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Time Travel & the Predestination Paradox Explained

May 16, 2017 James Miller Time Travel 3

A Predestination Paradox refers to a phenomenon in which a person traveling back in time becomes part of past events, and may even have caused the initial event that caused that person to travel back in time in the first place. In this theoretical paradox of time travel, history is presented as being unalterable and predestined, with any attempts to change past events merely resulting in that event being fulfilled.

Science fiction has provided fertile ground for exploring this paradox of time travel , and over the years has provided much entertainment in the form of countless books and movies on the subject, some of which are mentioned in this article.

Etymology of Predestination Paradox

Origin of the term ‘predestination’.

The word ‘predestination’ derives from the Greek word “proorizo” with “pro” meaning “before” and the verb “orizo” meaning to “determine”. It has been in use since classical times, with the Greek physician Hippocrates (460-370 BC) using it to describe an intended result following the administration of medication. It is mentioned four times in the Bible, or more specifically in the Epistles of Paul, and over time in theology has come to represent God having immutably determined all events throughout eternity that will come to pass.

Origin of the term ‘Predestination Paradox’

The concept of a predestination paradox has been explored by scientific writers in the past, most notably by Robert A. Heinlein in his short stories entitled “By His Bootstraps” (1941) and “All You Zombies” (1959). However, it was the Star Trek franchise that coined the phrase “Predestination Paradox” in a 1996 episode of Star Trek: Deep Space Nine episode titled “Trials and Tribble-ations”.

The Deep Space Nine episode Trials and Tribble-ations was a homage to Star Trek the Original Series, and involves agents from Starfleet’s Department of Temporal Investigations visiting DS-9. The Department are there to determine whether the timeline has been corrupted after Captain Sisko took the USS Defiant back in time 105 years to save Captain James T. Kirk from being assassinated. The expression Predestination Paradox is used twice throughout the show. The first time is by two time agents who are questioning Captain Sisko while trying to establish his motive for traveling back in time :

LUCSLY: “So you’re not contending it was a predestination paradox?” DULMUR: “A time loop. That you were meant to go back into the past?”

In the second instance, Doctor Bashir worries that after being invited on a date by a woman bearing his great-grandmother’s name, Watley, he could be destined to fall in love with her and become his own great-grandfather, who no one had ever met. As a worried Bashir then ponders: “If I don’t meet with her tomorrow, I may never be born.”

What type of paradox is the Predestination Paradox?

Time travel paradoxes are generally categorized into either:

1) Closed Causal Loops: When an action resulting from time travel to the past ensures the fulfillment of a cause. Examples include the Bootstrap Paradox and Predestination Paradox.

2) Consistency Paradoxes: When an action resulting from time travel to the past stops the cause from ever happening. Examples include the Grandfather Paradox , Hitler Paradox, and Polchinski’s Paradox.

Consistency Paradoxes vs. Causal Loops

To highlight the difference further, consistency paradoxes like the Grandfather Paradox create timeline inconsistencies caused by actually being able to change the past, including killing your own grandfather, thereby preventing your own existence. This would result in an inconsistent and altered version of a past event.

A Predestination Paradox, on the other hand, results in an internally consistent version of history, albeit involving an event that appears to predate the time traveler’s initial decision to travel to the past.  A  chrononaut visiting the past to prevent someone from being killed may still ultimately fail, but they are still able to use their time machine to return to their own present and continue living their lives in a linear fashion.

What is a Time Loop?

Time loops , on the other hand, are a favorite trope of time travel movies in which a person becomes stuck in a certain period of time after which the loop resets and they must repeat the time cycle endlessly. It is unclear whether these loops would be possible in our universe.

Predestination Paradoxes involving Objects

In Predestination (2014) , an intersex temporal agent who has undergone sexual reassignment surgery travels back in time to save his younger female self from falling in love and becoming pregnant by a mysterious male lover, who then disappears, completely ruining her life. Upon meeting his younger, female self, the time traveler subsequently falls in love and impregnates her, thus becoming the very stranger who caused all the heartache he traveled back in time to prevent.

As well as an example of a predestination paradox, the act of self-creation in which the time traveler is his own mother and father is an example of a bootstrap paradox, or a self-created entity (object, data, person) with no discernible point of origin.

A simpler predestination example involves a person traveling back in time to prevent a fire that broke out at a famous museum a century earlier resulting in the destruction of many valuable pieces of art, only to accidentally cause a kerosene lamp to fall, therefore creating the very fire that later motivated them to travel back in the first place. Likewise, a person traveling back in time to save a loved one from suffering a tragic death will be unable to save them from their fate as the event has already been determined.

– Movie Examples

In the 2002 remake of The Time Machine , the scientist Alex Hartdegen witnesses his girlfriend Emma being killed by a mugger looking to steal her engagement ring, after which Hartdegen devotes his life to building a time machine in order to change the past. Once completed, subsequent attempts to interfere with time sees Emma die under different circumstances, including being trampled by a horse, leading him to conclude that “I could come back a thousand times… and see her die a thousand ways.”

He then travels to the future to see whether scientists have discovered a solution on how to change the past, and during a conversation with the Über-Morlock in the distant future is told:

“You built your time machine because of Emma’s death. If she had lived, it would never have existed, so how could you use your machine to go back and save her? You are the inescapable result of your tragedy, just as I am the inescapable result of you.”

Other examples of predestination paradox movies involving physical time travel include the Terminator franchise (1984-2015), Back to the Future (1985), Bill and Ted’s Excellent Adventure (1989), Kate and Leopold (2001), Harry Potter and the Prisoner of Azkaban (2004), Timecrimes (2007), Looper (2012), and Interstellar (2014).

Finally, the movie 12 Monkeys (1995) also presents a worthy example, with the main protagonist James Cole traveling back thirty years in time to investigate a deadly plague that decimated humanity in 1996. During his investigation, he experiences flashbacks to when he was a boy and witnessed a man being shot at an airport, only at the end of the film becoming the very same man he witnessed being killed, while a younger version of himself in 1996 watches on from the airport.

Predestination Paradoxes involving Information

Instead of a person traveling back in time another type of predestination paradox involves information being sent from the future and causing a person to fulfill his part in an event yet to happen. Once again, any attempt to change either the past or future is doomed to ultimately fail.

Say, for instance, one day a man receives information from the future that he was fated to die from a heart attack. He subsequently takes up an active exercise regime in order to avoid his predestined fate but eventually ends up overexerting himself and dying from the very heart attack he set out to prevent. In another example, a person receives future information that they will die by drowning in the future, and so decides never to step foot off dry land. A decade later, her car falls off a collapsing bridge and she drowns in the river, having never learned to swim.

In both these examples, information from the future interacts with past events to form a causality loop, with both cause and effect running in a continuous circle. It is the fact that the information received from the future was truly known to occur that makes them examples of predestination paradoxes, though. Otherwise, it would just be a case of past events causing future actions.

– Literature and Movie Examples

The classic Greek tragedy Oedipus Rex (429 BC) includes a force beyond science component, as even the god Apollo warned King Laius about the supernatural curse placed on his family by King Pelops of Pisa.

The story centers around King Laius, Queen Jocasta and their son Oedipus, whom the oracle at Delphi prophecies will grow up to kill his father and marry his mother, thus bringing disaster on the city of Thebes. King Laius then leaves the infant on a mountainside side to die , which is subsequently found and raised by King Polybus and Queen Merope. After growing up, Oedipus learns of the prophecy and so leaves home to protect his adopted parents, but on his journey quarrels and kills a stranger (Laius), and after later saving the kingless Thebes from a monstrous Sphinx marries the king’s widow, Jocasta, thereby inadvertently fulfilling the prophecy.

In Star Wars Episode III: Revenge of the Sith (2005), Anakin Skywalker sees a premonition of the death of his wife Padmé Amidala while giving birth to Luke and Leia, leading him to turn to the Dark Side in an attempt to save his wife, ultimately causing her to lose the will to live, and die in childbirth.

Possible Solutions to the Predestination Paradox

In Predestination Paradox movies, the protagonist is usually depicted as helpless to change their fate either through a lack of free will, ignorance, or an external force seemingly controlling their actions and circumstances. This tallies with ‘Novikov’s self-consistency principle’ which asserts that a time traveler is constrained to only creating a consistent version of history. In other words, there must be zero probability of creating a time paradox.

According to another solution called the ‘ timeline-protection hypothesis ’, any attempts to change the timeline would result in a probability distortion being created to protect the timeline. Furthermore, a highly improbable event may occur in order to prevent a paradoxical, impossible event from taking place. The force which subsequently interferes with any attempts to alter past events may involve physical laws, fate, or even an improbable event.

A further possibility explored in sci-fi stories is that the time traveler is actually a willing participant in ensuring a paradox is maintained, such as in Predestination (2014), a movie inspired by the book All You Zombies (1959). In both instances, the time traveler not impregnating his younger transgender self would have resulted in him never having been born at all and therefore ceasing to exist.

History Must be Preserved

According to the Predestination Paradox, history is pre-written and anything interacting with past events will only be able to act in a consistent way that enables the already established past events to be preserved. One last classic example highlights this point nicely.

A person builds a time machine to prevent a loved one from being killed by a hit-and-run driver. After traveling to the past and driving to the scene of the crime, they accidentally run over their loved one and cause the very tragedy that they sought to prevent. They then flee the scene of the crime and return to their present and continue with their life knowing that history is pre-written, and that you cannot change an event in the past that has already taken place.

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Time Travel

There is an extensive literature on time travel in both philosophy and physics. Part of the great interest of the topic stems from the fact that reasons have been given both for thinking that time travel is physically possible—and for thinking that it is logically impossible! This entry deals primarily with philosophical issues; issues related to the physics of time travel are covered in the separate entries on time travel and modern physics and time machines . We begin with the definitional question: what is time travel? We then turn to the major objection to the possibility of backwards time travel: the Grandfather paradox. Next, issues concerning causation are discussed—and then, issues in the metaphysics of time and change. We end with a discussion of the question why, if backwards time travel will ever occur, we have not been visited by time travellers from the future.

1.1 Time Discrepancy

1.2 changing the past, 2.1 can and cannot, 2.2 improbable coincidences, 2.3 inexplicable occurrences, 3.1 backwards causation, 3.2 causal loops, 4.1 time travel and time, 4.2 time travel and change, 5. where are the time travellers, other internet resources, related entries, 1. what is time travel.

There is a number of rather different scenarios which would seem, intuitively, to count as ‘time travel’—and a number of scenarios which, while sharing certain features with some of the time travel cases, seem nevertheless not to count as genuine time travel: [ 1 ]

Time travel Doctor . Doctor Who steps into a machine in 2024. Observers outside the machine see it disappear. Inside the machine, time seems to Doctor Who to pass for ten minutes. Observers in 1984 (or 3072) see the machine appear out of nowhere. Doctor Who steps out. [ 2 ] Leap . The time traveller takes hold of a special device (or steps into a machine) and suddenly disappears; she appears at an earlier (or later) time. Unlike in Doctor , the time traveller experiences no lapse of time between her departure and arrival: from her point of view, she instantaneously appears at the destination time. [ 3 ] Putnam . Oscar Smith steps into a machine in 2024. From his point of view, things proceed much as in Doctor : time seems to Oscar Smith to pass for a while; then he steps out in 1984. For observers outside the machine, things proceed differently. Observers of Oscar’s arrival in the past see a time machine suddenly appear out of nowhere and immediately divide into two copies of itself: Oscar Smith steps out of one; and (through the window) they see inside the other something that looks just like what they would see if a film of Oscar Smith were played backwards (his hair gets shorter; food comes out of his mouth and goes back into his lunch box in a pristine, uneaten state; etc.). Observers of Oscar’s departure from the future do not simply see his time machine disappear after he gets into it: they see it collide with the apparently backwards-running machine just described, in such a way that both are simultaneously annihilated. [ 4 ] Gödel . The time traveller steps into an ordinary rocket ship (not a special time machine) and flies off on a certain course. At no point does she disappear (as in Leap ) or ‘turn back in time’ (as in Putnam )—yet thanks to the overall structure of spacetime (as conceived in the General Theory of Relativity), the traveller arrives at a point in the past (or future) of her departure. (Compare the way in which someone can travel continuously westwards, and arrive to the east of her departure point, thanks to the overall curved structure of the surface of the earth.) [ 5 ] Einstein . The time traveller steps into an ordinary rocket ship and flies off at high speed on a round trip. When he returns to Earth, thanks to certain effects predicted by the Special Theory of Relativity, only a very small amount of time has elapsed for him—he has aged only a few months—while a great deal of time has passed on Earth: it is now hundreds of years in the future of his time of departure. [ 6 ] Not time travel Sleep . One is very tired, and falls into a deep sleep. When one awakes twelve hours later, it seems from one’s own point of view that hardly any time has passed. Coma . One is in a coma for a number of years and then awakes, at which point it seems from one’s own point of view that hardly any time has passed. Cryogenics . One is cryogenically frozen for hundreds of years. Upon being woken, it seems from one’s own point of view that hardly any time has passed. Virtual . One enters a highly realistic, interactive virtual reality simulator in which some past era has been recreated down to the finest detail. Crystal . One looks into a crystal ball and sees what happened at some past time, or will happen at some future time. (Imagine that the crystal ball really works—like a closed-circuit security monitor, except that the vision genuinely comes from some past or future time. Even so, the person looking at the crystal ball is not thereby a time traveller.) Waiting . One enters one’s closet and stays there for seven hours. When one emerges, one has ‘arrived’ seven hours in the future of one’s ‘departure’. Dateline . One departs at 8pm on Monday, flies for fourteen hours, and arrives at 10pm on Monday.

A satisfactory definition of time travel would, at least, need to classify the cases in the right way. There might be some surprises—perhaps, on the best definition of ‘time travel’, Cryogenics turns out to be time travel after all—but it should certainly be the case, for example, that Gödel counts as time travel and that Sleep and Waiting do not. [ 7 ]

In fact there is no entirely satisfactory definition of ‘time travel’ in the literature. The most popular definition is the one given by Lewis (1976, 145–6):

What is time travel? Inevitably, it involves a discrepancy between time and time. Any traveller departs and then arrives at his destination; the time elapsed from departure to arrival…is the duration of the journey. But if he is a time traveller, the separation in time between departure and arrival does not equal the duration of his journey.…How can it be that the same two events, his departure and his arrival, are separated by two unequal amounts of time?…I reply by distinguishing time itself, external time as I shall also call it, from the personal time of a particular time traveller: roughly, that which is measured by his wristwatch. His journey takes an hour of his personal time, let us say…But the arrival is more than an hour after the departure in external time, if he travels toward the future; or the arrival is before the departure in external time…if he travels toward the past.

This correctly excludes Waiting —where the length of the ‘journey’ precisely matches the separation between ‘arrival’ and ‘departure’—and Crystal , where there is no journey at all—and it includes Doctor . It has trouble with Gödel , however—because when the overall structure of spacetime is as twisted as it is in the sort of case Gödel imagined, the notion of external time (“time itself”) loses its grip.

Another definition of time travel that one sometimes encounters in the literature (Arntzenius, 2006, 602) (Smeenk and Wüthrich, 2011, 5, 26) equates time travel with the existence of CTC’s: closed timelike curves. A curve in this context is a line in spacetime; it is timelike if it could represent the career of a material object; and it is closed if it returns to its starting point (i.e. in spacetime—not merely in space). This now includes Gödel —but it excludes Einstein .

The lack of an adequate definition of ‘time travel’ does not matter for our purposes here. [ 8 ] It suffices that we have clear cases of (what would count as) time travel—and that these cases give rise to all the problems that we shall wish to discuss.

Some authors (in philosophy, physics and science fiction) consider ‘time travel’ scenarios in which there are two temporal dimensions (e.g. Meiland (1974)), and others consider scenarios in which there are multiple ‘parallel’ universes—each one with its own four-dimensional spacetime (e.g. Deutsch and Lockwood (1994)). There is a question whether travelling to another version of 2001 (i.e. not the very same version one experienced in the past)—a version at a different point on the second time dimension, or in a different parallel universe—is really time travel, or whether it is more akin to Virtual . In any case, this kind of scenario does not give rise to many of the problems thrown up by the idea of travelling to the very same past one experienced in one’s younger days. It is these problems that form the primary focus of the present entry, and so we shall not have much to say about other kinds of ‘time travel’ scenario in what follows.

One objection to the possibility of time travel flows directly from attempts to define it in anything like Lewis’s way. The worry is that because time travel involves “a discrepancy between time and time”, time travel scenarios are simply incoherent. The time traveller traverses thirty years in one year; she is 51 years old 21 years after her birth; she dies at the age of 100, 200 years before her birth; and so on. The objection is that these are straightforward contradictions: the basic description of what time travel involves is inconsistent; therefore time travel is logically impossible. [ 9 ]

There must be something wrong with this objection, because it would show Einstein to be logically impossible—whereas this sort of future-directed time travel has actually been observed (albeit on a much smaller scale—but that does not affect the present point) (Hafele and Keating, 1972b,a). The most common response to the objection is that there is no contradiction because the interval of time traversed by the time traveller and the duration of her journey are measured with respect to different frames of reference: there is thus no reason why they should coincide. A similar point applies to the discrepancy between the time elapsed since the time traveller’s birth and her age upon arrival. There is no more of a contradiction here than in the fact that Melbourne is both 800 kilometres away from Sydney—along the main highway—and 1200 kilometres away—along the coast road. [ 10 ]

Before leaving the question ‘What is time travel?’ we should note the crucial distinction between changing the past and participating in (aka affecting or influencing) the past. [ 11 ] In the popular imagination, backwards time travel would allow one to change the past: to right the wrongs of history, to prevent one’s younger self doing things one later regretted, and so on. In a model with a single past, however, this idea is incoherent: the very description of the case involves a contradiction (e.g. the time traveller burns all her diaries at midnight on her fortieth birthday in 1976, and does not burn all her diaries at midnight on her fortieth birthday in 1976). It is not as if there are two versions of the past: the original one, without the time traveller present, and then a second version, with the time traveller playing a role. There is just one past—and two perspectives on it: the perspective of the younger self, and the perspective of the older time travelling self. If these perspectives are inconsistent (e.g. an event occurs in one but not the other) then the time travel scenario is incoherent.

This means that time travellers can do less than we might have hoped: they cannot right the wrongs of history; they cannot even stir a speck of dust on a certain day in the past if, on that day, the speck was in fact unmoved. But this does not mean that time travellers must be entirely powerless in the past: while they cannot do anything that did not actually happen, they can (in principle) do anything that did happen. Time travellers cannot change the past: they cannot make it different from the way it was—but they can participate in it: they can be amongst the people who did make the past the way it was. [ 12 ]

What about models involving two temporal dimensions, or parallel universes—do they allow for coherent scenarios in which the past is changed? [ 13 ] There is certainly no contradiction in saying that the time traveller burns all her diaries at midnight on her fortieth birthday in 1976 in universe 1 (or at hypertime A ), and does not burn all her diaries at midnight on her fortieth birthday in 1976 in universe 2 (or at hypertime B ). The question is whether this kind of story involves changing the past in the sense originally envisaged: righting the wrongs of history, preventing subsequently regretted actions, and so on. Goddu (2003) and van Inwagen (2010) argue that it does (in the context of particular hypertime models), while Smith (1997, 365–6; 2015) argues that it does not: that it involves avoiding the past—leaving it untouched while travelling to a different version of the past in which things proceed differently.

2. The Grandfather Paradox

The most important objection to the logical possibility of backwards time travel is the so-called Grandfather paradox. This paradox has actually convinced many people that backwards time travel is impossible:

The dead giveaway that true time-travel is flatly impossible arises from the well-known “paradoxes” it entails. The classic example is “What if you go back into the past and kill your grandfather when he was still a little boy?”…So complex and hopeless are the paradoxes…that the easiest way out of the irrational chaos that results is to suppose that true time-travel is, and forever will be, impossible. (Asimov 1995 [2003, 276–7]) travel into one’s past…would seem to give rise to all sorts of logical problems, if you were able to change history. For example, what would happen if you killed your parents before you were born. It might be that one could avoid such paradoxes by some modification of the concept of free will. But this will not be necessary if what I call the chronology protection conjecture is correct: The laws of physics prevent closed timelike curves from appearing . (Hawking, 1992, 604) [ 14 ]

The paradox comes in different forms. Here’s one version:

If time travel was logically possible then the time traveller could return to the past and in a suicidal rage destroy his time machine before it was completed and murder his younger self. But if this was so a necessary condition for the time trip to have occurred at all is removed, and we should then conclude that the time trip did not occur. Hence if the time trip did occur, then it did not occur. Hence it did not occur, and it is necessary that it did not occur. To reply, as it is standardly done, that our time traveller cannot change the past in this way, is a petitio principii . Why is it that the time traveller is constrained in this way? What mysterious force stills his sudden suicidal rage? (Smith, 1985, 58)

The idea is that backwards time travel is impossible because if it occurred, time travellers would attempt to do things such as kill their younger selves (or their grandfathers etc.). We know that doing these things—indeed, changing the past in any way—is impossible. But were there time travel, there would then be nothing left to stop these things happening. If we let things get to the stage where the time traveller is facing Grandfather with a loaded weapon, then there is nothing left to prevent the impossible from occurring. So we must draw the line earlier: it must be impossible for someone to get into this situation at all; that is, backwards time travel must be impossible.

In order to defend the possibility of time travel in the face of this argument we need to show that time travel is not a sure route to doing the impossible. So, given that a time traveller has gone to the past and is facing Grandfather, what could stop her killing Grandfather? Some science fiction authors resort to the idea of chaperones or time guardians who prevent time travellers from changing the past—or to mysterious forces of logic. But it is hard to take these ideas seriously—and more importantly, it is hard to make them work in detail when we remember that changing the past is impossible. (The chaperone is acting to ensure that the past remains as it was—but the only reason it ever was that way is because of his very actions.) [ 15 ] Fortunately there is a better response—also to be found in the science fiction literature, and brought to the attention of philosophers by Lewis (1976). What would stop the time traveller doing the impossible? She would fail “for some commonplace reason”, as Lewis (1976, 150) puts it. Her gun might jam, a noise might distract her, she might slip on a banana peel, etc. Nothing more than such ordinary occurrences is required to stop the time traveller killing Grandfather. Hence backwards time travel does not entail the occurrence of impossible events—and so the above objection is defused.

A problem remains. Suppose Tim, a time-traveller, is facing his grandfather with a loaded gun. Can Tim kill Grandfather? On the one hand, yes he can. He is an excellent shot; there is no chaperone to stop him; the laws of logic will not magically stay his hand; he hates Grandfather and will not hesitate to pull the trigger; etc. On the other hand, no he can’t. To kill Grandfather would be to change the past, and no-one can do that (not to mention the fact that if Grandfather died, then Tim would not have been born). So we have a contradiction: Tim can kill Grandfather and Tim cannot kill Grandfather. Time travel thus leads to a contradiction: so it is impossible.

Note the difference between this version of the Grandfather paradox and the version considered above. In the earlier version, the contradiction happens if Tim kills Grandfather. The solution was to say that Tim can go into the past without killing Grandfather—hence time travel does not entail a contradiction. In the new version, the contradiction happens as soon as Tim gets to the past. Of course Tim does not kill Grandfather—but we still have a contradiction anyway: for he both can do it, and cannot do it. As Lewis puts it:

Could a time traveler change the past? It seems not: the events of a past moment could no more change than numbers could. Yet it seems that he would be as able as anyone to do things that would change the past if he did them. If a time traveler visiting the past both could and couldn’t do something that would change it, then there cannot possibly be such a time traveler. (Lewis, 1976, 149)

Lewis’s own solution to this problem has been widely accepted. [ 16 ] It turns on the idea that to say that something can happen is to say that its occurrence is compossible with certain facts, where context determines (more or less) which facts are the relevant ones. Tim’s killing Grandfather in 1921 is compossible with the facts about his weapon, training, state of mind, and so on. It is not compossible with further facts, such as the fact that Grandfather did not die in 1921. Thus ‘Tim can kill Grandfather’ is true in one sense (relative to one set of facts) and false in another sense (relative to another set of facts)—but there is no single sense in which it is both true and false. So there is no contradiction here—merely an equivocation.

Another response is that of Vihvelin (1996), who argues that there is no contradiction here because ‘Tim can kill Grandfather’ is simply false (i.e. contra Lewis, there is no legitimate sense in which it is true). According to Vihvelin, for ‘Tim can kill Grandfather’ to be true, there must be at least some occasions on which ‘If Tim had tried to kill Grandfather, he would or at least might have succeeded’ is true—but, Vihvelin argues, at any world remotely like ours, the latter counterfactual is always false. [ 17 ]

Return to the original version of the Grandfather paradox and Lewis’s ‘commonplace reasons’ response to it. This response engenders a new objection—due to Horwich (1987)—not to the possibility but to the probability of backwards time travel.

Think about correlated events in general. Whenever we see two things frequently occurring together, this is because one of them causes the other, or some third thing causes both. Horwich calls this the Principle of V-Correlation:

if events of type A and B are associated with one another, then either there is always a chain of events between them…or else we find an earlier event of type C that links up with A and B by two such chains of events. What we do not see is…an inverse fork—in which A and B are connected only with a characteristic subsequent event, but no preceding one. (Horwich, 1987, 97–8)

For example, suppose that two students turn up to class wearing the same outfits. That could just be a coincidence (i.e. there is no common cause, and no direct causal link between the two events). If it happens every week for the whole semester, it is possible that it is a coincidence, but this is extremely unlikely . Normally, we see this sort of extensive correlation only if either there is a common cause (e.g. both students have product endorsement deals with the same clothing company, or both slavishly copy the same influencer) or a direct causal link (e.g. one student is copying the other).

Now consider the time traveller setting off to kill her younger self. As discussed, no contradiction need ensue—this is prevented not by chaperones or mysterious forces, but by a run of ordinary occurrences in which the trigger falls off the time traveller’s gun, a gust of wind pushes her bullet off course, she slips on a banana peel, and so on. But now consider this run of ordinary occurrences. Whenever the time traveller contemplates auto-infanticide, someone nearby will drop a banana peel ready for her to slip on, or a bird will begin to fly so that it will be in the path of the time traveller’s bullet by the time she fires, and so on. In general, there will be a correlation between auto-infanticide attempts and foiling occurrences such as the presence of banana peels—and this correlation will be of the type that does not involve a direct causal connection between the correlated events or a common cause of both. But extensive correlations of this sort are, as we saw, extremely rare—so backwards time travel will happen about as often as you will see two people wear the same outfits to class every day of semester, without there being any causal connection between what one wears and what the other wears.

We can set out Horwich’s argument this way:

• If time travel were ever to occur, we should see extensive uncaused correlations.
• It is extremely unlikely that we should ever see extensive uncaused correlations.
• Therefore time travel is extremely unlikely to occur.

The conclusion is not that time travel is impossible, but that we should treat it the way we treat the possibility of, say, tossing a fair coin and getting heads one thousand times in a row. As Price (1996, 278 n.7) puts it—in the context of endorsing Horwich’s conclusion: “the hypothesis of time travel can be made to imply propositions of arbitrarily low probability. This is not a classical reductio, but it is as close as science ever gets.”

Smith (1997) attacks both premisses of Horwich’s argument. Against the first premise, he argues that backwards time travel, in itself, does not entail extensive uncaused correlations. Rather, when we look more closely, we see that time travel scenarios involving extensive uncaused correlations always build in prior coincidences which are themselves highly unlikely. Against the second premise, he argues that, from the fact that we have never seen extensive uncaused correlations, it does not follow that we never shall. This is not inductive scepticism: let us assume (contra the inductive sceptic) that in the absence of any specific reason for thinking things should be different in the future, we are entitled to assume they will continue being the same; still we cannot dismiss a specific reason for thinking the future will be a certain way simply on the basis that things have never been that way in the past. You might reassure an anxious friend that the sun will certainly rise tomorrow because it always has in the past—but you cannot similarly refute an astronomer who claims to have discovered a specific reason for thinking that the earth will stop rotating overnight.

Sider (2002, 119–20) endorses Smith’s second objection. Dowe (2003) criticises Smith’s first objection, but agrees with the second, concluding overall that time travel has not been shown to be improbable. Ismael (2003) reaches a similar conclusion. Goddu (2007) criticises Smith’s first objection to Horwich. Further contributions to the debate include Arntzenius (2006), Smeenk and Wüthrich (2011, §2.2) and Elliott (2018). For other arguments to the same conclusion as Horwich’s—that time travel is improbable—see Ney (2000) and Effingham (2020).

Return again to the original version of the Grandfather paradox and Lewis’s ‘commonplace reasons’ response to it. This response engenders a further objection. The autoinfanticidal time traveller is attempting to do something impossible (render herself permanently dead from an age younger than her age at the time of the attempts). Suppose we accept that she will not succeed and that what will stop her is a succession of commonplace occurrences. The previous objection was that such a succession is improbable . The new objection is that the exclusion of the time traveler from successfully committing auto-infanticide is mysteriously inexplicable . The worry is as follows. Each particular event that foils the time traveller is explicable in a perfectly ordinary way; but the inevitable combination of these events amounts to a ring-fencing of the forbidden zone of autoinfanticide—and this ring-fencing is mystifying. It’s like a grand conspiracy to stop the time traveler from doing what she wants to do—and yet there are no conspirators: no time lords, no magical forces of logic. This is profoundly perplexing. Riggs (1997, 52) writes: “Lewis’s account may do for a once only attempt, but is untenable as a general explanation of Tim’s continual lack of success if he keeps on trying.” Ismael (2003, 308) writes: “Considered individually, there will be nothing anomalous in the explanations…It is almost irresistible to suppose, however, that there is something anomalous in the cases considered collectively, i.e., in our unfailing lack of success.” See also Gorovitz (1964, 366–7), Horwich (1987, 119–21) and Carroll (2010, 86).

There have been two different kinds of defense of time travel against the objection that it involves mysteriously inexplicable occurrences. Baron and Colyvan (2016, 70) agree with the objectors that a purely causal explanation of failure—e.g. Tim fails to kill Grandfather because first he slips on a banana peel, then his gun jams, and so on—is insufficient. However they argue that, in addition, Lewis offers a non-causal—a logical —explanation of failure: “What explains Tim’s failure to kill his grandfather, then, is something about logic; specifically: Tim fails to kill his grandfather because the law of non-contradiction holds.” Smith (2017) argues that the appearance of inexplicability is illusory. There are no scenarios satisfying the description ‘a time traveller commits autoinfanticide’ (or changes the past in any other way) because the description is self-contradictory (e.g. it involves the time traveller permanently dying at 20 and also being alive at 40). So whatever happens it will not be ‘that’. There is literally no way for the time traveller not to fail. Hence there is no need for—or even possibility of—a substantive explanation of why failure invariably occurs, and such failure is not perplexing.

3. Causation

Backwards time travel scenarios give rise to interesting issues concerning causation. In this section we examine two such issues.

Earlier we distinguished changing the past and affecting the past, and argued that while the former is impossible, backwards time travel need involve only the latter. Affecting the past would be an example of backwards causation (i.e. causation where the effect precedes its cause)—and it has been argued that this too is impossible, or at least problematic. [ 18 ] The classic argument against backwards causation is the bilking argument . [ 19 ] Faced with the claim that some event A causes an earlier event B , the proponent of the bilking objection recommends an attempt to decorrelate A and B —that is, to bring about A in cases in which B has not occurred, and to prevent A in cases in which B has occurred. If the attempt is successful, then B often occurs despite the subsequent nonoccurrence of A , and A often occurs without B occurring, and so A cannot be the cause of B . If, on the other hand, the attempt is unsuccessful—if, that is, A cannot be prevented when B has occurred, nor brought about when B has not occurred—then, it is argued, it must be B that is the cause of A , rather than vice versa.

The bilking procedure requires repeated manipulation of event A . Thus, it cannot get under way in cases in which A is either unrepeatable or unmanipulable. Furthermore, the procedure requires us to know whether or not B has occurred, prior to manipulating A —and thus, it cannot get under way in cases in which it cannot be known whether or not B has occurred until after the occurrence or nonoccurrence of A (Dummett, 1964). These three loopholes allow room for many claims of backwards causation that cannot be touched by the bilking argument, because the bilking procedure cannot be performed at all. But what about those cases in which it can be performed? If the procedure succeeds—that is, A and B are decorrelated—then the claim that A causes B is refuted, or at least weakened (depending upon the details of the case). But if the bilking attempt fails, it does not follow that it must be B that is the cause of A , rather than vice versa. Depending upon the situation, that B causes A might become a viable alternative to the hypothesis that A causes B —but there is no reason to think that this alternative must always be the superior one. For example, suppose that I see a photo of you in a paper dated well before your birth, accompanied by a report of your arrival from the future. I now try to bilk your upcoming time trip—but I slip on a banana peel while rushing to push you away from your time machine, my time travel horror stories only inspire you further, and so on. Or again, suppose that I know that you were not in Sydney yesterday. I now try to get you to go there in your time machine—but first I am struck by lightning, then I fall down a manhole, and so on. What does all this prove? Surely not that your arrival in the past causes your departure from the future. Depending upon the details of the case, it seems that we might well be entitled to describe it as involving backwards time travel and backwards causation. At least, if we are not so entitled, this must be because of other facts about the case: it would not follow simply from the repeated coincidental failures of my bilking attempts.

Backwards time travel would apparently allow for the possibility of causal loops, in which things come from nowhere. The things in question might be objects—imagine a time traveller who steals a time machine from the local museum in order to make his time trip and then donates the time machine to the same museum at the end of the trip (i.e. in the past). In this case the machine itself is never built by anyone—it simply exists. The things in question might be information—imagine a time traveller who explains the theory behind time travel to her younger self: theory that she herself knows only because it was explained to her in her youth by her time travelling older self. The things in question might be actions. Imagine a time traveller who visits his younger self. When he encounters his younger self, he suddenly has a vivid memory of being punched on the nose by a strange visitor. He realises that this is that very encounter—and resignedly proceeds to punch his younger self. Why did he do it? Because he knew that it would happen and so felt that he had to do it—but he only knew it would happen because he in fact did it. [ 20 ]

One might think that causal loops are impossible—and hence that insofar as backwards time travel entails such loops, it too is impossible. [ 21 ] There are two issues to consider here. First, does backwards time travel entail causal loops? Lewis (1976, 148) raises the question whether there must be causal loops whenever there is backwards causation; in response to the question, he says simply “I am not sure.” Mellor (1998, 131) appears to claim a positive answer to the question. [ 22 ] Hanley (2004, 130) defends a negative answer by telling a time travel story in which there is backwards time travel and backwards causation, but no causal loops. [ 23 ] Monton (2009) criticises Hanley’s counterexample, but also defends a negative answer via different counterexamples. Effingham (2020) too argues for a negative answer.

Second, are causal loops impossible, or in some other way objectionable? One objection is that causal loops are inexplicable . There have been two main kinds of response to this objection. One is to agree but deny that this is a problem. Lewis (1976, 149) accepts that a loop (as a whole) would be inexplicable—but thinks that this inexplicability (like that of the Big Bang or the decay of a tritium atom) is merely strange, not impossible. In a similar vein, Meyer (2012, 263) argues that if someone asked for an explanation of a loop (as a whole), “the blame would fall on the person asking the question, not on our inability to answer it.” The second kind of response (Hanley, 2004, §5) is to deny that (all) causal loops are inexplicable. A second objection to causal loops, due to Mellor (1998, ch.12), is that in such loops the chances of events would fail to be related to their frequencies in accordance with the law of large numbers. Berkovitz (2001) and Dowe (2001) both argue that Mellor’s objection fails to establish the impossibility of causal loops. [ 24 ] Effingham (2020) considers—and rebuts—some additional objections to the possibility of causal loops.

4. Time and Change

Gödel (1949a [1990a])—in which Gödel presents models of Einstein’s General Theory of Relativity in which there exist CTC’s—can well be regarded as initiating the modern academic literature on time travel, in both philosophy and physics. In a companion paper, Gödel discusses the significance of his results for more general issues in the philosophy of time (Gödel 1949b [1990b]). For the succeeding half century, the time travel literature focussed predominantly on objections to the possibility (or probability) of time travel. More recently, however, there has been renewed interest in the connections between time travel and more general issues in the metaphysics of time and change. We examine some of these in the present section. [ 25 ]

The first thing that we need to do is set up the various metaphysical positions whose relationships with time travel will then be discussed. Consider two metaphysical questions:

• Are the past, present and future equally real?
• Is there an objective flow or passage of time, and an objective now?

We can label some views on the first question as follows. Eternalism is the view that past and future times, objects and events are just as real as the present time and present events and objects. Nowism is the view that only the present time and present events and objects exist. Now-and-then-ism is the view that the past and present exist but the future does not. We can also label some views on the second question. The A-theory answers in the affirmative: the flow of time and division of events into past (before now), present (now) and future (after now) are objective features of reality (as opposed to mere features of our experience). Furthermore, they are linked: the objective flow of time arises from the movement, through time, of the objective now (from the past towards the future). The B-theory answers in the negative: while we certainly experience now as special, and time as flowing, the B-theory denies that what is going on here is that we are detecting objective features of reality in a way that corresponds transparently to how those features are in themselves. The flow of time and the now are not objective features of reality; they are merely features of our experience. By combining answers to our first and second questions we arrive at positions on the metaphysics of time such as: [ 26 ]

• the block universe view: eternalism + B-theory
• the moving spotlight view: eternalism + A-theory
• the presentist view: nowism + A-theory
• the growing block view: now-and-then-ism + A-theory.

So much for positions on time itself. Now for some views on temporal objects: objects that exist in (and, in general, change over) time. Three-dimensionalism is the view that persons, tables and other temporal objects are three-dimensional entities. On this view, what you see in the mirror is a whole person. [ 27 ] Tomorrow, when you look again, you will see the whole person again. On this view, persons and other temporal objects are wholly present at every time at which they exist. Four-dimensionalism is the view that persons, tables and other temporal objects are four-dimensional entities, extending through three dimensions of space and one dimension of time. On this view, what you see in the mirror is not a whole person: it is just a three-dimensional temporal part of a person. Tomorrow, when you look again, you will see a different such temporal part. Say that an object persists through time if it is around at some time and still around at a later time. Three- and four-dimensionalists agree that (some) objects persist, but they differ over how objects persist. According to three-dimensionalists, objects persist by enduring : an object persists from t 1 to t 2 by being wholly present at t 1 and t 2 and every instant in between. According to four-dimensionalists, objects persist by perduring : an object persists from t 1 to t 2 by having temporal parts at t 1 and t 2 and every instant in between. Perduring can be usefully compared with being extended in space: a road extends from Melbourne to Sydney not by being wholly located at every point in between, but by having a spatial part at every point in between.

It is natural to combine three-dimensionalism with presentism and four-dimensionalism with the block universe view—but other combinations of views are certainly possible.

Gödel (1949b [1990b]) argues from the possibility of time travel (more precisely, from the existence of solutions to the field equations of General Relativity in which there exist CTC’s) to the B-theory: that is, to the conclusion that there is no objective flow or passage of time and no objective now. Gödel begins by reviewing an argument from Special Relativity to the B-theory: because the notion of simultaneity becomes a relative one in Special Relativity, there is no room for the idea of an objective succession of “nows”. He then notes that this argument is disrupted in the context of General Relativity, because in models of the latter theory to date, the presence of matter does allow recovery of an objectively distinguished series of “nows”. Gödel then proposes a new model (Gödel 1949a [1990a]) in which no such recovery is possible. (This is the model that contains CTC’s.) Finally, he addresses the issue of how one can infer anything about the nonexistence of an objective flow of time in our universe from the existence of a merely possible universe in which there is no objectively distinguished series of “nows”. His main response is that while it would not be straightforwardly contradictory to suppose that the existence of an objective flow of time depends on the particular, contingent arrangement and motion of matter in the world, this would nevertheless be unsatisfactory. Responses to Gödel have been of two main kinds. Some have objected to the claim that there is no objective flow of time in his model universe (e.g. Savitt (2005); see also Savitt (1994)). Others have objected to the attempt to transfer conclusions about that model universe to our own universe (e.g. Earman (1995, 197–200); for a partial response to Earman see Belot (2005, §3.4)). [ 28 ]

Earlier we posed two questions:

Gödel’s argument is related to the second question. Let’s turn now to the first question. Godfrey-Smith (1980, 72) writes “The metaphysical picture which underlies time travel talk is that of the block universe [i.e. eternalism, in the terminology of the present entry], in which the world is conceived as extended in time as it is in space.” In his report on the Analysis problem to which Godfrey-Smith’s paper is a response, Harrison (1980, 67) replies that he would like an argument in support of this assertion. Here is an argument: [ 29 ]

A fundamental requirement for the possibility of time travel is the existence of the destination of the journey. That is, a journey into the past or the future would have to presuppose that the past or future were somehow real. (Grey, 1999, 56)

Dowe (2000, 442–5) responds that the destination does not have to exist at the time of departure: it only has to exist at the time of arrival—and this is quite compatible with non-eternalist views. And Keller and Nelson (2001, 338) argue that time travel is compatible with presentism:

There is four-dimensional [i.e. eternalist, in the terminology of the present entry] time-travel if the appropriate sorts of events occur at the appropriate sorts of times; events like people hopping into time-machines and disappearing, people reappearing with the right sorts of memories, and so on. But the presentist can have just the same patterns of events happening at just the same times. Or at least, it can be the case on the presentist model that the right sorts of events will happen, or did happen, or are happening, at the rights sorts of times. If it suffices for four-dimensionalist time-travel that Jennifer disappears in 2054 and appears in 1985 with the right sorts of memories, then why shouldn’t it suffice for presentist time-travel that Jennifer will disappear in 2054, and that she did appear in 1985 with the right sorts of memories?

Sider (2005) responds that there is still a problem reconciling presentism with time travel conceived in Lewis’s way: that conception of time travel requires that personal time is similar to external time—but presentists have trouble allowing this. Further contributions to the debate whether presentism—and other versions of the A-theory—are compatible with time travel include Monton (2003), Daniels (2012), Hall (2014) and Wasserman (2018) on the side of compatibility, and Miller (2005), Slater (2005), Miller (2008), Hales (2010) and Markosian (2020) on the side of incompatibility.

Leibniz’s Law says that if x = y (i.e. x and y are identical—one and the same entity) then x and y have exactly the same properties. There is a superficial conflict between this principle of logic and the fact that things change. If Bill is at one time thin and at another time not so—and yet it is the very same person both times—it looks as though the very same entity (Bill) both possesses and fails to possess the property of being thin. Three-dimensionalists and four-dimensionalists respond to this problem in different ways. According to the four-dimensionalist, what is thin is not Bill (who is a four-dimensional entity) but certain temporal parts of Bill; and what is not thin are other temporal parts of Bill. So there is no single entity that both possesses and fails to possess the property of being thin. Three-dimensionalists have several options. One is to deny that there are such properties as ‘thin’ (simpliciter): there are only temporally relativised properties such as ‘thin at time t ’. In that case, while Bill at t 1 and Bill at t 2 are the very same entity—Bill is wholly present at each time—there is no single property that this one entity both possesses and fails to possess: Bill possesses the property ‘thin at t 1 ’ and lacks the property ‘thin at t 2 ’. [ 30 ]

Now consider the case of a time traveller Ben who encounters his younger self at time t . Suppose that the younger self is thin and the older self not so. The four-dimensionalist can accommodate this scenario easily. Just as before, what we have are two different three-dimensional parts of the same four-dimensional entity, one of which possesses the property ‘thin’ and the other of which does not. The three-dimensionalist, however, faces a problem. Even if we relativise properties to times, we still get the contradiction that Ben possesses the property ‘thin at t ’ and also lacks that very same property. [ 31 ] There are several possible options for the three-dimensionalist here. One is to relativise properties not to external times but to personal times (Horwich, 1975, 434–5); another is to relativise properties to spatial locations as well as to times (or simply to spacetime points). Sider (2001, 101–6) criticises both options (and others besides), concluding that time travel is incompatible with three-dimensionalism. Markosian (2004) responds to Sider’s argument; [ 32 ] Miller (2006) also responds to Sider and argues for the compatibility of time travel and endurantism; Gilmore (2007) seeks to weaken the case against endurantism by constructing analogous arguments against perdurantism. Simon (2005) finds problems with Sider’s arguments, but presents different arguments for the same conclusion; Effingham and Robson (2007) and Benovsky (2011) also offer new arguments for this conclusion. For further discussion see Wasserman (2018) and Effingham (2020). [ 33 ]

We have seen arguments to the conclusions that time travel is impossible, improbable and inexplicable. Here’s an argument to the conclusion that backwards time travel simply will not occur. If backwards time travel is ever going to occur, we would already have seen the time travellers—but we have seen none such. [ 34 ] The argument is a weak one. [ 35 ] For a start, it is perhaps conceivable that time travellers have already visited the Earth [ 36 ] —but even granting that they have not, this is still compatible with the future actuality of backwards time travel. First, it may be that time travel is very expensive, difficult or dangerous—or for some other reason quite rare—and that by the time it is available, our present period of history is insufficiently high on the list of interesting destinations. Second, it may be—and indeed existing proposals in the physics literature have this feature—that backwards time travel works by creating a CTC that lies entirely in the future: in this case, backwards time travel becomes possible after the creation of the CTC, but travel to a time earlier than the time at which the CTC is created is not possible. [ 37 ]

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How does relativity theory resolve the Twin Paradox?

Ronald C. Lasky, a lecturer at Dartmouth College's Thayer School of Engineering, explains. Time must never be thought of as pre-existing in any sense; it is a manufactured quantity. --Hermann Bondi

Paul Davies's recent article "How to Build a Time Machine" has rekindled interest in the Twin Paradox, arguably the most famous thought experiment in relativity theory. In this supposed paradox, one of two twins travels at near the speed of light to a distant star and returns to the earth. Relativity dictates that when he comes back, he is younger than his identical twin brother.

The paradox lies in the question "Why is the traveling brother younger?" Special relativity tells us that an observed clock, traveling at a high speed past an observer, appears to run more slowly. (Many of us solved this problem in sophomore physics, to demonstrate one effect of the absolute nature of the speed of light.) Since relativity says that there is no absolute motion, wouldn?t the brother traveling to the star also see his brother?s clock on the earth move more slowly? If this were the case, wouldn?t they both be the same age? This paradox is discussed in many books but solved in very few. When the paradox is addressed, it is usually done so only briefly, by saying that the one who feels the acceleration is the one who is younger at the end of the trip. Hence, the brother who travels to the star is younger. While the result is correct, the explanation is misleading. Because of these types of incomplete explanations, to many partially informed people, the accelerations appear to be the issue. Therefore, it is believed that the general theory of relativity is required to explain the paradox. Of course, this conclusion is based on yet another mistake, since we don't need general relativity to handle accelerations. The paradox can be unraveled by special relativity alone, and the accelerations incurred by the traveler are incidental. An explanation follows.

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Let us assume that the two brothers, nicknamed the traveler and the homebody, live in Hanover, N.H. They differ in their wanderlust but share a common desire to build a spacecraft that can achieve 0.6 times the speed of light (0.6c). After working on the spacecraft for years, they are ready to launch it, manned by the traveler, toward a star six light-years away. His craft will quickly accelerate to 0.6c. For those who are interested, it would take a little more than 100 days to reach 0.6c at an acceleration of 2g's. Two g's is two times the acceleration of gravity, about what one experiences on a sharp loop on roller coaster. However, if the traveler were an electron, he could be accelerated to 0.6c in a tiny fraction of a second. Hence, the time to reach 0.6c is not central to the argument. The traveler uses the length-contraction equation of special relativity to measure distance. So the star six light-years away to the homebody appears to be only 4.8 light-years away to the traveler at a speed of 0.6c. Therefore, to the traveler, the trip to the star takes only eight years (4.8/0.6), whereas the homebody calculates it taking 10 years (6.0/0.6). It is instructive to discuss how each would view his and the other?s clocks during the trip. Let?s assume that each has a very powerful telescope that enables such observation. Surprisingly, with careful use of the time it takes light to travel between the two we can explain the paradox.

Both the traveler and homebody set their clocks at zero when the traveler leaves the earth for the star (event 1). When the traveler reaches the star (event 2) his clock reads eight years. ( Click here for graph.) However, when the homebody sees the traveler reach the star, the homebody?s clock reads 16 years. Why 16 years? Because, to the homebody, the craft takes 10 years to make it to the star and the light six additional years to come back to the earth showing the traveler at the star. So to the homebody, the traveler?s clock appears to be running at half the speed of his clock (8/16.)?

As the traveler reaches the star he reads his clock at eight years as mentioned, but he sees the homebody?s clock as it was six years ago (the amount of time it takes for the light from the earth to reach him), or at four years (10-6). So the traveler also views the homebody?s clock as running half the speed of his clock (4/8).

On the trip back, the homebody views the traveler?s clock going from eight years to 16 years in only four years' time, since his clock was at 16 years when he saw the traveler leave the star and will be at 20 years when the traveler arrives back home (event 3). So the homebody now sees the traveler's clock advance eight years in four years of his time; it is now twice as fast as his clock. On the trip back, the traveler sees the homebody?s clock advance from four to 20 years in eight years of his time. Therefore, he also sees his brother?s clock advancing at twice the speed of his. They both agree, however, that at the end of the trip the traveler?s clock reads 16 years and the homebody?s 20 years. So the traveler is four years younger. The asymmetry in the paradox is that the traveler leaves the earth?s reference frame and comes back, whereas the homebody never leaves the earth. It is also an asymmetry that the traveler and the homebody agree with the reading on the traveler?s clock at each event, but not vice versa. The traveler?s actions define the events.

The Doppler effect and relativity together explain this effect mathematically at any instant. The interested reader will find the combination of these effects discussed in The Fundamentals of Physics, by David Halliday et al. (John Wiley and Sons, 1996). Paul Davies also does a nice job explaining the Twin Paradox in his book About Time (Touchstone 1995, ppf 59.) My explanation follows Davies?s closely; I hope my graph adds further clarity. The reader should also note that the speed that an observed clock appears to run depends on whether it is traveling away from or toward the observer. The sophomore physics problem, mentioned earlier, is a special case as it applies only when the motion of the traveler passes the observer?s reference frame with no separating distance in the direction of motion.

For those with a little more formal physics background, a spacetime diagram also explains the paradox nicely. It is shown with the supporting calculations for the Doppler effect on the observed time. Proper time is time in the frame of the observer.?

The Time-Travel Paradoxes

What happens if a time traveler kills his or her grandfather? What is a time loop? How do you stop a time machine from just appearing somewhere in space, millions of kilometers from home? And is there such a thing as free will?

Congratulations! You have a time machine! You can pop over to see the dinosaurs, be in London for the Beatles’ rooftop concert, hear Jesus deliver his Sermon on the Mount, save the books of the Library of Alexandria, or kill Hitler. Past and future are in your hands. All you have to do is step inside and press the red button.

Wait! Don’t do it!

Seriously, if you value your lives, if you want to protect the fabric of reality – run for the hills! Physics and logical paradoxes will be your undoing. From the grandfather paradox to laws of classic mechanics, we have prepared a comprehensive guide to the hazards of time travel. Beware the dangers that lie ahead.

 The Grandfather Paradox

Want to change reality? First think carefully about your grandparents’ contribution to your lives.

The grandfather paradox basically describes the following situation: For some reason or another, you have decided to go back in time and kill your grandfather in his youth. Yeah, sure, of course you love him – but this is a scientific experiment; you don’t have a choice. So your grandmother will never give birth to your parent – and therefore you will never be born, which means that you cannot kill your grandfather. Oh boy! This is quite a contradiction!

The extended version of the paradox touches upon practically every single change that our hypothetical time traveler will make in the past. In a chaotic reality, there is no telling what the consequences of each step will be on the reality you came from. Just as a butterfly flapping its wings in the Amazon could cause a tornado in Texas, there is no way of predicting what one wrong move on your part might do to all of history, let alone a drastic move like killing someone.

There is a possible solution to this paradox – but it cancels out free will: Our time traveler can only do what has already been done. So don’t worry – everything you did in the past has already happened, so it’s impossible for you to kill grandpa, or create any sort of a contradiction in any other way. Another solution is that the time traveler's actions led to a splitting of the universe into two universes – one in which the time traveler was born, and the other in which he murdered his grandfather and was not born.

Information passage from the future to the past causes a similar paradox. Let’s say someone from the future who has my best interests in mind tries to warn me that a grand piano is about to fall on my head in the street, or that I have a type of cancer that is curable if it’s discovered early enough. Because of this warning, I could take steps to prevent the event – but then, there is no reason to send back the information from the future that saves my life. Another contradiction!

Marty finds himself in hot water with the grandfather paradox, from ‘Back to the Future’ 1985

Let’s now assume the information is different: A richer future me builds a time machine to let the late-90s me know that I should buy stock of a small company called “Google”, so that I can make a fortune. If I have free will, that means I can refuse. But future me knows I already did it. Do I have a choice but to do what I ask of myself?

 The Time Loop

In the book All You Zombies by science fiction writer Robert A. Heinlein the Hero is sent back in time in order to impregnate a young woman who is later revealed to be him, following a sex change operation. The offspring of this coupling is the young man himself, who will meet himself at a younger age and take him back to the past to impregnate you know whom.

Confused? This is just one extreme example of a time loop – a situation where a past event is the cause of an event at another time and also the result of it. A simpler example could be a time traveler giving the young William Shakespeare a copy of the complete works of Shakespeare so that he can copy them. If that happens, then who is the genius author of Macbeth?

This phenomenon is also known as the Bootstrap Paradox , based on another story by Heinlein, who likened it to a person trying to pull himself up by his bootstraps (a phrase which, in turn, comes from the classic book The Surprising Adventures of Baron Munchausen). The word ‘paradox’ here is a bit misleading, since there is no contradiction in the loop – it exists in a sequence of events and feeds itself. The only contradiction is in the order of things that we are acquainted with, where cause leads to effect and nothing further, and there is meaning to the question “how did it all begin?”

 Terminator 2 (1991). The shapeshifting android (Arnold Schwarzenegger) destroys himself in order to break the time loop in which his mere presence in the present enabled his production in the future

Time travelers – where have all they gone?

In 1950, over lunch physicist Enrico Fermi famously asked: “If there is intelligent extraterrestrial life in the Universe – then where are they?” indicating that we have never met aliens or came across evidence of their existence, such as radio signals which would be proof of a technological society.  We could pose that same question about time travelers: “If time travel is possible, where are all the time travelers?”

The question, known as the Fermi Paradox, is an important one. After all, if it were possible to travel through time, would we not have bumped into a bunch of observers from the future at critical junctures in history? It is unlikely to assume that they all managed to perfectly disguise themselves, without making any errors in the design of the clothes they wore, their accents, their vocabulary, etc. Another option is that time travel is possible, but it is used with the utmost care and tight control, due to all the dangers we discuss here.

 On June 28, 2009, physicist Stephen Hawking carried out a scientific experiment which was meant to answer this question once and for all. He brought snacks, balloons and champagne and hosted a secret party for time travelers only – but sent out the invitations only on the next day. If no one showed up, he argued, that would be proof that time travel to the past is not possible. The invitees failed to arrive. “I sat and waited for a while, but nobody came,” he reported at the Seattle Science Festival in 2012.

Multiple time travelers also undermine the possibility of a fixed and consistent timeline, assuming that the past can indeed be changed. Imagine, for example, a nail-biting derby between the top clubs, Hapoel Jericho and Maccabi Jericho. Originally Maccabi won, so a Hapoel fan traveled back in time and managed to lead to his team’s victory. Maccabi fans would not give up and did the same. Soon, the whole stadium is filled with time travelers and paradoxes.

 One way or round trip?

When considering travel, it is always continuous – from point A to point B, through all the points in between. Time travel should supposedly be the same: travelers get into their machine, push the button, and go from time A to time B, through all the times in between. But there’s a catch, if we are only travelling through time, then to the casual observer, the time machine continuously exists in the same space between the points in time. The result is that our journey is one-way and the time travelers will stay stuck in the future or the past because the machine itself will block the time-path back. And that is before we even start wondering how to even build this thing in the first place if it already exists in the place where we want to build it.

If that’s the case, then there’s no choice but to assume that there is some way to jump from time to time or place to place and materialize at the destination. How will our machine “know” to jump to an empty area, and to avoid materializing into a wall or a living creature unlucky enough to occupy that same spot? The passengers will undoubtedly need effective navigation and observation equipment to prevent unfortunate accidents at the point of entry.

 Advanced time travel

In addition to the problems that time travel poses for anyone trying to keep the notion of  cause and effect in order, time travelers may also face – or already have faced – other challenges from physics, even classical physics.

One issue you have to consider during time travel, and which science fiction writers usually prefer to ignore for convenience sake, is the question of arrival at the specified time destination and what would happen to us there.

It is usually assumed, with no good reason, that if someone is travelling through time, he or she will land in the same place, but at a different time – past or future. But this is where we hit a snag: the Earth rotates around the sun at a speed of 110,000 kph, and the Solar System itself is moving in its trajectory around the galaxy at a speed of 750,000 kph. If we time-travel for even a few seconds and stay in the same coordinates of space, we will probably find ourselves floating in outer space and perhaps even manage a quick glance around before we die. Our time machine will have to take into account this movement of the heavenly bodies and place us at exactly the right spot in space.

This alone may be resolved, since time travel, in any case, takes place between two points in the four-dimensional space-time continuum. According to the theory of general relativity, the theoretical foundation for time travel, space and time are a single physical entity, known as space-time. This entity can be bent and distorted – in fact gravity itself is an external manifestation of space-time distortion.

The Time Lord ,Doctor Who explains what “time” is exactly (Doctor Who, Season 3, Chapter 10: Blink).

Time travel would be possible if we could create a closed space-time loop, or if we could go from one point to another through a shortcut called a “Wormhole”. This would, in any case, not be just moving from one point in time to another, but would also include moving through space. Thus, from the outset, the journey is not only in time, but necessarily includes a destination point in space, which we will need to pre-program on our machine, of course .

In practice, the situation is more complicated – especially if we want to go into the distant past or distant future. The speed of the celestial bodies, and even the Earth’s shape and the structure of the continents, the seas, and mountains on the face of the Earth, change over the years. And because even a tiny deviation in our knowledge of the past can land us in the core of the Earth, in outer space or somewhere else that immediately reduces life expectancy to zero – time travel becomes a Russian roulette.

 How to travel in time and stay alive

 Let’s assume we coped with this problem and managed to get to the exact point in space-time that can sustain life. Careful – we’re not there yet; we still have to deal with momentum.

Momentum is a conserved quantity, which basically represents the potential of a body to continue moving at the speed and direction in which it is already travelling. If we were to jump out of a moving car (heaven forbid!), conservation of momentum is what would cause us to roll on the ground and probably get injured (in the best-case scenario). And so, if we leap in time – say, a month back – and land at the exact same point on Earth – we would discover, much to our dismay, that even if we started motionless in relation to the ground, now the ground underneath us is moving quickly at one angle or another towards us . Thus, even if we were lucky enough not to crash immediately on impact, we’re likely to hit some obstacle. And if by some miracle we were to survive, we would quickly find ourselves burning up in the atmosphere or gasping for air in space – because we have far exceeded the escape velocity from Earth.

A possible solution to this problem is to plan our landing point ahead, so that the ground speed will be equal in size and direction to our exit speed, but this places many constraints on our journey. We could always leap into space, where there are hardly any moving objects to be bumped into, and only then land again at our point of destination on Earth.

Having said all that, this problem arises chiefly when we assume that time hopping is immediate – that we disappear from one point in time and immediately appear in another, without losing mass, energy, or momentum. But since a “realistic” journey in time is not instantaneous, rather it involves travelling along space-time, it is no different from other types of journeys. This being the case, we can hope that we could adjust our speed to the desired value and direction prior to landing, just like a spacecraft slowing down before landing on a planet.

We should also keep in mind that thankfully, we will have access to a powerful technology that would enable us to cope with such problems: Time-travel technology itself. For example, we might decide to send thousands of tiny probes ahead of us, each to a slightly different point in space-time. Some of them, maybe even most, will be destroyed for one of the reasons already mentioned. The others will wait patiently until the present and then feed their programmed coordinates into the time machine. Thus by definition, the destination entered will be safe for us, except, perhaps for the annoying probe shower hitting the travellers. For the travellers themselves, the entire process will be immediate.

Time Travelling Grammar

Finally, we come to the question: How do you actually talk about time travel? The three tenses – past, present, and future – are insufficient to discuss a future event that happened some time in the past with someone who is in the present, which is another’s past and yet another’s future. And what is the correct grammatical tense to use when we talk about an alternative future that would have been created after we killed our grandfather? Or how do we express the future-past tense (or past-future, or past-future-past?), when we get stuck in a time loop where what will happen leads to what had already taken place, and so on? And of course the biggest question that Hebrew editors and translators have faced for years – is there really such a thing as present continuous?

It’s complicated.

Arguing about tenses and a time machine, The Big Bang Theory, Season 8, Episode 5, 2014

In his book, The Restaurant at the End of the Universe, science fiction writer Douglas Adams suggests to his readers to consult (by Dr. Dan Streetmentioner) Time Traveler's Handbook of 1001 Tense Formations (by Dr. Dan Streetmentioner) to find the answers to these questions. That’s all very well, but, Adams tells us, “most readers get as far as the Future Semi-Conditionally Modified Subinverted Plagal Past Subjunctive Intentional before giving up; and in fact in later editions of the book all pages beyond this point have been left blank to save on printing costs.”

If, despite all of the above, you’re still intent on travelling back to Mount Sinai or the Apollo 11 moon landing – let us then wish you bon voyage, and please give our regards to Neil Armstrong!

Time Travel Paradoxes

• First Online: 11 May 2018

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• S. V. Krasnikov 28  

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 193))

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It seems appropriate now to turn attention to the most controversial issue related to the time machines—the time travel paradoxes. On the one hand, paradoxes seem to be something inherent to time machines (their main attribute, perhaps). On the other hand, the (supposed) paradoxicalness of time travel is traditionally the main objection against it and a good pretext for dismissing causality violating spacetimes from consideration. Recall, however, that in studying physics one meets a lot of ‘paradoxes’ (Ehrenfest’s, Gibbs’, Olbers’, etc.). Today they are just interesting and instructive toy problems. Our aim in this chapter is to examine the ‘temporal paradoxes’ and to reduce them to the same status. In particular, we are going to show that they do not increase the tension between the relativistic concept of spacetime and ‘the simple notion of free will’ (S. W. Hawking and G. F. R. Ellis (1973). The Large Scale Structure of Spacetime. Cambridge University Press, Cambridge) [76]. As a by-product, we shall reveal, in the end of the chapter, a curious relation between the geometry of a spacetime and its matter content.

... Loads of them ended up killing their past or future selves by mistake! Hermiona in [158]

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Excerpts from: Time Travel and Time Machines

Physics and Our Intuitive Outlook on Time

Three facets of time-reversal symmetry

The term was coined by Tadasana.

In fact, this assumption is not that extravagant. I am not aware of a single strong argument against it. Note, in particular, that the apparent lack of contramotes in the everyday life and in astronomical observations is not an argument: the contramotes must be practically invisible to us comotes. Indeed, they almost do not radiate light. Instead, a contramote star, say, absorbs a powerful flux of photons emitted (for some mysterious reason) towards the star by other bodies.

For a collection of such pseudo paradoxes see [138].

We speak of the existence of the note and not of its appearance , because being a typical Cauchy demon, see Sect.  3 in Chap. 2, the note has always existed, without ever having come into being.

In fact, they often are too complex even when consist of billiard balls, see [39, 127].

As is known, ‘...either a tail is there or it isn’t there. You can’t make a mistake about it...’ [128]. The same is true for evolutions. So, we shall not speak of ‘self-inconsistent evolution’ or ‘trajectories with zero multiplicity’.

For a technical description see Example  74 in Chap. 1.

For a less trivial one see [65].

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Time travel could be possible, but only with parallel timelines

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Have you ever made a mistake that you wish you could undo? Correcting past mistakes is one of the reasons we find the concept of time travel so fascinating. As often portrayed in science fiction, with a time machine, nothing is permanent anymore — you can always go back and change it. But is time travel really possible in our universe , or is it just science fiction?

Read more: Curious Kids: is time travel possible for humans?

Our modern understanding of time and causality comes from general relativity . Theoretical physicist Albert Einstein’s theory combines space and time into a single entity — “spacetime” — and provides a remarkably intricate explanation of how they both work, at a level unmatched by any other established theory. This theory has existed for more than 100 years, and has been experimentally verified to extremely high precision, so physicists are fairly certain it provides an accurate description of the causal structure of our universe.

For decades, physicists have been trying to use general relativity to figure out if time travel is possible . It turns out that you can write down equations that describe time travel and are fully compatible and consistent with relativity. But physics is not mathematics, and equations are meaningless if they do not correspond to anything in reality.

Arguments against time travel

There are two main issues which make us think these equations may be unrealistic. The first issue is a practical one: building a time machine seems to require exotic matter , which is matter with negative energy. All the matter we see in our daily lives has positive energy — matter with negative energy is not something you can just find lying around. From quantum mechanics, we know that such matter can theoretically be created, but in too small quantities and for too short times .

However, there is no proof that it is impossible to create exotic matter in sufficient quantities. Furthermore, other equations may be discovered that allow time travel without requiring exotic matter. Therefore, this issue may just be a limitation of our current technology or understanding of quantum mechanics.

The other main issue is less practical, but more significant: it is the observation that time travel seems to contradict logic, in the form of time travel paradoxes . There are several types of such paradoxes, but the most problematic are consistency paradoxes .

A popular trope in science fiction, consistency paradoxes happen whenever there is a certain event that leads to changing the past, but the change itself prevents this event from happening in the first place.

For example, consider a scenario where I enter my time machine, use it to go back in time five minutes, and destroy the machine as soon as I get to the past. Now that I destroyed the time machine, it would be impossible for me to use it five minutes later.

But if I cannot use the time machine, then I cannot go back in time and destroy it. Therefore, it is not destroyed, so I can go back in time and destroy it. In other words, the time machine is destroyed if and only if it is not destroyed. Since it cannot be both destroyed and not destroyed simultaneously, this scenario is inconsistent and paradoxical.

Eliminating the paradoxes

There’s a common misconception in science fiction that paradoxes can be “created.” Time travellers are usually warned not to make significant changes to the past and to avoid meeting their past selves for this exact reason. Examples of this may be found in many time travel movies, such as the Back to the Future trilogy.

But in physics, a paradox is not an event that can actually happen — it is a purely theoretical concept that points towards an inconsistency in the theory itself. In other words, consistency paradoxes don’t merely imply time travel is a dangerous endeavour, they imply it simply cannot be possible.

This was one of the motivations for theoretical physicist Stephen Hawking to formulate his chronology protection conjecture , which states that time travel should be impossible. However, this conjecture so far remains unproven. Furthermore, the universe would be a much more interesting place if instead of eliminating time travel due to paradoxes, we could just eliminate the paradoxes themselves.

One attempt at resolving time travel paradoxes is theoretical physicist Igor Dmitriyevich Novikov’s self-consistency conjecture , which essentially states that you can travel to the past, but you cannot change it.

According to Novikov, if I tried to destroy my time machine five minutes in the past, I would find that it is impossible to do so. The laws of physics would somehow conspire to preserve consistency.

Introducing multiple histories

But what’s the point of going back in time if you cannot change the past? My recent work, together with my students Jacob Hauser and Jared Wogan, shows that there are time travel paradoxes that Novikov’s conjecture cannot resolve. This takes us back to square one, since if even just one paradox cannot be eliminated, time travel remains logically impossible.

So, is this the final nail in the coffin of time travel? Not quite. We showed that allowing for multiple histories (or in more familiar terms, parallel timelines) can resolve the paradoxes that Novikov’s conjecture cannot. In fact, it can resolve any paradox you throw at it.

The idea is very simple. When I exit the time machine, I exit into a different timeline. In that timeline, I can do whatever I want, including destroying the time machine, without changing anything in the original timeline I came from. Since I cannot destroy the time machine in the original timeline, which is the one I actually used to travel back in time, there is no paradox.

After working on time travel paradoxes for the last three years , I have become increasingly convinced that time travel could be possible, but only if our universe can allow multiple histories to coexist. So, can it?

Quantum mechanics certainly seems to imply so, at least if you subscribe to Everett’s “many-worlds” interpretation , where one history can “split” into multiple histories, one for each possible measurement outcome – for example, whether Schrödinger’s cat is alive or dead, or whether or not I arrived in the past.

But these are just speculations. My students and I are currently working on finding a concrete theory of time travel with multiple histories that is fully compatible with general relativity. Of course, even if we manage to find such a theory, this would not be sufficient to prove that time travel is possible, but it would at least mean that time travel is not ruled out by consistency paradoxes.

Time travel and parallel timelines almost always go hand-in-hand in science fiction, but now we have proof that they must go hand-in-hand in real science as well. General relativity and quantum mechanics tell us that time travel might be possible, but if it is, then multiple histories must also be possible.

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Paradoxes of Time Travel

Ryan Wasserman, Paradoxes of Time Travel , Oxford University Press, 2018, 240pp., $60.00, ISBN 9780198793335.

Reviewed by John W. Carroll, North Carolina State

Wasserman's book fills a gap in the academic literature on time travel. The gap was hidden among the journal articles on time travel written by physicists for physicists, the popular books on time travel by physicists for the curious folk, the books on the history of time travel in science fiction intended for a range of scholarly audiences, and the journal articles on time travel written for and by metaphysicians and philosophers of science. There are metaphysics books on time that give some attention to time travel, but, as far as I know, this is the first book length work devoted to the topic of time travel by a metaphysician homed in on the most important metaphysical issues. Wasserman addresses these issues while still managing to include pertinent scientific discussion and enjoyable time-travel snippets from science fiction. The book is well organized and is suitable for good undergraduate metaphysics students, for philosophy graduate students, and for professional philosophers. It reads like a sophisticated and excellent textbook even though it includes many novel ideas.

The research Wasserman has done is impressive. It reminds the reader that time travel as a topic of metaphysics did not start with David Lewis (1976). Wasserman (p. 2 n 4) identifies Walter B. Pitkin's 1914 journal article as (probably) the first academic discussion of time travel. The article includes a description of what has come to be called the double-occupancy problem, a puzzle about spatial location and time machines that trace a continuous path through space. The same note also includes a lovely passage, which anticipates paradoxes about changing the past, from Enrique Gaspar's 1887 book:

We may unwrap time but we don't know how to nullify it. If today is a consequence of yesterday and we are living examples of the present, we cannot unless we destroy ourselves, wipe out a cause of which we are the actual effects.

These are just two of the many useful bits of Wasserman's research.

Chapter 1 usefully introduces examples of time travel and some examples one might think would involve time travel, but do not (e.g., changing time zones). There is good discussion of Lewis's definition of time travel as a discrepancy between personal and external time, including a brief passage (p. 13) from a previously unpublished letter from Lewis to Jonathan Bennett on whether freezing and thawing is time travel. I had often wonder what Lewis would have said; now I know what he did say!

Chapter 2 dives into temporal paradoxes deriving from discussions of the status of tense and the ontology of time (presentism vs. eternalism vs. growing block vs. . . . ). Here, Wasserman also includes the double-occupancy problem as a problem for eternalism -- though it is not clear that it is only a problem for eternalism. Then he turns to the question of the compatibility of presentism and time travel, the compatibility of time travel and a version of growing block that accepts that there are no future-tensed truths, and finally to a section on relativity and time travel. The section on relativity is solid and seems to me to pull the rug out from under some earlier discussions. For example, Lewis's definition of time travel is shown not to work. It also becomes clear that presentism and the growing block are consistent with both time-dilation-style forward time travel and traveling-in-a-curved-spacetime "backwards" time travel.

Chapters 3 and 4 cover the granddaddies of all the time-travel paradoxes: the freedom paradoxes that include the grandfather paradox, the possibility of changing the past, and the prospects of such changes given models of branching time, models that invoke parallel worlds, and hyper time models. Chapter 4 gets serious about Lewis's treatment of the grandfather paradox and Kadri Vihvelin's treatment of the autoinfanticide paradox (about which I will have more to say).

Chapter 4 also includes discussion of "mechanical" paradoxes that, as stated, do not require modal premises about what something can and cannot do, and no notion of freedom or free will. (See Earman's bilking argument on p. 139 and the Polchinski paradox on p. 141.) Wasserman introduces modality to these paradoxes, but I would have liked them to be addressed on their own terms. As I see it, these paradoxes are introduced to show that backwards time travel or backwards causation in a certain situation validly lead to a contradiction. On their own terms, for these arguments to be valid, the premises of the arguments themselves must be inconsistent. How can one make trouble for backwards time travel if the argument is thus bound to be unsound?

Chapter 5 takes on the paradoxes generated by causal loops or more generally backwards causation including bilking arguments, the boot-strapping paradox (based on a presumption that self-causation is impossible), and the ex nihilo paradox with causal loops and object loops (i.e., jinn) that seem to have no cause or explanation.

Chapter 6 deals with paradoxes that arise from considerations regarding identity, with a focus on the self-visitation paradox from both perdurantist and endurantist perspectives. I was surprised to learn that Wasserman had defended an endurantist-friendly property compatibilism -- similar to my own -- to resolve the self-visitation paradox. I was then delighted to find out that he cleverly extends this sort of compatibilism to the time-travel-free problem of change (i.e., the so-called, temporary-intrinsics argument).

The outstanding scientific issue regarding backwards time travel is whether it is physically possible. There is no question that forwards time travel is actual, or even whether it is ubiquitous. There is also not much question that backwards time travel is consistent with general relativity. Still, we await more scientific progress before we will know whether backwards time travel really is consistent with the actual laws of nature. In the meantime, there is still much to be said about Lewis's treatment of the grandfather paradox and Vihvelin's stated challenge to that treatment in terms of the autoinfanticide paradox.

I will start by being somewhat critical of Lewis's approach. For his part (pp. 108-114), Wasserman does a terrific job of laying out Lewis's position as a metatheoretic discussion of the context sensitivity of 'can' and 'can't'. My concern is that not enough attention is given to the 'can' and 'can't' sentences that turn out true on the semantics. The semantics works only by a contextual restriction of possible worlds based on relevant facts -- the modal base -- associated with a conversational context. In meager contexts, false 'can' sentences will turn out true too easily. For example, suppose two people are having a conversation about Roger. Maybe all the two know about Roger is his name and that he is moving into the neighborhood. So, the proposition that Roger doesn't play the piano is not in the modal base. So, according to Lewis's semantics applied to 'can', 'Roger can play the piano' is true in this context. That seems wrong. This would be an unwarranted assertion for either of the participants in the conversation to make. Notice it is also true relative to the same meager context that Roger can play the harpsichord, the sousaphone, and the nyatiti. Quite a musician that Roger! [1]

Interestingly, though this problem arises for 'can', it does not arise for other "possibility" modals. For example, notice that, with the meager context described above, there is a big difference regarding the assertability of 'Roger could play the piano' and of 'Roger can play the piano'. Similarly, there is also no serious issue with regard to 'Roger might play the piano'. 'Could' and 'might' add tentativeness to the assertion that seems called for. There also seems to be no problem for the semantics insofar as it applies to 'is possible'. 'It is possible that Roger plays the piano' rings true relative to the context. But 'Roger can play the piano'? That shouldn't turn out true, especially if Roger is physically or psychologically unsuited for piano playing.

This issue has been frustrating for me, but Wasserman's book has me leaning toward the idea that what is needed is a contextual semantics that includes a distinguishing conditional treatment of 'can' of the sort Wasserman suggests:

(P1**) Necessarily, if someone would fail to do something no matter what she tried, then she cannot do it (p. 122).

This is a suggestion made by Wasserman on behalf of Vihvelin. I find (P1**) as a promising place to start in terms of the conditional treatment.

Speaking of Vihvelin, her thesis is "that no time traveler can kill the baby that in fact is her younger self, given what we ordinarily mean by 'can'" (1996, pp. 316-317). Vihvelin cites Paul Horwich as a defender of a can-kill solution, what she calls the standard reply :

The standard reply . . . goes something like this: Of course the time traveler . . . will not kill the baby who is her younger self . . . But that doesn't mean she can't . (Vihvelin 1996, p. 315)

Vihvelin's doing so is appropriate given what Horwich says about Charles attending the Battle of Hastings: "From the fact that someone did not do something it does not follow that he was not free to do it" (1975, 435). In contrast, it strikes me as odd that Vihvelin (1996, p. 329, fn. 1) also attributes the standard reply to Lewis. I presume that she does so based on some comments by Lewis. He says, "By any ordinary standards of ability , Tim can kill Grandfather," (1976, p. 150, my emphasis) and especially "what, in an ordinary sense , I can do" (1976, p. 151, my emphasis). So, admittedly, Vihvelin fairly highlights an aspect of Lewis's view as holding that, in the ordinary sense of 'can', Tim can kill Gramps. And I can see how this is a useful presentation of Lewis's position for her argumentative purposes.

Nevertheless, I take Lewis's talk of ordinary standards or an ordinary sense to just be a way to identify the ordinary contexts that arise with uses of 'can' in day-to-day dealings, where the possibility of time travel is not even on the table. Simple stuff like:

Hey, can you reach the pencil that fell on the floor?

Sure I can; here it is.

More importantly, we have to keep in mind that the basic semantics only has consequences about the truth of 'can' sentences once a modal base is in place. To me, the fact that Baby Suzy grows up to be Suzy is exactly the kind of fact that we do not ordinarily hold fixed. Lewis's commitment to the semantics does not make him either a can-kill guy or a can't-kill guy.

What is the upshot of this? There is a bit of underappreciation of Lewis's approach in Wasserman's discussion of Vihvelin's views. The pinching case on p. 119 provides a way to make the point. Consider:

(a) If Suzy were to try to kill Baby Suzy, then she would fail.

(b) If Suzy were to try to pinch Baby Suzy, then she would fail.

According to Wasserman, Vihvelin thinks that even in ordinary contexts (a) and (b) come apart (p. 119, note 32) -- (a) is true and (b) is false. As I see it, a natural context for (a) includes the fact that Baby Suzy grows up normally to be Suzy. That is a supposition that is crucial to the description of the scenario and so is likely to be part of the modal base. No canonical story or suppositions are tied to (b), though Vihvelin stipulates that Suzy travels back in time in both cases. We are not, however, told a story of Baby Suzy living a pinch-free life all the way to adulthood. We are not told whether Suzy decided go back in time because Baby Suzy deserved a pinch for some past transgression. My point is that the stories affect the context. So, with parallel background stories, (a) and (b) need not come apart.

I am not sure whether Wasserman was speaking for himself or for Vihvelin when he says about (a) and (b), "Self-defeating acts are paradoxical in a way other past-altering acts are not" (p. 120). Either way, I disagree. Lewis gives a more general way to resolve the past-alteration paradoxes that is not obviously in any serious conflict with Vihvelin's many utterances that turn out true relative to the contexts in which she asserts them. Wasserman also says, "The only disagreement between Lewis and Vihvelin is over whether Suzy's killing Baby Suzy is compatible with the kinds of facts we normally take as relevant in determining what someone can do" (p. 117). That is an odd thing for him to say. Lewis sketches a semantic theory that provides a framework for the truth conditions of 'can' and 'can't' sentences. He is not in disagreement with Vihvelin. For Lewis, there is one specification of truth conditions for 'can' that gives rise to both 'can kill' and 'can't kill' sentences turning out true relative to different contexts. Indeed, it is tempting to think that Vihvelin takes the fact that Baby Suzy grows up to be Adult Suzy as part of the modal base of the contexts from which she asserts the compelling 'can't-kill' sentences.

That all said, Wasserman's book is a significant contribution. There are those of us who focus a good chunk of our research on the paradoxes of time travel for their intrinsic interest, and especially because they are fun to teach. That is contribution enough for me. But, ultimately, from this somewhat esoteric, fun puzzle solving, we also learn more about the rest of metaphysics. The traditional issues of metaphysics: identity-over-time, freedom and determinism, causation, time and space, counterfactuals, personhood, mereology, and so on, all take on a new look when framed by the questions of whether time travel is possible and what time travel is or would be like. Wasserman's book is a wonderful source that spotlights these connections between the paradoxes of time travel and more traditional metaphysical issues.

Cargile, J., 1996. "Some Comments on Fatalism" The Philosophical Quarterly 46, No. 182 January 1996, 1-11.

Gaspar, E., 1887/2012. The Time-Ship: A Chronological Journey . Wesleyan University Press.

Horwich, P., 1975. "On Some Alleged Paradoxes of Time Travel" The Journal of Philosophy 72, 432-444.

Lewis, D., 1976 "The Paradoxes of Time Travel" American Philosophical Quarterly 13, 145-152.

Pitkin, W., 1914. "Time and Pure Activity" Journal of Philosophy, Psychology and Scientific Methods 11, 521-526.

Vihvelin, K., 1996. "What a Time Traveler Cannot Do" Philosophical Studies 81, 315-330.

[1] This criticism was first presented to me by Natalja Deng in the question-and-answer period for a presentation at the 2014 Philosophy of Time Society Conference. Later on, I found a parallel challenge in work by James Cargile (1996, 10-11) about Lewis's iconic, 'The ape can't speak Finnish, but I can'.

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Classic Time Travel Paradoxes (And How To Avoid Them)

[Movie still from  Time Machine , Warner Bros. and Dreamworks]

Editor’s Note: We’re bringing back one of our most loved posts because hey, time travel is always a relevant topic of discussion. Originally published 11/30/12.

Author’s Note: I assume that some day, this article will serve as an invaluable guide and warning for our time traveling ancestors-to-be (who will of course be unable to read books and learn these lessons for themselves, either because [a] all the books will have been burned, or [b] kids will have stopped reading books entirely, because grumble grumble, god damn kids, when I was your age, video games, blah blah, detriment to society, buncha hooligans, kids these days, no respect, etc). In the meantime, just enjoy it for all of its delightfully entertaining/convoluted/paradoxical pleasures.

As anyone who’s anyone who’s read any time travel story ever could easily tell you, time travel is a tricky subject. Temporal paradoxes might seem simple and straightforward at the start (no they don’t), but they always devolve quite quickly (linear time-wise) into some sort of trippy, philosophically complicated, timey-wimey conundrum that makes even the most convoluted middle school relationship make sense by comparison. Come to think of it, maybe the reason that all those cool kids in middle school suffer from impossibly complicated and melodramatic romances to begin with is because they’re all too “cool” to read time travel stories in the first place, which would obviously teach them the benefits of temporally linear dating, if nothing else.

I’m looking at you, River Song.

For the most part, any paradox related to time travel can generally be resolved or avoided by the Novikov self-consistency principle, which essentially asserts that for any scenario in which a paradox might arise, the probability of that event actually occurring is zero — or, to quote from LOST, “whatever happened, happened,” meaning that no matter what anyone does, they can’t actually create a paradox, because the laws of quantum physics will self-correct to avoid such a situation. Still, I’m wary of such a loose explanation for things, and so below, I’ve compiled a list of a few of the more popular time travel paradoxes — and what to do to avoid them.

ONTOLOGICAL PARADOX : Also known as the “Bootstraps Paradox,” an ontological paradox arises when a person or object is sent through time and recovered by another person, whose actions then lead to the original person or object back to the time from when it came in the first place, thus creating an endless loop with no discernible point of origin. Thus, the original person or object is essentially “pulling itself up by its own bootstraps,” hence the nickname (thanks in no small part to the Robert Heinlein story “By His Bootstraps”).

Example : The Terminator films are a prime and popular example of the Ontological Paradox. In the future, a Terminator is sent back in time to kill the mother of resistance leader John Connor before he is born. While the original T-800 is ultimately destroyed, the leftover pieces are found by scientists who use the technological to…develop and create Skynet, and the Terminator-series robots. Skynet would have never been created if Skynet hadn’t taken over the world and then sent a Terminator back in time to get destroyed and ultimately lead to the creation of Skynet. Trippy, right?

There’s also the fact that Future John Connor sends his buddy Kyle Reese back in time to protect his mother from the T-800, only Kyle ends up totally bangin’ John’s mom (dude high five! I mean, not cool, man) and impregnates her with his buddy John Connor. So to top it all off, if John hadn’t sent his friend back in time, his friend would never have had sex with John’s mom, and John would never have been born (meaning that Kyle Reese is either the best or worst friend, ever).

How to Avoid : No one’s really sure if a real-life ontological paradox would lead to some massive hemorrhaging of spacetime, or if the closed loop is kind of automatically self-corrected since it all works itself out evenly in the end anyway. Still, better to avoid these kind of complicated situations, and the best way to do that would simply be to stop taking candy from strangers — “candy” in this case being mysterious or alien artifacts with questionable origins, possibly given to you by mysterious people who may or may not come from the future. See? Maybe all those warnings that your Mom gave you when you were a little kid still mean something today. Or maybe all along she was just trying to prevent you from sending your friends back in time to sleep with her. Or perhaps encourage it…

PREDESTINATION PARADOX : The predestination paradox is similar to the ontological paradox in that the Cause leads to an Effect which then leads back to the initial Cause. The basic tenant of the predestination paradox is similar to that of a self-fulfilling prophecy: the motivation for the time traveler to travel in time is ultimately realized to have been the time traveler’s fault, due to his or her decision to time travel in the first place, or else otherwise unavoidable. Stories involving predestination paradoxes often involve a heavy sense of irony — the time traveler might go back in time in order to change something, for example, but his or her actions inadvertently lead to the exact situation that inspired the time traveler to have gone back and changed things. Thus, nothing ultimately changes. Determinism is a bleak friend.

Example : In Twelve Monkeys, James Cole is sent back in time to prevent a mysterious disaster involving the “Army of the Twelve Monkeys.” His wild rantings in the past about the terrible future from which he came are overheard by Jeffrey Goines, a mental patient who is remembered in the future as the leader of Army of the Twelve Monkeys. Ultimately, Cole’s efforts to prevent his future from happening inspire the actions that lead to his future coming to be. And in a cruel twist of irony, James Cole’s childhood memory of a man in a airport being shot and falling into the arms of a beautiful blonde — the memory that haunts him for the rest of his life — turns out that the guy who was shot was actually him, in the future, dooming young James Cole to grow up and repeat the cycle all over again.

How to Avoid : This one’s tricky, because philosophically, it’s all about free will (or lack thereof). So in fact, by trying to teach you to how to avoid falling victim to the tenants of the predestination paradox, I’m probably going to inspire you to go back in time and create the French film La jetée, which in turn inspires Terry Gilliam to make Twelve Monkeys, which in turn inspires me to use it as an example in this article, et cetera et cetera. Basically we’re all screwed, unless we avoid time travel and time travelers all together. Even a many worlds theory/alternate timeline thing can’t prevent this, because your actions wouldn’t even create a divergent timeline — they would just result in your present situation. So, sorry dude, nothing you can do is going to change anything. Again, unless you don’t do anything at all, although that still doesn’t guarantee anything.

GRANDFATHER PARADOX : This one perfectly demonstrates the aforementioned Novikov self-consistency principle. The basic idea is that, no matter how hard you try, you can’t go back in time and kill your grandfather, because if you did, your mother or father would never have been born, which means that you would never have been born, which means you couldn’t have gone back in time and killed your grandfather, which means that you didn’t go back in time and kill your grandfather, because you can’t go back in time and kill your grandfather, because if you did, you wouldn’t be born, which you obviously have already been born because if you were never born then you couldn’t have gone back in time and tried (and failed) to kill your grandfather in the first place.

That’s just a simple and straightforward summary though. You know, in Layman’s terms.

Basically, the Grandfather paradox conveys the idea of a self-correcting universe and/or fixed points in time. Even if you were able to go back in time and, I don’t know, shoot your Grandpa in the head before he ever meets your Grandma (jeez, you must really hate that guy, huh?), your Grandfather would turn out to be an early sperm donor or something, who would still manage even posthumously to impregnate your Grandmother, because you would have to exist in order to have shot him in the head in the first place. So you might be able to fudge a few temporal details here and there, but no matter what you do, the end result stays the same.

Example : Let’s just say that when you’re LOST on a magical tropical island somewhere in the Pacific Ocean (ish?) and you end up skipping through time and decide to try to kill that evil guy while he’s still a kid and/or stop a nuclear bomb you’ve so affectionately nicknamed “The Jughead” from exploding and causing all kinds of electromagnetic problems and inconsistencies on your already-mystical island home, the best that’s going to happen is you get some kind of weird Hindu sideways limbo reality that works as a parallel narrative to the entire last season of your television show. Oh, and that little kid you shot still turns out to be pretty evil, and it’s all your fault.

How to Avoid : Uhh, don’t try to kill your grandfather in the past before the birth of your father? Take that as a metaphor all you’d like.

HITLER’S MURDER PARADOX : This is similar to the Grandfather Paradox, in that the time traveller goes back in time to change something significant that has already happened. Unlike the Grandfather Paradox (which we assume would self-correct despite our best efforts), the change that one wishes to affect in the Hitler’s Murder Paradox is one that is more technically feasible — as in not intrinsically paradoxical — but still ultimately problematic.

The name comes from the idea that one could theoretically go back in time and kill Adolf Hitler before the Holocaust happened, thus preventing the systematic annihilation of some six million Jews and other minorities. Which, ya know, all sounds good and well, except that it tends to lead to some kind of downward spiraling domino effect with plenty of other consequences that the well-intentioned time traveler probably didn’t consider, and which ultimately might lead to a worse situation than that which the time traveler had hoped to prevent.

Example : This kind of stuff is rampant in comic books, especially X-Men, but the best example of it was the early 90s Age of Apocalypse storyline, in which Professor Xavier’s schizophrenic mutant son, Legion, decides to make daddy proud by helping his dream of mutant-human co-existence come true. Legion concludes that the best way to do this is to go back in time and kill Magneto before he becomes, ya know, Magneto. The only problem is, Magneto and Xavier were like totally BFF back then, so Xavier ends up taking the bullet for Magneto and dies (so yes, Legion does technically end up killing his own father, but that’s not the point).

As a result of there being no Charles Xavier, the psycho evil Darwinist uber-mutant Apocalypse ends up taking over the world before Magneto’s team of X-Men (named in honor of his deceased friend) are able to stop him, which leads to all kinds of crazy situations like evil Hank McCoy aka Dark Beast, who works alongside the evil versions of Cyclops and Havok, or a Sabretooth who is actually a pretty likeable superhero and a member of the X-Men. Oh, also, Magneto and Rogue totally have the sex, and humans are being systematically slaughtered in concentration camps by Apocalypse and his cronies. So basically, in his attempt to kill a perceived “Hitler” in the form of Magneto, Legion caused a real and even more twisted Holocaust to happen. WHOOPS.

How to Avoid : In addition to the whole alternate-reality-that-is-ironically-worse-than-the-world-as-it-used-to-be problem, there’s also the moral compromise of killing an innocent child, even though you know that child is going to grow up to become pretty much the worst (greatest?) mass murderer in history. The best way to avoid it is simply and sadly to accept that you cannot change the past and shouldn’t even try. That is, unless you’re smart enough to have eliminated any possibility of negative domino effect resulting out of your actions.

For example, if you went back in time and eliminated M. Night Shyamalan shortly before the release of Signs, there would be nothing but positive results; the world would mourn the tragic and mysterious loss of a gifted young filmmaker taken before his time, we would all be so blinded by the shock of his death that we’d be able to ignore how bad the aliens looked in that movie (and the fact that seeing them at all was completely unnecessary), and the rest of us wouldn’t have been forced to endure such awful schlock as The Happening or Lady in the Water. See? That way everyone wins!

BUTTERFLY EFFECT : Similar to the cascading domino effect of the Hitler’s Murder Paradox, but on a different level. Whereas killing Hitler would obviously be a landmark event with quite a significant historical impact, something like, say, accidentally stepping on a bug in the past probably wouldn’t have as big of an effect, right?

Have you even been paying attention? Of course it will! That’s the whole point of a time travel paradox! Just like the way that a butterfly flapping its wings in Brazil can affect a weather system in Texas, one tiny change in the past can lead to all kinds of Rube Goldbergian complications that can subtly — or seriously — affect the present. The term “Butterfly Effect” is actually derived from “A Sound of Thunder,” a short story by Ray Bradbury, in which a character accidentally steps on a butterfly in prehistoric times and causes catastrophic changes in the future from which he came.

Example : In Orpheus With Clay Feet by Philip K. Dick, the main character, Jesse Slade, enlists in the services of a time travel tourism agency, who set him up with a trip that allows him to go back in time and act as a muse for some significant historical figure. Slade chooses to go back and inspire his favorite science fiction writer Jack Dowland (which was also Dick’s pen name). Unfortunately, in his efforts to inspire Dowland’s monumental science fiction work, Slade directly reveals to Dowland that he is a time traveler hoping to inspire his work. Dowland takes this as an insulting ruse, and as a result, never becomes the great science fiction writer that he is meant to be. He does, however, publish a single science short story, under the pen name Philip K. Dick: a story called Orpheus With Clay Feet, about a time traveler that goes back in time to inspire his favorite science fiction writer, a man named Jack Dowland.

How to Avoid : Watch your step

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1 Introduction

• Published: November 2017
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Chapter 1 explains the concept of time travel, clarifies the main question to be addressed, and previews the paradoxes to come. Section 1 explains the traditional view of time travel as involving a discrepancy between “personal” and “external” time. Section 2 contrasts this kind of time travel with other, purported examples of time travel. Section 3 distinguishes a number of different questions about time travel, including the question of whether or not time travel is compatible with the laws of metaphysics—particularly those having to do with the nature of time, freedom, causation, and identity. Finally, section 4 provides an outline of the rest of the book by introducing some of the key paradoxes to be addressed. Other topics in this chapter include time, causation, and metaphysical grounding.

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What Is the Fermi Paradox?

The fermi paradox explores the haunting contradiction: if alien civilizations exist, why haven’t we found them nasa advisor paul sutter unpacks this cosmic mystery..

The Fermi paradox boils down to a simple question: where is everybody? In other words, if we’re not alone in the universe, then why haven’t we seen any evidence for aliens yet? To date, there is no consensus resolution to the Fermi Paradox…and we still have no evidence for aliens.

Who Came Up With the Fermi Paradox?

Lore has it that in the summer of 1950, famed Italian-American physicist Enrico Fermi was out to lunch one day with some friends and colleagues. The conversation turned to talk of UFO sightings, space travel, and alien civilization. In response to the conversation, Fermi simply blurted out “But where is everybody?”

After further calculations to back up his original interjection, this statement came to be known the Fermi paradox in his honor. If the universe is full of advanced alien civilizations, then we should have ample evidence for their existence by now. Instead, we have found absolutely nothing, and for all intents and purposes the cosmos is empty of life.

The argument that the universe should be full of life is a good one. There’s nothing particularly special about us. The Milky Way is just another spiral galaxy. The Sun is just another medium-sized star. The Earth is just another small, rocky world. All the ingredients needed to make life: water, hydrogen, carbon, and so on, are all fantastically abundant in the universe.

Plus, life emerged on Earth roughly four billion years ago, but the universe itself is over three times that age. The Milky Way galaxy is roughly 13 billion years old and contains hundreds of billions of stars. The Earth was certainly not the first rocky planet to form in all that time, and life in the galaxy should be ancient, giving any sufficiently advanced civilization more than enough time to spread throughout the galaxy…making them easily detectable.

So…where is everybody?

Read More: Fact or Fiction: What Is The Truth Behind Alien Conspiracy Theories?

What Are Some Solutions to the Fermi Paradox?

In the decades since Fermi’s question, many scientists and creative thinkers have come up with a variety of possible solutions to the paradox.

1. Intelligence Is Rare

One solution is to confront the basic assumptions of the paradox head-on. Maybe there is something special about life, especially intelligent life. Maybe the emergence of intelligence is a fundamentally rare occurrence. Yes, there are many stars and planets out there, but if intelligence is rare enough, then we shouldn’t expect to encounter any aliens. In this scenario, we are well and truly alone in the universe.

2. Great Filter Approach

Another solution is that life, especially intelligent life, may be relatively common , but the ability of advanced civilizations to make themselves undetectable is likely rare.

For example, there could be “great filters” that prevent the rise of advanced civilizations above a certain level. We only need to point to our own propensity for self-destruction in the form of nuclear weapons or climate change for ready examples of how a great filter might work. And if we don’t do it ourselves, maybe nature can do it for us: there have been many mass extinctions in the history of the Earth, and it wouldn’t take much to destroy an aspiring spacefaring civilization.

3. Zoo and Dark Forest Hypotheses

Another set of approaches is to argue that aliens are common, but for some reason we have a hard time detecting them. For example, in the zoo hypothesis , advanced aliens are out there and know we exist, but they have chosen to isolate the Earth to allow humanity to progress along its natural course without outside interference. Or in the “dark forest” hypothesis, aliens prefer to stay quiet and hidden, fearing that an aggressive, expansionist species may wipe them out.

4. Distance of Extraterrestrial Life

Or it might be that our math is off. Life might be common, with hundreds or even thousands of intelligent species spread throughout the galaxy at any one time. But the combination of extreme distances and long travel times makes these disparate civilizations effectively isolated from each other, despite whatever feats of technological sophistication they may be able to achieve.

Read More: The Drake Equation: What Are the Odds That Aliens Exist?

Are We Alone in the Universe?

Ultimately we do not know if we are alone in the universe. To date, we have found no evidence for life outside the Earth. We have detected no radio signals from intelligent species, and we have not found any artifacts, like mega-engineering projects, in our surveys.

Searches in the universe continue. While private groups largely focus on detecting signals from intelligence, most astronomers instead focus on broader searches for any signs of life, to the point that finding an analog of Earth is a man priority for NASA’s next generation of space telescopes.

Read More: New SETI Tool Expands the Search for Intelligent Life in the Universe

Article Sources

Our writers at Discovermagazine.com use peer-reviewed studies and high-quality sources for our articles, and our editors review for scientific accuracy and editorial standards. Review the sources used below for this article:

Britannica. The Fermi Paradox: Where Are All the Aliens?

NASA. The Milky Way Galaxy

Astronomy. The Great Filter: a possible solution to the Fermi Paradox

NASA. Archaeology, Anthropology, and Interstellar Communication

Paul M. Sutter is a theoretical cosmologist, NASA advisor, host of the "Ask a Spaceman" podcast, and a U.S. Cultural Ambassador. He is the author of "Your Place in the Universe" and "How to Die in Space."

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• space exploration

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What is the grandfather paradox?

Can you go back in time and kill an ancestor without creating a logical paradox? Surprisingly, the answer may be yes.

Grandfather paradox explained

• Is it possible?
• Parallel worlds

Grandfather paradox solved?

Grandfather paradox and the butterfly effect.

• Additional resoources

Bibliography

The grandfather paradox is a self-contradictory situation that arises in some time travel scenarios that is illustrated by the impossible scenario in which a person travels back in time only to kill their grandfather (who could no longer go on to produce one's parent, and hence where does that leave you and your ancestor-killing event?). The paradox is sometimes taken as an argument against the logical possibility of traveling backward in time, according to the Stanford Encyclopedia of Philosophy . Within the framework of modern physics, however, there are ways to avoid the paradox without dispensing with time travel altogether.

Related: 5 sci-fi concepts that are possible (in theory)

Let's suppose you have a time machine that allows you to travel back into the past. While you're there, you accidentally kill one of your grandparents — or any other direct ancestor — before they have any offspring. That would alter a whole chain of future events, including your own birth, which would no longer happen. But if you weren't born in the future, then you couldn't kill your ancestor in the past — hence the paradox. It's a scenario that became popular in the science-fiction magazines of the 1920s and 1930s, according to the Historical Dictionary of Science Fiction , and the name "grandfather paradox" was firmly established by 1950.

Actually, you don't even need to kill anyone; there are many other ways you could change history that would result in your future non-existence. Perhaps the best known example is the movie "Back to the Future," in which the time-traveling protagonist inadvertently drives a wedge between his parents before they were married — and then has to work frantically to bring them together again.

Is the grandfather paradox possible?

Moving from science fiction to science fact, one person who was eminently qualified to talk about the realities of time travel was the late Stephen Hawking, arguably the most brilliant physicist of recent times. In 1999, he gave a lecture on "space and time warps," which showed how Einstein 's theory of general relativity might make time travel possible, by bending space-time back on itself. 

One theoretical possibility that would allow time travel (and thus the ability to somehow kill off a critical ancestor) is a special kind of wormhole . Among the most dramatic consequences of general relativity, wormholes are often described as shortcuts between one point in space and another. But, as Hawking explained in his lecture, a wormhole could possibly loop back to an earlier point in time — a situation technically known as a "closed time-like curve" (CTC).

But if physics allows backward time travel, wouldn't the grandfather paradox still cause issues? Hawking suggested two possible ways to get around the paradox in this scenario. First, there's what he referred to as the "consistent histories" model, in which the whole of time — past, present and future — is rigidly predetermined; in that way, you can only travel back to an earlier point in time if you had already been there in your own history. In this "block universe" model, as it's sometimes called, one could travel to the past but doing so would not alter it, according to the Australian Broadcasting Corporation . Taking this view, the grandfather paradox could never arise. With Hawking's second option, on the other hand, the situation is more subtle.

Grandfather paradox and parallel worlds

This second approach to traveling back in time invokes quantum physics , where an event may have several possible outcomes with different likelihoods of occurring.

As described by the Stanford Encyclopedia of Philosophy , the "many worlds" interpretation of quantum theory sees all these various outcomes as occurring in different, "parallel" timelines. In this view, the grandfather paradox could be resolved if the time traveler starts out in a timeline where their grandfather lived long enough to have children, and then — after going back and killing their forebear — continue along a parallel time track in which they will never be born. ( Stanford Encyclopedia has a more detailed look at why you can’t jump back and forth between parallel timelines at will.) As Hawking pointed out in his 1999 lecture, this seems to be the implicit assumption behind sci-fi treatments such as "Back to the Future."

At the time that movie was made in 1985, the "parallel world" explanation of the grandfather paradox was merely a philosophical conjecture. In 1991, however, it was put on firmer ground by the physicist David Deutsch, as New Scientist reported at the time. Deutsch showed that, while parallel timelines are normally incapable of interacting with each other, the situation changes in the vicinity of a closed time-like curve (CTC), when a wormhole curves back on itself. Here, just as the sci-fi writers imagined, the different timelines are able to cross over — so that when a CTC loops back into the past, it's the past of a different timeline. If that's proven, then you really could kill an infant grandparent without paradoxically eliminating yourself in the process. In that case, your grandfather would never have existed only in one parallel world. And you, the grandfather-killer, would only have existed in the other.

As surprising as it sounds, there's actually some experimental support for Deutsch's solution to the grandfather paradox. In 2014, a team at the University of Queensland examined a simpler time-travel scenario that entailed a similar logical paradox. The researchers described the work in their paper published that year in the journal Nature Communications . The idea was that a subatomic particle had to go back in time to flip the switch that resulted in its creation; if the switch wasn't flipped, the particle would never exist in the first place.

A key feature of Deutsch's theory is that the various probabilities have to be self-consistent. For instance, in the Queensland research example, if there's a 50:50 chance the particle travels back in time, then there must also be a 50:50 chance that the switch gets flipped to create that particle in the first place. In the absence of a time machine, the researchers set up an experiment involving a pair of photons, which they claimed was logically equivalent to a single photon traveling back in time to "create" itself. The experiment was a success, with the results validating Deutsch's self-consistency theory.

Killing your grandfather when he was a child is a sure-fire way to ensure you're never born. But there are also subtler possibilities for messing up the timeline. In a sufficiently complex system, even the tiniest change can have serious long-term consequences — as in the butterfly effect , by which the flapping of a butterfly's wings can eventually trigger a tornado thousands of miles away. Sci-fi writer Ray Bradbury produced a time travel counterpart to this in his 1952 story "A Sound of Thunder," which can be read online at the Internet Archive . Bradbury's protagonist travels back to the time of the dinosaurs , where he accidentally steps on a butterfly — then returns to the present to find society changed beyond recognition. It's easy to imagine that, if the societal changes were sweeping enough, the time traveler might have prevented his own birth as surely as if he'd slain a grandparent.

But would that really be the case, using the quantum approach to the grandfather paradox? Recent work at the Los Alamos National Laboratory indicates that the course of history is more resilient than the butterfly effect might suggest. The researchers used a quantum computer to simulate time travel into the past, where a piece of information was deliberately damaged — the computational equivalent of stepping on a Jurassic-era butterfly. But unlike Bradbury's story, the knock-on effect in the "present" of the computer simulation turned out to be relatively small and insignificant. That, of course, is great news for would-be time travelers. As long as you refrain from blatantly silly acts like killing a direct ancestor, it may be possible to go back in time without any paradoxical consequences at all.

Additional resources

• Watch a YouTube video about the science behind the grandfather paradox
• Take Ten Short Lessons in time travel from Brian Clegg
• Explore dozens of fictional time travel paradoxes at the Science Fiction Encyclopedia and TV Tropes

Historical Dictionary of Science Fiction. https://sfdictionary.com/view/2178/grandfather-paradox

"Many-Worlds Interpretation of Quantum Mechanics," Stanford Encyclopedia of Philosophy, 2021. https://plato.stanford.edu/entries/qm-manyworlds/  

"Time Travel without the Paradoxes," New Scientist, 1992. https://www.newscientist.com/article/mg13318143-000-science-time-travel-without-the-paradoxes/

"The block universe theory, where time travel is possible but time passing is an illusion," Australian Broadcasting Corporation, 2018. https://www.abc.net.au/news/science/2018-09-02/block-universe-theory-time-past-present-future-travel/10178386  

"Experimental simulation of closed timelike curves," Nature Communications, 2014. https://www.nature.com/articles/ncomms5145  

"A Sound of Thunder," Ray Bradbury, Internet Archive. https://archive.org/details/Planet_Stories_v06n04_1954-01/page/n5/mode/2up

"Simulating quantum 'time travel' disproves butterfly effect in quantum realm," Los Alamos National Laboratory, 2020. https://www.lanl.gov/discover/news-release-archive/2020/July/0728-quantum-time-travel.php

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Andrew May holds a Ph.D. in astrophysics from Manchester University, U.K. For 30 years, he worked in the academic, government and private sectors, before becoming a science writer where he has written for Fortean Times, How It Works, All About Space, BBC Science Focus, among others. He has also written a selection of books including Cosmic Impact and Astrobiology: The Search for Life Elsewhere in the Universe, published by Icon Books.

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Physical Review D

Covering particles, fields, gravitation, and cosmology.

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Time travel paradoxes and multiple histories

Jacob hauser and barak shoshany, phys. rev. d 102 , 064062 – published 24 september 2020.

• Citing Articles (2)
• INTRODUCTION
• KRASNIKOV’S PARADOX MODEL
• GENERALIZING THE MODEL
• THE CASE OF UNLIMITED HISTORIES
• THE CASE OF FINITE CYCLIC HISTORIES
• ANALYSIS OF OUR MODEL
• SUMMARY AND FUTURE PLANS
• ACKNOWLEDGMENTS

If time travel is possible, it seems to inevitably lead to paradoxes. These include consistency paradoxes, such as the famous grandfather paradox, and bootstrap paradoxes, where something is created out of nothing. One proposed class of resolutions to these paradoxes allows for multiple histories (or timelines) such that any changes to the past occur in a new history, independent of the one where the time traveler originated. We introduce a simple mathematical model for a spacetime with a time machine and suggest two possible multiple-histories models, making use of branching spacetimes and covering spaces, respectively. We use these models to construct novel and concrete examples of multiple-histories resolutions to time travel paradoxes, and we explore questions such as whether one can ever come back to a previously visited history and whether a finite or infinite number of histories is required. Interestingly, we find that the histories may be finite and cyclic under certain assumptions, in a way which extends the Novikov self-consistency conjecture to multiple histories and exhibits hybrid behavior combining the two. Investigating these cyclic histories, we rigorously determine how many histories are needed to fully resolve time travel paradoxes for particular laws of physics. Finally, we discuss how observers may experimentally distinguish between multiple histories and the Hawking and Novikov conjectures.

• Received 10 January 2020
• Accepted 21 August 2020

DOI: https://doi.org/10.1103/PhysRevD.102.064062

© 2020 American Physical Society

Physics Subject Headings (PhySH)

• Research Areas

Authors & Affiliations

• 1 Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada
• 2 Pomona College, 333 North College Way, Claremont, California 91711, USA
• 3 Department of Physics, Brock University, 1812 Sir Isaac Brock Way, St. Catharines, Ontario L2S 3A1, Canada
• * [email protected]
• † [email protected];

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Vol. 102, Iss. 6 — 15 September 2020

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In the DP space, the line ( 1 , x ) is associated with ( − 1 , x ) for − 1 < x < 1 in Minkowski space. This is a simplified model for a wormhole time machine [ 2 ]. After traversing the wormhole, the particle emerges at an earlier value of t and travels in the same direction in x .

In the TDP space, ( 1 , x ) is instead associated with ( − 1 , − x ) for − 1 < x < 1 . After emerging from the wormhole, the particle will travel in the opposite direction in x .

The causality-violating region J 0 ( M ) for the TDP space M is contained between the two associated lines in x . The gray spacelike line indicates a choice of a reasonable surface on which to define initial conditions. We also see particles of two different colors, blue and green, emerging from the right and left; the meaning of these colors is explained in Sec.  2b .

The four possible distinct vertices for particle collisions in Krasnikov’s model. Time is the vertical axis, so the particles always come from the bottom. Note how each blue particle changes into a green particle, and vice versa, in every collision.

An illustration of the consistency and bootstrap paradoxes in Krasnikov’s model. The blue and green lines represent the two possible particle colors, as above. The gray lines indicate a particle which cannot be assigned a consistent color.

(a) Given the identification between colors and elements of Z C , this single general vertex captures all four vertices of Fig.  4 for C = 2 , as well as those for any other values of C . For illustration, the four colors in the figure—blue, green, orange, and magenta—represent any of the C possible colors for the case C ≥ 4 . (b) This vertex is the result of reversing time and parity and conjugating color with respect to the vertex in (a). Since each particle still leaves with a color one greater than it starts with, the result is a valid vertex. In fact, performing C T or P transformations independently also yields a valid vertex. In this example, we took blue = 0 , orange = 1 , green = 2 , magenta = 3 , c = 0 , c ′ = 2 , and C = 4 in both (a) and (b).

In the branching model, when the blue particle enters the time machine at h = 1 , it comes out twisted (since we are in a TDP space) at h = 2 . The new history has an identical copy of the initial blue particle, but this time it encounters itself (or more precisely, its copy from h = 1 ) and the two particles change their colors. A green particle then enters the time machine and continues to h = 3 , and so on. Thus, we have avoided both consistency and bootstrap paradoxes.

Unlike the branching model, the covering space model has no unique first history. Therefore, we depict two consecutive histories k and k + 1 . Without loss of generality, a green particle emerges from the time machine in history k , where it collides with the incoming blue particle; here we are using the color convention of Fig.  6 . Both particles increase their colors as in Fig.  6 : blue = 0 to orange = 1 and green = 2 to magenta = 3 . In history k + 1 , the same process occurs with a magenta particle emerging from the time machine instead of a green particle, and the magenta particle increases its color to blue = 4 (mod 4). Since there is a countably infinite number of time machines, the particle traversing the time machines never completes a CCC, nor does any copy of the incoming blue particle. Thus, we have again avoided both consistency and bootstrap paradoxes.

Since m is a point along the associated wormhole line, it appears twice in our representation of the TDP space—once at t = − 1 and once at t = + 1 . Therefore, our ball U around m is actually U = U + ∪ U − , the union of balls around each wormhole mouth. It is always possible to select such a ball which does not intersect a singularity: if m is a distance ϵ > 0 away from a singularity, then the ball can be chosen to have radius ϵ / 2 .

In our extension of the TDP space, wormhole points are now associated between adjacent histories. As a result, the ball around the point m k + 1 (the point overlapping histories k and k + 1 , which projects down to m under the map p ) is equal to U k + ∪ U k + 1 − . The preimage p − 1 ( U ) = ⋃ k ( U k + ∪ U k + 1 − ) is composed of a countably infinite number of such balls, each of which is homeomorphic to U + ∪ U − from Fig.  9 .

When C = 2 , the consistency paradox can be solved with two cyclic histories. The blue particle entering the time machine in h = 1 comes out of the time machine in h = 2 , and the green particle entering the time machine in h = 2 comes out of the time machine back in h = 1 . Since we interpret the vertices as elastic collisions, we now have a bootstrap paradox: the particle traveling along the CCC only exists within the CCC itself. We will discuss how to resolve this in Sec.  5b . Unlike in the scenario of Fig.  7 , here there is no first history where nothing has come out of the time machine yet (in fact, in Fig.  7 the past exit of the time machine does not even exist for h = 1 ).

A collision of p particles from the left and q particles from the right.

A single history’s causality-violating region can be partitioned into three zones, each of which contains a group collision of particles.

Here, a reflected version of the h = 2 causality-violating region is stacked on top of the h = 1 causality-violating region. These two regions lie in different spaces, as indicated by the separate coordinate axes. However, this representation makes it easy to see how particles evolve over multiple histories, and what the consistency constraints are: that particles on the last wormhole surface match those on the first one.

In this illustration, with C = 2 and H = 2 , one particle is solid and the other is dashed. The illustration demonstrates an interpretation in which the particles do not collide; instead, they pass through each other. This allows us to avoid a bootstrap paradox. However, the same vertices in Fig.  4 still apply.

One of the two consistent solutions obtained by sending particles toward the causality-violating region from both sides.

The second of the two consistent solutions obtained by sending particles toward the causality-violating region from both sides. Note that the initial conditions and final outcomes are the same as in Fig.  16 —two blue particles coming in and two green particles coming out—but the evolution inside the causality-violating region is different. Thus, evolution in this region cannot be predicted.

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What is the grandfather paradox?

Perhaps no implication of time travel is as troubling as the grandfather paradox.

The grandfather paradox explained

Can quantum physics save grandfather.

• Experimental demonstration?

Additional resources

The grandfather paradox is an example of a problem arising from the effect of time travel on causality, the idea that a cause must precede its effect. The paradox suggests that a cause is eliminated by its own effect, thus preventing its own cause and essentially becoming reverse causation. 

The classic analogy for this, and the one that gives the paradox its name, is a time traveler journeying back in time and killing their own biological grandfather before they can sire children. This means the time traveler could never have come to exist and, as a consequence, can't travel back in time and thus can't kill their own grandfather. That means they then are born and can go back in time, hence the paradox. 

The grandfather paradox has been a trope of science fiction, appearing in Ray Bradbury's short story " A Sound of Thunder, " the classic movie "Back to the Future" and many other works. But the grandfather paradox isn't limited to the realm of fiction. Philosophers and physicists began seriously thinking about the grandfather paradox when Albert Einstein 's theories of special and general relativity suggested that time travel may be a theoretical possibility.

Related: Was Einstein wrong? The case against space-time theory

Einstein's theory of special relativity proposes that space and time are actually one unified entity called space-time and also introduced a universal speed limit for particles of mass, setting this at the speed of light (c).

So no particle with mass could accelerate to the speed of light, as this would take an infinite amount of energy. But scientists following Einstein's work, including Columbia University physicist Gerald Feinberg, suggested the existence of hypothetical particles that could be caught speeding. Traveling faster than light, these massless particles — which Feinberg dubbed " tachyons " in a 1967 paper — would travel backward through time, thus introducing the concept of time travel to physics that went way beyond idle speculation.

Einstein would take this idea further with general relativity , the idea that space-time itself can be shaped by mass and energy and that gravity is a result of this influence. The idea that space and time were no longer static stages on which the events of the universe simply play out earned general relativity the alternative name "the geometric theory of gravity."

From general relativity, mathematician Kurt Gödel formulated the idea of closed timelike curves (CTCs) , paths through space-time that return to their starting point without violating special relativity. CTCs come in two primary types, unimaginatively titled Type 1 and Type 2. 

Type 1 allows a time traveler to journey along a CTC through space and time and into the past and, when there, interfere with their past self. This is therefore a model of CTC that allows the grandfather paradox to happen, at least in theory.

In the Type 2 model, CTCs follow a principle of self-consistency also known as the Novikov self-consistency principle , or Niven's law of the conservation of history, that forbids time-travel paradoxes from being created.

This places certain events in order along the same CTC. These events would be effects and their causes, ensuring that causality never ran "backward." This self-consistency programmed into time travel would mean our time traveler couldn't kill their grandfather no matter how hard they tried. Some aspect of the universe would prevent it, the rifle would jam, the car would be diverted or some other intervention would save grandfather. 

The message from this is clear: The grandfather paradox doesn't prevent time travel; it just prevents traveling back in time and doing something to violate causality. 

But is there any way time travelers hopping on a Type 1 CTC into the past can be prevented from triggering the grandfather paradox? One interpretation of quantum mechanics, the physics of the subatomic, suggests yes.

Quantum physics could prevent the grandfather paradox via physicist Hugh Everett's many-worlds interpretation of quantum mechanics, according to the Stanford Encyclopedia of Philosophy .

The fact that a quantum system is described with wave mechanics means that a system can be depicted in overlapping states or a superposition of states, according to George Mason University . This means that a system described quantum mechanically can simultaneously have seemingly contradictory values.

So an electron could be in a superposition with both "up" and "down" spin states simultaneously. This persists until the electron is measured or interacts with another system and its spin resolves as either up or down. This concept is described as a collapse of the superposition in the most favored interpretations of quantum physics. 

Why this collapse occurs has been a long-standing mystery, but Everett avoided this superposition collapse altogether. Instead, he suggested that the superposition grows exponentially to envelop the entire universe and then create an individual "world" for each potential value of the quantum system. So, in effect, according to Everett, an experimenter measuring the spin of an electron is swallowed by the experiment and is actually discovering if they are in a world in which the spin is up or one in which it is down.

In a 1991 paper in the journal Physical Review D , quantum computing pioneer and physicist David Deutsch imagined how the many-worlds concept would apply to time travel, envisioning a particle traveling along a CTC loop through time in a superposition of states. He posited that to avoid paradoxes during the journey and when the particle follows the CTC back to its starting point, a new world would be created for each possible state.

Imagine this is the case of a human time traveler journeying back in time to kill their grandfather. When the time traveler arrives back in 1963 from 2022, they leave world A and create a distinct world, World B, the world in which they arrive. World B would be different from World A, because in the established timeline of World A, a time machine carrying our time traveler never appeared in 1963. 

That means that if the time traveler were to kill their grandfather during this excursion into the past, their existence wouldn't be threatened because it would not be their World A grandfather who died. Instead, it would be a World B copy of him — split away as soon as the time machine materialized in 1963 — who would be killed. 

One of Everett's provisos for the many-worlds interpretation was that worlds can't interact, so conceivably, a time traveler creating World B and finding themselves in its past couldn't return to World A and their present. 

This also could explain why we've never seen a time traveler from the future announce their arrival in our time. We could be in a primary world, World A, from which time travelers depart, never to return.

Can an experiment demonstrate the grandfather paradox?

As far as we know — possibly because all time travelers are caught in other worlds — time travel isn't experimentally possible. 

But Seth Lloyd, a professor of mechanical engineering at the Massachusetts Institute of Technology and a self-described 'quantum mechanic," has been experimenting with the "next best thing" to time travel in the lab for over a decade.

In 2010, Lloyd and his team developed a quantum simulation that replicated an "in principle" time machine that combined CTCs with quantum teleportation, a technique for transferring quantum information from a sender to a receiver. The transfers is based on quantum entanglement and is analogous to travel through a CTC. 

To this idea, they added a post-selection mechanism, a way of giving a quantum computer the power to choose the outcomes of certain measurements, thus making the quantum system deterministic rather than probabilistic as quantum physics usually is.

Using the simulation, Lloyd then sent photons a few billionths of a second backward in time with a mission to "terminate" their previous selves. 

The team found something remarkable: The closer a photon got to fulfilling this "Terminator"-like mission — and thus achieving reverse causality and something logically inconsistent — the more frequently the experiment failed. The results suggest that actual time travel would work in the same way: Any journey that would result in the grandfather paradox being triggered would be doomed to failure before it could begin. So Granddad can breathe a sigh of relief … for now.

Explore the grandfather paradox and time travel in more detail with these articles published on Astronomy Trek and Scientific American . Read about the Futurama episode "Roswell That Ends Well," in which Phillip J. Fry takes an NSFR (not safe for robots) trip back to Roswell in 1947 to visit his grandfather and grandmother — possibly the most disturbing trip back through time ever told in fiction. 

Bibliography

Time Travel and Modern Physics, Stanford Encyclopedia of Philosophy, [Accessed 12/11/22], [ https://plato.stanford.edu/entries/time-travel-phys/ ]

S. Lloyd, et al, 'The quantum mechanics of time travel through post-selected teleportation,' [2010], [ https://arxiv.org/abs/1007.2615 ]

Time Travel, Stanford Encyclopedia of Philosophy, [Accessed 12/11/22], [ https://plato.stanford.edu/entries/time-travel/#GraPar ]

The Grandfather Paradox, A Time Travel Website, [Accessed 12/11/22], [ http://timetravelphilosophy.net/topics/grandfather/ ] D, Deutsch, Quantum mechanics near closed timelike lines, [1991], Physical Review D, [ https://journals.aps.org/prd/abstract/10.1103/PhysRevD.44.3197 ] 

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Robert Lea is a science journalist in the U.K. whose articles have been published in Physics World, New Scientist, Astronomy Magazine, All About Space, Newsweek and ZME Science. He also writes about science communication for Elsevier and the European Journal of Physics. Rob holds a bachelor of science degree in physics and astronomy from the U.K.’s Open University. Follow him on Twitter @sciencef1rst.

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