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 machine from H. G. Wells’ “The Time Machine”. Credit: Shutterstock.

 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.

But where is everybody? A painting of the Italian physicist Enrico Fermi – Emilio Segrè Visual Archives SPL

 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.

While travelling from one point in time to another are passengers passing through all the moments in between? Good question! Photo: Shutterstock

 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.

We still have to deal with the issue of momentum in our time travels / Illustrative picture, Shutterstock

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!

all time travel paradoxes

all time travel paradoxes


How Time Travel Works

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Time Travel Paradoxes

all time travel paradoxes

As we mentioned before, the concept of traveling into the past becomes a bit murky the second causality rears its head. Cause comes before effect, at least in this universe, which manages to muck up even the best-laid time traveling plans.

For starters, if you traveled back in time 200 years, you'd emerge in a time before you were born. Think about that for a second. In the flow of time, the effect (you) would exist before the cause (your birth).

To better understand what we're dealing with here, consider the famous grandfather paradox . You're a time-traveling assassin, and your target just happens to be your own grandfather. So you pop through the nearest wormhole and walk up to a spry 18-year-old version of your father's father. You raise your laser blaster , but just what happens when you pull the trigger?

Think about it. You haven't been born yet. Neither has your father. If you kill your own grandfather in the past, he'll never have a son. That son will never have you, and you'll never happen to take that job as a time-traveling assassin. You wouldn't exist to pull the trigger, thus negating the entire string of events. We call this an inconsistent causal loop .

On the other hand, we have to consider the idea of a consistent causal loop . While equally thought-provoking, this theoretical model of time travel is paradox free. According to physicist Paul Davies, such a loop might play out like this: A math professor travels into the future and steals a groundbreaking math theorem. The professor then gives the theorem to a promising student. Then, that promising student grows up to be the very person from whom the professor stole the theorem to begin with.

Then there's the post-selected model of time travel, which involves distorted probability close to any paradoxical situation [source: Sanders]. What does this mean? Well, put yourself in the shoes of the time-traveling assassin again. This time travel model would make your grandfather virtually death proof. You can pull the trigger, but the laser will malfunction. Perhaps a bird will poop at just the right moment, but some quantum fluctuation will occur to prevent a paradoxical situation from taking place.

But then there's another possibility: The quantum theory that the future or past you travel into might just be a parallel universe . Think of it as a separate sandbox: You can build or destroy all the castles you want in it, but it doesn't affect your home sandbox in the slightest. So if the past you travel into exists in a separate timeline, killing your grandfather in cold blood is no big whoop. Of course, this might mean that every time jaunt would land you in a new parallel universe and you might never return to your original sandbox.

Confused yet? Welcome to the world of time travel.

Explore the links below for even more mind-blowing cosmology.

Related Articles

  • How Time Works
  • How Special Relativity Works
  • What is relativity?
  • Is Time Travel Possible?
  • How Black Holes Work
  • How would time travel affect life as we know it?

More Great Links

  • NOVA Online: Time Travel
  • Into the Universe with Stephen Hawking
  • Cleland, Andrew. Personal interview. April 2010.
  • Davies, Paul. "How to Build a Time Machine." Penguin. March 25, 2003.
  • Davies, Paul. Personal interview. April 2010.
  • Franknoi, Andrew. "Light as a Cosmic Time Machine." PBS: Seeing in the Dark. March 2008. (March 1, 2011)
  • Hawking, Stephen. "How to build a time machine." Mail Online. May 3, 2010. (March 1, 2011)
  • "Into the Universe with Stephen Hawking." Discovery Channel.
  • Kaku, Michio. "Parallel Worlds: A Journey Through Creation, Higher Dimensions, and the Future of the Cosmos." Anchor. Feb. 14, 2006.
  • "Kerr Black Holes and time travel." NASA. Dec. 8, 2008. (March 1, 2011)
  • Sanders, Laura. "Physicists Tame Time Travel by Forbidding You to Kill Your Grandfather." WIRED. July 20, 2010. (Mach 1, 2011)

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Paradoxes of Time Travel

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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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A brief history of time travel

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Of all time travel's paradoxes, here's the strangest of them all: hop on a TARDIS back to 1894 and the concept didn't even exist. "Time travel is a new idea," explains New York-based author James Gleick, 62. "It's a very modern myth." Gleick's entertaining Time Travel: A History , out in hardback in February, quantum leaps from HG Wells's The Time Machine - the original - via Proust and alt-history right up to your Twitter timeline. Until we get the DeLorean working for real, fellow travellers, consider it the next best thing.

The Mahabharata

Time travel appears in Hindu text The Mahabharata, and in stories such as Washington Irving's Rip Van Winkle (1819) - but it usually only involved a one-way trip. "People fell asleep, and woke 
up in the future," says Gleick.

HG Wells's The Time Machine

"The idea of time travel with volition, in either direction, didn't arrive until Wells," says Gleick. It explains that time is a dimension - something not widely accepted until Einstein's theories in 1905.

Henri Bergson's Time And Free Will

Bergson's thesis is published soon after Wells's novel. "Bergson is a friend of Marcel Proust," says Gleick. Soon Proust et al are jumping on the idea of time travel to explore free will - and influencing new sci-fi in return.

Time Capsules

The idea of preserving a time stamp only arose in the 1930s in Scientific American. "It's the most pedestrian form of time travel: sending something into the future at a rate of one minute per minute."

Robert A Heinlein's By His Bootstraps

Heinlein's short story, published in Astounding Science Fiction, introduces the idea of a character appearing in multiple timelines, meeting themselves amid complex - and funny - paradoxes.

William Gibson's The Peripheral

Gleick cites Gibson's unique twist on the genre: "We can't send people, but what if you could send information back to the past?" It's a chilling new take. "It shows how our cultural conception of time is changing."

This article was originally published by WIRED UK

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Time Travel Paradoxes

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  • S. V. Krasnikov 28  

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

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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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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Krasnikov, S.V. (2018). Time Travel Paradoxes. In: Back-in-Time and Faster-than-Light Travel in General Relativity. Fundamental Theories of Physics, vol 193. Springer, Cham.

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Paradox-Free Time Travel Is Theoretically Possible, Researchers Say

Matthew S. Schwartz 2018 square

Matthew S. Schwartz

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A dog dressed as Marty McFly from Back to the Future attends the Tompkins Square Halloween Dog Parade in 2015. New research says time travel might be possible without the problems McFly encountered. Timothy A. Clary/AFP via Getty Images hide caption

A dog dressed as Marty McFly from Back to the Future attends the Tompkins Square Halloween Dog Parade in 2015. New research says time travel might be possible without the problems McFly encountered.

"The past is obdurate," Stephen King wrote in his book about a man who goes back in time to prevent the Kennedy assassination. "It doesn't want to be changed."

Turns out, King might have been on to something.

Countless science fiction tales have explored the paradox of what would happen if you went back in time and did something in the past that endangered the future. Perhaps one of the most famous pop culture examples is in Back to the Future , when Marty McFly goes back in time and accidentally stops his parents from meeting, putting his own existence in jeopardy.

But maybe McFly wasn't in much danger after all. According a new paper from researchers at the University of Queensland, even if time travel were possible, the paradox couldn't actually exist.

Researchers ran the numbers and determined that even if you made a change in the past, the timeline would essentially self-correct, ensuring that whatever happened to send you back in time would still happen.

"Say you traveled in time in an attempt to stop COVID-19's patient zero from being exposed to the virus," University of Queensland scientist Fabio Costa told the university's news service .

"However, if you stopped that individual from becoming infected, that would eliminate the motivation for you to go back and stop the pandemic in the first place," said Costa, who co-authored the paper with honors undergraduate student Germain Tobar.

"This is a paradox — an inconsistency that often leads people to think that time travel cannot occur in our universe."

A variation is known as the "grandfather paradox" — in which a time traveler kills their own grandfather, in the process preventing the time traveler's birth.

The logical paradox has given researchers a headache, in part because according to Einstein's theory of general relativity, "closed timelike curves" are possible, theoretically allowing an observer to travel back in time and interact with their past self — potentially endangering their own existence.

But these researchers say that such a paradox wouldn't necessarily exist, because events would adjust themselves.

Take the coronavirus patient zero example. "You might try and stop patient zero from becoming infected, but in doing so, you would catch the virus and become patient zero, or someone else would," Tobar told the university's news service.

In other words, a time traveler could make changes, but the original outcome would still find a way to happen — maybe not the same way it happened in the first timeline but close enough so that the time traveler would still exist and would still be motivated to go back in time.

"No matter what you did, the salient events would just recalibrate around you," Tobar said.

The paper, "Reversible dynamics with closed time-like curves and freedom of choice," was published last week in the peer-reviewed journal Classical and Quantum Gravity . The findings seem consistent with another time travel study published this summer in the peer-reviewed journal Physical Review Letters. That study found that changes made in the past won't drastically alter the future.

Bestselling science fiction author Blake Crouch, who has written extensively about time travel, said the new study seems to support what certain time travel tropes have posited all along.

"The universe is deterministic and attempts to alter Past Event X are destined to be the forces which bring Past Event X into being," Crouch told NPR via email. "So the future can affect the past. Or maybe time is just an illusion. But I guess it's cool that the math checks out."

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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)

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


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  • 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
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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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Is time travel even possible? An astrophysicist explains the science behind the science fiction

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Curious Kids is a series for children of all ages. If you have a question you’d like an expert to answer, send it to [email protected] .

Will it ever be possible for time travel to occur? – Alana C., age 12, Queens, New York

Have you ever dreamed of traveling through time, like characters do in science fiction movies? For centuries, the concept of time travel has captivated people’s imaginations. Time travel is the concept of moving between different points in time, just like you move between different places. In movies, you might have seen characters using special machines, magical devices or even hopping into a futuristic car to travel backward or forward in time.

But is this just a fun idea for movies, or could it really happen?

The question of whether time is reversible remains one of the biggest unresolved questions in science. If the universe follows the laws of thermodynamics , it may not be possible. The second law of thermodynamics states that things in the universe can either remain the same or become more disordered over time.

It’s a bit like saying you can’t unscramble eggs once they’ve been cooked. According to this law, the universe can never go back exactly to how it was before. Time can only go forward, like a one-way street.

Time is relative

However, physicist Albert Einstein’s theory of special relativity suggests that time passes at different rates for different people. Someone speeding along on a spaceship moving close to the speed of light – 671 million miles per hour! – will experience time slower than a person on Earth.

People have yet to build spaceships that can move at speeds anywhere near as fast as light, but astronauts who visit the International Space Station orbit around the Earth at speeds close to 17,500 mph. Astronaut Scott Kelly has spent 520 days at the International Space Station, and as a result has aged a little more slowly than his twin brother – and fellow astronaut – Mark Kelly. Scott used to be 6 minutes younger than his twin brother. Now, because Scott was traveling so much faster than Mark and for so many days, he is 6 minutes and 5 milliseconds younger .

Some scientists are exploring other ideas that could theoretically allow time travel. One concept involves wormholes , or hypothetical tunnels in space that could create shortcuts for journeys across the universe. If someone could build a wormhole and then figure out a way to move one end at close to the speed of light – like the hypothetical spaceship mentioned above – the moving end would age more slowly than the stationary end. Someone who entered the moving end and exited the wormhole through the stationary end would come out in their past.

However, wormholes remain theoretical: Scientists have yet to spot one. It also looks like it would be incredibly challenging to send humans through a wormhole space tunnel.

Paradoxes and failed dinner parties

There are also paradoxes associated with time travel. The famous “ grandfather paradox ” is a hypothetical problem that could arise if someone traveled back in time and accidentally prevented their grandparents from meeting. This would create a paradox where you were never born, which raises the question: How could you have traveled back in time in the first place? It’s a mind-boggling puzzle that adds to the mystery of time travel.

Famously, physicist Stephen Hawking tested the possibility of time travel by throwing a dinner party where invitations noting the date, time and coordinates were not sent out until after it had happened. His hope was that his invitation would be read by someone living in the future, who had capabilities to travel back in time. But no one showed up.

As he pointed out : “The best evidence we have that time travel is not possible, and never will be, is that we have not been invaded by hordes of tourists from the future.”

Telescopes are time machines

Interestingly, astrophysicists armed with powerful telescopes possess a unique form of time travel. As they peer into the vast expanse of the cosmos, they gaze into the past universe. Light from all galaxies and stars takes time to travel, and these beams of light carry information from the distant past. When astrophysicists observe a star or a galaxy through a telescope, they are not seeing it as it is in the present, but as it existed when the light began its journey to Earth millions to billions of years ago.

NASA’s newest space telescope, the James Webb Space Telescope , is peering at galaxies that were formed at the very beginning of the Big Bang, about 13.7 billion years ago.

While we aren’t likely to have time machines like the ones in movies anytime soon, scientists are actively researching and exploring new ideas. But for now, we’ll have to enjoy the idea of time travel in our favorite books, movies and dreams.

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And since curiosity has no age limit – adults, let us know what you’re wondering, too. We won’t be able to answer every question, but we will do our best.

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20 Paradoxes That Will Boggle Your Mind

By paul anthony jones | jun 7, 2023, 2:35 pm edt.

These paradoxes will melt your brain.

A paradox is a statement or problem that either appears to produce two entirely contradictory (yet possible) outcomes, or provides proof for something that goes against what we intuitively expect. Paradoxes have been a central part of philosophical thinking for centuries, and are always ready to challenge our interpretation of otherwise simple situations, turning what we might think to be true on its head and presenting us with provably plausible situations that are in fact just as provably impossible. Confused? You should be.

Table Of Contents

1. the paradox of achilles and the tortoise, 2. the grandfather paradox, 3. the bootstrap paradox, 4. the ship of theseus paradox, 5. and 6. the sorites paradox and the horn paradox, 7. the liar paradox, 8. the pinocchio paradox, 9. the card paradox, 10. the crocodile paradox, 11. newcomb’s paradox, 12. the dichotomy paradox, 13. the boy or girl paradox, 14. the fletcher’s paradox, 14. galileo’s paradox of the infinite, 15. the potato paradox, 16. the raven paradox, 17. the penrose triangle, 19. hilbert’s paradox of the grand hotel, 20. the interesting number paradox.

Two Galapagos tortoises

The Paradox of Achilles and the Tortoise is one of a number of theoretical discussions of movement put forward by the Greek philosopher Zeno of Elea in the 5th century BCE. It begins with the great hero Achilles challenging a tortoise to a footrace. To keep things fair, he agrees to give the tortoise a head start of, say, 500 meters. When the race begins, Achilles unsurprisingly starts running at a speed much faster than the tortoise, so that by the time he has reached the 500-meter mark, the tortoise has only walked 50 meters further than him. But by the time Achilles has reached the 550-meter mark, the tortoise has walked another 5 meters. And by the time he has reached the 555-meter mark, the tortoise has walked another 0.5 meters, then 0.25 meters, then 0.125 meters, and so on. This process continues again and again over an infinite series of smaller and smaller distances, with the tortoise always moving forwards while Achilles always plays catch up.

Logically, this seems to prove that Achilles can never overtake the tortoise—whenever he reaches somewhere the tortoise has been, he will always have some distance still left to go no matter how small it might be. Except, of course, we know intuitively that he can overtake the tortoise. The trick here is not to think of Zeno’s Achilles Paradox in terms of distances and races, but rather as an example of how any finite value can always be divided an infinite number of times, no matter how small its divisions might become.

A grandfather and his grandson walking with their backs to camera.

All of us know that if you ever travel back in time, you should definitely not kill your own grandfather, lest you create some kind of temporal paradox-slash-rift in the space-time continuum. This problem, known as the Grandfather Paradox , presents the main problem of time travel: If you go back and prevent yourself from being born, how would you ever have been able to go back in time in the first place?

The Cobbe Portrait of William Shakespeare

The Bootstrap Paradox is another paradox of time travel that questions how something that is taken from the future and placed in the past could ever come into being in the first place. It’s a common trope used by science fiction writers and has inspired plotlines in everything from Doctor Who to the Bill and Ted movies, but one of the most memorable and straightforward examples—by Professor David Toomey of the University of Massachusetts and used in his book The New Time Travelers —involves an author and his manuscript.

Imagine that a time traveler buys a copy of Hamlet from a bookstore, travels back in time to Elizabethan London, and hands the book to Shakespeare, who then copies it out and claims it as his own work. Over the centuries that follow, Hamlet is reprinted and reproduced countless times until finally a copy of it ends up back in the same original bookstore, where the time traveler finds it, buys it, and takes it back to Shakespeare. Who, then, wrote Hamlet ?

Theseus And The Minotaur (Minotaurum Theseus Vincit)

One of the more famous paradoxes, thanks in part to the Marvel show WandaVision , is the Ship of Theseus Paradox . Here’s a brief summary.

Theseus was a mythical king and the hero of Athens. (He was the guy who slayed the Minotaur, amongst other feats.) He did a lot of sailing, and his famed ship was eventually kept in an Athenian harbor as a sort of memorial/museum piece. As time went on, the ship’s wood began to rot in various places. Those wooden pieces were replaced, one by one. As time went on, more pieces needed replacing. The process of replacing rotten planks with new ones continued, at least in modern versions of the paradox, until the entire ship was made up of new pieces of wood. This thought experiment asks the question: Is this completely refurbished vessel still the ship of Theseus?

Let’s take it a step further: What if someone else took all of the discarded, original pieces of wood and reassembled them into a ship. Would this object be Theseus’s ship? And if so, what do we make of the restored ship sitting in the harbor? Which is the original ship?

This paradox is all about the nature of identity over time, and has been the subject of philosophical discussions for thousands of years. It appears in other forms, such as the Question of the Grandfather’s Axe and Trigger’s Broom, both of which ask whether an object remains the same after all the aggregate parts have been replaced. 

The idea even expands to questions of personal identity. If a person changes drastically over time, so much so that who they are no longer matches any part of who they once were, are they still the same person?

A pile of sand with more sand pouring on it.

Another paradox about the vague nature of identity is the Sorites Paradox . The premise is fairly simple. It generally involves a heap of sand. If you take away a single grain of sand from the heap, it’s still, almost certainly, a heap of sand. Now take away another grain. Still a heap. If we continue this enough times, eventually it will be down to one grain of sand, which is, almost certainly, not a heap anymore. When did the sand cease being a heap and start being something else? 

The Sorites Paradox is all about the vagueness of language. Because the word heap doesn’t have a specific quantity assigned to it, the nature of a heap is subjective. It also leads to false premises. For example, if you try the paradox in reverse, you start with a single grain of sand, which is not a heap. Then, one could argue that one grain of sand plus another grain of sand is also not a heap. Then, two grains of sand plus another grain of sand is also not a heap. This continues until even the statement “a million grains of sand is not a heap” which, as we know, does not make sense. 

The name of the paradox, Sorites, comes from the Greek word soros , which means “heap” or “pile.” It’s often attributed to Eubulides of Miletus, a logician from the 4th century BCE who was basically a paradox machine. Most of his paradoxes deal with semantic fallacies, like the Horn Paradox. If we accept the idea that “What you have not lost, you have,” then consider the fact that you have not lost your horns. Therefore, you must have horns. And yes, most of his paradoxes are just as infuriating.

A woman with a question mark drawn above her head

One of Eubulides of Miletus’s more famous paradoxes, the Liar Paradox , is still discussed today. It has a very simple premise but a very mind-boggling result. Here it is: This sentence is false.

Think about it for a moment. If the statement is true, then that means that the sentence is in fact false, as it claims. But that would then mean that the sentence is false. And if the sentence “this sentence is false” is false, then that means it’s true. But, if it’s true that it’s false, then—you get the picture. It goes on and on, forever. 

One version of the Liar Paradox involves Pinocchio.

The Liar’s Paradox has been discussed and adapted many times, eventually leading to the Pinocchio Paradox. It follows the same general structure, but with an added visual component. Imagine Pinocchio uttering the statement “My nose grows longer now.” If he’s telling the truth, then his nose should grow longer, like he said. But as we know, Pinocchio’s nose only grows if he’s telling a lie. Which means that if his nose did grow longer, then the statement would have been false. But if “my nose grows longer now” is false, then it should not have grown in the first place … Has your brain exploded yet?

This version of the paradox was created in 2001 by philosopher Peter Eldridge-Smith’s 11-year-old daughter. He summarized it neatly like this: "Pinocchio’s nose will grow if and only if it does not.”

A card that reads "the statement on the other side of this card is true" in a red envelope on a teal background

Imagine you’re holding a postcard in your hand, on one side of which is written, “The statement on the other side of this card is true.” We’ll call that Statement A. Turn the card over, and the opposite side reads, “The statement on the other side of this card is false” (Statement B). Trying to assign any truth to either Statement A or B, however, leads to a paradox: If A is true then B must be as well, but for B to be true, A has to be false. Oppositely, if A is false then B must be false too, which must ultimately make A true. The Card Paradox is a simple variation on the Liar Paradox that was invented by the British logician Philip Jourdain in the early 1900s.

A side profile of a Nile crocodile

Another variant of the Liar Paradox actually helped shape language in the 16th century. A crocodile snatches a young boy from a riverbank. His mother pleads with the crocodile to return him, to which the crocodile replies that he will only return the boy safely if the mother can guess correctly whether or not he will indeed return the boy. There’s no problem if the mother guesses that the crocodile will return him—if she’s right, he is returned; if she’s wrong, the crocodile keeps him.

If she answers that the crocodile will not return him, however, we end up with a paradox: If she’s right and the crocodile never intended to return her child, then the crocodile has to return him, but in doing so breaks his word and contradicts the mother’s answer. On the other hand, if she’s wrong and the crocodile actually did intend to return the boy, the crocodile must then keep him even though he intended not to, thereby also breaking his word.

The Crocodile Paradox is such an ancient and enduring logic problem that in the Middle Ages the word crocodilite came to be used to refer to any similarly brain-twisting dilemma where you admit something that is later used against you, and crocodility is an equally ancient word for captious or fallacious reasoning

An open box with $100 bills in it.

Another place where having to make a choice pops up is Newcomb’s Paradox. Imagine that you walk into a room where there are two boxes. You can see that the first box contains $1000. But the second box is a mystery. 

Before you came into the room, an omniscient entity made a prediction about the choice you will make. If it predicted that you’d take only the second box, that box would contain $1 million. But if it predicted that if you’d take both boxes, the second box would be empty, and you’d walk away with $1000 and two boxes. 

So what to do? One side argues to take only the second box—this is an omniscient entity doing the predicting, after all. The other side would argue that the entity’s decision has already been made. Nothing you do now in that room will have any effect on the dollar values in the boxes, so might as well take the gamble. And people can be surprisingly split on what to do—in 2016, a nonscientific online poll by The Guardian —which called the paradox “one of philosophy’s most contentious conundrums”—found 53.5 percent chose just the second box and 46.5 percent chose both boxes.

A man walking

Imagine that you’re about to set off walking down a street. To reach the other end, you’d first have to walk half way there. And to walk half way there, you’d first have to walk a quarter of the way there. And to walk a quarter of the way there, you’d first have to walk an eighth of the way there. And before that a 16th of the way there, and then a 32nd of the way there, a 64th of the way there, and so on.

Ultimately, in order to perform even the simplest of tasks like walking down a street, you’d have to perform an infinite number of smaller tasks—something that, by definition, is utterly impossible. Not only that, but no matter how small the first part of the journey is said to be, it can always be halved to create another task; the only way in which it cannot be halved would be to consider the first part of the journey to be of absolutely no distance whatsoever, and in order to complete the task of moving no distance whatsoever, you can’t even start your journey in the first place.

A little sister with her baby brother

Imagine that a family has two children, one of whom we know to be a boy. What, then, is the probability that the other child is a boy? The obvious answer is to say that the probability is 1/2—after all, the other child can only be either a boy or a girl, and the chances of a baby being born a boy or a girl are ( essentially ) equal. In a two-child family, however, there are actually four possible combinations of children: two boys (MM), two girls (FF), an older boy and a younger girl (MF), and an older girl and a younger boy (FM). We already know that one of the children is a boy, meaning we can eliminate the combination FF, but that leaves us with three equally possible combinations of children in which at least one is a boy—namely MM, MF, and FM. This means that the probability that the other child is a boy—MM—must be 1/3, not 1/2.

An arrow flying through the air

Imagine a fletcher (i.e. an arrow-maker) has fired one of his arrows into the air. For the arrow to be considered to be moving, it has to be continually repositioning itself from the place where it is now to any place where it currently isn’t. The Fletcher’s Paradox, however, states that throughout its trajectory the arrow is actually not moving at all. At any given instant of no real duration (in other words, a snapshot in time) during its flight, the arrow cannot move to somewhere it isn’t because there isn’t time for it to do so. And it can’t move to where it is now, because it’s already there. So, for that instant in time, the arrow must be stationary. But because all time is comprised entirely of instants—in every one of which the arrow must also be stationary—then the arrow must in fact be stationary the entire time. Except, of course, it isn’t.

Galileo Galilei (1564-1642) italian physicist, mathematician and astronomer, engraving colorized document

In his final written work, Discourses and Mathematical Demonstrations Relating to Two New Sciences (1638), the legendary Italian polymath Galileo Galilei proposed a mathematical paradox based on the relationships between different sets of numbers. On the one hand, he proposed, there are square numbers—like 1, 4, 9, 16, 25, 36, and so on. On the other, there are those numbers that are not squares—like 2, 3, 5, 6, 7, 8, 10, and so on. Put these two groups together, and surely there have to be more numbers in general than there are just square numbers—or, to put it another way, the total number of square numbers must be less than the total number of square and non-square numbers together. However, because every positive number has to have a corresponding square and every square number has to have a positive number as its square root, there cannot possibly be more of one than the other.

Confused? You’re not the only one. In his discussion of his paradox, Galileo was left with no alternative than to conclude that numerical concepts like more , less , or fewer can only be applied to finite sets of numbers, and as there are an infinite number of square and non-square numbers, these concepts simply cannot be used in this context.

A basket of potatoes.

Imagine that a farmer has a sack containing 100 pounds of potatoes. The potatoes, he discovers, are comprised of 99 percent water and 1 percent solids, so he leaves them in the heat of the sun for a day to let the amount of water in them reduce to 98 percent. But when he returns to them the day after, he finds his 100-pound sack now weighs just 50 pounds. How can this be true?

Well, if 99 percent of 100 pounds of potatoes is water then the water must weigh 99 pounds. The 1 percent of solids must ultimately weigh just 1 pound, giving a ratio of solids to liquids of 1:99. But if the potatoes are allowed to dehydrate to 98 percent water, the solids must now account for 2 percent of the weight—a ratio of 2:98, or 1:49—even though the solids must still only weigh 1 pound. The water, ultimately, must now weigh 49 pounds, giving a total weight of 50 pounds despite just a 1 percent reduction in water content. Or must it?

Although not a true paradox in the strictest sense, the counterintuitive Potato Paradox is a famous example of what is known as a veridical paradox, in which a basic theory is taken to a logical but apparently absurd conclusion.

Close-up of a raven

Also known as Hempel’s Paradox, for the German logician who proposed it in the mid-1940s, the Raven Paradox begins with the apparently straightforward and entirely true statement that “all ravens are black.” This is matched by a “logically contrapositive” (i.e. negative and contradictory) statement that “everything that is not black is not a raven”—which, despite seeming like a fairly unnecessary point to make, is also true given that we know “all ravens are black.” Hempel argues that whenever we see a black raven, this provides evidence to support the first statement. But by extension, whenever we see anything that is not black, like an apple, this too must be taken as evidence supporting the second statement—after all, an apple is not black, and nor is it a raven.

The paradox here is that Hempel has apparently proved that seeing an apple provides us with evidence, no matter how unrelated it may seem, that ravens are black. It’s the equivalent of saying that you live in New York is evidence that you don’t live in L.A., or that saying you are 30 years old is evidence that you are not 29. Just how much information can one statement actually imply anyway?

A Penrose Triangle

While most paradoxes are presented through a spoken or written philosophical prompt, some are visual in nature. Take, for example, the Penrose triangle. It’s an object that is described by one of its creators as “impossibility … in its purest form,” but you can build one and show it to people. Obviously it’s a trick of proportions and viewing angles, but even after you reveal the trick , people will still see it as an impossible triangle.

You might know variations of these “visual paradoxes” from their representations in the works of MC Escher, who is the poster child for mind-bending art. His Waterfall from 1961, for example, depicts an impossible object.

A corridor of hotel room doors.

Hilbert’s Paradox of the Grand Hotel is a famous thought experiment that is meant to show the counterintuitive nature of infinity. Imagine walking into a big, beautiful, hotel, looking for a room. How big? Infinitely big. This hotel has a countably infinite number of rooms. However, all the rooms are currently occupied by a countably infinite number of guests. (Countably infinite means you can one-to-one attach a natural number to everything in the set.) One might assume that the hotel would not be able to accommodate you, let alone more guests, but Hilbert’s paradox proves that this is not the case. 

In order to accommodate you, the hotel could, hypothetically, move the guest in room one to room two. Simultaneously, the guest in room two could be moved to three, and so on, which would move every guest from their current room, x, to a new room, x+1. As there are infinite rooms, everyone would get a new room, and now, room one is totally vacant. Enjoy your stay. 

What if we wanted to apply this idea to any number of finite guests? Let’s say 3000 people arrive and want rooms. No problem, just the repeat process but instead of x+1, simply do x+y—y, in this case, being 3000. 

What if a countably infinite number of people line up behind you, each of which wants a room? There’s a solution to that, too. The pattern would now be 2x. Simply move the guest in room one to room two, the guest in room two to room four, and the guest in room three to room six, and so on. This would leave all the odd-numbered rooms open, so each new guest could take one of the newly vacated odd-numbered rooms and the previous patrons would all be moved to the next even room. 

The basis of the Grand Hotel Paradox is the idea of counterintuitive results that are still provably true. In this example, the statements “there is a guest in every room” and “no more guests can be accommodated” are not the same thing because of the nature of infinity. In a normal set of numbers, such as the number of rooms in a normal hotel, the number of odd-numbered rooms would obviously be smaller than the total number of rooms. But in the case of infinity, this isn’t the case, as there are an infinite number of odd numbers, and an infinite number of total numbers. 

This paradox was first introduced by philosopher David Hilbert in a 1924 lecture and has been used to demonstrate various principles of infinity ever since. 

Numbers on a blue background

The interesting number paradox is debatably not a paradox at all, though it’s often called one. It basically goes to prove that all numbers are “interesting”—even the boring ones … which are actually interesting, of course, and not boring at all … because they’re boring.

Interesting, in this case, means it has something unique to it. For example, 1 is the first non-zero natural number; 2 is the smallest prime number; 3 is the first odd prime number. The list can go on and on, until you reach the first “uninteresting” number. It doesn’t have anything special or fascinating about it. But, being the first uninteresting number you stumbled upon, it is, in fact, unique, and therefore interesting.

This process can be repeated indefinitely, hypothetically. This idea was born out of a discussion between the mathematicians Srinivasa Ramanujan and G.H. Hardy. Hardy remarked that the number of the taxicab he had recently ridden in, 1729, was “rather a dull one.” Ramanujan responded that it actually was interesting, being the smallest number that is the sum of two cubes in two different ways. 

This story combines a piece written in 2016 with a list adapted from an episode of The List Show on YouTube.

Time travel: Is it possible?

Science says time travel is possible, but probably not in the way you're thinking.

time travel graphic illustration of a tunnel with a clock face swirling through the tunnel.

Albert Einstein's theory

  • General relativity and GPS
  • Wormhole travel
  • Alternate theories

Science fiction

Is time travel possible? Short answer: Yes, and you're doing it right now — hurtling into the future at the impressive rate of one second per second. 

You're pretty much always moving through time at the same speed, whether you're watching paint dry or wishing you had more hours to visit with a friend from out of town. 

But this isn't the kind of time travel that's captivated countless science fiction writers, or spurred a genre so extensive that Wikipedia lists over 400 titles in the category "Movies about Time Travel." In franchises like " Doctor Who ," " Star Trek ," and "Back to the Future" characters climb into some wild vehicle to blast into the past or spin into the future. Once the characters have traveled through time, they grapple with what happens if you change the past or present based on information from the future (which is where time travel stories intersect with the idea of parallel universes or alternate timelines). 

Related: The best sci-fi time machines ever

Although many people are fascinated by the idea of changing the past or seeing the future before it's due, no person has ever demonstrated the kind of back-and-forth time travel seen in science fiction or proposed a method of sending a person through significant periods of time that wouldn't destroy them on the way. And, as physicist Stephen Hawking pointed out in his book " Black Holes and Baby Universes" (Bantam, 1994), "The best evidence we have that time travel is not possible, and never will be, is that we have not been invaded by hordes of tourists from the future."

Science does support some amount of time-bending, though. For example, physicist Albert Einstein 's theory of special relativity proposes that time is an illusion that moves relative to an observer. An observer traveling near the speed of light will experience time, with all its aftereffects (boredom, aging, etc.) much more slowly than an observer at rest. That's why astronaut Scott Kelly aged ever so slightly less over the course of a year in orbit than his twin brother who stayed here on Earth. 

Related: Controversially, physicist argues that time is real

There are other scientific theories about time travel, including some weird physics that arise around wormholes , black holes and string theory . For the most part, though, time travel remains the domain of an ever-growing array of science fiction books, movies, television shows, comics, video games and more. 

Scott and Mark Kelly sit side by side wearing a blue NASA jacket and jeans

Einstein developed his theory of special relativity in 1905. Along with his later expansion, the theory of general relativity , it has become one of the foundational tenets of modern physics. Special relativity describes the relationship between space and time for objects moving at constant speeds in a straight line. 

The short version of the theory is deceptively simple. First, all things are measured in relation to something else — that is to say, there is no "absolute" frame of reference. Second, the speed of light is constant. It stays the same no matter what, and no matter where it's measured from. And third, nothing can go faster than the speed of light.

From those simple tenets unfolds actual, real-life time travel. An observer traveling at high velocity will experience time at a slower rate than an observer who isn't speeding through space. 

While we don't accelerate humans to near-light-speed, we do send them swinging around the planet at 17,500 mph (28,160 km/h) aboard the International Space Station . Astronaut Scott Kelly was born after his twin brother, and fellow astronaut, Mark Kelly . Scott Kelly spent 520 days in orbit, while Mark logged 54 days in space. The difference in the speed at which they experienced time over the course of their lifetimes has actually widened the age gap between the two men.

"So, where[as] I used to be just 6 minutes older, now I am 6 minutes and 5 milliseconds older," Mark Kelly said in a panel discussion on July 12, 2020, previously reported . "Now I've got that over his head."

General relativity and GPS time travel

Graphic showing the path of GPS satellites around Earth at the center of the image.

The difference that low earth orbit makes in an astronaut's life span may be negligible — better suited for jokes among siblings than actual life extension or visiting the distant future — but the dilation in time between people on Earth and GPS satellites flying through space does make a difference. 

Read more: Can we stop time?

The Global Positioning System , or GPS, helps us know exactly where we are by communicating with a network of a few dozen satellites positioned in a high Earth orbit. The satellites circle the planet from 12,500 miles (20,100 kilometers) away, moving at 8,700 mph (14,000 km/h). 

According to special relativity, the faster an object moves relative to another object, the slower that first object experiences time. For GPS satellites with atomic clocks, this effect cuts 7 microseconds, or 7 millionths of a second, off each day, according to the American Physical Society publication Physics Central .  

Read more: Could Star Trek's faster-than-light warp drive actually work?

Then, according to general relativity, clocks closer to the center of a large gravitational mass like Earth tick more slowly than those farther away. So, because the GPS satellites are much farther from the center of Earth compared to clocks on the surface, Physics Central added, that adds another 45 microseconds onto the GPS satellite clocks each day. Combined with the negative 7 microseconds from the special relativity calculation, the net result is an added 38 microseconds. 

This means that in order to maintain the accuracy needed to pinpoint your car or phone — or, since the system is run by the U.S. Department of Defense, a military drone — engineers must account for an extra 38 microseconds in each satellite's day. The atomic clocks onboard don’t tick over to the next day until they have run 38 microseconds longer than comparable clocks on Earth.

Given those numbers, it would take more than seven years for the atomic clock in a GPS satellite to un-sync itself from an Earth clock by more than a blink of an eye. (We did the math: If you estimate a blink to last at least 100,000 microseconds, as the Harvard Database of Useful Biological Numbers does, it would take thousands of days for those 38 microsecond shifts to add up.) 

This kind of time travel may seem as negligible as the Kelly brothers' age gap, but given the hyper-accuracy of modern GPS technology, it actually does matter. If it can communicate with the satellites whizzing overhead, your phone can nail down your location in space and time with incredible accuracy. 

Can wormholes take us back in time?

General relativity might also provide scenarios that could allow travelers to go back in time, according to NASA . But the physical reality of those time-travel methods is no piece of cake. 

Wormholes are theoretical "tunnels" through the fabric of space-time that could connect different moments or locations in reality to others. Also known as Einstein-Rosen bridges or white holes, as opposed to black holes, speculation about wormholes abounds. But despite taking up a lot of space (or space-time) in science fiction, no wormholes of any kind have been identified in real life. 

Related: Best time travel movies

"The whole thing is very hypothetical at this point," Stephen Hsu, a professor of theoretical physics at the University of Oregon, told sister site Live Science . "No one thinks we're going to find a wormhole anytime soon."

Primordial wormholes are predicted to be just 10^-34 inches (10^-33 centimeters) at the tunnel's "mouth". Previously, they were expected to be too unstable for anything to be able to travel through them. However, a study claims that this is not the case, Live Science reported . 

The theory, which suggests that wormholes could work as viable space-time shortcuts, was described by physicist Pascal Koiran. As part of the study, Koiran used the Eddington-Finkelstein metric, as opposed to the Schwarzschild metric which has been used in the majority of previous analyses.

In the past, the path of a particle could not be traced through a hypothetical wormhole. However, using the Eddington-Finkelstein metric, the physicist was able to achieve just that.

Koiran's paper was described in October 2021, in the preprint database arXiv , before being published in the Journal of Modern Physics D.

Graphic illustration of a wormhole

Alternate time travel theories

While Einstein's theories appear to make time travel difficult, some researchers have proposed other solutions that could allow jumps back and forth in time. These alternate theories share one major flaw: As far as scientists can tell, there's no way a person could survive the kind of gravitational pulling and pushing that each solution requires.

Infinite cylinder theory

Astronomer Frank Tipler proposed a mechanism (sometimes known as a Tipler Cylinder ) where one could take matter that is 10 times the sun's mass, then roll it into a very long, but very dense cylinder. The Anderson Institute , a time travel research organization, described the cylinder as "a black hole that has passed through a spaghetti factory."

After spinning this black hole spaghetti a few billion revolutions per minute, a spaceship nearby — following a very precise spiral around the cylinder — could travel backward in time on a "closed, time-like curve," according to the Anderson Institute. 

The major problem is that in order for the Tipler Cylinder to become reality, the cylinder would need to be infinitely long or be made of some unknown kind of matter. At least for the foreseeable future, endless interstellar pasta is beyond our reach.

Time donuts

Theoretical physicist Amos Ori at the Technion-Israel Institute of Technology in Haifa, Israel, proposed a model for a time machine made out of curved space-time — a donut-shaped vacuum surrounded by a sphere of normal matter.

"The machine is space-time itself," Ori told Live Science . "If we were to create an area with a warp like this in space that would enable time lines to close on themselves, it might enable future generations to return to visit our time."

Amos Ori is a theoretical physicist at the Technion-Israel Institute of Technology in Haifa, Israel. His research interests and publications span the fields of general relativity, black holes, gravitational waves and closed time lines.

There are a few caveats to Ori's time machine. First, visitors to the past wouldn't be able to travel to times earlier than the invention and construction of the time donut. Second, and more importantly, the invention and construction of this machine would depend on our ability to manipulate gravitational fields at will — a feat that may be theoretically possible but is certainly beyond our immediate reach.

Graphic illustration of the TARDIS (Time and Relative Dimensions in Space) traveling through space, surrounded by stars.

Time travel has long occupied a significant place in fiction. Since as early as the "Mahabharata," an ancient Sanskrit epic poem compiled around 400 B.C., humans have dreamed of warping time, Lisa Yaszek, a professor of science fiction studies at the Georgia Institute of Technology in Atlanta, told Live Science .  

Every work of time-travel fiction creates its own version of space-time, glossing over one or more scientific hurdles and paradoxes to achieve its plot requirements. 

Some make a nod to research and physics, like " Interstellar ," a 2014 film directed by Christopher Nolan. In the movie, a character played by Matthew McConaughey spends a few hours on a planet orbiting a supermassive black hole, but because of time dilation, observers on Earth experience those hours as a matter of decades. 

Others take a more whimsical approach, like the "Doctor Who" television series. The series features the Doctor, an extraterrestrial "Time Lord" who travels in a spaceship resembling a blue British police box. "People assume," the Doctor explained in the show, "that time is a strict progression from cause to effect, but actually from a non-linear, non-subjective viewpoint, it's more like a big ball of wibbly-wobbly, timey-wimey stuff." 

Long-standing franchises like the "Star Trek" movies and television series, as well as comic universes like DC and Marvel Comics, revisit the idea of time travel over and over. 

Related: Marvel movies in order: chronological & release order

Here is an incomplete (and deeply subjective) list of some influential or notable works of time travel fiction:

Books about time travel:

A sketch from the Christmas Carol shows a cloaked figure on the left and a person kneeling and clutching their head with their hands.

  • Rip Van Winkle (Cornelius S. Van Winkle, 1819) by Washington Irving
  • A Christmas Carol (Chapman & Hall, 1843) by Charles Dickens
  • The Time Machine (William Heinemann, 1895) by H. G. Wells
  • A Connecticut Yankee in King Arthur's Court (Charles L. Webster and Co., 1889) by Mark Twain
  • The Restaurant at the End of the Universe (Pan Books, 1980) by Douglas Adams
  • A Tale of Time City (Methuen, 1987) by Diana Wynn Jones
  • The Outlander series (Delacorte Press, 1991-present) by Diana Gabaldon
  • Harry Potter and the Prisoner of Azkaban (Bloomsbury/Scholastic, 1999) by J. K. Rowling
  • Thief of Time (Doubleday, 2001) by Terry Pratchett
  • The Time Traveler's Wife (MacAdam/Cage, 2003) by Audrey Niffenegger
  • All You Need is Kill (Shueisha, 2004) by Hiroshi Sakurazaka

Movies about time travel:

  • Planet of the Apes (1968)
  • Superman (1978)
  • Time Bandits (1981)
  • The Terminator (1984)
  • Back to the Future series (1985, 1989, 1990)
  • Star Trek IV: The Voyage Home (1986)
  • Bill & Ted's Excellent Adventure (1989)
  • Groundhog Day (1993)
  • Galaxy Quest (1999)
  • The Butterfly Effect (2004)
  • 13 Going on 30 (2004)
  • The Lake House (2006)
  • Meet the Robinsons (2007)
  • Hot Tub Time Machine (2010)
  • Midnight in Paris (2011)
  • Looper (2012)
  • X-Men: Days of Future Past (2014)
  • Edge of Tomorrow (2014)
  • Interstellar (2014)
  • Doctor Strange (2016)
  • A Wrinkle in Time (2018)
  • The Last Sharknado: It's About Time (2018)
  • Avengers: Endgame (2019)
  • Tenet (2020)
  • Palm Springs (2020)
  • Zach Snyder's Justice League (2021)
  • The Tomorrow War (2021)

Television about time travel:

Image of the Star Trek spaceship USS Enterprise

  • Doctor Who (1963-present)
  • The Twilight Zone (1959-1964) (multiple episodes)
  • Star Trek (multiple series, multiple episodes)
  • Samurai Jack (2001-2004)
  • Lost (2004-2010)
  • Phil of the Future (2004-2006)
  • Steins;Gate (2011)
  • Outlander (2014-2023)
  • Loki (2021-present)

Games about time travel:

  • Chrono Trigger (1995)
  • TimeSplitters (2000-2005)
  • Kingdom Hearts (2002-2019)
  • Prince of Persia: Sands of Time (2003)
  • God of War II (2007)
  • Ratchet and Clank Future: A Crack In Time (2009)
  • Sly Cooper: Thieves in Time (2013)
  • Dishonored 2 (2016)
  • Titanfall 2 (2016)
  • Outer Wilds (2019)

Additional resources

Explore physicist Peter Millington's thoughts about Stephen Hawking's time travel theories at The Conversation . Check out a kid-friendly explanation of real-world time travel from NASA's Space Place . For an overview of time travel in fiction and the collective consciousness, read " Time Travel: A History " (Pantheon, 2016) by James Gleik. 

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Ailsa is a staff writer for How It Works magazine, where she writes science, technology, space, history and environment features. Based in the U.K., she graduated from the University of Stirling with a BA (Hons) journalism degree. Previously, Ailsa has written for Cardiff Times magazine, Psychology Now and numerous science bookazines. 

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The real time-travel paradox was the friends we made along the way

  • Rodrigo Culagovski 0

Rodrigo is a Chilean architect, designer and web developer. He currently heads a web development agency and is a researcher and professor at Universidad Católica in Chile. He has published in Dark Matter Presents: Monstrous Futures , Solarpunk Magazine and Future Science Fiction Digest . On Mastodon as @[email protected] . He misses his Commodore 64. Pronouns he/him/él.

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Illustration: Jacey

She was taller than me. Prettier and with better muscle tone. Shinier hair and perfect skin and teeth. Which was odd because she claimed she was me — from the future.

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Time Travel & the Predestination Paradox Explained

May 16, 2017 James Miller Time Travel 2


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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Notes to Time Travel and Modern Physics

1. There is a large philosophical literature on the first two paradoxes (and others), see, e.g., the entry on time travel , Wasserman (2018), and Effingham (2020), but very little on the easy knowledge paradox (emphasized by Deutsch 1991, discussed further below). Our approach differs from the literature surveyed in these two books by focusing on the physical—rather than metaphysical—possibility of time travel.

2. Multiple collisions are handled in the obvious way by continuity considerations: just continue straight lines through the collision point and identify which particle is which by their ordering in space.

3. The dynamics here is radically non-time-reversible. Indeed, the dynamics is deterministic in the future direction but not in the past direction.

4. One might hope that fixed point theorems can be used to prove the existence of solutions in this type of cases too. Consider, for instance, a fixed initial state of motion I of the ball. Then consider all the possible velocities and locations and times \(\langle v,x,t\rangle\) at which such a ball could enter mouth 1 of the wormhole. Each such triple \(\langle v,x,t\rangle\) will determine the trajectory of that ball out of mouth 2. One can then look at the continuation of the trajectory from state I and that from state s , and see whether these trajectories collide. Then one can see for each possible triple \(\langle v,x,t\rangle\) whether the ball that starts in state I will be collided into mouth 1, and if it is, with which speed at what location and at which time this will occur. Thus given state I , each triple \(\langle v,x,t\rangle\) maps onto another triple \(\langle v',x',t'\rangle\). One might then suggest appealing to a fixed point theorem to argue that there must be a solution for each initial state I . However, in the first place the set of possible speeds and times are open sets. And in the second place there can be multiple wormhole traversals. Thus the relevant total state-space of wormhole mouth crossings consists of discretely many completely disconnected state-spaces (with increasing numbers of dimensions). So standard fixed point theorems do not apply directly. It should be noted that the results that have been achieved regarding this case do make use of fixed points theorems quite extensively. But their application is limited to certain sub-problems, and do not yield a fully general proof of the lack of constraints for arbitrary I .

5. This argument, especially the second illustration of it, is similar to the one in Horwich (1987: 124–128). However, we do not share Horwich’s view that it only tells against time travel of humans into their local past.

6. Recently physicists have developed a similar computational approach (called the process matrix formalism) to describe interactions among systems with indefinite causal structure. See Adlam (unpublished) for a philosophical discussion and references to the physics literature.

7. In this section we will presume familiarity with quantum mechanics. See, for example, the entry on quantum mechanics , and its extremely useful guide to further reading, for an entry point to this subject.

Copyright © 2023 by Christopher Smeenk < csmeenk2 @ uwo . ca > Frank Arntzenius Tim Maudlin

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Time Travel Movies Rely on the ‘Bootstrap Paradox.’ It Could Explain Real-Life Destiny

It may not be as famous as the so-called “grandfather paradox,” but that doesn’t make the idea of an infinite causal loop any less troubling ... or fascinating .

astronaut entering portal transportation

Arriving back slightly before your time, you watch your friend as she teaches her younger self how to build the time machine in the first place. “But … ” you stammer, cautious in case your friend—or her younger counterpart—takes offense and travels back in time to wipe you from existence, “if you used the time machine to travel back in time to inform yourself how to build the time machine, isn’t that a paradox?” It is , because no one in this story ever actually sat down to figure out how to create a time machine. This is the bootstrap paradox, which details an infinite cause-and-effect loop that develops around information, an object, or even a person that can no longer be given a discernible point of origin in a time travel scenario.

This results in a “closed causal loop,” in which some event or object is a key player in its own origin and couldn’t exist without its later self. The idea is woven through the imaginations of science fiction writers, theoretical physicists, and philosophers, meaning its roots in science and pop culture may be irrevocably interwoven.

Though less famous than the grandfather paradox —in which a time traveler kills their grandfather before they have children, and can no longer exist to go back in time and perform grand patricide—the bootstrap paradox is still an idea that philosophers and physicists have been grappling with for almost 100 years.

“The bootstrap paradox in time travel occurs when a piece of information that has no right to exist, nonetheless exists,” Seth Lloyd, a professor of mechanical engineering at the Massachusetts Institute of Technology and a self-described “quantum mechanic,” tells Popular Mechanics . “To illustrate the bootstrap paradox, consider the version known as the ‘unproved theorem paradox.’”

Lloyd explains that in the unproved theorem paradox, a time traveler finds a beautiful and elegant proof of a theorem in a book, then goes back in time and shows the proof to a mathematician, who includes the proof in his book. “The book, of course, is the same book in which the time traveler found the proof in the future,” he adds. “So who proved the theorem? No one proved the theorem! Where did the proof come from? Nowhere!”

Tim Maudlin, a philosopher of science who investigates the metaphysical foundations of physics and logic, says there is a key difference between the bootstrap paradox and the grandfather paradox.

“The bootstrap paradox occurs in certain logically consistent time travel scenarios. Unlike the grandfather paradox, which is a self-contradictory and hence an impossible scenario, in a bootstrap story, everything fits together in a logically coherent way,” Maudlin tells Popular Mechanics. “Still, the paradox arises because certain things or information [are] ‘self-caused’ or ‘come from itself.’” That means, in a sense, that these bits of information appear in the story without ever having been created, just like the instructions for building your friend’s time machine.

Maudlin — who alongside Oxford University philosopher Frank Arntzenius wrote the Stanford Encyclopedia of Philosophy article “Time Travel and Modern Physics”— adds that since it is not a matter of self-contradiction or logical incoherence, logic alone cannot rule out these bootstrap paradox scenarios. This has helped make the concept a staple of time travel stories in popular culture.

The Origins of the Bootstrap Paradox

zoom in of city lights view from high

Physicists first began to pay serious attention to the concept of time travel in the early years of the 20th century, following the work of Albert Einstein .

As he formulated the theory of special relativity, published in 1905, Einstein united the concepts of space and time into a single four-dimensional entity — spacetime — and also imposed the rule that particles with mass would need infinite energy to accelerate to the speed of light . This led to speculation about hypothetical massless particles called “tachyons” that could exceed the speed of light, but as a consequence, would travel back through time.

.css-2l0eat{font-family:UnitedSans,UnitedSans-roboto,UnitedSans-local,Helvetica,Arial,Sans-serif;font-size:1.625rem;line-height:1.2;margin:0rem;padding:0.9rem 1rem 1rem;}@media(max-width: 48rem){.css-2l0eat{font-size:1.75rem;line-height:1;}}@media(min-width: 48rem){.css-2l0eat{font-size:1.875rem;line-height:1;}}@media(min-width: 64rem){.css-2l0eat{font-size:2.25rem;line-height:1;}}.css-2l0eat b,.css-2l0eat strong{font-family:inherit;font-weight:bold;}.css-2l0eat em,.css-2l0eat i{font-style:italic;font-family:inherit;} “The paradox suggests the potential for ‘predestination’ to causality, or the idea that the past is dependent on the future.”

While this opened the door to physicists thinking about time travel, Einstein would violently tear that hypothetical door down ten years later when he formulated the theory of general relativity . Primarily a theory that describes the effect of mass on spacetime, general relativity implies that four-dimensional spacetime could be twisted into any shape. This means it could be possible to create a path that forms a loop passing back through time, returning to its original starting point — which would become known as a “closed time-like curve” or CTC.

The idea of time travel caused a serious threat to causality, the relationship between cause and effect, in that it could make an effect precede its own cause—a clear contradiction. The bootstrap paradox is more subtle than this (cause still precedes effect), but there is no starting point in the process. Instead, the paradox suggests the potential for “predestination” to causality, or the idea that the past is dependent on the future.

As the bootstrap paradox worked its way into physicists’ notebooks and blackboards, it was also making its mark on pop culture, with the two occasionally overlapping.

The Bootstrap Paradox in Pop Culture

on the set of terminator

The bootstrap paradox takes its name from an expression that dates back to 1834: to “pull oneself over a fence by one’s bootstraps,” which came to represent the idea of performing a ludicrous or impossible task. (In the startup world, it’s come to mark the idea of launching a company with your own money or whatever you can scrounge from friends and family—certainly a Herculean task.)

In popular culture, the paradox lent its name to the 1941 Robert A. Heinlein story, By His Bootstraps , likely one of the paradox’s earliest presentations to the public. In the story, a similar scenario plays out to the one we described about your time-traveling friend:

“A time travel machine is built by following the instructions in a book, which itself is sent back from the future. But how did the information get into the book? By being copied into a newly made notebook from the older version of itself,” Maudlin explains. “That is, no one ever sat down and figured out how to build a time machine, the information about how to do it is just there in a closed causal loop.”

Since the publication of Heinlein’s tale, the bootstrap paradox has made its way into a wealth of science fiction tales, though it often goes unnamed. For instance, in the popular Doctor Who episode “Blink,” the time-traveler that David Tennett plays must combat a menace called the Weeping Angels by passing messages from the past—when he is trapped without his own method of time travel, the TARDIS—to the present.

At the end of the story, with evil defeated, a log of the messages is passed back to the timelord before he is trapped in the past. Therefore, the log of messages has no set origin; It cycles between the past and the future in a closed causal loop.

Meanwhile, the Terminator franchise features a wealth of potential time travel paradoxes across the series. For example, the main mission of the earliest film is for Arnold Schwarzenegger’s T-800 to prevent the birth of John Connor. Yet, if the Terminator kills his mother Sarah, and prevents the birth of John Conner before he can lead the rebellion, then he never existed as a threat to the Terminator controlling Skynet in the first place; That means they’d never need to send a Terminator back to kill him at all,eEssentially creating a version of the Grandfather paradox with more robots.

Artificial intelligence-based boogeyman Skynet is itself, however, an example of the bootstrap paradox. The AI system that would go on to rule Earth and subjugate mankind was created from the leftover parts of the T-800 Terminator that was sent back in time to kill Sarah Connor and prevent the birth of John Connor in the first place. Eventually, Skynet’s own killing machines, including the T-800, were retro-engineered from these parts, meaning the T-800 is the source of its own origin. Classic bootstrap!

These are just a few of the more infamous examples of the bootstrap paradox in fiction, and some of these tales have even helped inform scientific theory on the subject.

“As part of our efforts to construct a self-consistent quantum theory of time travel via closed timelike curves, I did extensive reading of time travel narratives and viewing of time travel films,” Lloyd explains. “All time travel paradoxes seem to be versions of either the grandfather paradox or of the bootstrap paradox.”

Escaping the Bootstrap Paradox

woman jumping into a rectangular portal

Hugh Everett’s Many-Worlds Interpretation of quantum mechanics suggests that for every quantum possibility, a distinct universe is created. This can provide a solution to apparent contradictions in time travel.

“It has been suggested that paradoxes such as the grandfather paradox could be avoided by Everett’s Many Worlds—or more accurately, ‘relative state’—interpretation of quantum mechanics ,” Lloyd says. “When the time traveler goes back and kills her grandfather, she is simply forcing a transition into a separate ‘world,’ or branch of the wave function, from the world in which she came.”

That means a time traveler hitching a ride on a closed time-like curve into the past actually causes the universe to diverge, and the world she arrives in is distinct from the one she left. Therefore, it is not her grandfather she kills in the past, but a version of him that will never go on to have a child or grandchild. Our time traveler’s birth, therefore, is not prevented.

So in the case of the bootstrap paradox, returning to our earlier scenario, our friend doesn’t pass the information for building a time machine to her earlier self, but a version of herself in the past in a separate world.

That means each backward leap passes the information to a new universe.

Even so, this doesn’t fully solve the Bootstrap paradox, as it doesn’t explain where this information came from in the first place; The instructions for the time travel machine still don’t have an origin point.

“Since no contradiction is involved, one can’t raise the same logical objection as in the grandfather paradox case,” Maudlin says. “But still, many people think that such ‘self-causation’ or lack of an originator of the information, makes the scenario impossible. And of course, if reverse causation is not possible, then this closed causal loop is not either.”

Maudlin does point out that the bootstrap paradox isn’t as intrinsically intractable as the grandfather paradox, however. In fact, it could be replete with a wealth of hitherto undiscovered exit routes.

“If one allows for closed causal loops, then in a way, the opposite thing happens as in the grandfather paradox case. With the grandfather paradox, there seems to be no logically self-consistent solution,” Maudlin concludes. “But in the bootstrapping cases, there are often several different solutions, with the closed loops taking different forms.

“In fact, there would not seem to be any explanation of why one, rather than another, of these solutions would be realized.”

Testing the Bootstrap Paradox

While Maudlin doesn’t believe that the bootstrap paradox could ever be experimentally tested, Lloyd disagrees; He has suggested an experiment to investigate the unproved theorem paradox version of the bootstrap paradox.

“We devised experiments to test the pre/retrodictions of our theory for both of the central paradoxes of time travel—the grandfather paradox and the bootstrap paradox—a simple experiment to test the pre/retrodictions of our theory for the unproved theorem paradox,” Lloyd says. “The test can be performed on a simple quantum computer . In the experiment, a bit of information—call it Bit A—is copied to a second bit (Bit B).

“Bit B is sent back into the past, where it turns out that B in the past is in fact the same bit that becomes A in the future. Rather than engendering a self-inconsistency, however, the bootstrap/unproved theorem experiment is entirely self-consistent.”

This means for Lloyd, perhaps the greatest paradox surrounding the bootstrap paradox is that it doesn’t have to be a paradox at all.

“The bootstrap paradox isn’t always paradoxical. In our proposed experiment, for example, we predict that the ‘unproved’ bit will turn out to be entirely random,” he says. “This makes sense, as at no point in the future or the past was there any bias introduced to make it anything other than random .”

For now, however, Lloyd doesn’t intend to attempt such an experiment. Instead, alongside his colleague Michele Reilly and artist Andrey Kezzyn, Lloyd expressed his interest in time travel in the form of the 2022 movie Steeplechase .

“The experimental demonstration of the grandfather paradox gave rise to so much publicity—not to say notoriety—however, that we decided to hold off on further time travel experiments for the foreseeable future,” the physicist explains.

Headshot of Robert Lea

Robert Lea is a freelance science journalist focusing on space, astronomy, and physics. Rob’s articles have been published in Newsweek , Space , Live Science , Astronomy magazine and New Scientist . He lives in the North West of England with too many cats and comic books.  

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Paradoxes of Time Travel

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Paradoxes of Time Travel

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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    Abstract. 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 ...

  16. Time Travel and Modern Physics

    Time Travel and Modern Physics. First published Thu Feb 17, 2000; substantive revision Wed Dec 23, 2009. Time travel has been a staple of science fiction. With the advent of general relativity it has been entertained by serious physicists. But, especially in the philosophy literature, there have been arguments that time travel is inherently ...

  17. Paradoxes of Time Travel

    Abstract. Paradoxes of Time Travel is a comprehensive study of the philosophical issues raised by the possibility of time travel. The book begins, in Chapter 1, by explaining the concept of time travel and clarifying the central question to be addressed: Is time travel compatible with the laws of metaphysics and, in particular, the laws concerning time, freedom, causation, and identity?

  18. Is time travel even possible? An astrophysicist explains the science

    There are also paradoxes associated with time travel. The famous " grandfather paradox " is a hypothetical problem that could arise if someone traveled back in time and accidentally prevented ...

  19. 20 Paradoxes That Will Boggle Your Mind

    9. The Card Paradox. Imagine you're holding a postcard in your hand, on one side of which is written, "The statement on the other side of this card is true.". We'll call that Statement A ...

  20. Time travel

    Every work of time-travel fiction creates its own version of space-time, glossing over one or more scientific hurdles and paradoxes to achieve its plot requirements.

  21. The real time-travel paradox was the friends we made along the way

    The real time-travel paradox was the friends we made along the way. Life at the cutting edge. She was taller than me. Prettier and with better muscle tone. Shinier hair and perfect skin and teeth ...

  22. Time Travel & the Predestination Paradox Explained

    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 ...

  23. Notes to Time Travel and Modern Physics

    Notes to Time Travel and Modern Physics. 1. There is a large philosophical literature on the first two paradoxes (and others), see, e.g., the entry on time travel , Wasserman (2018), and Effingham (2020), but very little on the easy knowledge paradox (emphasized by Deutsch 1991, discussed further below).

  24. Paradoxes of Time Travel

    Ryan Wasserman presents a wide-ranging exploration of puzzles raised by the possibility of time travel, including the grandfather paradox, the bootstrapping paradox, and the twin paradox of special relativity. He draws out their implications for our understanding of time, tense, freedom, fatalism, causation, counterfactuals, laws of nature, persistence, change, and mereology.

  25. How Time Travel's 'Bootstrap Paradox' Could Explain Destiny

    Meanwhile, the Terminator franchise features a wealth of potential time travel paradoxes across the series. For example, the main mission of the earliest film is for Arnold Schwarzenegger's T ...

  26. Introduction

    Abstract. 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 ...