terça-feira, 18 de novembro de 2008

Temporal Paradoxes in Science Fiction: an article by Eduardo Torres

It's well established that, at subatomic level, there is not preferential orientation for time, and that subatomic particles can be seen as suffering interactions and alterations that can be interpreted as going in positive or negative direction of time, with the same laws of nature being applied in each case. An 'intelligent' electron would be able to, therefore, discover ways to move forward or backward in time at ease.
Isaac Asimov

Of all the basic themes of science fiction, I think that of voyaging in the time is the most fundamental, the closest of the heart of the matter.
Stories of spaceships journeying toward distant suns, of flawless robots transforming human civilization, of mutants with strange mental or physical powers are all very fine so far as they go; but they are only aspects of the essential science-fiction thing, which for me it is to reveal the future. (...) …the stories of travel in the time gave me the future itself, the fundamental thing, the unattainable world to come. As a reader and then as a writer I was drawn constantly attracted to that.

Robert Silverberg

Imagination is more important than knowledge.
Albert Einstein

One complicated thing for SF readers aficionados of time travel is having to deal with temporal paradoxes. Don't misunderstand me. They are one of the most fascinating things in time travel stories. But they have to be treated with ability, otherwise we have the sensation of being cheated, or being abused in our good faith. Some authors dive deep in the paradoxes, without fear. Others avoid them, seeming intimidated. The thing is still more complex when we read books from different writers, because each one creates his own 'rule of the game' to handle the paradoxes. And sometimes the same author, in the same book, treats the same paradox in a different way.

I will try to expose in this article a summary of my ideas and impressions on the temporal paradoxes in science fiction, describing them and analysing how the theme was treated by three authors of SF: Robert Silverberg (Up the Line), Poul Anderson (The Guardians of Time) and Isaac Asimov (The End of Eternity).

Let's begin with Up the Line, where Silverberg goes deep into the paradoxes, getting to play with them. The narrative is made through the main character, a Time Courier (member of a organization specialized in temporal tourism). So, we go 'learning' with him about the paradoxes in his ' training' course. The Silverbergian paradoxes are:

1) Accumulation Paradox:
It happens when the same person leaves from several points in the timeline to the same point of the past. It happened a lot with the Time Couriers. There was one, for instance, that was specialized in tourist visits to Christ's crucifixion. He had already done that trip 22 times along several years. So we had 22 versions of that Courier at the same time attending the event. That paradox created other paradoxes. If all those trips happened and the basic principle of time travel is that the past, the present and the future are part of an only continuum, why all were not there all the time?
And, taking into account that the temporal tourism continued for the subsequent centuries, why there weren't hordes of thousands of tourists from the future attending the Crucifixion? Why was not that gigantic crowd registered in History? Silverberg makes all those inquiries through Jud Elliott (the new Courier). The solution? Silverberg doesn't give it. In the novel, that paradox stayed insoluble even for the best minds of the time (2059). Apparently they 'went happening' as they were 'introduced' in the continuum. Paradoxically, in the first trips of a Courier to a place where he would appear later, there were not copies initially. They went appearing in elapsing of 'time'. But what time? Would not time be one only thing? A continuum? Well, I think that's why Silverberg left that part unexplained: He must also have tied a knot in his head.

2) Transit Displacement Paradox:
Travelers to the past took with themselves their 'own time', as if they were 'encapsulated' in a bubble of the present time just as it existed in the occasion of their trip. That means that modifications of History subsequent to their trip could not reach them, since they stayed out of their temporal matrix (the present from where they left). So, you could kill your grandfather when he was still child. You would not stop existing immediately, only if you returned to the present, where you would not have more any temporal connection, since you would never have been born.

3) Discontinuity Paradox:
It happened when you found in the past somebody that left from a point of the future different from yours. He could not recognize you, because in his present you had not still found if. Or the opposite could happen. You could find somebody that left from a point ahead of your future, and that knew what will happen with you in the next months or even years. There was a rigid code of ethics followed by Couriers to avoid those contacts and, if they happened, to avoid any exchange of information. That paradox, for its turn, also opened other paradoxes. If all events are part of an only continuum, they always happened. So, when being presented in the distant past to somebody who you had already found before in the present, but you are knowing 'now' (in the distant past) coming from another point of future when you had not still been introduced, should he maintain memory of that previous encounter, isn't it? Later he would know you 'actually' in the present time of both. But would that first encounter always have happened, sure? Silverberg gives contradictory treatments to such paradoxes in the book. Just once happened a 'remembering', and even so in a vague way. In general, he passed the idea that those 'discontinuous meetings', just as in the Accumulation Paradox, seemed to happen in the past in ' parallel' with the present.

4) Duplication Paradox:
It happened in Silverberg's book when our hero Jud tried to avoid that a tourist used an altered timer to travel in time independently (the timers were stuck to the body by a plastic strip and the ones used by tourists were locked and they could only be operated by the Courier). The tourist was fast and jumped first in time. Then Jud went back some seconds in the past to try again, finding the tourist and his own version of some seconds before, when he had not still made the first attempt of stopping the undisciplined visitor. But the tourist was really smart and escaped again. And the first Jud, shocked by the sudden arrival of his future version, altered his actions and did not return to the past those same seconds, as he had done in the first time, altering History. Then the two Juds stayed, existing in parallel in the same time line, as permanent copies, just one having lived and possessing memories of some seconds more than the other. (Actually, Silverberg described just one of the two possible types of Duplication Paradox, in the case that we could classify as Duplication Paradox due to History Alteration. It also exists the Cumulative Duplication Paradox, as we will see ahead).

5) Final Paradox:
In the 'course' that expression was reserved for an event caused by a time traveler in the past that changed History so that the time travel were never discovered.

6) Law of Lesser Paradoxes:
Ingenious invention of Silverberg: When events could cause multiple paradoxes, it happened before the least unlikely (for instance: the Transit Displacement Paradox happened with precedence over the Final Paradox).

In that point it is convenient to explain that in Up the Line trips to the future were not possible. That is, you could return to the past, but you could only come back to the future until the date of the departure added to the 'absolut' time (or 'physiotime', to use the expression adopted by Isaac Asimov in the End of Eternity) that you spent in the past. Another limitation was that the 'timer', like the Time Machine of H. G. Wells, only allowed trips in time, not in space. So, the time traveler would have to do first a physical trip in the present to the destiny place and only then jump to the desired time.
The Time Courier was one of the divisions of the Time Service. The other was the Time Patrol, which function was to avoid any alteration of the temporal continuum. Those non- authorized alterations were considered time crimes, being the only case of capital punishment of the time.
Silverberg describes a flowing and editable past. Was there an accident with a temporal tourist during a trip? The Courier could return some minutes in time and avoid it. Of course the 'edition' would be forever registered in the temporal continuum, with two Couriers appearing simultaneously for some minutes (that practice was subject to sanctions by the Patrol).

The Time Patrol used that same fluidity of the past to correct the time crimes. Did anybody go back to the past to kill Mohammed before him creating Islamism or to poison Jesus Christ while child? The criminal was traced, located and impeded of doing the trip to the past immediately before commiting his crimes. All the resulting events of his actions turned non-events then. They never happened.
They were removed from the continuum and they didn't leave any consequence nor memories (except in those protected by the Transit Displacement Paradox).
The thing is becoming complicated, isn't it? And that Paradox of Retroactive Alteration of History opened, as always, other paradoxes. For instance, an alteration of the past in a key-point, like the murders of Mohammed or Jesus, would reflect immediately in the continuum? Would the present be immediately modified? The own time travel could stop existing? How would there be the subsequent correction by the Time Patrol if it had never been created? Silverberg adopts in that case a solution similar to the Accumulation and the Discontinuity Paradoxes, that is, the changes go 'propagating' in the continuum in 'parallel' with the present. But how, if everything is only one continuum? Jud himself wonders and he doesn't know the answer. We can observe here a lack of self-consistence in the book, because, in the mentioned case of the time traveler going to the past to kill his grandfather when child, Silverberg admits that his existence in the present would be canceled immediately. That event is even described as a suicide form adopted at that time (those time crimes were always discovered and reverted by the Time Patrol, but, as the criminal was executed, the transtemporal suicide ended well succeeded anyway). In Up the Line the murder of Jesus as a small boy (yes, it happened!) was discovered when a Courier was to take a group of tourists to the scene of the Crucifixion and he didn't see any Jesus there. Only the two thieves. The Patrol located the criminal and made the retroactive correction, avoiding that he traveled to the past to kill Jesus.
As Jesus was killed when he was 11 and the crime discovered when he was supposed to be 33, only 22 years were affected. And as the Christianity only provoked historical effects a long time after Christ's death, the alterations of the continuum were irrelevant. After the 'edition' by the Time Patrol, even those alterations were totally eliminated. The murderer? He was executed. Even with his victim 'resurrected' by the Time Patrol. Another interesting thing in the 'temporal rules of the game' of Silverberg: The Couriers could 'escape' during the trips. They could jump to other times for hours or days, to relax. And what about the poor tourists trapped in a distant past? The Couriers just had to go back some minutes after having departed. For all practical effects they had never been far for long.

Concerning the problem of the languages of past times, the Couriers, Patrolmen and tourists took fast hipno-courses before the trips or missions and they maintained perfect fluency for one or two months. I think Silverberg thought in almost all possible temporal paradoxes in Up the Line, and for that I extended more in the analysis of his book. Only two other paradoxical events were left out: The loops and the cumulative duplications. The first are of two types: The loops of temporal repetition and the loops of objects or people (sometimes called the 'Egg and Chicken' Paradoxes).

The loops of temporal repetition have been found more frequently in motion pictures. Those paradoxes happen when you travel in time not in the traditional way, with a physical transport to another moment of the past or of the future, but when you 'revive' several times a past time, like in the films Groundhog Day, 12:01 pm (TV short movie) and 12:01 pm (feature film). In stories involving loops of temporal repetition we have two paradoxes, one the time repetition itself, and the other the person (or people) that is (are) 'outside' the loop, keeping memories of the previous time loops and acting differently in each repetition loop. It's interesting that this temporal paradox can create comical stories, like Groundhog Day, and also anguishing terror tales, like 12:01 pm, the TV movie of 1990 that was the pioneer in the theme. The paradoxical loops of objects or people are more common in films as well. A very known one, in the modality object, appeared in the movie Somewhere in Past, based on the book by Richard Matheson, where the main character receives a clock from an old lady and he found out later that she was a lover that he met in a trip to the past. He ends up getting that time travel through a mental process, but it travels materially, leaving registrations in the past and, the most surprising, taking with him that same clock that he received from the old lady to give it to the same woman when she was a beautiful girl. Then he returns to the present. And she will always remember him and keep the clock to give him in the future when she finally meets her old/young love. What she only gets to do when she is already an old lady, closing the loop. The paradox here is: Who manufactured that clock? How did it appear in the temporal continuum if it begins and finishes in that transtemporal loop between the two lovers? Another film with paradoxical loop, this time of person, is The Terminator, where the leader of the human resistance in the future sends to the past a protector for his mother before him being born. And that protector ends up becoming his father. In other words, the leader's own existence in his present depended on him to send his future father to the past in such way this man could make pregnant his future mother, closing the loop.
In the sequel of that film we have a temporal loop of object, when it is revealed that the company that had created the technology that would generate the domain of the machines in the future actually based its researches in the chip and in the remaining components of the destroyed first Terminator, that, for its turn, was created as development of that same technology. Another famous example of 'temporal loop' in films appeared in the series of The Planet of Apes, where the son of a couple of apes coming from the future would come to lead the anthropoid revolt that would end up generating a world dominated by the apes, from where his own parents would arrive, in an infinite cycle.

The Cumulative Duplication Paradox can be considered a variation of the Accumulation Paradox, but with different characteristics. It is not very used in books of SF, or at least I have not found it frequently. It happens when we remove an object or person from a certain point in the time line and we transport them to the past (or other instant of time, depending on the author's transtemporal criteria). Later we return to one moment immediately previous to the first removal and we repeat the operation, placing the person or object near the first 'duplicate', being the two in the same time line. We can repeat that operation indefinitely, accumulating how many copies we want, starting from the 'original', always collecting some instants before the last removal. We could ask: Would not the second removal make the first to disappear, since only in a subsequent point of the time you transported the first object? Would you arrive there (in the removal or delivery point) and find nothing? No, because all removed objects would not be subject any more to subsequent alterations of History (like the successive removals), due to the fact that they would be out of their temporal matrix and protected by the Transit Displacement Paradox. Interesting way of becoming rich with a 100 dollars bill, isn't it? (Since, of course, that nobody notices the identical series numbers). We note that, in the duplication by alteration of History, as in Up the Line, the paradox happens because we alter our own course of time retroactively, doing, for some reason, our self to alter his past actions in such a way to follow a different path from wich he had proceeded previously and that had taken to the own altering action. In the cumulative duplication the duplicated entity is not the agent of the History alteration, but, as it is removed successively from several points to an only point of the time line, it happens a 'permanent accumulation', different from the accumulation of Up the Line, where, actually, there is a 'line' tying all copies, since it is the same person going and returning in successive time trips with several starting points and only one of arrival. We cannot trace that same line tying the objects removed from the time line in the Cumulative Duplication Paradox. A last comment about the cumulative duplication: In the Silverbergian temporal universe, that paradox would have two restrictions, firstly, the objects would have always to be transported to the past (there's no trips to 'absolute' future), and secondly, you could not take the objects back to the time from which they where removed. Why? Because it would happen with the copies the same that would happen to you if you came back to present from a trip to the past where you killed your grandfather when he was a child. You would stop existing. We have to have in mind that each successive removal of the object or person in a previous point of the time line altered their History, turning to non-events all previous removals, because the object or person would not be there to be removed. In other points of the time, all copies would be protected by the Transit Displacement Paradox, but if they returned to their original time matrix, they would disappear, just remaining an entity, the last one removed. We see therefore that the Silverbergian cumulative duplication doesn't violate the law of conservation of mass, although in other temporal universes this apparent violation occurs, as we will see later.

Let's talk now about Poul Anderson's The Guardians of Time: This is an excellent book of time travel, formed by five stories, but it doesn't have the same involvement with paradoxes as in Up the Line. Accumulation and Discontinuity Paradoxes aren't even imagined. It has also a Time Patrol that tries to maintain the continuum and has the power to correct the History retroactively, transforming eventual alterations in non-events, but the time trips don't show, in my opinion, all their paradoxical potential, at least not with the Silverberg's voluptuousness. Instead of timers stuck to the waist, Anderson's agents use vehicles (as in the Time Machine of H. G. Wells), but, besides of being more advanced (Anderson defines them as 'antigravity scooters'), they don't suffer the limitations imposed by Silverberg and Wells in their books, and can travel simultaneously to any instant of time and point of space. In the story 'Delenda Est' History is changed when the Roman general Scipio is killed by a temporal criminal before he can combat with success Hannibal, and, in consequence, Carthage defeats and razes Rome, radically altering the future. But, in other difference from Silverberg's intertemporal universe, Poul Anderson states that, in that case, History changes instantly, just preserving the agents that were traveling in time in points previous to the change. These, for their turn, also differently from the 'rules of the game'of Silverberg, were permanently encapsulated in their 'time bubble', even if they returned to the modified present, where they probably would not have existence, taking into account the historical alterations along millennia - what is actually as paradoxical as the solution proposed by Silverberg of 'slow propagation of changings'. On the other hand, Anderson makes the agents go frequently to the past, sometimes to tourist points like the 'Falls of Gibraltar' millions of years ago, without any discontinuity concerns. An academy of the Time Patrol exists in the Oligocenic period, but those problems don't show up either, even with agents coming from several points in the continuum to the same point in the past (those points were sometimes used for decades, which, theoretically, would allow a schedule, but that is not mentioned in the book).

The stories are very good and imaginative. Like Silverberg's Couriers, Anderson's Patrolmen could also 'escape' during missions. Actually, Anderson raised a point, not refered by Silverberg, that they could take several years of vacation between missions. How? It would be enough to come back at the exact time established for their report for the next duty. For all practical effects they would be accomplishing strictly their schedules (Anderson guarantees that the Patrolmen avoided those abuses). The Patrol sometimes ended up accepting a permanent History alteration, as when an agent assumes for years the role of the great Persian king Cyrus, and that period is not edited. But, if the continuum embraces all times, who could guarantee that this apparent alteration wouldn't be the 'true' History? That to maintain it wouldn't be to preserve the continuum? This, of course, introduces the Retroactive History Paradox, i.e., people of the future, that had not been born at the time of events already happened and historically registered, end up being revealed protagonists of those same events. We can interpret that paradox as a variant of the Loop Paradox or, if we prefer, a variant of the History Alteration Paradox, because the 'Retroactive History' is nothing more than a retroactive alteration of History that was not corrected, being incorporated permanently into the continuum. That opens even a philosophical discussion on what criteria would have to be used to define the 'true' History in a world where time travel were possible.

No Duplication Paradox appears in Anderson's book, but, if they happened, the Cumulative Duplication one would not suffer the restrictions imposed by Silverberg. As the trips to the future are not forbidden in the Andersonian universe, and the only demand to be protected by the Transit Displacement Paradox is to be in a point of time line before the alteration of History, it would be enough, after having concluded all the removals, to transport the duplicates to any desired point of the time line. It would not happen any more the disappearance of the copies, even if they were brought back to their original time, in an apparent violation of the law of conservation of mass. On the other hand (it seems that when we deal with temporal paradoxes there is always another hand), we can interpret the temporal continuum as an infinite succession of 'moments' - infinitesimals of time - each one with a 'copy' of everything that exists. In that case it would be pointless to reason if the Cumulative Duplication Paradox violates or not the law of conservation of mass.

We come now to the Good Doctor. The End of Eternity is a good book indeed. It catches the reader and has the Asimov's fluent and linear text. In fact, too linear. That is the problem. Isaac Asimov, in the foreword, tells us that the temporal paradoxes cause such vertiginous speculations, that the easiest solution would be to suppose that time travel would be impossible. But that he would face them and write a story that would be the ultimate example of the gender. Then he invents the 'Eternity' and the ' Eternals'. What is the Eternity? It is a mysterious dimension created by a Temporal Field of high energy that is provided by the future Nova Sun, billions of years in future. It is formed by Sections that extend for all the eternity and there live the Eternals, humans recruited to be Modifiers of Time. In the Eternity they are immune to time and have unrestricted access to every century. And the Good Doctor is not shy in showing the reach of the Eternals. The thing goes from our time to the century 150,000! Yes, 15 million years! Asimov later concedes that the humanity won't exist then. It will have evolved to something unknown. The plot is very imaginative and the role of the Eternals is opposed to the one of the Time Patrols of Silverberg and Anderson. Their work is continually to alter the continuum, changing History. Computers calculate the Minimum Necessary Changes (MNC) to obtain the Maximum Desired Results (MDR). And the Eternals are never affected, because they are in the Eternity. Interesting, isn't it? But, in my opinion, unplausible. Asimov actually eluded from the problem, because, although he defines it as immune to time, time passes in the Eternity. The events happen, people know people, things are planned and done, events cause other events. There are past, present and future. Asimov creates Eternals 'watching' each Section of the Eternity, i.e., centuries of the normal time. But that is, as I see, absurd. To accompany a time is to live the time. Let's say that an Eternal had, for instance, the mission of watching the century 1000. After 100 years it would accomplish his task. Would he return 100 years in the past and watch everything again? Would he find him working in the first mission? What means 'to watch each century', if all are part of a continuum? Is not everything 'happening' at the same time? Asimov created a solution that I consider inconsistent. When the plot refers to the Reality (the normal time) and to the events 'inside' the Eternity, things are more coherent and involving, but without exploring much the paradoxes. There is an interesting loop when apparently the invention of the Temporal Field depended on help of the Eternity, that, for its turn, only became possible after the invention of the Temporal Field. There was an Eternal that was sent by accident to the distant past and had to leave a message to be read in the future (as in one of the films of the trilogy Back to the Future). But the point is: Why not to solve the problem returning to the past and avoiding the accident? Because, without explanations, the Eternals cannot travel in time in the Eternity. But they can travel from Eternity to Reality and back to Eternity any time. How can you accompany the temporal continuum if you are stuck to an unalterable time line in Eternity? How to reconcile that with the time travels in Reality in parallel to the Eternity? The conclusion of the book - that, obviously, leads to the End of Eternity - is very interesting, and we find out the causes and consequences of all those modifications of History.

The Good Doctor was, to the best of my knowledge, the only author to conceive that singular concept of Eternity in time travel stories. Asimov also introduced in the End of Eternity an inedited component of probability in the History Alteration Paradox. In the Asimovian 'rules of the game', an alteration of the past might not be reflected immediately in the present if could happen a subsequent probable correction. If things were still in the present as they were before the alteration, there would be a significant probability that came to happen a new restoring alteration, that would already be part of the continuum, and due to this fact the reality had not still changed. Only when the probability fell below a - to use an Asimov's expression - 'crucial value', the alteration would be instantly 'propagated' along the whole continuum. But this was not guaranteed. Something that you did could avoid that probable reversion of the change. And that could happen due to a simple irreversible decision of to do or not to do something. That gave to the End of Eternity a new type of suspense in time travel. In the introduction of the book, Asimov also raised a point that usually passes unperceived by readers and writers of time travel: The space travel is implicit in time travel. If not, how would you always appear on the surface of Earth? If we travel one day in the future maintaining our position in space, the Earth will already be far in its orbit around the Sun. Will we materialize in the interplanetary vacuum? And any mechanism of 'fixation' of the temporal trip in the surface of our planet would implicate in an instantaneous trip in space to cover the distance between the Earth of departure and the Earth of arrival. As the Earth is on average about 150 million kilometers from the Sun, if you left in Summer and arrived in Winter (opposed points of the orbit), it would take a bit more than 16 minutes to cross the distance of the terrestrial orbital diameter at the speed of light (actually more than that, because the own Sun also has a movement in relation to the galactic center, and it drags with him the planets - not taking into account a possible deviation of the traveler's path to avoid passing inside the Sun). But perhaps, for you, the trip seemed instantaneous, due to the relativistic dilation of time that would happen in the itinerary; and your time machine could discount the time consumed in the trip, automatically adjusting the selected arrival time. And we cannot eliminate the hypothesis that time travel implicates, as secondary effect, in a space travel at superluminal speed (after all, in relativistic terms, time and space form an only continuum). It would remain the subject of the energy involved, but we can only speculate if the energy necessary to travel at a velocity close to the light speed for 16 minutes, or even above this value, is larger than the energy needed to transport someone, say, a thousand years in the past.

The stories of time travel commented in this article are just a small sample of a vast sub-gender that composes the universe of science fiction since the end of nineteenth century, with the pioneer book The Time Machine, by H. G. Wells. With all their disconcerting paradoxes, those stories continue being my favorite in SF. I like to think that perhaps time travel is physically possible in macroscopic level, as apparently it is in subatomic scale, and that one day the science and the human technology can make a true Time Machine. Meanwhile, we rely on our imagination to travel to the past and to the future. But didn't all the great accomplishments of Humanity begin as dreams?

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