite occurring sequentially after.  To clarify, it was possible that the first trip anyone ever made was when the Turtles departed from 2000 for 1400, and then in the revised history which their presence in 1400 created, April eventually departs for 1603.  It was possible instead that the first trip made to the past was when April replaced Kenshin, departing from 1992, and that after all the anomalies created by the journeys in the film were resolved we added one more journey from 2000 to 1400 which rewrote the history into which everyone traveled.  Our discussion of events of 1400 suggested that as long as the Norinaga family lost their war either way, and no important individuals lived or died who needed to do otherwise, it was not important to our starting point.

Yet it might be important to our ending point.  The problem arises in tracing the movements of our scepter.  There are three distinct possibilities, each with different ramifications.

We have been assuming the first:  April bought the sceptor in 1992 and all their time travel adventures happened then; then they stored it until, for some reason, they used it again in 2000 to travel to 1400.  As previously noted, this means that in 2000 they knew clearly what the scepter did; it also means that the scroll bearing their images did not exist when they first reached 1603 but was part of a revised 1603.  It also raises questions about the route the scepter took from 1400 to 1603:  if you owned a scepter which had been demonstrated to call demons from the future, would you handle it the same way as an expensive-looking family heirloom which had never done anything?  Would Kenshin have the scepter in 1603 given the altered 1400 events?

In the alternative it is possible that April did not originally find the scepter in 1992, but that it reached the Turtles by a different course in 2000, and then because of their trip to 1400 they changed the future history of the scepter such that April found it in 1992 instead.  This is more complex.  It means that in the original history the scepter never did anything until 2000, and then it created the alternate history beginning in 1400; in this altered history it did not work for Kenshin in 1603 but was activated in 1992, changing history again from 1603 forward, all the adventures then occurred, and then in 2000 the Turtles, with full knowledge of what the scepter did and having visited the Norinaga house in 1603, made the same trip at the same moment to 1400.

Since the moment is controlled by the alignment of the device with itself and nothing done in 1603 will change what happened in 1400, that moment is easily secured:  the device was activated from the past at this moment.  The Turtles do not know when it will happen, though, so it is a serious question whether they will be in the right place at the right time to make the trip; and they will be different Turtles, having already visited the descendants of the people they are visiting and knowing something of the future they ought to create.  They will not take the same actions; it might change the future.

A third possibility not yet mentioned is that April finds the scepter in 1992, but it does nothing at that time and is saved by Splinter until 2000, when it activates for the first time, taking the Turtles to 1400.  This construction has two advantages, first that we do not need to find two ways of bringing the scepter to the Turtles in 2000, and second that we do not have a history of 1603 in which Turtles arrived then that does not already have the earlier history of 1400 in which Turtles arrived.  The only issue is whether the Turtles would treat the scepter the same in the rewritten history between 1992 and 2000.  After all, they now have an appointment to keep; but they will not be the same Turtles traveling to 1400 that they were in the original history, because those Turtles never visited 1603 and these have.

That presents more complications to consider.

We considered the complications involved in the relationship between the trip from (we suppose) 2000 to 1400 and the trips from 1992 to 1603, noting that if the 1603 arrivals occur first the Norinaga family is going to do something different with the scepter than they would if it brought Turtle demons against them in 1400, making it unlikely that those trips would happen in that replay of history, but that if the 2000 to 1400 trip is first we have the problem that in the replay of history the Turtles know before 2000 what they did not know in the original history, that the scepter will take them to 1400 and that they will revisit in 1603.  This puts the 2000 to 1400 trip in jeopardy, because it is possible that the Turtles might not make that trip and certain that they would not be quite the same, er, people that they were the previous time.

Yet in a sense that does not matter to our analysis.

Don't misunderstand.  In a sense it matters very much.  Having changed their identities by altering their experience and knowledge, the Turtles guarantee that any trip they make to the past will result in a sawtooth snap at best, as they change what they did and so change who they will be in a cycle that will have to stabilize.  There is a very real danger, indeed, that their trip from 1992 to 1603 will so alter their lives that they will fail to make the trip from 2000 to 1400, and that means that they undo the history they have created.  Their non-arrival in 1400 will restore the original history, leading into a convoluted mess of temporal problems in 1603 when Kenshin will not use the scepter and so there will be no 1992 departures.  All of this leads back to a 2000 departure, and a complex infinity loop.  We will have destroyed time, as there will never be a stable history between 1400 and 2000 and time cannot advance a moment beyond that point.

The sense in which it does not matter, though, is that the movie never tells us otherwise.  It is entirely possible that the Turtles left from 2000 and arrived in 1400, and then died in the past (they would do so on their first trip back anyway, because they have to stabilize history in order for someone in 2000 to replace them in the past and return them to their own time), and then have the universe end in 2000.  Just because time as we know it did not end in 2000 does not mean that it did not do so in the universe of the Turtles.  The movie does not tell us that the last trip was not a disaster, that there was a future beyond the moment of their next departure.  It does not even tell us when they made that trip--we chose 2000, but already by then those who were teenagers in 1992 are unlikely to be so still, and their crime fighting careers might extend into their early fifties, so the end of their world could easily be in the early 2030s on that timeline.  Just because we predict a temporal disaster does not mean that the movie fails; one can have a good story (such as perhaps The Perpetual Barbecue) built around a temporal disaster that still works because the disaster does not prevent the story.

Further, there is nothing here, once again, that makes the events we see impossible.  It might be improbable that the Turtles would make the 2000 trip after making the 1992 trip; it might be improbable that Kenshin's family would keep the scepter in the same place after fighting demons in 1400 as they did after not fighting demons in 1400.  Yet in no case are the events impossible.  Nothing anyone does in the film absolutely prevents anything anyone does in the film.  It is doubtful whether such improbable event sequences would occur, but all specific event sequences are inherently improbable, and one of them will occur, so it could happen.

Despite the temporal improbabilities, Teenage Mutant Ninja Turtles III remains a fun movie, and not an impossible one.  There remains, however, one issue.

Several times we have suggested that no one can leave from the past until history has reached the moment in the future to which they are headed.  In this, the system is like Timeline, in which the recall devices must send a signal to the future, where it must be received to activate the beam.  Thus all of history must be written between the moment the signal is sent and the moment it is received, and then the travelers leave the past, causing history to rewrite itself again so they can arrive in that future which follows from that past.

Yet it might be asked why that must be so in this case.  After all, in Warlock we suggested that the travelers from the past might be dropped in a temporal pocket, emerging at their destination.  Could not our Turtle time travelers have a similar experience?

It is evident that in two cases this solution is inadequate.  When the device is activated in 1992, first by the Turtles and later by Kenshin, it is apparent that the history of the world leading to the moment of activation must exist before it can be activated.  In these instances it is very like the Timeline travel:  a decision made in 1992 causes travelers to be plucked from 1603.

What, though, of when Kenshin activates the scepter in 1603, or when Michelangelo presumably similarly does so?  Could they not be pulled out of history to re-emerge in 1992?  The problem becomes clear when we attempt to picture what happens to the scepter.  The best guess is that in 1603, Kensin vanishes, the scepter crashes to the floor, and we rewrite one hundred eighty-nine years of history in which he simply disappeared; then in 1992 he appears, April disappears, and she leaps back to 1603.  But we know this does not happen because we are given the principle of equal mass displacement, and thus Kenshin cannot leave the past until the scepter connects with its future self and can claim April to replace him.  Regardless of from which end the scepter is activated, it must connect with itself to operate, and therefore the past version must find a future version built on the events which followed from that moment.  No one vanishes from the past until their future replacement can be summoned.

While the analysis has been difficult and confusing, we can be fairly certain at least that there is never a timeline in which someone vanishes and is not immediately replaced by someone else, and thus that there are timelines in which the device simply does nothing at all, replaced when the device activates in the future and so changes the past.