Tuesday, 24 April 2012

The Logic of Time Travel: Part II

See Part I.

The End Of Eternity by Isaac Asimov assumes a successive timelines theory. Asimov’s time travellers (“Eternals”) have a base (“Eternity”) outside normal space-time, presumably in a fourth spatial dimension. From Eternity, they enter successive timelines (“Realities”) either to observe events or to violate causality (“Change Reality”), thus generating subsequent timelines. After many such causality violations, and thus after many successive timelines, an Eternal enters the current timeline at a point further back in its past than usual. His task is to complete a causal circle that will bring Eternity into existence. Surely, to do this, he would need to get back into the original timeline from which the first Eternals had come before they constructed Eternity? Asimov does not realise this difficulty.

There are other problems with the Eternals. They academically discuss whether a time traveller can meet himself instead of experimenting to see whether he can.


The Eternal who has travelled to the twentieth century in order to ensure the founding of Eternity decides not to complete his mission. When he has made this decision, the vehicle in which he has travelled disappears. Why? And, if it disappears, why doesn’t he? Eternity is staffed by Eternals who continue to exist even though their Realities of origin have been superseded. Eternity itself has survived its original Reality. Why should it cease to exist now because of subsequent changes made to the course of events in the twentieth century of a later Reality?

In the earlier, shorter version of The End Of Eternity, the characters state that Eternity is outside of normal time and then seem to assume that the same amount of time is elapsing for themselves in Eternity as for one of their number who has travelled to the twentieth century, as if they were simply in different places at the same time. Then it is said that it is standard practice, having spent, e.g., a year in “time” to arrive back in Eternity exactly a year after one’s departure as time is experienced by those who have remained in Eternity. It is an unusual procedure when someone arranges to arrive back a moment after his departure. Why should this be unusual? Time travellers should be able to do it all the time. There is no reason, having left time t1 and spent a year in an earlier period, to “return” to t1 plus one year instead of just to t1. You can travel to any time if you are a time traveller. 

I think that The End Of Eternity, particularly the shorter version, is too full of auctorially unnoticed inconsistencies to be salvageable as a coherent narrative. In addition, its action is set almost entirely in the artificial environment of Eternity (like a large spaceship in hyperspace), its few references to events in “Time” are to our future, not to the past, and it does not give any real sense of historical process in the future. Therefore, it lacks any of the saving graces as fiction and as literature that are possessed by Poul Anderson’s Time Patrol series and by Jack Finney’s Time novels.

In “The Red Queen’s Race” by Asimov, the characters know that a chemistry text book has been translated into Greek and sent to ancient Greece. They do not yet know that this book was the source of the fragmentary atomic theory in Greek philosophy, thus that there has been a causal circle. Instead, they fear a causality violation, i.e., an industrial revolution in ancient Greece. Further, they know that the book should have aged by the equivalent of twenty four hours for every hundred years that it travelled into the past. Since it travelled back two thousand years, they expect the causality violation to come into effect twenty days after the book was sent. Thus, they imagine this impossible sequence of events: 

the book containing knowledge expected to cause an industrial revolution arrived in ancient Greece;
for two thousand years, history unfolded without any effects of an industrial revolution in ancient Greece;
the book was sent from the twentieth century;
twenty days after that, the whole world changes into whatever state it would have been in if there had been an industrial revolution in ancient Greece.


Any effects of the book’s arrival should have occurred in ancient Greece, not two thousand years and twenty days later. This is eventually pointed out to the characters who had thought that they would be annihilated after twenty days but they still do not seem to realise the absurdity of their original hypothesis. However, “The Red Queen’s Race” does make more sense than The End Of Eternity.

Some novels (The Big Time by Fritz Leiber, The Legion of Time by Jack Williamson and Up The Line by Robert Silverberg) are even less coherent than The End Of Eternity so that it would be both more difficult to clarify what their failings are and less enjoyable to try to do so. However, one scene from Up The Line is easy to analyse and sets the tone for the rest of the book. A time traveller stands in a group watching an approaching Emperor. A woman standing in front of the time traveller and under his protection runs in front of the Emperor and is killed by a bodyguard. The time traveller moves one step forward and a few seconds pastwards. He is now standing between his slightly younger self and the woman. He grabs the woman, thus preventing her leap forward and summary execution. Seconds later, the version of himself whom he is standing in front of disappears. Why? And where/when does he reappear?

Let us call the time traveller who is holding the woman Traveller One and the one standing behind him Traveller Two. Traveller One remembers seeing the woman killed and has taken action to prevent this. Traveller Two does not see the woman being killed. He sees Traveller One appear and grab her. Therefore, Traveller Two does not know that it is his job to move one step forward and a few seconds pastwards and grab the woman. Even if he does try to do this, he will arrive a few seconds earlier to see Traveller One grabbing the woman and we must now talk about Traveller Three standing behind them. Thus, the time traveller irretrievably duplicates or triplicates himself but the events described by Silverberg cannot have happened on any hypothesis.

In Hawksbill Station by Silverberg, a time traveller thinks that, if he kills a trilobite, thus preventing the evolution of humanity, then he himself will disappear immediately after killing the trilobite. Why? If humanity had not evolved, then the time traveller would never have been born. Someone who has not been born cannot exist into adulthood, then disappear. Either there is a single discontinuous timeline in which a time traveller from a merely possible future appears, kills the trilobite and continues to exist, because there is no reason why he shouldn’t, or there are two timelines such that he is born in one and kills the trilobite in the other.

Also in Hawksbill Station, a repressive future regime sends political prisoners on a one-way trip to the remote past. Years later, a more liberal regime learns how to bring them back and begins to do so after they have been imprisoned in the past for years. Why does the liberal regime not rescue them from the past mere moments after their arrival there? The method of time travel used may be such that this is not possible but that should be elucidated in the story. Instead, it seems to be assumed that two times are really just two places co-existing at the same time with the same rate of duration. The prisoners might as well be teleported to a more primitive planet.

The Man Who Folded Himself by David Gerrold expounds a successive timelines scenario but immediately contradicts it in practice. Gerrold’s scenario: Moving either backwards or forwards in time takes a time traveller into a second timeline identical with the first except for any changes made by the time traveller, the first such change being his arrival. He leaves timeline 1 forever. If he continues to travel, then timeline 3 incorporates his arrival from timeline 2 and duplicates his arrival in timeline 2 unless this duplication is prevented by the time traveller after arriving in timeline 3, e.g., if he had arrived in timeline 2 during World War II but, then, in timeline 3, prevented World War II, then this would also prevent his arrival in the 1939-1945 period in timeline 3.

After expounding this scenario, Gerrold then describes the following transaction: the time traveller travels a short distance into the future, confers with his future self, then returns to the present to make use of his knowledge from the future. This could happen in a single timeline but, in Gerrold’s scenario, the transaction should be as follows:

the time traveller disappears forever from timeline 1;
no future self greets him in timeline 2;
he returns to the present in timeline 3;
later in timeline 3, he greets that timeline’s duplicate of his past self who had originally arrived in timeline 2;
that duplicate returns to the present in timeline 4 and there meets the duplicate of the self who had returned to the present in timeline 3.





Thus, by pulling this stunt, the time traveller should have unintentionally duplicated himself, although Gerrold does not realise this.


Harry Harrison wrote a definitive historical circular causality novel, The Technicolor Time Machine, but was less successful with Rebel In Time. In the latter novel, our hero knows that the villain has travelled back to a particular time in order to help the Confederates win the American Civil War. Hero travels back to thwart villain. The method of time travel used ensures that he arrives at the same place. (They are transmitted back from a particular research establishment rather than travelling in a vehicle.) Hero arranges to arrive a few hours after villain and then has to find him. Why did he not arrive before him in order to apprehend him on arrival?

It may be replied that this would have deprived the novel of the drama of pursuit in a historical period but this is not the point. The method and circumstances of time travel could have been adjusted to allow for this, e.g., if it is not possible to be precise about arrival times, then the hero might have to arrive a considerable time beforehand and hide elsewhere while waiting. Then, circumstances could prevent him from returning to the arrival point in time to catch the villain arriving. The point is that both the author and the characters seem to confuse time travel with travel through space or on the Earth’s surface. In familiar travel, if we depart after someone else, then we arrive after him as well. It seems to be taken for granted that this should also apply to time travel. That none of the people experimenting with time travel realises this amounts almost to a logical contradiction in the novel.

I have read half a dozen sequels to The Time Machine, most of them disappointing. (Christopher Priest’s The Space Machine is more of a sequel to The War Of The Worlds.) In Time After Time by Karl Alexander, where Wells is the Time Traveller, his Time Machine changes in the middle of the novel and without explanation, from a vehicle that carries the Traveller through time into a static machine that merely endures through time while the Traveller moves backwards or forwards in time within it. Thus, when he arrives in his future/our present, he is in the U. S. because the Machine, which no one else knows how to use, has been moved to an American museum since Wells’ lifetime. Wells’ original Time Machine, even if it was going to be moved to the States after his death, remained spatially stationary during a time journey.

In another sequel, The Time Ships by Stephen Baxter, it is established that, whenever the Time Traveller visits the future and returns to the present, he changes events so that his next forward trip is to a different future. One such future is a twentieth century in which the Time Traveller had never returned to the nineteenth century but there are technologies based on what was found in his laboratory. On his next past-wards trip, he not only visits his pre-time travelling self but also brings that younger self with him to the twentieth century and never returns him to the nineteenth century. Despite this, the twentieth century which they enter is still that in which the nineteenth century Time Traveller had travelled through time and disappeared, leaving significant materials in his laboratory. I have other problems with the novel:

I find it arbitary and unacceptable that the White Sphinx and the Morlocks exist in an earlier period in a later timeline;
it is questionable whether, after innumerable causality violations and successive timelines, the Time Traveller would be able to return, as he does, to his original timeline;
when he does, his attempted intervention in the Morlock-Eloi society is minimal compared with what could have been done by marshalling the resources of earlier periods, e.g., exterminate the Morlocks, put the Eloi in a reservation and repopulate the paradisal Earth with un-devolved humanity;
since Wells’ story did not involve causality violation, I do not think it is appropriate to introduce it in a sequel;
there is more than enough scope for a sequel simply in exploring the timeline and future history that Wells had outlined;
I do not think it is appropriate to use the name “Plattner” without introducing the title character of “The Plattner Story” or to apply the name “Nebogipfel” from “The Chronic Argonauts” to a Morlock;
The novel summarises post-Wellsian ideas but does not innovate as Wells did and would more appropriately have been written, as it was originally conceived, as an independent time travel novel, not as a sequel to The Time Machine.


“The Dark Tower” by C. S. Lewis is modelled on The Time Machine. It begins with a group discussion of time travel theory and proceeds to a practical demonstration, albeit of chronoscopy, not of chronokinesis. Orfieu argues against the possibility of bodily time travel as follows:


no particle can be in two places at the same time;
the particles which at present make up the tip of someone’s nose will, by 3000 A.D., be doing something else, e.g., forming part of a chair;
therefore, if he travels to 3000 A.D., taking his present body with him, then the same particles would be both in his nose and in the chair, which is absurd.


It is true that it is usually regarded as impossible for one particle to be in two places at one time, if only because, when we detect a particle in one place and a particle in another, then we automatically regard them as different particles. However, there is a situation in quantum mechanics when two particles emerge from one point, then one of them mutually annihilates with an already existing particle. This can be interpreted not as creation and annihilation but as one particle travelling briefly backwards in time and therefore momentarily existing in three places simultaneously. Orfieu’s argument amounts to saying that time travel is impossible because time travel is impossible.

Even on Orfieu’s argument, a human body from the twentieth century would be able to spend a week in 3000 A.D. if only the atoms that had composed it could be detected in 3000 and sent back to the twentieth century to fill the gap. (There would not have to be corresponding weeks: the time traveller could spend a week in the future and return to the present a second after leaving it; the particles from the future could spend a second in the present and return to the future a week after leaving it.)

Another way around Orfieu’s objections would be to assemble a duplicate body with the appropriate memories and sense of identity in 3000 A. D., then, after a week, disassemble the body while transmitting its newly acquired memories back into the brain of the original body in the twentieth century. In this case, only information would have time travelled. 

Lewis’ chronoscope reveals not a past or future time but a divergent or parallel timeline. Lewis hypothesizes that identical bodies could exist in different timelines and that their minds could be swapped through the chronoscope. Thus, he describes not physical travel backwards or forwards in time but mental travel sideways in time. This does not count as time travel but his opening discussion is about time travel.

In “A Little Something For Us Tempunauts” by Philip K. Dick, three U. S. “tempunauts”:

set out to travel a week into the future;
arrive back from the future;
die instantaneously in an implosion on their return (“re-entry”);
arrive in the future a week later;
attend their own funeral;
are told that the implosion occurred because one of them disobeyed orders by carrying too much mass back with him.


Each event in this sequence occurs only once, is experienced only once and is remembered as having happened only once. Despite this, the characters speak as if it is possible, though not certain, that the tempunauts and, by extension, everyone else are somehow re-experiencing the sequence endlessly. I cannot see either that this idea means anything or that it should matter to anyone if it does since they do not remember the endless repetition. There is evidence that the world does continue to exist after the tempunauts start their return journey because two Russian “chrononauts” are said to have gone fifty years into the future.

The suicidal tempunaut has feelings of tiredness and déjà vu that convince him alone of endless recurrence. This would make sense as an irrational fear in the mind of a disturbed time traveller but everyone else accepts that his idea is possible. Next, he develops two nonsensical ideas. First, having already accepted that the implosion is part of the repetition, he now thinks that, by causing the implosion, he will end the repetition. Secondly, he is informed that, if there is a repetition, then it is probably caused by the implosion. He then decides to cause the implosion because he has suddenly identified the repetition with eternal life. This does provide a comprehensible, if insane, motivation for the tempunaut who disobeys orders by carrying back too much mass.

The film Back To The Future is a mixture of good, questionable and atrocious time travel theory. There is good circular causality. The hero, having seen the Professor shot, travels into the past and gives the younger Professor a letter warning him about being shot but the younger Professor tears up the letter unread on the grounds that no one should know their future. The hero returns to the present, witnesses the shooting plus his younger self’s disappearance into the past and runs over to the Professor’s body. The Professor then sits up, revealing that he had stuck the letter back together and has been wearing a bullet-proof vest. 

That could happen in a single timeline. However, there has also been causality violation. Because of the hero’s activities in the past, his family is now conventionally successful whereas he remembers them as failures. Either he is now in a different timeline, in which case the circular causality will not work, or there is still only a single timeline allowing for both circular causality and causal discontinuity. The latter would mean that the time traveller “remembers” some events that did not occur. He correctly remembers seeing the Professor shot but incorrectly remembers his family’s social status. The successful parents recognize him as their son so what has become of the version of him that knew them? Or, if there is only one him, why does he arrive in the past with partly incorrect memories? It is difficult to fit both causality paradoxes into a single timeline.

It is atrocious that, when he is in the past and the probability that his parents will not marry has increased, his image disappears from a family photograph that he has brought with him. The younger Professor immediately interprets this as evidence that the hero’s birth is in jeopardy instead of just classifying it as an inexplicable event. Later in the film series, the headline on a newspaper held in the Professor’s hand instantly changes as he changes the events described in the newspaper. Why should this happen and, if it does, why do all other records, including the Professor’s own memories, not change as well? 

On another occasion, the hero’s girlfriend was last seen in a dangerous situation in an undesirable timeline. The Professor’s solution is simply to leave her there but change the past so that she will be alright when everything changes around her. Everything will not change around her. A new timeline will be created but she will still exist in the old one. The time travellers having left that timeline may now regard it as past and therefore no longer existent but, to the girl in that past timeline, her dangerous situation will not have ceased to exist. 

In a film whose title I forget (TimeCop?), the hero travels to the past and there encounters villainous characters who discuss preventing his birth. They conclude that his birth has not been prevented because “he is still here”. If he has travelled from the “present” of timeline 1 to the “past” of timeline 2, then it is possible that someone else has travelled from timeline 1 to timeline 2 and prevented his birth in timeline 2. His appearance in timeline 2 proves only that his birth has not been prevented in timeline 1. Births in timeline 1 are prevented by sexual abstinence, contraception, abortion or accidents preventing encounters between potential parents but not by time travellers from any previous timeline. Thus, if someone’s birth had been prevented in timeline 1, then he would have no existence whatsoever and would not even be remembered by any time travellers. No one would have set out to prevent his birth.

In a Dr. Who episode, the Doctor sends his assistant forward a minute. To him, she disappears for a minute. To her on arrival, he disappears temporarily because “he has not got there yet”! This is nonsensical. If three dimensional bodies move uniformly along another dimension and she jumps ahead for a minute’s worth of travel, then the whole universe, not just the Doctor, will disappear from her view because “they have not got there yet”. Further, she will have jumped ahead not in time but in a fourth spatial dimension and motion along that dimension will take time. If she moved forward in time, then she would arrive at the moment when the whole universe, including the Doctor, had moved forward for a minute’s worth of travel in the fourth spatial dimension. And if she moved forward only in time and not also in space, then she would have been left behind.

In the Star Trek episode “Tomorrow Is Yesterday”, the Enterprise, approaching Earth, accidentally slips back to the twentieth century, focuses a tractor beam on a USAF fighter plane that buzzes it and has to ”transport” (teleport) the pilot aboard when his plane breaks up in the tractor beam. Later, the Enterprise crew want to return the pilot to Earth without his memories of having met anyone from the future. Superior technology, futuristic drugs or Vulcan mind meld should be able to remove his memories. Instead, they go briefly back in time before returning home. While doing this, they return the pilot to the cockpit of his plane a moment before they had taken him out of it. This is meant to deprive him of his memories. The problems are: 

Why is there suddenly a rule that anyone who travels back to a particular time forgets everything that happened after that time?
If there is such a rule, then why have the Enterprise crew not suffered total amnesia because they have travelled to a time before their births?
There should now be two versions of the pilot sitting in the cockpit, unless he occupies the same space as his younger self and they both explode.


The Enterprise crew have done nothing to change the fact that the fighter plane is breaking up. Thus, the pilot whom they have just returned to the plane should now die in it unless he can bail out, which is what they were trying to save him from in the first place. Instead, he is shown inexplicably losing sight of the Enterprise and flying away unharmed. 

I heard this described as a “neat solution” to the problem in the story.

I have heard it argued that it should be impossible to travel forward to a time after your own death presumably because it is usually impossible to be alive after you have died. Someone who travels into a remote future and stays there will die there and thus will not have travelled forward to a time after his death. Someone who travels into the remote future, returns to the present and does not time travel again will die in the near future and thus will exist in the remote future after his death. Someone who travels to and stays in the remote past has already died before he was born. The uncanniness of meeting someone after you have known that he was dead is an emotional hazard of time travel noted in The Door Into Summer by Robert Heinlein. In The Time Traveller’s Wife by Audrey Niffenegger, a child who is used to it can say that her father is not dead all the time because he is a time traveller.

Although “A Sound Of Thunder” by Ray Bradbury is the best known, most anthologised, definitive causality violation story, it has its oddities which can be left to the attentive reader to find. All of this shows that time travel fiction can be both more satisfying and more dissatisfying than any other sf.



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