time travel summary essay

1000-Word Philosophy: An Introductory Anthology

Philosophy, One Thousand Words at a Time

Time Travel

Author: Taylor W. Cyr Category: Metaphysics Word Count: 1000

Time travel is familiar from science fiction and is interesting to philosophers because of the metaphysical issues it raises: the nature of time, causation, personal identity, and freedom, among others. [1]

It’s widely accepted that time travel to the future is possible, but the possibility of backward time travel remains hotly debated. [2] This article will sketch some models of backward time travel (hereafter simply “time travel”) before addressing the main objections to its possibility. [3]

1. Models of Time Travel

According to the standard model of time travel, time is linear so a time traveler’s journey may be depicted along a single timeline, with some events that occur earlier in the timeline’s being experienced as later by the traveler: [4]

On another model, time travel results in the creation of a new universe that branches out from the same trunk (shared past) as the original:

A third model of time travel maintains that there is a second temporal dimension, and so, in addition to times, there are “hyper-times.” [5] On this model, time is more like a plane than like a line, and a time traveler may, in returning to an earlier time, reach that time at a later hyper-time, with the result that the aforementioned time bears different properties at the different hyper-times: [6]

2. Changing the Past

It is natural to suppose that time travel would change the past, which many believe is impossible. Changing the past would require that the past have a certain property at one “time” and then lack that property at another “time.” This is incoherent on the standard model of time travel, which maintains that time is linear (there is no “second time around”), so the standard model precludes changing the past.

But time travel doesn’t require changing the past. We may distinguish changing the past from affecting the past, where the latter requires only that the time traveler’s travels have effects in the past. [7] For example, suppose a time traveler finds her younger self and attempts to convince herself not to time travel. [8] Assuming the standard model of time travel, she will fail to prevent herself from time traveling, but the attempt will affect how the past was “all along,” so to speak. From the outside, the scene will look like an ordinary conversation between two people, but, assuming the time traveler remembers the scene, she will remember an older version of herself trying to convince her not to time travel. [9]

Moreover, according to the other two models of time travel, one and the same time may exist in two different universes or hyper-times, and so it isn’t obviously incoherent to state that some past time may have a property at one “time” (either in one universe, or at one hyper-time) that it lacks at another “time” (in another universe, or at another hyper-time). [10]

3. Causal Loops

Consider some events from the television show Lost . [11] At one point, Richard gives a compass to Locke, telling him to return it the next time they meet. Locke then travels back in time, sees a younger Richard, and returns the compass, which Richard keeps until he gives it to Locke in the aforementioned meeting.

The Lost compass is strange. It was not created in the usual way—in fact, it has no creator! It appeared (with Locke) at time t1 (when it was given to Richard), remained with Richard at a later time t2, and then was given to Locke at t3, when Locke set out for t1, resulting in a “causal loop.” At each time t1-t3, there is a causal explanation for the compass’s presence by reference to the prior stage in the loop. But no explanation can be given for the loop itself. (Where did the compass come from to begin with? There is no answer.)

Now, if such cases are impossible, this might cast doubt on the possibility of time travel. As David Lewis says in response, however, such cases “are not too different from inexplicabilities we are already inured to” such as “God, or the Big Bang, or the decay of a tritium atom,” all of which are “uncaused and inexplicable” (1976: 149).

Note that this objection assumes the standard model of time travel, since these strange loops do not necessarily result from time travel on the other models. Moreover, it may be possible for there to be cases of time travel that don’t generate causal loops even assuming the standard model. [12]

4. Time Travelers’ Abilities

Suppose Tim time travels and attempts to kill his Grandfather before his parents are conceived. Assuming Tim has a gun, is a good shot, etc., it would seem that Tim can kill Grandfather. But Tim can’t kill Grandfather, for doing so would preclude his own existence. Tim both can and can’t kill Grandfather: that’s a contradiction, so we should give up the assumption that led to it, namely that time travel is possible.

This is the Grandfather Paradox, and it is the main objection to the possibility of time travel. Here are two responses, both of which assume the standard model of time travel. [13]

First, one might understand “can” claims like “Tim can kill Grandfather” as claims about what is possible in view of certain facts—and which facts are held fixed is determined by the context of utterance. [14] For example, in view of Tim’s possession of a gun, his reliable aim, etc., it is true that Tim can kill Grandfather. But if we also hold fixed the fact that Grandfather lives , then Tim’s killing Grandfather isn’t possible, and thus he can’t kill Grandfather. So, there is no contradiction; it is true that Tim can kill Grandfather holding certain facts fixed, and it is false holding more fixed, but the claim is not both true and false in the same context. [15]

A second approach denies that Tim can kill Grandfather. [16] This denial follows from certain independently motivated views of agents’ abilities, and it avoids the Paradox by restricting the freedom of time travelers.

5. Conclusion

Perhaps time travel is (metaphysically) possible, but it doesn’t follow that it’s technologically feasible, or that it will ever actually occur. Only time will tell.

[1]   While not the first philosophical discussion of time travel, David Lewis’s classic 1976 essay “The Paradoxes of Time Travel” popularized the subject in metaphysics. For a recent philosophical discussion of time travel—an excellent summary of several facets of the debate, as well as some new developments—see Wasserman (2018).

[2]   By “possibility” I mean metaphysical possibility—consistency with the laws of metaphysics, such as the laws of causation, identity, etc. For more on the discussion of the various senses of possibility we might be asking about in connection with time travel, see Wasserman (2018, chapter 1), and see the rest of the same book for a summary of the debate about the metaphysical possibility of backward time travel.

[3]   There are other objections, but there isn’t space to consider all of them here. One objection concerns its likelihood rather than its possibility . As we will see below, there are certain things that it would seem time travelers cannot do, and so if time travelers attempted the impossible, something would prevent them from succeeding (perhaps the time traveler would have a change of heart, or perhaps she would slip on a banana peel, or…). Horwich (1987) argues that since backward time travel would result in such improbable events, this casts doubt on the likelihood of time travel. See Smith (1997) for discussion and a response to Horwich.

[4]   See the first figure. Reprinted from Wasserman (2018, chapter 3) with permission of Ryan Wasserman and Oxford University Press.

[5]   For developments of the hyper-time model, see Meiland (1974), Goddu (2003), and van Inwagen (2010).

[6]   If we graphed the two dimensions of time on a plane, with the temporal dimension along the x- axis and the hyper-temporal dimension along the y -axis, as in the third figure, time travel would amount to moving leftward (back in time) and upward (forward in hyper-time).

[7]   As Brier explains, “One cannot change the past or undo what has been done. Rather, what is at issue is whether one can affect the past; that is, by a present action cause something to have happened which would not have happened otherwise” (1973: 361).

[8]   For a simple example of this from science-fiction, see the film Interstellar . After leaving Earth, Cooper is able to send messages back in time, and he uses his first message to try to get his daughter to make him stay on Earth, as seen here .

[9]   For another example of affecting (but not changing) the past, see J. K. Rowling’s Harry Potter and the Prisoner of Azkaban . An especially excellent case of time travel occurs toward the end of the book when Hermione takes Harry back in time, allowing him to save himself from Dementors. In the film version, we see Harry attacked by (but saved from) Dementors here , and then we see Hermione take Harry back in time here , and finally, we see Harry save himself here .

[10]   It is contentious whether these models of time travel really allow for changing the past. See Smith (1997, 2015) and Baron (2017) for arguments against, and see Law (Forthcoming) for a response.

[11]   The first of these occurs in the third episode of season five, “Jughead,” from 39:44-41:19,  and the second scene occurs in the first episode of season five, “Because You Left,” from 29:30-34:34.

[12]   For example, suppose I travel back in time by twenty seconds but set my machine to a destination on the other side of the planet. Presumably, my appearance in the past will not have any causal consequences across the globe, despite its occurring twenty seconds earlier than my departure, and thus no causal loop will be generated. For a similar example, see Hanley (2004: 130).

[13]   On the other models, there is no reason to think that Tim can’t kill Grandfather, for doing so would preclude Tim’s future birth in the new timeline (the new branch or hyper-time), but Grandfather would not have been killed in the original, and thus Tim is still born in that timeline.

[14] See Kratzer (1977).

[15]   While Lewis’s (1776: 149-152) influential response to the Paradox also relies on the Kratzer semantics for “can,” his proposed resolution is slightly different, for he sees the fact that Grandfather lives as one that it would be illegitimate to hold fixed. Holding it fixed, he thinks, amounts to “fatalist trickery,” as such a fact “is an irrelevant fact about the future masquerading as a relevant fact about the past” (1976: 151).

[16]   See Vihvelin (1996).

Baron, Sam (2017). “Back to the Unchanging Past,” Pacific Philosophical Quarterly 98: 129–147.

Brier, Bob (1973). “Magicians, Alarm Clocks, and Backward Causation,” Southern Journal of Philosophy 11: 359-364.

Goddu, G. C. (2003). “Time Travel and Changing the Past (or How to Kill Yourself and Live to Tell the Tale),” Ratio 16: 16-32.

Hanley, Richard (2004). “No End in Sight: Causal Loops in Philosophy, Physics, and Fiction,” Synthese 141: 123-152.

Horwich, Paul (1997). Asymmetries In Time: Problems In the Philosophy of Science . Cambridge, MA: MIT Press.

Kratzer, Angelika (1977). “What ‘Must’ and ‘Can’ Must and Can Mean,” Linguistics and Philosophy 1: 337-355.

Law, Andrew (Forthcoming). “The Puzzle of Hyper-Change,” Ratio .

Lewis, David (1976). “The Paradoxes of Time Travel,” American Philosophical Quarterly 13: 145-152.

Meiland, Jack (1974). “A Two-Dimensional Passage Model of Time for Time Travel,” Philosophical Studies 26: 152-173.

Smith, Nicholas J. J. (1997). “Bananas Enough for Time Travel?” The British Journal for the Philosophy of Science 48: 363-389.

Smith, Nicholas J. J. (2015). “Why Time Travellers (Still) Cannot Change the Past,” Revista Portuguesa de Filosofia 71: 677–694.

van Inwagen, Peter (2010). “Changing the Past,” in D. Zimmerman, ed., Oxford Studies in Metaphysics , vol. 5. Oxford: Oxford University Press.

Vihvelin, Kadri (1996). “What Time Travelers Cannot Do,” Philosophical Studies 81: 315-330.

Wasserman, Ryan (2018). Paradoxes of Time Travel . New York: Oxford University Press.

Related Essays

Philosophy of Space and Time: Are  the  Past and Future Real ?  by Dan Peterson

Personal Identity by Chad Vance

Free Will and Free Choice  by Jonah Nagashima

Translation

This essay has been translated into Italian for the Italian cultural magazine  L’Indiscreto .

About the Author

Taylor W. Cyr is an Assistant Professor of Philosophy at Samford University. His main research interests lie at the intersection of ethics and metaphysics, including such topics as free will, moral responsibility, death, and time. His work has appeared in such journals as Ethics , Philosophical Studies , Philosophical Quarterly , and Erkenntnis . TaylorWCyr.com

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Paradoxes of Time Travel

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

Reviewed by John W. Carroll, North Carolina State

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Sure I can; here it is.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Time Travel and Modern Physics

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 paradoxical. The most famous paradox is the grandfather paradox: you travel back in time and kill your grandfather, thereby preventing your own existence. To avoid inconsistency some circumstance will have to occur which makes you fail in this attempt to kill your grandfather. Doesn’t this require some implausible constraint on otherwise unrelated circumstances? We examine such worries in the context of modern physics.

1. Paradoxes Lost?

2. topology and constraints, 3. the general possibility of time travel in general relativity, 4. two toy models, 5. slightly more realistic models of time travel, 6. the possibility of time travel redux, 7. even if there are constraints, so what, 8. computational models, 9. quantum mechanics to the rescue, 10. conclusions, other internet resources, related entries.

• Supplement: Remarks and Limitations on the Toy Models

Modern physics strips away many aspects of the manifest image of time. Time as it appears in the equations of classical mechanics has no need for a distinguished present moment, for example. Relativity theory leads to even sharper contrasts. It replaces absolute simultaneity, according to which it is possible to unambiguously determine the time order of distant events, with relative simultaneity: extending an “instant of time” throughout space is not unique, but depends on the state of motion of an observer. More dramatically, in general relativity the mathematical properties of time (or better, of spacetime)—its topology and geometry—depend upon how matter is arranged rather than being fixed once and for all. So physics can be, and indeed has to be, formulated without treating time as a universal, fixed background structure. Since general relativity represents gravity through spacetime geometry, the allowed geometries must be as varied as the ways in which matter can be arranged. Alongside geometrical models used to describe the solar system, black holes, and much else, the scope of variation extends to include some exotic structures unlike anything astrophysicists have observed. In particular, there are spacetime geometries with curves that loop back on themselves: closed timelike curves (CTCs), which describe the possible trajectory of an observer who returns exactly back to their earlier state—without any funny business, such as going faster than the speed of light. These geometries satisfy the relevant physical laws, the equations of general relativity, and in that sense time travel is physically possible.

Yet circular time generates paradoxes, familiar from science fiction stories featuring time travel: [ 1 ]

• Consistency: Kurt plans to murder his own grandfather Adolph, by traveling along a CTC to an appropriate moment in the past. He is an able marksman, and waits until he has a clear shot at grandpa. Normally he would not miss. Yet if he succeeds, there is no way that he will then exist to plan and carry out the mission. Kurt pulls the trigger: what can happen?
• Underdetermination: Suppose that Kurt first travels back in order to give his earlier self a copy of How to Build a Time Machine. This is the same book that allows him to build a time machine, which he then carries with him on his journey to the past. Who wrote the book?
• Easy Knowledge: A fan of classical music enhances their computer with a circuit that exploits a CTC. This machine efficiently solves problems at a higher level of computational complexity than conventional computers, leading (among other things) to finding the smallest circuits that can generate Bach’s oeuvre—and to compose new pieces in the same style. Such easy knowledge is at odds with our understanding of our epistemic predicament. (This third paradox has not drawn as much attention.)

The first two paradoxes were once routinely taken to show that solutions with CTCs should be rejected—with charges varying from violating logic, to being “physically unreasonable”, to undermining the notion of free will. Closer analysis of the paradoxes has largely reversed this consensus. Physicists have discovered many solutions with CTCs and have explored their properties in pursuing foundational questions, such as whether physics is compatible with the idea of objective temporal passage (starting with Gödel 1949). Philosophers have also used time travel scenarios to probe questions about, among other things, causation, modality, free will, and identity (see, e.g., Earman 1972 and Lewis’s seminal 1976 paper).

We begin below with Consistency , turning to the other paradoxes in later sections. A standard, stone-walling response is to insist that the past cannot be changed, as a matter of logic, even by a time traveler (e.g., Gödel 1949, Clarke 1977, Horwich 1987). Adolph cannot both die and survive, as a matter of logic, so any scheme to alter the past must fail. In many of the best time travel fictions, the actions of a time traveler are constrained in novel and unexpected ways. Attempts to change the past fail, and they fail, often tragically, in just such a way that they set the stage for the time traveler’s self-defeating journey. The first question is whether there is an analog of the consistent story when it comes to physics in the presence of CTCs. As we will see, there is a remarkable general argument establishing the existence of consistent solutions. Yet a second question persists: why can’t time-traveling Kurt kill his own grandfather? Doesn’t the necessity of failures to change the past put unusual and unexpected constraints on time travelers, or objects that move along CTCs? The same argument shows that there are in fact no constraints imposed by the existence of CTCs, in some cases. After discussing this line of argument, we will turn to the palatability and further implications of such constraints if they are required, and then turn to the implications of quantum mechanics.

Wheeler and Feynman (1949) were the first to claim that the fact that nature is continuous could be used to argue that causal influences from later events to earlier events, as are made possible by time travel, will not lead to paradox without the need for any constraints. Maudlin (1990) showed how to make their argument precise and more general, and argued that nonetheless it was not completely general.

Imagine the following set-up. We start off having a camera with a black and white film ready to take a picture of whatever comes out of the time machine. An object, in fact a developed film, comes out of the time machine. We photograph it, and develop the film. The developed film is subsequently put in the time machine, and set to come out of the time machine at the time the picture is taken. This surely will create a paradox: the developed film will have the opposite distribution of black, white, and shades of gray, from the object that comes out of the time machine. For developed black and white films (i.e., negatives) have the opposite shades of gray from the objects they are pictures of. But since the object that comes out of the time machine is the developed film itself it we surely have a paradox.

However, it does not take much thought to realize that there is no paradox here. What will happen is that a uniformly gray picture will emerge, which produces a developed film that has exactly the same uniform shade of gray. No matter what the sensitivity of the film is, as long as the dependence of the brightness of the developed film depends in a continuous manner on the brightness of the object being photographed, there will be a shade of gray that, when photographed, will produce exactly the same shade of gray on the developed film. This is the essence of Wheeler and Feynman’s idea. Let us first be a bit more precise and then a bit more general.

For simplicity let us suppose that the film is always a uniform shade of gray (i.e., at any time the shade of gray does not vary by location on the film). The possible shades of gray of the film can then be represented by the (real) numbers from 0, representing pure black, to 1, representing pure white.

Let us now distinguish various stages in the chronological order of the life of the film. In stage \(S_1\) the film is young; it has just been placed in the camera and is ready to be exposed. It is then exposed to the object that comes out of the time machine. (That object in fact is a later stage of the film itself). By the time we come to stage \(S_2\) of the life of the film, it has been developed and is about to enter the time machine. Stage \(S_3\) occurs just after it exits the time machine and just before it is photographed. Stage \(S_4\) occurs after it has been photographed and before it starts fading away. Let us assume that the film starts out in stage \(S_1\) in some uniform shade of gray, and that the only significant change in the shade of gray of the film occurs between stages \(S_1\) and \(S_2\). During that period it acquires a shade of gray that depends on the shade of gray of the object that was photographed. In other words, the shade of gray that the film acquires at stage \(S_2\) depends on the shade of gray it has at stage \(S_3\). The influence of the shade of gray of the film at stage \(S_3\), on the shade of gray of the film at stage \(S_2\), can be represented as a mapping, or function, from the real numbers between 0 and 1 (inclusive), to the real numbers between 0 and 1 (inclusive). Let us suppose that the process of photography is such that if one imagines varying the shade of gray of an object in a smooth, continuous manner then the shade of gray of the developed picture of that object will also vary in a smooth, continuous manner. This implies that the function in question will be a continuous function. Now any continuous function from the real numbers between 0 and 1 (inclusive) to the real numbers between 0 and 1 (inclusive) must map at least one number to itself. One can quickly convince oneself of this by graphing such functions. For one will quickly see that any continuous function \(f\) from \([0,1]\) to \([0,1]\) must intersect the line \(x=y\) somewhere, and thus there must be at least one point \(x\) such that \(f(x)=x\). Such points are called fixed points of the function. Now let us think about what such a fixed point represents. It represents a shade of gray such that, when photographed, it will produce a developed film with exactly that same shade of gray. The existence of such a fixed point implies a solution to the apparent paradox.

Let us now be more general and allow color photography. One can represent each possible color of an object (of uniform color) by the proportions of blue, green and red that make up that color. (This is why television screens can produce all possible colors.) Thus one can represent all possible colors of an object by three points on three orthogonal lines \(x, y\) and \(z\), that is to say, by a point in a three-dimensional cube. This cube is also known as the “Cartesian product” of the three line segments. Now, one can also show that any continuous map from such a cube to itself must have at least one fixed point. So color photography can not be used to create time travel paradoxes either!

Even more generally, consider some system \(P\) which, as in the above example, has the following life. It starts in some state \(S_1\), it interacts with an object that comes out of a time machine (which happens to be its older self), it travels back in time, it interacts with some object (which happens to be its younger self), and finally it grows old and dies. Let us assume that the set of possible states of \(P\) can be represented by a Cartesian product of \(n\) closed intervals of the reals, i.e., let us assume that the topology of the state-space of \(P\) is isomorphic to a finite Cartesian product of closed intervals of the reals. Let us further assume that the development of \(P\) in time, and the dependence of that development on the state of objects that it interacts with, is continuous. Then, by a well-known fixed point theorem in topology (see, e.g., Hocking & Young 1961: 273), no matter what the nature of the interaction is, and no matter what the initial state of the object is, there will be at least one state \(S_3\) of the older system (as it emerges from the time travel machine) that will influence the initial state \(S_1\) of the younger system (when it encounters the older system) so that, as the younger system becomes older, it develops exactly into state \(S_3\). Thus without imposing any constraints on the initial state \(S_1\) of the system \(P\), we have shown that there will always be perfectly ordinary, non-paradoxical, solutions, in which everything that happens, happens according to the usual laws of development. Of course, there is looped causation, hence presumably also looped explanation, but what do you expect if there is looped time?

Unfortunately, for the fan of time travel, a little reflection suggests that there are systems for which the needed fixed point theorem does not hold. Imagine, for instance, that we have a dial that can only rotate in a plane. We are going to put the dial in the time machine. Indeed we have decided that if we see the later stage of the dial come out of the time machine set at angle \(x\), then we will set the dial to \(x+90\), and throw it into the time machine. Now it seems we have a paradox, since the mapping that consists of a rotation of all points in a circular state-space by 90 degrees does not have a fixed point. And why wouldn’t some state-spaces have the topology of a circle?

However, we have so far not used another continuity assumption which is also a reasonable assumption. So far we have only made the following demand: the state the dial is in at stage \(S_2\) must be a continuous function of the state of the dial at stage \(S_3\). But, the state of the dial at stage \(S_2\) is arrived at by taking the state of the dial at stage \(S_1\), and rotating it over some angle. It is not merely the case that the effect of the interaction, namely the state of the dial at stage \(S_2\), should be a continuous function of the cause, namely the state of the dial at stage \(S_3\). It is additionally the case that path taken to get there, the way the dial is rotated between stages \(S_1\) and \(S_2\) must be a continuous function of the state at stage \(S_3\). And, rather surprisingly, it turns out that this can not be done. Let us illustrate what the problem is before going to a more general demonstration that there must be a fixed point solution in the dial case.

Forget time travel for the moment. Suppose that you and I each have a watch with a single dial neither of which is running. My watch is set at 12. You are going to announce what your watch is set at. My task is going to be to adjust my watch to yours no matter what announcement you make. And my actions should have a continuous (single valued) dependence on the time that you announce. Surprisingly, this is not possible! For instance, suppose that if you announce “12”, then I achieve that setting on my watch by doing nothing. Now imagine slowly and continuously increasing the announced times, starting at 12. By continuity, I must achieve each of those settings by rotating my dial to the right. If at some point I switch and achieve the announced goal by a rotation of my dial to the left, I will have introduced a discontinuity in my actions, a discontinuity in the actions that I take as a function of the announced angle. So I will be forced, by continuity, to achieve every announcement by rotating the dial to the right. But, this rotation to the right will have to be abruptly discontinued as the announcements grow larger and I eventually approach 12 again, since I achieved 12 by not rotating the dial at all. So, there will be a discontinuity at 12 at the latest. In general, continuity of my actions as a function of announced times can not be maintained throughout if I am to be able to replicate all possible settings. Another way to see the problem is that one can similarly reason that, as one starts with 12, and imagines continuously making the announced times earlier, one will be forced, by continuity, to achieve the announced times by rotating the dial to the left. But the conclusions drawn from the assumption of continuous increases and the assumption of continuous decreases are inconsistent. So we have an inconsistency following from the assumption of continuity and the assumption that I always manage to set my watch to your watch. So, a dial developing according to a continuous dynamics from a given initial state, can not be set up so as to react to a second dial, with which it interacts, in such a way that it is guaranteed to always end up set at the same angle as the second dial. Similarly, it can not be set up so that it is guaranteed to always end up set at 90 degrees to the setting of the second dial. All of this has nothing to do with time travel. However, the impossibility of such set ups is what prevents us from enacting the rotation by 90 degrees that would create paradox in the time travel setting.

Let us now give the positive result that with such dials there will always be fixed point solutions, as long as the dynamics is continuous. Let us call the state of the dial before it interacts with its older self the initial state of the dial. And let us call the state of the dial after it emerges from the time machine the final state of the dial. There is also an intermediate state of the dial, after it interacts with its older self and before it is put into the time machine. We can represent the initial or intermediate states of the dial, before it goes into the time machine, as an angle \(x\) in the horizontal plane and the final state of the dial, after it comes out of the time machine, as an angle \(y\) in the vertical plane. All possible \(\langle x,y\rangle\) pairs can thus be visualized as a torus with each \(x\) value picking out a vertical circular cross-section and each \(y\) picking out a point on that cross-section. See figure 1 .

Figure 1 [An extended description of figure 1 is in the supplement.]

Suppose that the dial starts at angle \(i\) which picks out vertical circle \(I\) on the torus. The initial angle \(i\) that the dial is at before it encounters its older self, and the set of all possible final angles that the dial can have when it emerges from the time machine is represented by the circle \(I\) on the torus (see figure 1 ). Given any possible angle of the emerging dial, the dial initially at angle \(i\) will develop to some other angle. One can picture this development by rotating each point on \(I\) in the horizontal direction by the relevant amount. Since the rotation has to depend continuously on the angle of the emerging dial, circle \(I\) during this development will deform into some loop \(L\) on the torus. Loop \(L\) thus represents all possible intermediate angles \(x\) that the dial is at when it is thrown into the time machine, given that it started at angle \(i\) and then encountered a dial (its older self) which was at angle \(y\) when it emerged from the time machine. We therefore have consistency if \(x=y\) for some \(x\) and \(y\) on loop \(L\). Now, let loop \(C\) be the loop which consists of all the points on the torus for which \(x=y\). Ring \(I\) intersects \(C\) at point \(\langle i,i\rangle\). Obviously any continuous deformation of \(I\) must still intersect \(C\) somewhere. So \(L\) must intersect \(C\) somewhere, say at \(\langle j,j\rangle\). But that means that no matter how the development of the dial starting at \(I\) depends on the angle of the emerging dial, there will be some angle for the emerging dial such that the dial will develop exactly into that angle (by the time it enters the time machine) under the influence of that emerging dial. This is so no matter what angle one starts with, and no matter how the development depends on the angle of the emerging dial. Thus even for a circular state-space there are no constraints needed other than continuity.

Unfortunately there are state-spaces that escape even this argument. Consider for instance a pointer that can be set to all values between 0 and 1, where 0 and 1 are not possible values. That is, suppose that we have a state-space that is isomorphic to an open set of real numbers. Now suppose that we have a machine that sets the pointer to half the value that the pointer is set at when it emerges from the time machine.

Figure 2 [An extended description of figure 2 is in the supplement.]

Suppose the pointer starts at value \(I\). As before we can represent the combination of this initial position and all possible final positions by the line \(I\). Under the influence of the pointer coming out of the time machine the pointer value will develop to a value that equals half the value of the final value that it encountered. We can represent this development as the continuous deformation of line \(I\) into line \(L\), which is indicated by the arrows in figure 2 . This development is fully continuous. Points \(\langle x,y\rangle\) on line \(I\) represent the initial position \(x=I\) of the (young) pointer, and the position \(y\) of the older pointer as it emerges from the time machine. Points \(\langle x,y\rangle\) on line \(L\) represent the position \(x\) that the younger pointer should develop into, given that it encountered the older pointer emerging from the time machine set at position \(y\). Since the pointer is designed to develop to half the value of the pointer that it encounters, the line \(L\) corresponds to \(x=1/2 y\). We have consistency if there is some point such that it develops into that point, if it encounters that point. Thus, we have consistency if there is some point \(\langle x,y\rangle\) on line \(L\) such that \(x=y\). However, there is no such point: lines \(L\) and \(C\) do not intersect. Thus there is no consistent solution, despite the fact that the dynamics is fully continuous.

Of course if 0 were a possible value, \(L\) and \(C\) would intersect at 0. This is surprising and strange: adding one point to the set of possible values of a quantity here makes the difference between paradox and peace. One might be tempted to just add the extra point to the state-space in order to avoid problems. After all, one might say, surely no measurements could ever tell us whether the set of possible values includes that exact point or not. Unfortunately there can be good theoretical reasons for supposing that some quantity has a state-space that is open: the set of all possible speeds of massive objects in special relativity surely is an open set, since it includes all speeds up to, but not including, the speed of light. Quantities that have possible values that are not bounded also lead to counter examples to the presented fixed point argument. And it is not obvious to us why one should exclude such possibilities. So the argument that no constraints are needed is not fully general.

An interesting question of course is: exactly for which state-spaces must there be such fixed points? The arguments above depend on a well-known fixed point theorem (due to Schauder) that guarantees the existence of a fixed point for compact, convex state spaces. We do not know what subsequent extensions of this result imply regarding fixed points for a wider variety of systems, or whether there are other general results along these lines. (See Kutach 2003 for more on this issue.)

A further interesting question is whether this line of argument is sufficient to resolve Consistency (see also Dowe 2007). When they apply, these results establish the existence of a solution, such as the shade of uniform gray in the first example. But physicists routinely demand more than merely the existence of a solution, namely that solutions to the equations are stable—such that “small” changes of the initial state lead to “small” changes of the resulting trajectory. (Clarifying the two senses of “small” in this statement requires further work, specifying the relevant topology.) Stability in this sense underwrites the possibility of applying equations to real systems given our inability to fix initial states with indefinite precision. (See Fletcher 2020 for further discussion.) The fixed point theorems guarantee that for an initial state \(S_1\) there is a solution, but this solution may not be “close” to the solution for a nearby initial state, \(S'\). We are not aware of any proofs that the solutions guaranteed to exist by the fixed point theorems are also stable in this sense.

Time travel has recently been discussed quite extensively in the context of general relativity. General relativity places few constraints on the global structure of space and time. This flexibility leads to a possibility first described in print by Hermann Weyl:

Every world-point is the origin of the double-cone of the active future and the passive past [i.e., the two lobes of the light cone]. Whereas in the special theory of relativity these two portions are separated by an intervening region, it is certainly possible in the present case [i.e., general relativity] for the cone of the active future to overlap with that of the passive past; so that, in principle, it is possible to experience events now that will in part be an effect of my future resolves and actions. Moreover, it is not impossible for a world-line (in particular, that of my body), although it has a timelike direction at every point, to return to the neighborhood of a point which it has already once passed through. (Weyl 1918/1920 [1952: 274])

A time-like curve is simply a space-time trajectory such that the speed of light is never equaled or exceeded along this trajectory. Time-like curves represent possible trajectories of ordinary objects. In general relativity a curve that is everywhere timelike locally can nonetheless loop back on itself, forming a CTC. Weyl makes the point vividly in terms of the light cones: along such a curve, the future lobe of the light cone (the “active future”) intersects the past lobe of the light cone (the “passive past”). Traveling along such a curve one would never exceed the speed of light, and yet after a certain amount of (proper) time one would return to a point in space-time that one previously visited. Or, by staying close to such a CTC, one could come arbitrarily close to a point in space-time that one previously visited. General relativity, in a straightforward sense, allows time travel: there appear to be many space-times compatible with the fundamental equations of general relativity in which there are CTC’s. Space-time, for instance, could have a Minkowski metric everywhere, and yet have CTC’s everywhere by having the temporal dimension (topologically) rolled up as a circle. Or, one can have wormhole connections between different parts of space-time which allow one to enter “mouth \(A\)” of such a wormhole connection, travel through the wormhole, exit the wormhole at “mouth \(B\)” and re-enter “mouth \(A\)” again. CTCs can even arise when the spacetime is topologically \(\mathbb{R}^4\), due to the “tilting” of light cones produced by rotating matter (as in Gödel 1949’s spacetime).

General relativity thus appears to provide ample opportunity for time travel. Note that just because there are CTC’s in a space-time, this does not mean that one can get from any point in the space-time to any other point by following some future directed timelike curve—there may be insurmountable practical obstacles. In Gödel’s spacetime, it is the case that there are CTCs passing through every point in the spacetime. Yet these CTCs are not geodesics, so traversing them requires acceleration. Calculations of the minimal fuel required to travel along the appropriate curve should discourage any would-be time travelers (Malament 1984, 1985; Manchak 2011). But more generally CTCs may be confined to smaller regions; some parts of space-time can have CTC’s while other parts do not. Let us call the part of a space-time that has CTC’s the “time travel region” of that space-time, while calling the rest of that space-time the “normal region”. More precisely, the “time travel region” consists of all the space-time points \(p\) such that there exists a (non-zero length) timelike curve that starts at \(p\) and returns to \(p\). Now let us turn to examining space-times with CTC’s a bit more closely for potential problems.

In order to get a feeling for the sorts of implications that closed timelike curves can have, it may be useful to consider two simple models. In space-times with closed timelike curves the traditional initial value problem cannot be framed in the usual way. For it presupposes the existence of Cauchy surfaces, and if there are CTCs then no Cauchy surface exists. (A Cauchy surface is a spacelike surface such that every inextendable timelike curve crosses it exactly once. One normally specifies initial conditions by giving the conditions on such a surface.) Nonetheless, if the topological complexities of the manifold are appropriately localized, we can come quite close. Let us call an edgeless spacelike surface \(S\) a quasi-Cauchy surface if it divides the rest of the manifold into two parts such that

• every point in the manifold can be connected by a timelike curve to \(S\), and
• any timelike curve which connects a point in one region to a point in the other region intersects \(S\) exactly once.

It is obvious that a quasi-Cauchy surface must entirely inhabit the normal region of the space-time; if any point \(p\) of \(S\) is in the time travel region, then any timelike curve which intersects \(p\) can be extended to a timelike curve which intersects \(S\) near \(p\) again. In extreme cases of time travel, a model may have no normal region at all (e.g., Minkowski space-time rolled up like a cylinder in a time-like direction), in which case our usual notions of temporal precedence will not apply. But temporal anomalies like wormholes (and time machines) can be sufficiently localized to permit the existence of quasi-Cauchy surfaces.

Given a timelike orientation, a quasi-Cauchy surface unproblematically divides the manifold into its past (i.e., all points that can be reached by past-directed timelike curves from \(S)\) and its future (ditto mutatis mutandis ). If the whole past of \(S\) is in the normal region of the manifold, then \(S\) is a partial Cauchy surface : every inextendable timelike curve which exists to the past of \(S\) intersects \(S\) exactly once, but (if there is time travel in the future) not every inextendable timelike curve which exists to the future of \(S\) intersects \(S\). Now we can ask a particularly clear question: consider a manifold which contains a time travel region, but also has a partial Cauchy surface \(S\), such that all of the temporal funny business is to the future of \(S\). If all you could see were \(S\) and its past, you would not know that the space-time had any time travel at all. The question is: are there any constraints on the sort of data which can be put on \(S\) and continued to a global solution of the dynamics which are different from the constraints (if any) on the data which can be put on a Cauchy surface in a simply connected manifold and continued to a global solution? If there is time travel to our future, might we we able to tell this now, because of some implied oddity in the arrangement of present things?

It is not at all surprising that there might be constraints on the data which can be put on a locally space-like surface which passes through the time travel region: after all, we never think we can freely specify what happens on a space-like surface and on another such surface to its future, but in this case the surface at issue lies to its own future. But if there were particular constraints for data on a partial Cauchy surface then we would apparently need to have to rule out some sorts of otherwise acceptable states on \(S\) if there is to be time travel to the future of \(S\). We then might be able to establish that there will be no time travel in the future by simple inspection of the present state of the universe. As we will see, there is reason to suspect that such constraints on the partial Cauchy surface are non-generic. But we are getting ahead of ourselves: first let’s consider the effect of time travel on a very simple dynamics.

The simplest possible example is the Newtonian theory of perfectly elastic collisions among equally massive particles in one spatial dimension. The space-time is two-dimensional, so we can represent it initially as the Euclidean plane, and the dynamics is completely specified by two conditions. When particles are traveling freely, their world lines are straight lines in the space-time, and when two particles collide, they exchange momenta, so the collision looks like an “\(X\)” in space-time, with each particle changing its momentum at the impact. [ 2 ] The dynamics is purely local, in that one can check that a set of world-lines constitutes a model of the dynamics by checking that the dynamics is obeyed in every arbitrarily small region. It is also trivial to generate solutions from arbitrary initial data if there are no CTCs: given the initial positions and momenta of a set of particles, one simply draws a straight line from each particle in the appropriate direction and continues it indefinitely. Once all the lines are drawn, the worldline of each particle can be traced from collision to collision. The boundary value problem for this dynamics is obviously well-posed: any set of data at an instant yields a unique global solution, constructed by the method sketched above.

What happens if we change the topology of the space-time by hand to produce CTCs? The simplest way to do this is depicted in figure 3 : we cut and paste the space-time so it is no longer simply connected by identifying the line \(L-\) with the line \(L+\). Particles “going in” to \(L+\) from below “emerge” from \(L-\) , and particles “going in” to \(L-\) from below “emerge” from \(L+\).

Figure 3: Inserting CTCs by Cut and Paste. [An extended description of figure 3 is in the supplement.]

How is the boundary-value problem changed by this alteration in the space-time? Before the cut and paste, we can put arbitrary data on the simultaneity slice \(S\) and continue it to a unique solution. After the change in topology, \(S\) is no longer a Cauchy surface, since a CTC will never intersect it, but it is a partial Cauchy surface. So we can ask two questions. First, can arbitrary data on \(S\) always be continued to a global solution? Second, is that solution unique? If the answer to the first question is \(no\), then we have a backward-temporal constraint: the existence of the region with CTCs places constraints on what can happen on \(S\) even though that region lies completely to the future of \(S\). If the answer to the second question is \(no\), then we have an odd sort of indeterminism, analogous to the unwritten book: the complete physical state on \(S\) does not determine the physical state in the future, even though the local dynamics is perfectly deterministic and even though there is no other past edge to the space-time region in \(S\)’s future (i.e., there is nowhere else for boundary values to come from which could influence the state of the region).

In this case the answer to the first question is yes and to the second is no : there are no constraints on the data which can be put on \(S\), but those data are always consistent with an infinitude of different global solutions. The easy way to see that there always is a solution is to construct the minimal solution in the following way. Start drawing straight lines from \(S\) as required by the initial data. If a line hits \(L-\) from the bottom, just continue it coming out of the top of \(L+\) in the appropriate place, and if a line hits \(L+\) from the bottom, continue it emerging from \(L-\) at the appropriate place. Figure 4 represents the minimal solution for a single particle which enters the time-travel region from the left:

Figure 4: The Minimal Solution. [An extended description of figure 4 is in the supplement.]

The particle “travels back in time” three times. It is obvious that this minimal solution is a global solution, since the particle always travels inertially.

But the same initial state on \(S\) is also consistent with other global solutions. The new requirement imposed by the topology is just that the data going into \(L+\) from the bottom match the data coming out of \(L-\) from the top, and the data going into \(L-\) from the bottom match the data coming out of \(L+\) from the top. So we can add any number of vertical lines connecting \(L-\) and \(L+\) to a solution and still have a solution. For example, adding a few such lines to the minimal solution yields:

Figure 5: A Non-Minimal Solution. [An extended description of figure 5 is in the supplement.]

The particle now collides with itself twice: first before it reaches \(L+\) for the first time, and again shortly before it exits the CTC region. From the particle’s point of view, it is traveling to the right at a constant speed until it hits an older version of itself and comes to rest. It remains at rest until it is hit from the right by a younger version of itself, and then continues moving off, and the same process repeats later. It is clear that this is a global model of the dynamics, and that any number of distinct models could be generating by varying the number and placement of vertical lines.

Knowing the data on \(S\), then, gives us only incomplete information about how things will go for the particle. We know that the particle will enter the CTC region, and will reach \(L+\), we know that it will be the only particle in the universe, we know exactly where and with what speed it will exit the CTC region. But we cannot determine how many collisions the particle will undergo (if any), nor how long (in proper time) it will stay in the CTC region. If the particle were a clock, we could not predict what time it would indicate when exiting the region. Furthermore, the dynamics gives us no handle on what to think of the various possibilities: there are no probabilities assigned to the various distinct possible outcomes.

Changing the topology has changed the mathematics of the situation in two ways, which tend to pull in opposite directions. On the one hand, \(S\) is no longer a Cauchy surface, so it is perhaps not surprising that data on \(S\) do not suffice to fix a unique global solution. But on the other hand, there is an added constraint: data “coming out” of \(L-\) must exactly match data “going in” to \(L+\), even though what comes out of \(L-\) helps to determine what goes into \(L+\). This added consistency constraint tends to cut down on solutions, although in this case the additional constraint is more than outweighed by the freedom to consider various sorts of data on \({L+}/{L-}\).

The fact that the extra freedom outweighs the extra constraint also points up one unexpected way that the supposed paradoxes of time travel may be overcome. Let’s try to set up a paradoxical situation using the little closed time loop above. If we send a single particle into the loop from the left and do nothing else, we know exactly where it will exit the right side of the time travel region. Now suppose we station someone at the other side of the region with the following charge: if the particle should come out on the right side, the person is to do something to prevent the particle from going in on the left in the first place. In fact, this is quite easy to do: if we send a particle in from the right, it seems that it can exit on the left and deflect the incoming left-hand particle.

Carrying on our reflection in this way, we further realize that if the particle comes out on the right, we might as well send it back in order to deflect itself from entering in the first place. So all we really need to do is the following: set up a perfectly reflecting particle mirror on the right-hand side of the time travel region, and launch the particle from the left so that— if nothing interferes with it —it will just barely hit \(L+\). Our paradox is now apparently complete. If, on the one hand, nothing interferes with the particle it will enter the time-travel region on the left, exit on the right, be reflected from the mirror, re-enter from the right, and come out on the left to prevent itself from ever entering. So if it enters, it gets deflected and never enters. On the other hand, if it never enters then nothing goes in on the left, so nothing comes out on the right, so nothing is reflected back, and there is nothing to deflect it from entering. So if it doesn’t enter, then there is nothing to deflect it and it enters. If it enters, then it is deflected and doesn’t enter; if it doesn’t enter then there is nothing to deflect it and it enters: paradox complete.

But at least one solution to the supposed paradox is easy to construct: just follow the recipe for constructing the minimal solution, continuing the initial trajectory of the particle (reflecting it the mirror in the obvious way) and then read of the number and trajectories of the particles from the resulting diagram. We get the result of figure 6 :

Figure 6: Resolving the “Paradox”. [An extended description of figure 6 is in the supplement.]

As we can see, the particle approaching from the left never reaches \(L+\): it is deflected first by a particle which emerges from \(L-\). But it is not deflected by itself , as the paradox suggests, it is deflected by another particle. Indeed, there are now four particles in the diagram: the original particle and three particles which are confined to closed time-like curves. It is not the leftmost particle which is reflected by the mirror, nor even the particle which deflects the leftmost particle; it is another particle altogether.

The paradox gets it traction from an incorrect presupposition. If there is only one particle in the world at \(S\) then there is only one particle which could participate in an interaction in the time travel region: the single particle would have to interact with its earlier (or later) self. But there is no telling what might come out of \(L-\): the only requirement is that whatever comes out must match what goes in at \(L+\). So if you go to the trouble of constructing a working time machine, you should be prepared for a different kind of disappointment when you attempt to go back and kill yourself: you may be prevented from entering the machine in the first place by some completely unpredictable entity which emerges from it. And once again a peculiar sort of indeterminism appears: if there are many self-consistent things which could prevent you from entering, there is no telling which is even likely to materialize. This is just like the case of the unwritten book: the book is never written, so nothing determines what fills its pages.

So when the freedom to put data on \(L-\) outweighs the constraint that the same data go into \(L+\), instead of paradox we get an embarrassment of riches: many solution consistent with the data on \(S\), or many possible books. To see a case where the constraint “outweighs” the freedom, we need to construct a very particular, and frankly artificial, dynamics and topology. Consider the space of all linear dynamics for a scalar field on a lattice. (The lattice can be though of as a simple discrete space-time.) We will depict the space-time lattice as a directed graph. There is to be a scalar field defined at every node of the graph, whose value at a given node depends linearly on the values of the field at nodes which have arrows which lead to it. Each edge of the graph can be assigned a weighting factor which determines how much the field at the input node contributes to the field at the output node. If we name the nodes by the letters a , b , c , etc., and the edges by their endpoints in the obvious way, then we can label the weighting factors by the edges they are associated with in an equally obvious way.

Suppose that the graph of the space-time lattice is acyclic , as in figure 7 . (A graph is Acyclic if one can not travel in the direction of the arrows and go in a loop.)

Figure 7: An Acyclic Lattice. [An extended description of figure 7 is in the supplement.]

It is easy to regard a set of nodes as the analog of a Cauchy surface, e.g., the set \(\{a, b, c\}\), and it is obvious if arbitrary data are put on those nodes the data will generate a unique solution in the future. [ 3 ] If the value of the field at node \(a\) is 3 and at node \(b\) is 7, then its value at node \(d\) will be \(3W_{ad}\) and its value at node \(e\) will be \(3W_{ae} + 7W_{be}\). By varying the weighting factors we can adjust the dynamics, but in an acyclic graph the future evolution of the field will always be unique.

Let us now again artificially alter the topology of the lattice to admit CTCs, so that the graph now is cyclic. One of the simplest such graphs is depicted in figure 8 : there are now paths which lead from \(z\) back to itself, e.g., \(z\) to \(y\) to \(z\).

Figure 8: Time Travel on a Lattice. [An extended description of figure 8 is in the supplement.]

Can we now put arbitrary data on \(v\) and \(w\), and continue that data to a global solution? Will the solution be unique?

In the generic case, there will be a solution and the solution will be unique. The equations for the value of the field at \(x, y\), and \(z\) are:

Solving these equations for \(z\) yields

which gives a unique value for \(z\) in the generic case. But looking at the space of all possible dynamics for this lattice (i.e., the space of all possible weighting factors), we find a singularity in the case where \(1-W_{zx}W_{xz} - W_{zy}W_{yz} = 0\). If we choose weighting factors in just this way, then arbitrary data at \(v\) and \(w\) cannot be continued to a global solution. Indeed, if the scalar field is everywhere non-negative, then this particular choice of dynamics puts ironclad constraints on the value of the field at \(v\) and \(w\): the field there must be zero (assuming \(W_{vx}\) and \(W_{wy}\) to be non-zero), and similarly all nodes in their past must have field value zero. If the field can take negative values, then the values at \(v\) and \(w\) must be so chosen that \(vW_{vx}W_{xz} = -wW_{wy}W_{yz}\). In either case, the field values at \(v\) and \(w\) are severely constrained by the existence of the CTC region even though these nodes lie completely to the past of that region. It is this sort of constraint which we find to be unlike anything which appears in standard physics.

Our toy models suggest three things. The first is that it may be impossible to prove in complete generality that arbitrary data on a partial Cauchy surface can always be continued to a global solution: our artificial case provides an example where it cannot. The second is that such odd constraints are not likely to be generic: we had to delicately fine-tune the dynamics to get a problem. The third is that the opposite problem, namely data on a partial Cauchy surface being consistent with many different global solutions, is likely to be generic: we did not have to do any fine-tuning to get this result.

This third point leads to a peculiar sort of indeterminism, illustrated by the case of the unwritten book: the entire state on \(S\) does not determine what will happen in the future even though the local dynamics is deterministic and there are no other “edges” to space-time from which data could influence the result. What happens in the time travel region is constrained but not determined by what happens on \(S\), and the dynamics does not even supply any probabilities for the various possibilities. The example of the photographic negative discussed in section 2, then, seems likely to be unusual, for in that case there is a unique fixed point for the dynamics, and the set-up plus the dynamical laws determine the outcome. In the generic case one would rather expect multiple fixed points, with no room for anything to influence, even probabilistically, which would be realized. (See the supplement on

Remarks and Limitations on the Toy Models .

It is ironic that time travel should lead generically not to contradictions or to constraints (in the normal region) but to underdetermination of what happens in the time travel region by what happens everywhere else (an underdetermination tied neither to a probabilistic dynamics nor to a free edge to space-time). The traditional objection to time travel is that it leads to contradictions: there is no consistent way to complete an arbitrarily constructed story about how the time traveler intends to act. Instead, though, it appears that the more significant problem is underdetermination: the story can be consistently completed in many different ways.

Echeverria, Klinkhammer, and Thorne (1991) considered the case of 3-dimensional single hard spherical ball that can go through a single time travel wormhole so as to collide with its younger self.

Figure 9 [An extended description of figure 9 is in the supplement.]

The threat of paradox in this case arises in the following form. Consider the initial trajectory of a ball as it approaches the time travel region. For some initial trajectories, the ball does not undergo a collision before reaching mouth 1, but upon exiting mouth 2 it will collide with its earlier self. This leads to a contradiction if the collision is strong enough to knock the ball off its trajectory and deflect it from entering mouth 1. Of course, the Wheeler-Feynman strategy is to look for a “glancing blow” solution: a collision which will produce exactly the (small) deviation in trajectory of the earlier ball that produces exactly that collision. Are there always such solutions? [ 4 ]

Echeverria, Klinkhammer & Thorne found a large class of initial trajectories that have consistent “glancing blow” continuations, and found none that do not (but their search was not completely general). They did not produce a rigorous proof that every initial trajectory has a consistent continuation, but suggested that it is very plausible that every initial trajectory has a consistent continuation. That is to say, they have made it very plausible that, in the billiard ball wormhole case, the time travel structure of such a wormhole space-time does not result in constraints on states on spacelike surfaces in the non-time travel region.

In fact, as one might expect from our discussion in the previous section, they found the opposite problem from that of inconsistency: they found underdetermination. For a large class of initial trajectories there are multiple different consistent “glancing blow” continuations of that trajectory (many of which involve multiple wormhole traversals). For example, if one initially has a ball that is traveling on a trajectory aimed straight between the two mouths, then one obvious solution is that the ball passes between the two mouths and never time travels. But another solution is that the younger ball gets knocked into mouth 1 exactly so as to come out of mouth 2 and produce that collision. Echeverria et al. do not note the possibility (which we pointed out in the previous section) of the existence of additional balls in the time travel region. We conjecture (but have no proof) that for every initial trajectory of \(A\) there are some, and generically many, multiple-ball continuations.

Friedman, Morris, et al. (1990) examined the case of source-free non-self-interacting scalar fields traveling through such a time travel wormhole and found that no constraints on initial conditions in the non-time travel region are imposed by the existence of such time travel wormholes. In general there appear to be no known counter examples to the claim that in “somewhat realistic” time-travel space-times with a partial Cauchy surface there are no constraints imposed on the state on such a partial Cauchy surface by the existence of CTC’s. (See, e.g., Friedman & Morris 1991; Thorne 1994; Earman 1995; Earman, Smeenk, & Wüthrich 2009; and Dowe 2007.)

How about the issue of constraints in the time travel region \(T\)? Prima facie , constraints in such a region would not appear to be surprising. But one might still expect that there should be no constraints on states on a spacelike surface, provided one keeps the surface “small enough”. In the physics literature the following question has been asked: for any point \(p\) in \(T\), and any space-like surface \(S\) that includes \(p\) is there a neighborhood \(E\) of \(p\) in \(S\) such that any solution on \(E\) can be extended to a solution on the whole space-time? With respect to this question, there are some simple models in which one has this kind of extendability of local solutions to global ones, and some simple models in which one does not have such extendability, with no clear general pattern. The technical mathematical problems are amplified by the more conceptual problem of what it might mean to say that one could create a situation which forces the creation of closed timelike curves. (See, e.g., Yurtsever 1990; Friedman, Morris, et al. 1990; Novikov 1992; Earman 1995; and Earman, Smeenk, & Wüthrich 2009). What are we to think of all of this?

The toy models above all treat billiard balls, fields, and other objects propagating through a background spacetime with CTCs. Even if we can show that a consistent solution exists, there is a further question: what kind of matter and dynamics could generate CTCs to begin with? There are various solutions of Einstein’s equations with CTCs, but how do these exotic spacetimes relate to the models actually used in describing the world? In other words, what positive reasons might we have to take CTCs seriously as a feature of the actual universe, rather than an exotic possibility of primarily mathematical interest?

We should distinguish two different kinds of “possibility” that we might have in mind in posing such questions (following Stein 1970). First, we can consider a solution as a candidate cosmological model, describing the (large-scale gravitational degrees of freedom of the) entire universe. The case for ruling out spacetimes with CTCs as potential cosmological models strikes us as, surprisingly, fairly weak. Physicists used to simply rule out solutions with CTCs as unreasonable by fiat, due to the threat of paradoxes, which we have dismantled above. But it is also challenging to make an observational case. Observations tell us very little about global features, such as the existence of CTCs, because signals can only reach an observer from a limited region of spacetime, called the past light cone. Our past light cone—and indeed the collection of all the past light cones for possible observers in a given spacetime—can be embedded in spacetimes with quite different global features (Malament 1977, Manchak 2009). This undercuts the possibility of using observations to constrain global topology, including (among other things) ruling out the existence of CTCs.

Yet the case in favor of taking cosmological models with CTCs seriously is also not particularly strong. Some solutions used to describe black holes, which are clearly relevant in a variety of astrophysical contexts, include CTCs. But the question of whether the CTCs themselves play an essential representational role is subtle: the CTCs arise in the maximal extensions of these solutions, and can plausibly be regarded as extraneous to successful applications. Furthermore, many of the known solutions with CTCs have symmetries, raising the possibility that CTCs are not a stable or robust feature. Slight departures from symmetry may lead to a solution without CTCs, suggesting that the CTCs may be an artifact of an idealized model.

The second sense of possibility regards whether “reasonable” initial conditions can be shown to lead to, or not to lead to, the formation of CTCs. As with the toy models above, suppose that we have a partial Cauchy surface \(S\), such that all the temporal funny business lies to the future. Rather than simply assuming that there is a region with CTCs to the future, we can ask instead whether it is possible to create CTCs by manipulating matter in the initial, well-behaved region—that is, whether it is possible to build a time machine. Several physicists have pursued “chronology protection theorems” aiming to show that the dynamics of general relativity (or some other aspects of physics) rules this out, and to clarify why this is the case. The proof of such a theorem would justify neglecting solutions with CTCs as a source of insight into the nature of time in the actual world. But as of yet there are several partial results that do not fully settle the question. One further intriguing possibility is that even if general relativity by itself does protect chronology, it may not be possible to formulate a sensible theory describing matter and fields in solutions with CTCs. (See SEP entry on Time Machines; Smeenk and Wüthrich 2011 for more.)

There is a different question regarding the limitations of these toy models. The toy models and related examples show that there are consistent solutions for simple systems in the presence of CTCs. As usual we have made the analysis tractable by building toy models, selecting only a few dynamical degrees of freedom and tracking their evolution. But there is a large gap between the systems we have described and the time travel stories they evoke, with Kurt traveling along a CTC with murderous intentions. In particular, many features of the manifest image of time are tied to the thermodynamical properties of macroscopic systems. Rovelli (unpublished) considers a extremely simple system to illustrate the problem: can a clock move along a CTC? A clock consists of something in periodic motion, such as a pendulum bob, and something that counts the oscillations, such as an escapement mechanism. The escapement mechanism cannot work without friction; this requires dissipation and increasing entropy. For a clock that counts oscillations as it moves along a time-like trajectory, the entropy must be a monotonically increasing function. But that is obviously incompatible with the clock returning to precisely the same state at some future time as it completes a loop. The point generalizes, obviously, to imply that anything like a human, with memory and agency, cannot move along a CTC.

Since it is not obvious that one can rid oneself of all constraints in realistic models, let us examine the argument that time travel is implausible, and we should think it unlikely to exist in our world, in so far as it implies such constraints. The argument goes something like the following. In order to satisfy such constraints one needs some pre-established divine harmony between the global (time travel) structure of space-time and the distribution of particles and fields on space-like surfaces in it. But it is not plausible that the actual world, or any world even remotely like ours, is constructed with divine harmony as part of the plan. In fact, one might argue, we have empirical evidence that conditions in any spatial region can vary quite arbitrarily. So we have evidence that such constraints, whatever they are, do not in fact exist in our world. So we have evidence that there are no closed time-like lines in our world or one remotely like it. We will now examine this argument in more detail by presenting four possible responses, with counterresponses, to this argument.

Response 1. There is nothing implausible or new about such constraints. For instance, if the universe is spatially closed, there has to be enough matter to produce the needed curvature, and this puts constraints on the matter distribution on a space-like hypersurface. Thus global space-time structure can quite unproblematically constrain matter distributions on space-like hypersurfaces in it. Moreover we have no realistic idea what these constraints look like, so we hardly can be said to have evidence that they do not obtain.

Counterresponse 1. Of course there are constraining relations between the global structure of space-time and the matter in it. The Einstein equations relate curvature of the manifold to the matter distribution in it. But what is so strange and implausible about the constraints imposed by the existence of closed time-like curves is that these constraints in essence have nothing to do with the Einstein equations. When investigating such constraints one typically treats the particles and/or field in question as test particles and/or fields in a given space-time, i.e., they are assumed not to affect the metric of space-time in any way. In typical space-times without closed time-like curves this means that one has, in essence, complete freedom of matter distribution on a space-like hypersurface. (See response 2 for some more discussion of this issue). The constraints imposed by the possibility of time travel have a quite different origin and are implausible. In the ordinary case there is a causal interaction between matter and space-time that results in relations between global structure of space-time and the matter distribution in it. In the time travel case there is no such causal story to be told: there simply has to be some pre-established harmony between the global space-time structure and the matter distribution on some space-like surfaces. This is implausible.

Response 2. Constraints upon matter distributions are nothing new. For instance, Maxwell’s equations constrain electric fields \(\boldsymbol{E}\) on an initial surface to be related to the (simultaneous) charge density distribution \(\varrho\) by the equation \(\varrho = \text{div}(\boldsymbol{E})\). (If we assume that the \(E\) field is generated solely by the charge distribution, this conditions amounts to requiring that the \(E\) field at any point in space simply be the one generated by the charge distribution according to Coulomb’s inverse square law of electrostatics.) This is not implausible divine harmony. Such constraints can hold as a matter of physical law. Moreover, if we had inferred from the apparent free variation of conditions on spatial regions that there could be no such constraints we would have mistakenly inferred that \(\varrho = \text{div}(\boldsymbol{E})\) could not be a law of nature.

Counterresponse 2. The constraints imposed by the existence of closed time-like lines are of quite a different character from the constraint imposed by \(\varrho = \text{div}(\boldsymbol{E})\). The constraints imposed by \(\varrho = \text{div}(\boldsymbol{E})\) on the state on a space-like hypersurface are:

• local constraints (i.e., to check whether the constraint holds in a region you just need to see whether it holds at each point in the region),
• quite independent of the global space-time structure,
• quite independent of how the space-like surface in question is embedded in a given space-time, and
• very simply and generally stateable.

On the other hand, the consistency constraints imposed by the existence of closed time-like curves (i) are not local, (ii) are dependent on the global structure of space-time, (iii) depend on the location of the space-like surface in question in a given space-time, and (iv) appear not to be simply stateable other than as the demand that the state on that space-like surface embedded in such and such a way in a given space-time, do not lead to inconsistency. On some views of laws (e.g., David Lewis’ view) this plausibly implies that such constraints, even if they hold, could not possibly be laws. But even if one does not accept such a view of laws, one could claim that the bizarre features of such constraints imply that it is implausible that such constraints hold in our world or in any world remotely like ours.

Response 3. It would be strange if there are constraints in the non-time travel region. It is not strange if there are constraints in the time travel region. They should be explained in terms of the strange, self-interactive, character of time travel regions. In this region there are time-like trajectories from points to themselves. Thus the state at such a point, in such a region, will, in a sense, interact with itself. It is a well-known fact that systems that interact with themselves will develop into an equilibrium state, if there is such an equilibrium state, or else will develop towards some singularity. Normally, of course, self-interaction isn’t true instantaneous self-interaction, but consists of a feed-back mechanism that takes time. But in time travel regions something like true instantaneous self-interaction occurs. This explains why constraints on states occur in such time travel regions: the states “ ab initio ” have to be “equilibrium states”. Indeed in a way this also provides some picture of why indeterminism occurs in time travel regions: at the onset of self-interaction states can fork into different equi-possible equilibrium states.

Counterresponse 3. This is explanation by woolly analogy. It all goes to show that time travel leads to such bizarre consequences that it is unlikely that it occurs in a world remotely like ours.

Response 4. All of the previous discussion completely misses the point. So far we have been taking the space-time structure as given, and asked the question whether a given time travel space-time structure imposes constraints on states on (parts of) space-like surfaces. However, space-time and matter interact. Suppose that one is in a space-time with closed time-like lines, such that certain counterfactual distributions of matter on some neighborhood of a point \(p\) are ruled out if one holds that space-time structure fixed. One might then ask

Why does the actual state near \(p\) in fact satisfy these constraints? By what divine luck or plan is this local state compatible with the global space-time structure? What if conditions near \(p\) had been slightly different?

And one might take it that the lack of normal answers to these questions indicates that it is very implausible that our world, or any remotely like it, is such a time travel universe. However the proper response to these question is the following. There are no constraints in any significant sense. If they hold they hold as a matter of accidental fact, not of law. There is no more explanation of them possible than there is of any contingent fact. Had conditions in a neighborhood of \(p\) been otherwise, the global structure of space-time would have been different. So what? The only question relevant to the issue of constraints is whether an arbitrary state on an arbitrary spatial surface \(S\) can always be embedded into a space-time such that that state on \(S\) consistently extends to a solution on the entire space-time.

But we know the answer to that question. A well-known theorem in general relativity says the following: any initial data set on a three dimensional manifold \(S\) with positive definite metric has a unique embedding into a maximal space-time in which \(S\) is a Cauchy surface (see, e.g., Geroch & Horowitz 1979: 284 for more detail), i.e., there is a unique largest space-time which has \(S\) as a Cauchy surface and contains a consistent evolution of the initial value data on \(S\). Now since \(S\) is a Cauchy surface this space-time does not have closed time like curves. But it may have extensions (in which \(S\) is not a Cauchy surface) which include closed timelike curves, indeed it may be that any maximal extension of it would include closed timelike curves. (This appears to be the case for extensions of states on certain surfaces of Taub-NUT space-times. See Earman, Smeenk, & Wüthrich 2009). But these extensions, of course, will be consistent. So properly speaking, there are no constraints on states on space-like surfaces. Nonetheless the space-time in which these are embedded may or may not include closed time-like curves.

Counterresponse 4. This, in essence, is the stonewalling answer which we indicated in section 1. However, whether or not you call the constraints imposed by a given space-time on distributions of matter on certain space-like surfaces “genuine constraints”, whether or not they can be considered lawlike, and whether or not they need to be explained, the existence of such constraints can still be used to argue that time travel worlds are so bizarre that it is implausible that our world or any world remotely like ours is a time travel world.

Suppose that one is in a time travel world. Suppose that given the global space-time structure of this world, there are constraints imposed upon, say, the state of motion of a ball on some space-like surface when it is treated as a test particle, i.e., when it is assumed that the ball does not affect the metric properties of the space-time it is in. (There is lots of other matter that, via the Einstein equation, corresponds exactly to the curvature that there is everywhere in this time travel worlds.) Now a real ball of course does have some effect on the metric of the space-time it is in. But let us consider a ball that is so small that its effect on the metric is negligible. Presumably it will still be the case that certain states of this ball on that space-like surface are not compatible with the global time travel structure of this universe.

This means that the actual distribution of matter on such a space-like surface can be extended into a space-time with closed time-like lines, but that certain counterfactual distributions of matter on this space-like surface can not be extended into the same space-time. But note that the changes made in the matter distribution (when going from the actual to the counterfactual distribution) do not in any non-negligible way affect the metric properties of the space-time. (Recall that the changes only effect test particles.) Thus the reason why the global time travel properties of the counterfactual space-time have to be significantly different from the actual space-time is not that there are problems with metric singularities or alterations in the metric that force significant global changes when we go to the counterfactual matter distribution. The reason that the counterfactual space-time has to be different is that in the counterfactual world the ball’s initial state of motion starting on the space-like surface, could not “meet up” in a consistent way with its earlier self (could not be consistently extended) if we were to let the global structure of the counterfactual space-time be the same as that of the actual space-time. Now, it is not bizarre or implausible that there is a counterfactual dependence of manifold structure, even of its topology, on matter distributions on spacelike surfaces. For instance, certain matter distributions may lead to singularities, others may not. We may indeed in some sense have causal power over the topology of the space-time we live in. But this power normally comes via the Einstein equations. But it is bizarre to think that there could be a counterfactual dependence of global space-time structure on the arrangement of certain tiny bits of matter on some space-like surface, where changes in that arrangement by assumption do not affect the metric anywhere in space-time in any significant way . It is implausible that we live in such a world, or that a world even remotely like ours is like that.

Let us illustrate this argument in a different way by assuming that wormhole time travel imposes constraints upon the states of people prior to such time travel, where the people have so little mass/energy that they have negligible effect, via the Einstein equation, on the local metric properties of space-time. Do you think it more plausible that we live in a world where wormhole time travel occurs but it only occurs when people’s states are such that these local states happen to combine with time travel in such a way that nobody ever succeeds in killing their younger self, or do you think it more plausible that we are not in a wormhole time travel world? [ 5 ]

An alternative approach to time travel (initiated by Deutsch 1991) abstracts away from the idealized toy models described above. [ 6 ] This computational approach considers instead the evolution of bits (simple physical systems with two discrete states) through a network of interactions, which can be represented by a circuit diagram with gates corresponding to the interactions. Motivated by the possibility of CTCs, Deutsch proposed adding a new kind of channel that connects the output of a given gate back to its input —in essence, a backwards-time step. More concretely, given a gate that takes \(n\) bits as input, we can imagine taking some number \(i \lt n\) of these bits through a channel that loops back and then do double-duty as inputs. Consistency requires that the state of these \(i\) bits is the same for output and input. (We will consider an illustration of this kind of system in the next section.) Working through examples of circuit diagrams with a CTC channel leads to similar treatments of Consistency and Underdetermination as the discussion above (see, e.g., Wallace 2012: § 10.6). But the approach offers two new insights (both originally due to Deutsch): the Easy Knowledge paradox, and a particularly clear extension to time travel in quantum mechanics.

A computer equipped with a CTC channel can exploit the need to find consistent evolution to solve remarkably hard problems. (This is quite different than the first idea that comes to mind to enhance computational power: namely to just devote more time to a computation, and then send the result back on the CTC to an earlier state.) The gate in a circuit incorporating a CTC implements a function from the input bits to the output bits, under the constraint that the output and input match the i bits going through the CTC channel. This requires, in effect, finding the fixed point of the relevant function. Given the generality of the model, there are few limits on the functions that could be implemented on the CTC circuit. Nature has to solve a hard computational problem just to ensure consistent evolution. This can then be extended to other complex computational problems—leading, more precisely, to solutions of NP -complete problems in polynomial time (see Aaronson 2013: Chapter 20 for an overview and further references). The limits imposed by computational complexity are an essential part of our epistemic situation, and computers with CTCs would radically change this.

We now turn to the application of the computational approach to the quantum physics of time travel (see Deutsch 1991; Deutsch & Lockwood 1994). By contrast with the earlier discussions of constraints in classical systems, they claim to show that time travel never imposes any constraints on the pre-time travel state of quantum systems. The essence of this account is as follows. [ 7 ]

A quantum system starts in state \(S_1\), interacts with its older self, after the interaction is in state \(S_2\), time travels while developing into state \(S_3\), then interacts with its younger self, and ends in state \(S_4\) (see figure 10 ).

Figure 10 [An extended description of figure 10 is in the supplement.]

Deutsch assumes that the set of possible states of this system are the mixed states, i.e., are represented by the density matrices over the Hilbert space of that system. Deutsch then shows that for any initial state \(S_1\), any unitary interaction between the older and younger self, and any unitary development during time travel, there is a consistent solution, i.e., there is at least one pair of states \(S_2\) and \(S_3\) such that when \(S_1\) interacts with \(S_3\) it will change to state \(S_2\) and \(S_2\) will then develop into \(S_3\). The states \(S_2, S_3\) and \(S_4\) will typically be not be pure states, i.e., will be non-trivial mixed states, even if \(S_1\) is pure. In order to understand how this leads to interpretational problems let us give an example. Consider a system that has a two dimensional Hilbert space with as a basis the states \(\vc{+}\) and \(\vc{-}\). Let us suppose that when state \(\vc{+}\) of the young system encounters state \(\vc{+}\) of the older system, they interact and the young system develops into state \(\vc{-}\) and the old system remains in state \(\vc{+}\). In obvious notation:

Similarly, suppose that:

Let us furthermore assume that there is no development of the state of the system during time travel, i.e., that \(\vc{+}_2\) develops into \(\vc{+}_3\), and that \(\vc{-}_2\) develops into \(\vc{-}_3\).

Now, if the only possible states of the system were \(\vc{+}\) and \(\vc{-}\) (i.e., if there were no superpositions or mixtures of these states), then there is a constraint on initial states: initial state \(\vc{+}_1\) is impossible. For if \(\vc{+}_1\) interacts with \(\vc{+}_3\) then it will develop into \(\vc{-}_2\), which, during time travel, will develop into \(\vc{-}_3\), which inconsistent with the assumed state \(\vc{+}_3\). Similarly if \(\vc{+}_1\) interacts with \(\vc{-}_3\) it will develop into \(\vc{+}_2\), which will then develop into \(\vc{+}_3\) which is also inconsistent. Thus the system can not start in state \(\vc{+}_1\).

But, says Deutsch, in quantum mechanics such a system can also be in any mixture of the states \(\vc{+}\) and \(\vc{-}\). Suppose that the older system, prior to the interaction, is in a state \(S_3\) which is an equal mixture of 50% \(\vc{+}_3\) and 50% \(\vc{-}_3\). Then the younger system during the interaction will develop into a mixture of 50% \(\vc{+}_2\) and 50% \(\vc{-}_2\), which will then develop into a mixture of 50% \(\vc{+}_3\) and 50% \(\vc{-}_3\), which is consistent! More generally Deutsch uses a fixed point theorem to show that no matter what the unitary development during interaction is, and no matter what the unitary development during time travel is, for any state \(S_1\) there is always a state \(S_3\) (which typically is not a pure state) which causes \(S_1\) to develop into a state \(S_2\) which develops into that state \(S_3\). Thus quantum mechanics comes to the rescue: it shows in all generality that no constraints on initial states are needed!

One might wonder why Deutsch appeals to mixed states: will superpositions of states \(\vc{+}\) and \(\vc{-}\) not suffice? Unfortunately such an idea does not work. Suppose again that the initial state is \(\vc{+}_1\). One might suggest that that if state \(S_3\) is

one will obtain a consistent development. For one might think that when initial state \(\vc{+}_1\) encounters the superposition

it will develop into superposition

and that this in turn will develop into

as desired. However this is not correct. For initial state \(\vc{+}_1\) when it encounters

will develop into the entangled state

In so far as one can speak of the state of the young system after this interaction, it is in the mixture of 50% \(\vc{+}_2\) and 50% \(\vc{-}_2\), not in the superposition

So Deutsch does need his recourse to mixed states.

This clarification of why Deutsch needs his mixtures does however indicate a serious worry about the simplifications that are part of Deutsch’s account. After the interaction the old and young system will (typically) be in an entangled state. Although for purposes of a measurement on one of the two systems one can say that this system is in a mixed state, one can not represent the full state of the two systems by specifying the mixed state of each separate part, as there are correlations between observables of the two systems that are not represented by these two mixed states, but are represented in the joint entangled state. But if there really is an entangled state of the old and young systems directly after the interaction, how is one to represent the subsequent development of this entangled state? Will the state of the younger system remain entangled with the state of the older system as the younger system time travels and the older system moves on into the future? On what space-like surfaces are we to imagine this total entangled state to be? At this point it becomes clear that there is no obvious and simple way to extend elementary non-relativistic quantum mechanics to space-times with closed time-like curves: we apparently need to characterize not just the entanglement between two systems, but entanglement relative to specific spacetime descriptions.

How does Deutsch avoid these complications? Deutsch assumes a mixed state \(S_3\) of the older system prior to the interaction with the younger system. He lets it interact with an arbitrary pure state \(S_1\) younger system. After this interaction there is an entangled state \(S'\) of the two systems. Deutsch computes the mixed state \(S_2\) of the younger system which is implied by this entangled state \(S'\). His demand for consistency then is just that this mixed state \(S_2\) develops into the mixed state \(S_3\). Now it is not at all clear that this is a legitimate way to simplify the problem of time travel in quantum mechanics. But even if we grant him this simplification there is a problem: how are we to understand these mixtures?

If we take an ignorance interpretation of mixtures we run into trouble. For suppose that we assume that in each individual case each older system is either in state \(\vc{+}_3\) or in state \(\vc{-}_3\) prior to the interaction. Then we regain our paradox. Deutsch instead recommends the following, many worlds, picture of mixtures. Suppose we start with state \(\vc{+}_1\) in all worlds. In some of the many worlds the older system will be in the \(\vc{+}_3\) state, let us call them A -worlds, and in some worlds, B -worlds, it will be in the \(\vc{-}_3\) state. Thus in A -worlds after interaction we will have state \(\vc{-}_2\) , and in B -worlds we will have state \(\vc{+}_2\). During time travel the \(\vc{-}_2\) state will remain the same, i.e., turn into state \(\vc{-}_3\), but the systems in question will travel from A -worlds to B -worlds. Similarly the \(\vc{+}\) \(_2\) states will travel from the B -worlds to the A -worlds, thus preserving consistency.

Now whatever one thinks of the merits of many worlds interpretations, and of this understanding of it applied to mixtures, in the end one does not obtain genuine time travel in Deutsch’s account. The systems in question travel from one time in one world to another time in another world, but no system travels to an earlier time in the same world. (This is so at least in the normal sense of the word “world”, the sense that one means when, for instance, one says “there was, and will be, only one Elvis Presley in this world.”) Thus, even if it were a reasonable view, it is not quite as interesting as it may have initially seemed. (See Wallace 2012 for a more sympathetic treatment, that explores several further implications of accepting time travel in conjunction with the many worlds interpretation.)

We close by acknowledging that Deutsch’s starting point—the claim that this computational model captures the essential features of quantum systems in a spacetime with CTCs—has been the subject of some debate. Several physicists have pursued a quite different treatment of evolution of quantum systems through CTC’s, based on considering the “post-selected” state (see Lloyd et al. 2011). Their motivations for implementing the consistency condition in terms of the post-selected state reflects a different stance towards quantum foundations. A different line of argument aims to determine whether Deutsch’s treatment holds as an appropriate limiting case of a more rigorous treatment, such as quantum field theory in curved spacetimes. For example, Verch (2020) establishes several results challenging the assumption that Deutsch’s treatment is tied to the presence of CTC’s, or that it is compatible with the entanglement structure of quantum fields.

What remains of the grandfather paradox in general relativistic time travel worlds is the fact that in some cases the states on edgeless spacelike surfaces are “overconstrained”, so that one has less than the usual freedom in specifying conditions on such a surface, given the time-travel structure, and in some cases such states are “underconstrained”, so that states on edgeless space-like surfaces do not determine what happens elsewhere in the way that they usually do, given the time travel structure. There can also be mixtures of those two types of cases. The extent to which states are overconstrained and/or underconstrained in realistic models is as yet unclear, though it would be very surprising if neither obtained. The extant literature has primarily focused on the problem of overconstraint, since that, often, either is regarded as a metaphysical obstacle to the possibility time travel, or as an epistemological obstacle to the plausibility of time travel in our world. While it is true that our world would be quite different from the way we normally think it is if states were overconstrained, underconstraint seems at least as bizarre as overconstraint. Nonetheless, neither directly rules out the possibility of time travel.

If time travel entailed contradictions then the issue would be settled. And indeed, most of the stories employing time travel in popular culture are logically incoherent: one cannot “change” the past to be different from what it was, since the past (like the present and the future) only occurs once. But if the only requirement demanded is logical coherence, then it seems all too easy. A clever author can devise a coherent time-travel scenario in which everything happens just once and in a consistent way. This is just too cheap: logical coherence is a very weak condition, and many things we take to be metaphysically impossible are logically coherent. For example, it involves no logical contradiction to suppose that water is not molecular, but if both chemistry and Kripke are right it is a metaphysical impossibility. We have been interested not in logical possibility but in physical possibility. But even so, our conditions have been relatively weak: we have asked only whether time-travel is consistent with the universal validity of certain fundamental physical laws and with the notion that the physical state on a surface prior to the time travel region be unconstrained. It is perfectly possible that the physical laws obey this condition, but still that time travel is not metaphysically possible because of the nature of time itself. Consider an analogy. Aristotle believed that water is homoiomerous and infinitely divisible: any bit of water could be subdivided, in principle, into smaller bits of water. Aristotle’s view contains no logical contradiction. It was certainly consistent with Aristotle’s conception of water that it be homoiomerous, so this was, for him, a conceptual possibility. But if chemistry is right, Aristotle was wrong both about what water is like and what is possible for it. It can’t be infinitely divided, even though no logical or conceptual analysis would reveal that.

Similarly, even if all of our consistency conditions can be met, it does not follow that time travel is physically possible, only that some specific physical considerations cannot rule it out. The only serious proof of the possibility of time travel would be a demonstration of its actuality. For if we agree that there is no actual time travel in our universe, the supposition that there might have been involves postulating a substantial difference from actuality, a difference unlike in kind from anything we could know if firsthand. It is unclear to us exactly what the content of possible would be if one were to either maintain or deny the possibility of time travel in these circumstances, unless one merely meant that the possibility is not ruled out by some delineated set of constraints. As the example of Aristotle’s theory of water shows, conceptual and logical “possibility” do not entail possibility in a full-blooded sense. What exactly such a full-blooded sense would be in case of time travel, and whether one could have reason to believe it to obtain, remain to us obscure.

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How to cite this entry . Preview the PDF version of this entry at the Friends of the SEP Society . Look up topics and thinkers related to this entry at the Internet Philosophy Ontology Project (InPhO). Enhanced bibliography for this entry at PhilPapers , with links to its database.

• Adlam, Emily, unpublished, “ Is There Causation in Fundamental Physics? New Insights from Process Matrices and Quantum Causal Modelling ”, 2022, arXiv: 2208.02721. doi:10.48550/ARXIV.2208.02721
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Past, present, paradox: writing about time travel.

Time travel in fiction can open your story to infinite possibilities. Ever wondered what it would be like if somebody taught the Romans how to make a nuclear bomb? Do you need to retcon an event in your story? Time travel!

It may seem simple for your time-traveling characters to hop in Tony’s Terrific Temporal Transport and whiz through time, but there are many hurdles to overcome when writing about time travel.

Chief among these is dealing with time travel paradoxes, so let’s look at those, discuss how you can write convincing time travel stories, and explore how some popular stories handle it.

The Problem With Time Travel

Consider an ordinary day in your life. It follows a sequence of events where one thing leads to another. This is called causality , the concept that everything that happens results from events that happened before it. The problem with time travel in fiction, especially travel to the past, is that it often breaks the rules of causality.

This can lead to time travel paradoxes and unforeseen results , including:

• Continuity paradoxes: The act of time travel renders itself impossible.
• Closed causal loop paradoxes: Traveling to the past creates a condition where an idea, object, or person has no identifiable origin and exists in a closed loop in time that repeats infinitely.
• The butterfly effect: Even the smallest action can have massive consequences.

With all that in mind, let’s embark on a journey through time and explore these further!

Grandfather Paradox

This thought experiment posits the idea of somebody traveling back in time and killing their grandfather before their parents were born. Because the grandfather never has children, the time traveler—his grandchild—cannot exist.

However, if the time traveler never existed, they couldn’t kill their grandfather, so he would go on to have children and grandchildren. One of those grandchildren is the time traveler, though, who might go back in time and kill their grandfather. If that seems confusing, it’s okay—it’s supposed to be.

The bottom line is that if somebody travels to the past and changes something that prevents them from ever traveling to the past, they have broken the timeline's continuity.

Polchinski’s Paradox

American theoretical physicist Joseph Polchinski removed human intervention from the time travel equation.

Imagine a billiard ball travels into a wormhole, tunnels through time in a closed loop, and emerges from the same wormhole just in time to knock its past self away.

Doing so prevents it from ever entering the wormhole and traveling through time, to begin with. However, if it does not travel back in time, it cannot emerge to knock itself out of the way, giving it a clear path to travel back in time.

Bootstrap Paradox

The Bootstrap Paradox is the first closed causal loop paradox we will explore. This presents a situation where an object, idea, or person traveling to the past creates the conditions for their existence, leading to it having no identifiable origin in the timeline.

Imagine sending the schematics for your time machine to your past self, from which you create a time machine. Where did the knowledge of how to create the time machine begin?

Predestination Paradox

The most nihilistic of paradoxes explores the idea that nothing we do matters, no matter what. Events are predetermined to still occur regardless of when and where you travel in time.

Suppose you time travel to the past to talk Alexander the Great out of invading Persia, but he hadn’t even considered this until you mentioned it. By traveling to the past to prevent Alexander’s conquest, you caused it.

Butterfly Effec t

Less of a paradox and more an exploration of unintended consequences, the butterfly effect explores the idea that any action can have sweeping repercussions, no matter how small.

In the 1960s, meteorologist Edward Lorenz discovered that adding tiny changes to computer-based meteorological models resulted in unpredictable changes far from the origin point. In traveling back in time, we don’t know what effect even minor changes might have on the timeline.

How to Write Convincing Time Travel Stories

Time travel can be pretty complex at the best of times, but that doesn't mean writing about it has to be a challenge. Here are a few practical tips to craft narratives that crack the temporal code.

Ask Yourself, "Why Time Travel?"

If your story has time travel, to begin with, it likely plays a pretty significant role in the narrative. Define the purpose that time travel has in your story by asking yourself questions like:

• How and why is time travel possible in your setting?
• What does it mean for your story and your characters?
• What are your characters meant to use time travel for?
• Is the actual practice of time travel different from its intent?

If you can't be clear about time travel's purpose in your story, how can you convincingly write about it? To get crafty with time, you first need to master its relevant mechanics.

Keep a Record of Everything

You're asking your reader to potentially make several mental leaps when time travel is involved in a story, so it's imperative to have all of your details sorted. Do the work of planning out dates and events ahead of time by creating a time map for yourself—like a mindmap, but for a timeline.

You'll be able to keep a birds-eye view of the narrative at all times, be more strategic about moving the order of events around, and ensure that you never miss a detail. You may even want to have multiple versions—a strictly linear timeline and a more loosely structured time map where you draw connections between events and in the order they appear in the narrative.

In Campfire, you can do both with the Timeline Module —create as many Timelines as you want by using the Page feature in the element. You can also connect your Timeline(s) to a custom calendar from the Calendar Module for extra fun with time wonkiness in your world.

If a new idea pops up while writing, don't stress! You'll have your handy time map already laid out so you can easily see if a new scene or chapter makes sense, as well as where it will best fit into the narrative.

Never Forget Causality

I mentioned this concept earlier in the article, but it should be reiterated: The most important rule of time travel is that every action results in a consequence. Remember cause and effect : an action is taken (your character time travels to the past), and causes an effect, the consequence (the timeline is forever changed).

"Consequence" doesn't have to be a negative thing, either, even though the word has that connotation. The resulting consequence of a given action could be a positive effect, too.

Regardless, seek to maintain causality so you don't confuse your readers (or yourself, for that matter). Establishing clear rules for how time travel works in your setting and sticking to them will help you keep your time logic consistent and avoid running into narrative dead ends or plot holes.

Tips & Tricks For the Time-Traveling Author

Now that we’ve examined several obstacles you can encounter when writing about time travel, let’s see how you can either avoid them or exploit them. That’s right! Even time travel paradoxes present opportunities for superb storytelling.

Focus on the Future

Fortunately, all the named paradoxes here involve the past, so the easy way to avoid them is to not go there! Thanks to Einstein’s theory of special relativity, you don’t even have to invent a clever way to travel instead to the future.

An aspect of Einstein's theory is time dilation , in which the faster an object moves through space, the slower it moves through time. With this, you need only zip around at near the speed of light for a few weeks or months, and when you come back to Earth, years or centuries will have gone by.

Create a Multiverse

A popular trope in science fiction today, and a theory gaining popularity among theoretical quantum physicists, is the multiverse concept. According to multiverse theory, whenever an event occurs, every possible outcome of the event happens simultaneously, splitting the universe into parallels that each contain differing outcomes.

Since all these realities exist, perhaps changing the past is simply a way for time travelers to travel between realities, shifting their perspective to a timeline where things occurred differently than in their original reality.

Get Creative With Consequences

Instead of avoiding paradoxes, maybe you want them to occur. Leading to some fascinating stories, this can be approached in a variety of ways. Perhaps you want to examine the unintended consequences of the butterfly effect, create a time-traveling police force that enforces the laws of time travel, or simply break time itself and revel in the chaos that ensues.

Just be sure to remember the action-consequence rule and keep your timeline handy for easy reference—especially if you're toying around with multiple timelines!

Best Time Travel Stories

What follows are what I think are some of the best time travel stories. As you will see, the first two fall victim to time travel paradoxes, while the other two do a great job of exploring various elements we’ve discussed.

Terminator 2: Judgment Day

The corporation Cyberdyne Systems has remnants of the Terminator from the first movie, which they use to create an artificial intelligence system called Skynet. Skynet then actually creates the terminators and sends one back in time. Thus, it gives humanity the technology to create itself in a classic example of a bootstrap paradox.

Back to the Future

In this film, Marty McFly travels to the past and inadvertently interrupts the event where his parents first meet. This causes a chain of events where Marty’s parents never get married and have children, threatening to erase Marty and his siblings from the timeline.

Some argue that the McFly offspring ceasing to exist is a great exploration of the consequences of time travel. However, they would never have been at risk had Marty not been in the past to impede their parents’ romance. And if he ceases to exist, he’ll never go back and get in the way, thus creating a grandfather paradox.

War of the Twins

In this second volume of the Dragonlance Legends trilogy by Margaret Weis and Tracy Hickman, the mage Raistlin Majere travels into the past, kills a wizard named Fistandantilus in a battle for power, and assumes his identity. Throughout the book, Raistlin unwittingly follows the historical fate of Fistandantilus, in a wonderful exploration of the predestination paradox.

It’s hard to talk about time travel in fiction these days without mentioning Loki. The show explores two suggestions from my list above: the multiverse and policing the timeline. In this series, varying outcomes of events lead to branching timelines, creating a multiverse of possibilities. However, an agency called the Time Variance Authority exists to prevent this from happening, and they set out to eliminate any branches separate from what they consider the Sacred Timeline.

Bon Voyage!

I hope this exploration of time travel leaves you prepared to tackle these obstacles and opportunities that naturally present themselves when playing around with time.

Just knowing about the complexities of time travel and the paradoxes it can bring about is the best way to avoid trouble and create innovative storytelling moments. So, dust off your DeLorean, polish your paradox-proof plot, and get ready to write your adventure through the ages!

Learn more about making a timeline with Campfire in the dedicated Timeline Module tutorial . And be sure to check out the other plotting and planning articles and videos here on Learn, for advice on how to plan your very own time travel adventures!

Where Does the Concept of Time Travel Come From?

Time; he's waiting in the wings.

The dream of traveling through time is both ancient and universal. But where did humanity's fascination with time travel begin, and why is the idea so appealing?

The concept of time travel — moving through time the way we move through three-dimensional space — may in fact be hardwired into our perception of time . Linguists have recognized that we are essentially incapable of talking about temporal matters without referencing spatial ones. "In language — any language — no two domains are more intimately linked than space and time," wrote Israeli linguist Guy Deutscher in his 2005 book "The Unfolding of Language." "Even if we are not always aware of it, we invariably speak of time in terms of space, and this reflects the fact that we think of time in terms of space."

Deutscher reminds us that when we plan to meet a friend "around" lunchtime, we are using a metaphor, since lunchtime doesn't have any physical sides. He similarly points out that time can not literally be "long" or "short" like a stick, nor "pass" like a train, or even go "forward" or "backward" any more than it goes sideways, diagonal or down.

Related: Why Does Time Fly When You're Having Fun?

Perhaps because of this connection between space and time, the possibility that time can be experienced in different ways and traveled through has surprisingly early roots. One of the first known examples of time travel appears in the Mahabharata, an ancient Sanskrit epic poem compiled around 400 B.C., Lisa Yaszek, a professor of science fiction studies at the Georgia Institute of Technology in Atlanta, told Live Science 

In the Mahabharata is a story about King Kakudmi, who lived millions of years ago and sought a suitable husband for his beautiful and accomplished daughter, Revati. The two travel to the home of the creator god Brahma to ask for advice. But while in Brahma's plane of existence, they must wait as the god listens to a 20-minute song, after which Brahma explains that time moves differently in the heavens than on Earth. It turned out that "27 chatur-yugas" had passed, or more than 116 million years, according to an online summary , and so everyone Kakudmi and Revati had ever known, including family members and potential suitors, was dead. After this shock, the story closes on a somewhat happy ending in that Revati is betrothed to Balarama, twin brother of the deity Krishna. 

Time is fleeting

To Yaszek, the tale provides an example of what we now call time dilation , in which different observers measure different lengths of time based on their relative frames of reference, a part of Einstein's theory of relativity.

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Such time-slip stories are widespread throughout the world, Yaszek said, citing a Middle Eastern tale from the first century BCE about a Jewish miracle worker who sleeps beneath a newly-planted carob tree and wakes up 70 years later to find it has now matured and borne fruit (carob trees are notorious for how long they take to produce their first harvest). Another instance can be found in an eighth-century Japanese fable about a fisherman named Urashima Tarō who travels to an undersea palace and falls in love with a princess. Tarō finds that, when he returns home, 100 years have passed, according to a translation of the tale published online by the University of South Florida . 

In the early-modern era of the 1700 and 1800s, the sleep-story version of time travel grew more popular, Yaszek said. Examples include the classic tale of Rip Van Winkle, as well as books like Edward Belamy's utopian 1888 novel "Looking Backwards," in which a man wakes up in the year 2000, and the H.G. Wells 1899 novel "The Sleeper Awakes," about a man who slumbers for centuries and wakes to a completely transformed London. 

Related: Science Fiction or Fact: Is Time Travel Possible ?

In other stories from this period, people also start to be able to move backward in time. In Mark Twain’s 1889 satire "A Connecticut Yankee in King Arthur's Court," a blow to the head propels an engineer back to the reign of the legendary British monarch. Objects that can send someone through time begin to appear as well, mainly clocks, such as in Edward Page Mitchell's 1881 story "The Clock that Went Backwards" or Lewis Carrol's 1889 children's fantasy "Sylvie and Bruno," where the characters possess a watch that is a type of time machine . 

The explosion of such stories during this era might come from the fact that people were "beginning to standardize time, and orient themselves to clocks more frequently," Yaszek said. 

Time after time

Wells provided one of the most enduring time-travel plots in his 1895 novella "The Time Machine," which included the innovation of a craft that can move forward and backward through long spans of time. "This is when we’re getting steam engines and trains and the first automobiles," Yaszek said. "I think it’s no surprise that Wells suddenly thinks: 'Hey, maybe we can use a vehicle to travel through time.'"

Because it is such a rich visual icon, many beloved time-travel stories written after this have included a striking time machine, Yaszek said, referencing The Doctor's blue police box — the TARDIS — in the long-running BBC series "Doctor Who," and "Back to the Future"'s silver luxury speedster, the DeLorean . 

More recently, time travel has been used to examine our relationship with the past, Yaszek said, in particular in pieces written by women and people of color. Octavia Butler's 1979 novel "Kindred" about a modern woman who visits her pre-Civil-War ancestors is "a marvelous story that really asks us to rethink black and white relations through history," she said. And a contemporary web series called " Send Me " involves an African-American psychic who can guide people back to antebellum times and witness slavery. 

"I'm really excited about stories like that," Yaszek said. "They help us re-see history from new perspectives."

Time travel has found a home in a wide variety of genres and media, including comedies such as "Groundhog Day" and "Bill and Ted's Excellent Adventure" as well as video games like Nintendo's "The Legend of Zelda: Majora's Mask" and the indie game "Braid." 

Yaszek suggested that this malleability and ubiquity speaks to time travel tales' ability to offer an escape from our normal reality. "They let us imagine that we can break free from the grip of linear time," she said. "And somehow get a new perspective on the human experience, either our own or humanity as a whole, and I think that feels so exciting to us." 

That modern people are often drawn to time-machine stories in particular might reflect the fact that we live in a technological world, she added. Yet time travel's appeal certainly has deeper roots, interwoven into the very fabric of our language and appearing in some of our earliest imaginings. 

"I think it's a way to make sense of the otherwise intangible and inexplicable, because it's hard to grasp time," Yaszek said. "But this is one of the final frontiers, the frontier of time, of life and death. And we're all moving forward, we're all traveling through time."

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Originally published on Live Science .

Adam Mann is a freelance journalist with over a decade of experience, specializing in astronomy and physics stories. He has a bachelor's degree in astrophysics from UC Berkeley. His work has appeared in the New Yorker, New York Times, National Geographic, Wall Street Journal, Wired, Nature, Science, and many other places. He lives in Oakland, California, where he enjoys riding his bike. 

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Time Travel: A History by James Gleick review – why haven’t we realised the dream?

W e all travel in time mentally when we think about the past or the future, and I for one close my eyes every night and travel instantaneously into tomorrow. But the idea of some kind of technology that allows us to literally transport ourselves to a different era is surprisingly recent. James Gleick’s historical survey of the concept concludes that, apart from a couple of vague anticipations in the 19th century, the idea really was invented in 1895, in HG Wells’s novel The Time Machine .

Cue more than a century of literary, philosophical and scientific investigations into the topic. There are logical knots aplenty, as when people travel back in time to kill their ancestors (the Grandfather Paradox). There are alt-history fantasies of killing Hitler. There is a flux capacitor powering a DeLorean time machine; there is a Time Lord zooming around in an old police phone box; and there is the head-spinning set of nested time loops in Shane Carruth’s extraordinary micro-budget first film, Primer .

The last example is not mentioned in this book, but a lot else is, including more metaphorical forms of time travel: there is a fascinating, wry chapter, for example, on the craze for burying cultural objects inside “time capsules” in the hope that our descendants won’t think we were all complete idiots. (The time capsule, Gleick writes, is “a tragi-comic time machine. It lacks an engine, goes nowhere, sits and waits.”) From Jorge Luis Borges’s story “The Garden of Forking Paths” to TS Eliot, entropy and free will, the book is rich with associative detail.

At first, time travel seemed a harmless fantasy, until Kurt Gödel showed Albert Einstein that his equations of relativity allowed solutions in which time travel appeared to be possible, although no one yet knows exactly how. Mathematicians and physicists got to work, and they haven’t stopped yet. The best argument against the possibility of time travel is probably that supplied by Stephen Hawking , who has pointed out that we are not invaded by hordes of tourists from the future. (Hawking posits that somehow metaphysically embedded within the universe is a “Chronology Protection Principle”.) But that is not a knockdown argument, because many serious scientific hypotheses about time travel forbid travelling back to a time before the first time machine was invented. In that case, unfortunately, we will never be able to go back and see the dinosaurs. But also it means that we are not invaded by time travellers from the future simply because the first time machine has not yet been invented.

Curiously, though, Gleick does not go into much detail about the scientific work on time travel of the last few decades, because he is convinced that physicists working on the subject have just read too much science fiction (they have, he condescendingly writes, been “unwittingly conditioned” by it), and are wasting their own and everyone else’s, um, time. There is, for example, no reference at all to one of the leading such researchers, the astrophysicist J Richard Gott. (Interested readers should consult his excellent book Time Travel in Einstein’s Universe .) On the other hand, the book expends very many pages on laborious plot summaries of more-or-less obscure time-travel fictions of the last century.

Nor, moreover, is Gleick much impressed by what he considers the “futile” philosophical writing on time that he has consulted. One example is the famous 1962 paper on fatalism by Richard Taylor, which begins: “A fatalist – if there is any such – thinks he cannot do anything about the future”, so it is “pointless for him to deliberate about what he is going to do”. This started a long and complicated argument in the philosophical literature, an unimportant footnote to which is that, after David Foster Wallace ’s death, his undergraduate essay on the topic was published, along with Taylor’s original paper, as Fate, Time and Language, in order, or so a cynic might think, to cash in on DFW’s posthumous literary celebrity. Gleick here seems to have just swallowed the publisher’s claim that the future novelist managed to refute Taylor wholesale. At the end of another chapter, with the air of revealing a profound truth, Gleick writes: “What is time? Things change, and time is how we keep track.” A fair response would be to ask: “OK, what is change?”

What, then, is Gleick’s cultural diagnosis? He argues that the persistent dream of time travel is a cultural fantasy of escaping the worries of the present, and in particular of eluding death. This is perceptive and no doubt true, but it would still be true even if time travel were in fact theoretically possible. The author, however, seems too impatient to keep an open mind on the matter.

This is all rather baffling for any fan of Gleick’s earlier, brilliant works such as Genius , his biography of Richard Feynman, and Chaos : this writer, after all, more or less invented the modern style of mind-bending scientific non-fiction that does not talk down to its audience. Time Travel is written with his usual elegance, but there is something morose about it, as though, having embarked on the work, he now can’t believe he is obliged to put all these supposedly clever people right about their stupid fantasies. Indeed, one ends the book intrigued mostly by the quirk of authorial psychology by which someone would choose to write a history of an idea that he is convinced is not only impossible but ridiculous.

So I prefer the cheerier hypothesis that someone has already made the first time machine in their garage, and the widespread adoption of the technology is going to lead to utter disaster. Luckily, there is a hero who will stop this happening: future James Gleick, who has travelled back in time to smash the time machine he emerges from and write this book to convince everybody that there’s no point ever trying to build another one. Let’s hope it works.

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Tips and Tricks to Writing Time Travel Into Your Story

Time travel and time manipulation is a very common conflict in science fiction, fantasy, and even more action-based genres of fiction. However, despite it being so common, it is possibly one of the hardest supernatural qualities to write effectively into a story.

Time travel can be very confusing, and you can lose your readers if you are not careful about how you approach it. Not only that, but since time travel has been done so many times, authors may feel the need to be original in their works which can cause even more confusion.

However, writing time travel can be fun and easy if you know what you’re dealing with! When writing a story with any sort of time manipulation, make sure you first answer the question: what are the rules of time travel in my story? Once you’ve asked this, there are common writing tips that can help you write these rules effectively into your story.

Rules of Time Travel

Before we worry about what your characters understand, let’s focus on you, the writer. Before writing a story with time travel, we want to make sure that you understand exactly the type of time travel you are writing (there are many different kinds!).

But what exactly is a rule of time travel? Well, since you’re the one writing the story, the rules are what you make them. However, there are common types of time travel that writers tend to fall into, whether they are trying or not.

The Different Types of Time Travel:

When discussing time travel, there are four categories to choose from:

Traveling back in time

Traveling forward in time

The gift of foresight

Of course, within each of these categories, there are many subcategories and creative possibilities. But looking only at the broad strokes, every time travel story has one of these.

In choosing which type of time travel to include, it’s important to consider what you want from your story. A story of time loops, like Groundhog Day , usually focuses on the character development of the person in the loop. Meanwhile foresight and traveling forward usually deal with morality. And traveling to the past is a great way to discuss free will. It’s all about what you want.

There are so many options with time travel. The important thing is to find the type of time travel that fits your story best, create rules for it, and stick to those rules . This leads us to the first tip in writing time travel:

Consistency

These rules are just for you. You don’t necessarily need to tell your readers about them. There’s no need for some sort of exposition explanation (although if you want to, feel free). But deciding what time travel can and can’t do in your story will stop plot holes from forming. Keeping your time travel consistent is important.

For example, let’s look at Supernatural . Supernatural is great at giving us examples of what not to do.

In season 4 of Supernatural , Dean Winchester is sent back in time to when his parents were his age. Dean attempts to kill a demon that will kill his mother in the future. At the end, he fails and ultimately causes the events that will happen (classic unchangeable past time travel rules). Castiel tells him that it is impossible to change the present by traveling to the past.

We then jump to season five. Anna, a runaway angel, goes back in time to kill Sam and Dean’s parents before they can have Sam. Castiel and the brothers become worried about this. But why? If we can’t alter the past, then what’s the problem? Even if Anna doesn’t realize her goals are futile, why would Castiel be concerned?

Backstory :

This leads us to our next point. After you decide your own time travel rules, you have to consider how much each character knows about these rules . If you have decided that a seer has unchangeable visions, and they know this, then that character should never try to change their fate.

The time travel rule of Twelve Monkeys is that you cannot change the past. However, the movie only has a plot because the main character doesn’t know this. He believes he can change the past until the very end when he realizes his goal is fruitless.

However, the Prisoner of Azkaban has the same rules of time travel and Dumbledore and Hermione both know they can’t change the past. There is still conflict in the book because that is not their goal.

If a character has a backstory where they studied time travel for years, and has traveled hundreds of times before, they shouldn’t be shocked by the rules of time travel. Withholding the information from your characters can create interesting conflict, but make sure each character understands a plausible amount.

Show, Don’t Tell:

Having your characters have a long conversation about time travel can be fun to write, but it’s important to remember that the best way to ensure your audience understands time travel is to show characters traveling through time .

As long as you stick to your rules, your time travel will eventually make sense to your audience. And, when it comes to time travel, you’d be surprised just how long your readers will be okay with being in the dark.

In Avengers: Endgame , Hulk/Bruce Banner goes on a long explanation about how time travel works in this universe. They bring up Hot Tub Time Machine and Back to the Future . But in the end, did anyone in the audience completely understand what that time travel was about from the Hulk’s rant? From what I can gather, no.

About the Author: Susan Matteucci is an author, editor, and reader currently finishing up her BFA in Creative Writing at Emerson College. She has two publish short stories and hopefully has many more on the way. She has a passion for Sci-Fi, particularly time travel, and fantasy. It is her belief that straying from the realistic is the best way to comment on society.

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Summary of “The Paradoxes of Time Travel” by Lewis

Time travel is a fascinating fantasy idea that has a logical justification in addition to its obviously entertaining function. In particular, such travel is inextricably associated with the endless paradoxes generated whenever the traveler decides to move into the past or the future. This raises legitimate questions about whether the traveler can change the course of events, about the objective measure of time, and what justifies the discrepancy between the two temporal functions.

These are all questions Lewis sought to answer in his reflections on “The Paradoxes of Time Travel.” More specifically, the author conducted an eclectic analysis of the phenomenon of time travel from the perspective of precise terminology, logical validity, and explanations of apparent paradoxes. The article is full of Lewis’s personal statements and illustrative cases to facilitate understanding such confusing material.

It is paramount to recognize that Lewis’s article is a summarizing and multifaceted work that adequately covers the basic philosophical and logical questions outlined as early as the first paragraphs of the material. Broadly speaking, this includes defining the permissibility of time travel, finding a terminological description of the basic elements, and explaining the geometry of time from the perspective of an outside observer and time traveler. Thus, the reader reading “The Paradoxes of Time Travel” may feel the initial confusion and logical incoherence of the text’s components, but through the scenarios and descriptions given by the author that accompany almost every page, the overall point is reached.

Consequently, Lewis began his work by attempting to explain the spatial geometry of time. Acknowledging the fiction of time travel — but, more importantly, not pointing out the impossibility of it — the researcher makes a cursory comparison of linear, planar, and four-dimensional time. Lewis originally adhered to the concept of a Cartesian model of time, in which the traveler is free to move between axes, whereas the average person lives by a linear function symmetrical about two axes.

However, this idea of two-dimensional time is not supported by logic from the point of view that the same event cannot be dissected into two axes. In other words, the nature of time is inseparable and represents one line rather without division into directions: straight or cyclic. Straight time aligns perfectly with what Lewis proposed, namely the four-dimensional model. Aligning the three spatial coordinates with the time axis allows the traveler to cascade along with one of the axes without splitting events into different versions at different times.

The difference between the stages of travel in time constitutes change. In attempting to formulate a definition of qualitative change, Lewis was particularly careful to refer to illustrations. In particular, a person’s growing up or hair growth determines the passage of time, and in this sense, the traveler can go back to a time when he was still a child without hair, for example, this forms the Cambridge change model (Lewis 146). However, some elements are constant at all times, such as numbers or the laws of physics. In this sense, even when traveling through time, the traveler will find that unchanging elements or events have not been subject to transformation.

A key idea, set at the beginning of the paper and found up to the last paragraph, was the division of the nature of time into personal and external. To better convey the meaning of this division, Lewis gives an example concerning the time it took to travel. For instance, if a traveler moves one thousand years into the past, the journey itself may take him about an hour, but the final destination will have a chronological difference from the point of departure of minus a thousand years.

Thus, to respond to the seeming inconsistency of time — Lewis, as mentioned above, adheres to the hypothesis of the inseparability of time along the axes — the author introduces the terms “personal” and “external” time. The hour elapsed for the traveler determines his personal account, indicated on his wristwatch, while external time characterizes the difference that objectively exists between the beginning and the end of the journey.

Near the middle of his text, Lewis raises the most intriguing questions concerning time teleportations: the phenomenon of the traveler’s personal identity and the grandfather paradox. There is no doubt that the individual who has returned to the not-too-distant past is in the same reality system as the younger version of him. For example, a twenty-year-old man who has gone back ten years may be in contact with a ten-year-old himself. Lewis urges the reader not to make the mistake of differentiating between the two individuals and especially emphasizes that both the young and adult versions of the individual are the same person, bound together by a mental connection. For outsiders and even the young version of the traveler, all given events occur according to the course of external time, while the return to the past is the man’s personal experience.

On the other hand, such an effect raises the question of the existence of a causal link between the past and the present. In particular, in the case when an adult traveler tells a young one about the device of a time machine, this knowledge as a timeless phenomenon is transferred from the present to the past so that it then turns into the present. Simply put, a young explorer could not have created the time machine without encountering a more adult copy of himself. Lewis emphasizes that similar connections produce casual cycles and loops, which, however, do not explain the origin of the time machine’s knowledge.

Approaching the second half of the article, Lewis discusses the grandfather paradox, which best covers time travel’s causal mechanism. In particular, if a grandson from his own time returns to 1921 to kill his hated grandfather, this obviously raises a number of questions about the permissibility of such a situation (Lewis 148). On the one hand, the grandson’s personal reality does not exclude changes in the past, so there is no contradiction in killing his grandfather.

However, this version is untenable from the point of view that the events in time are interconnected. The murder of the grandfather, according to Lewis, would lead to the impossibility of the birth of the father and then of the grandchild proper in the future. In other words, the grandchild would not have to exist and could not go back in time to kill the grandfather. Consequently, the grandfather would not die, and the grandson would survive. Obviously, such thinking leads to untenable conclusions and logical fallacies, which is why this effect is called the time paradox.

One of the last thoughts mentioned in the paper is the hypothesis of the branching of time when events occur during travel. Although this idea has been mentioned cursorily, it is an important thought that allows considering the phenomenon of time in an alternative way (Lewis 152). Thus, time is not linear and does not represent an axis on a four-dimensional coordinate plane; instead, it can branch. The grandfather paradox perfectly describes this model: in the case of murder, the world continues to develop along one path, but the unkilled grandfather forms a parallel, alternate reality.

Lewis, David. “The Paradoxes of Time Travel.” American Philosophical Quarterly , vol. 13, no. 2, 1976, pp. 145-152.

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The Definitive Writer’s Guide to Time Travel (historical fiction tips and tricks)

Any writer can travel in time (it’s true), but to do it well takes effort…and a plan. Here is your complete plan to write convincing historical fiction or non-fiction.

Jenna Coleman did it.  You can, too.

Jenna played the role of The Doctor’s companion , first as Oswin Oswald, then as Clara Oswin Oswald and finally flying off in the Tardis as Clara Oswald for three seasons.

After all that time travel to shake her up, you’d think she would be eager to plant her feet firmly in her own time. But, no, she went straight back to the mid 1800s, playing Queen Victoria in Victoria .

Writers often find that themselves zipping back and forth through time just to complete one novel.

Ghostwriters get even worse jet lag. They often live in multiple time zones, all at once. They might be working simultaneously on a romance novel set in early San Francisco, a drama unfolding in the court of Alexander the Great and a sci fi adventure at some unknown date in a dystopian future.

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Any writer can travel in time, but to do it well takes effort. Future travel is easy. We all know we’ll wear fish in our ears and scramble our particles in transporter beams.

Getting the past right in historical fiction is a little more challenging. Here is a good starter guide to getting the past right. Of course, it’s just a guide.  Every book is different.

Time Travel Tips for Writers

Work with timelines

You should have at least two timelines before you even start writing. The first timeline, which is probably most obvious, is the timeline of the story you are writing about.

You might create several timelines for this, covering the protagonist, the antagonist and perhaps a few of the other main characters. You might even set out their events on two sides of a single line.

The second timeline should be a history line. It should include all major external events that could impact the story.  For instance, you might want to include the start and end of World War II, even if the story is not war-related. It should also include all lesser events that are close to the story.

Time is a lot like space. You need to know where a story takes place and the major physical or visual aspects of the setting. You need also to know the time aspects of the setting.

With the two timelines in hand, you can cross reference the two.  Make sure your story fits well into the historical timeline, and make adjustments if it does not.

If you plan to outsource your writing, you will save yourself a lot of frustration by getting this done before hiring a ghostwriter .

Technology and style of the day

No, they did not have flush toilets in the court of Kublai Khan.  How will you deal with that? Technology touches everything.  While transportation and communications might be obvious, simple home implements – such as flush toilets – can really color your story.

If someone drops by unexpectedly in colonial America, you can’t have the host just put a kettle on.  They first have to load the stove up with wood.

As important as is the functionality of things in a different era, the appearance of those things makes a difference, too. Here are some questions to ask:

What would this person be wearing in this era? More specifically, it’s important to figure out what the person would be wearing in various situations, just as we have different outfits for different situations.

What about architecture and home décor? How did things look in the garden (were there gardens?) and in the various rooms? Your story might come before plastic was invented or before wall paper was in style, for example.

Vocabulary of the day

As soon as you have dialogue in historical fiction, you have language to contend with.  How did people speak in those days.

If you go far enough back in time, you won’t be able to be totally authentic. After all, what type of English did the ancient Greeks speak? Even if you go back to Shakespeare’s time, the English of the day would make tough reading for us. Much better to use modern English vocabulary with some tweaks that give our modern minds a sense of days gone by.

Just as today, there were curses and there was slang in almost every era. Interjecting this more colorful language, where it would have been appropriate, gives your manuscript an air of authenticity.  But be careful, because not all slang will be understood and not all curses will seem very sharp to today’s reader.

And that’s another thing to get right – social norms.  Throughout history, the pendulum has swung between repressive and libertine. Make sure your manuscript reflects where the pendulum was at that time in history.

Time Travel Research Guide for Writers

If getting historical fiction right seems like a daunting task, there’s a reason.  It is a daunting task. In fact, it might be a writer’s most daunting task.

There is a lot of information to seek that we just take for granted in our own time. And the information is not readily available.  There are no year-by-year lists one can run to.

But there are places to turn:

Museums: There are history museums and there are art museums.  Photos and paintings give us some idea of how the upper classes dressed, how they wore their hair, etc. Village museums give a glimpse of how ordinary people lived at a certain time.

Books: Many old novels describe the surroundings, and sometimes pictures give an idea of what people and their abodes looked like. Novels from the era can also give you a good idea how to color your dialogue.

Documentaries: Whenever a film is available, make a point to watch. It will give you a feel for how things might have been.  Keep an open mind, though, because it will be mostly an educated guess.

Internet: Of course, the Internet is full of information and images.

Academics: If you are lucky enough to find an academic willing to work with you on historical accuracy, you have it made. Academics can provide input in advance, then “proofread” for historical accuracy.

Enthusiasts: Less reliable than academics, historical enthusiasts can also be helpful.  You’ll find plenty of Civil War enthusiasts, but likely fewer with knowledge of 17 th century Finland.

Time travel is fun.  And it’s even more fun if you are a writer or a singer in Hamilton . Or a Tardis passenger. Since Broadway is a long shot and blue boxes are in short supply these days, you might as well time travel as a writer.

David Leonhardt is President of The Happy Guy Marketing, a published author, a "Distinguished Toastmaster", a former consumer advocate, a social media addict and experienced with media relations and government reports.

Read more about David Leonhardt

Hi David, Awesome post……. your article is really informative and helpful for me and other bloggers too because writing a quality content is not a cup of tea. Really you have described everything in descriptive, simply yet effective too. You’ve done a great job with this. Thanks to share this informative article.

Hi Dave What a joy to be here again after a long gap. I am here today via your Quora question. Time Travel Tips for Writers” A lot of tips to pick for writers. Well written post with a lot of practical tips for a genuine writer. Yes, a writer needs to have a lot of patience. As you said: “Perfecting time travel might be a writer’s most daunting task. if one can achieve this area, I am sure he will succeed in his task. Thanks Dave for this wonderful and informative shout out especially for a writer like me. Learned a lot from it. Keep writing Best ~ Phil

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Home — Essay Samples — Science — Scientific Theories — Time Travel

Essays on Time Travel

What makes a captivating time travel essay topic.

When it comes to selecting a topic for your time travel essay, it's crucial to consider various factors that will set your essay apart from the rest. Here are some recommendations on how to brainstorm and choose the perfect essay topic:

- Brainstorm: Start by generating ideas related to time travel. Explore different time periods, whether fictional or real, and consider how they can be examined in your essay.

- Research: Conduct extensive research on the chosen time period or concept to gather enough information to craft a compelling essay.

- Uniqueness: Look for topics that are extraordinary and avoid those that have been overdone. Select something that will captivate readers' attention and offer a fresh perspective.

- Relevance: Evaluate the relevance of the chosen time travel topic. Does it hold significance in history, literature, or popular culture?

- Controversy: Controversial topics often ignite interest and discussion. If your time travel topic touches upon controversial themes or theories, it can make your essay more intriguing.

- Personal interest: Choose a topic that genuinely interests you. This will help you stay motivated and engaged throughout the writing process.

- Creativity: Think outside the box and explore unconventional ideas related to time travel. Don't hesitate to push boundaries and present a unique perspective.

- Impact: Consider the potential impact of your chosen topic. Can it challenge existing beliefs or open up new discussions about time travel?

A good time travel essay topic combines elements of originality, relevance, and creativity, captivating readers and making them eager to delve into the essay's content.

The Best Time Travel Essay Topics

Looking for some extraordinary time travel essay topics to get your creative juices flowing? Here are 20 unique and thought-provoking ideas:

1. The Butterfly Effect: Exploring the consequences of altering small events in history through time travel.

2. Time Loops: Analyzing the concept of being trapped in a never-ending cycle of time.

3. The Ethics of Time Travel: Examining the moral implications and dilemmas faced by time travelers.

4. Time Travel in Literature: Analyzing the portrayal of time travel in famous novels and its impact on the story.

5. Time Travel and Paradoxes: Investigating the logical paradoxes that arise when contemplating time travel.

6. Time Travel and Ancient Civilizations: Imagining the influence of time travel on shaping ancient civilizations.

7. Time Travel and Quantum Physics: Exploring the connection between time travel theories and quantum physics concepts.

8. Time Travel and Popular Culture: Analyzing the portrayal of time travel in movies, TV shows, and music.

9. Time Travel and Historical Events: Examining how pivotal historical events could have unfolded differently with time travel intervention.

10. Time Travel and Future Predictions: Speculating on how time travel could be used to predict and shape the future.

11. Time Travel and Artificial Intelligence: Investigating the intersection of time travel and AI advancements.

12. Time Travel and Multiverse Theory: Exploring the idea of multiple universes and their relation to time travel.

13. Time Travel and Evolution: Examining the impact of time travel on the evolution of species.

14. Time Travel and Alternate Realities: Imagining how time travel could lead to the existence of alternate realities.

15. Time Travel and Philosophy: Analyzing the philosophical implications and theories surrounding time travel.

16. Time Travel and Time Perception: Examining how time perception changes when traveling through time.

17. Time Travel and Ancient Mysteries: Investigating how time travel could help unravel ancient mysteries and secrets.

18. Time Travel and Cultural Exchange: Imagining the cultural exchanges that could occur through time travel between different civilizations.

19. Time Travel and Technological Advances: Speculating on how future technological advancements might enable time travel.

20. Time Travel and Personal Transformation: Exploring how time travel experiences can transform an individual's perspective on life.

These unique time travel essay topics will surely make your writing stand out and captivate your readers' imagination.

Time Travel Essay Questions

Here are ten thought-provoking essay questions to explore your chosen time travel topic in greater depth:

1. How would altering a major historical event through time travel impact the present world?

2. Can time travel paradoxes be resolved, or are they inherent in the concept?

3. What ethical concerns arise when considering the potential consequences of time travel on future generations?

4. How does time travel in literature reflect the societal context in which the works were written?

5. Is it possible to change the course of history through time travel, or is everything predestined?

6. How does time travel challenge our understanding of cause and effect?

7. If time travel were possible, would you choose to visit the past or the future? Why?

8. How does time travel intersect with our perception of reality and the nature of existence?

9. Can time travel be reconciled with the laws of physics, or does it require new scientific principles?

10. What role does time travel play in shaping our collective imagination and popular culture?

These essay questions will encourage critical thinking and prompt in-depth analysis of your time travel topic.

Time Travel Essay Prompts

Here are five creative essay prompts to spark your imagination and inspire unique perspectives on time travel:

1. Write a fictional letter from a time traveler warning humanity about a future catastrophe.

2. Imagine a world where time travel tourism is a booming industry. Explore the positive and negative implications of this phenomenon.

3. Create a short story where a time traveler accidentally alters a minor event that has significant consequences for the present.

4. Write an essay exploring the psychological and emotional challenges faced by a time traveler who is unable to return to their original timeline.

5. Imagine a society where time travel is a common occurrence. Discuss the impact of this technology on social, economic, and cultural aspects of life.

These essay prompts will encourage imaginative thinking and allow you to explore time travel from unconventional angles.

Answering Your Time Travel Essay FAQs

Q: Can I write a time travel essay without any scientific background?

A: Absolutely! While scientific knowledge can enhance your understanding of time travel concepts, it is not a prerequisite. Focus on exploring the philosophical, ethical, and cultural aspects of time travel instead.

Q: Should I choose a specific time period for my time travel essay?

A: It depends on your topic and interests. While a specific time period can provide a focused approach, broader concepts such as alternate realities or time loops may not require a specific era.

Q: Can I mix fictional and real-life elements in my time travel essay?

A: Yes, blending fictional and real-life elements can add depth and intrigue to your essay. Just ensure that the narrative remains coherent and logical.

Q: How do I ensure my time travel essay stands out from others?

A: Choose a unique topic, conduct thorough research, present fresh perspectives, and maintain a captivating writing style. Incorporate personal insights and engage readers through clear arguments and imaginative storytelling.

Q: Can I propose new time travel theories in my essay?

A: Absolutely! Time travel is a subject that invites speculation and exploration. Feel free to propose new theories, but ensure you support them with logical reasoning and evidence.

Remember, writing a time travel essay should be an enjoyable experience where you can unleash your creativity and explore intriguing concepts. Embrace the adventure of time travel and let your imagination soar!

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The Paradoxes of Time Travel by David Lewis Term Paper

Introduction, lewis on time travel, the criticism, lewis’ revision strategy of the story, works cited.

David Lewis, in his work, The Paradoxes of Time Travel, posits that time travel is possible and adds that; paradoxes surrounding time travel are not impossibilities but oddments. In this paper, the writer imagines that an author writes a science fiction story about time travel.

In the story, a poor scientist in 2010 uses a time machine to travel back to 2008, where he/she tells his younger self the winning lottery numbers for 2009. The time traveler uses the time machine to return to 2010, where he is now rich. The writer then uses Lewis’ arguments to criticize the story and suggest how Lewis would revise it. To understand this story, it is important to understand some of Lewis’ arguments.

Lewis observes that, “time must not be a line but a plane” (146). This implies if two events are separated more than once in time dimensions, then they can have two one-sided separations. In normal life, people live on straightforward aslope lines cutting across the plane of time. However, a time traveler lives on bent-line slopes on the same time plane. Moreover, according to Gott, time traveler has a personal time that does not comply with the rules of the normal time, also called external time (5).

In this case, the time traveler’s personal time can go back into ancient time in the present external time. Nevertheless, this phenomenon is relative and Lewis notes that the probability of a time traveler going back in time to change the past depends on some set facts. Lewis therefore would find a foothold to criticize the aforementioned fiction.

As aforementioned, the author writes a story where a poor scientist in 2010, goes back to 2008, reveals to his younger self the winning numbers of a 2009 lottery; wins the lottery, and comes back to 2010 where he or she is rich. Lewis would say that this scenario could not happen because of inconsistency.

Lewis would consider some few facts here. The poor scientist cannot be rich in 2010. This poor scientist is poor right now, therefore going back in 2008 and reveal to his/her younger self the winning numbers of a 2009 lottery, would be tantamount to changing the past, which cannot change.

Lewis would argue that, events surrounding “past moments are not sub divisible into temporal parts; therefore, cannot change” (151). Events of 2008 can either timelessly include the poor scientist revealing to his/her younger self the lottery winning numbers or timelessly do not include the events; however, the two events cannot occur simultaneously.

If the fiction story were to be considered true, the possibility of describing two events referring to same thing would be inevitable. In this case, there would be ‘original’ 2008 and ‘new’ 2008.

The ‘original’ 2008 would represent the actual time when the poor scientist lived and did not know anything about the winning lottery numbers; on the other hand, the ‘new’ 2008 would represent a counterfactual time when the poor scientist is revealing to his/her younger self the winning numbers of the lottery. In the time traveling world of this poor scientist, both the ‘original’ and the ‘new’ 2008 exist in his/her extended timeline; however, in the external time people would be referring to the same thing.

Unfortunately, one event cannot be defined or described by two different events. If the poor scientist did not reveal to his or her younger self the winning numbers in the ‘original’ 2008, but he reveals the numbers in the ‘new’ 2008, then he/she must both reveal and not reveal the winning numbers in 2008, because there can only be one 2008 which is both the ‘new’ and the ‘original’ 2008.

Therefore, logically speaking, the poor scientist cannot reveal to his/her younger self the winning numbers of the lottery; consequently, he or she cannot be rich in 2010.

Instead of giving a one sided story, Lewis would opt to give it two sides considering what the poor scientist could do and what he/she could not. The first scenario is that of the poor scientist not revealing to his/her younger self the winning numbers of the lottery as explicated in Lewis’ criticism. In revising this story, Lewis would argue that the poor scientist would reveal to his/her younger self the winning of the lottery.

Here are some facts that would facilitate this occasion. The poor scientist would change his/her poverty status in the past by revealing to his younger self the winning lottery numbers; however, he/she would fail to do that, not because of any impossibility but because of some inefficiencies. Given the fact that the poor scientist did not reveal the winning numbers in the original 2008, consistency requires that he/she does not reveal them in the ‘new’ 2008; why?

There has to be a reason why the poor scientist could not reveal the winning numbers to his/her younger self. Maybe he/she lost the paper containing the numbers or simply doubted the authenticity of the numbers. In this case, the poor scientist has the potential to reveal to his/her younger self the winning lottery numbers; however, something crops up which changes the fate of this poor scientist. This is normal in life; people try hard to do things that they would wish to; however, fate has it that they fail.

Not because it is impossible to do such things, it is only that luck does not allow it. In this case, some eminent contradictions would sabotage the consistency of the story. One, the poor scientist does not reveal the numbers even though he can for he/she has them. Two, the poor scientist does not reveal the numbers, and he/she cannot for the past is unchangeable. According to Sider, Lewis would argue that, ‘can’ is equivocal; hence, the two scenarios are compatible (1).

To say the poor scientist ‘could’ reveal the winning lottery numbers is compossible with contextual facts; that is, he had the numbers. The poor scientist could reveal to his/her younger self the winning lottery numbers just the way a teacher can read out answers to students. However, the poor scientist could not reveal the numbers to his young self because this scenario is not compossible with some other facts, he/she is poor in 2010, and this is the fact.

Nevertheless, interpreting these two scenarios calls to choose either a wide delineation and conclude that the poor scientist cannot reveal the numbers or a narrow delineation of relevant facts and conclude that he/she can reveal the numbers.

Relativity takes precedence here and either of the arguments can pass as true; however, one cannot afford to conclude that the poor scientist could and could not reveal the numbers simultaneously. The call to make choice here is to root out contradiction, which would otherwise refute the possibility of time travel.

Lewis points out that time travel is possible; however, one has to make a choice and argue his/her case out based on relativity of facts surrounding the subject under study. In the case of a poor scientist in 2010 traveling through a time machine to 2008, revealing to his younger self the winning numbers of a 2009 lottery, winning it and becoming rich in 2010, Lewis would criticize it on basis that, the past is unchangeable.

However, Lewis would revise the story and throw in a possibility of such an event happening depending on the relativity of facts surrounding it. The poor scientist did not reveal the numbers to his younger self but he/she could do so because he/she had the numbers; however, he/she failed for he/she either misplaced the paper containing the numbers or simply doubted the authenticity of the same.

On the other hand, the poor scientist did not reveal the numbers to his younger self and cannot because the past is unchangeable. The fact is, in 2010, the scientist is poor, and it depends on the stand that one takes in interpreting the possibility of this poor scientist going back to 2008 to reveal the winning numbers to his young self. Nevertheless, one cannot say that the poor scientist can and cannot travel back to 2008 simultaneously.

Gott, Richard. “Time Travel in Einstein’s Universe: The Physical Possibilities of Travel.” New York; Houghton Mifflin Company, 2001.

Lewis, David. “The Paradoxes of Time Travel.” American Philosophical Quarterly. 1976: 13(2); 146-152.

Sider, Ted. “Lewis on Time Travel.” Nd. Web.

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Editor’s Note: We know that many of you are looking for help writing travel experience essays for school or simply writing about a trip for your friends or family. To inspire you and help you write your next trip essay—whether it’s an essay about a trip with family or simply a way to remember your best trip ever (so far)—we enlisted the help of Professor Kathleen Boardman, whose decades of teaching have helped many college students learn the fine art of autobiography and life writing. Here’s advice on how to turn a simple “my best trip” essay into a story that will inspire others to explore the world.

Welcome home! Now that you’re back from your trip, you’d like to share it with others in a travel essay. You’re a good writer and a good editor of your work, but you’ve never tried travel writing before. As your potential reader, I have some advice and some requests for you as you write your travel experience essay.

Trip Essays: What to Avoid

Please don’t tell me everything about your trip. I don’t want to know your travel schedule or the names of all the castles or restaurants you visited. I don’t care about the plane trip that got you there (unless, of course, that trip is the story).

I have a friend who, when I return from a trip, never asks me, “How was your trip?” She knows that I would give her a long, rambling answer: “… and then … and then … and then.” So instead, she says, “Tell me about one thing that really stood out for you.” That’s what I’d like you to do in this travel essay you’re writing.

The Power of Compelling Scenes

One or two “snapshots” are enough—but make them great. Many good writers jump right into the middle of their account with a vivid written “snapshot” of an important scene. Then, having aroused their readers’ interest or curiosity, they fill in the story or background. I think this technique works great for travel writing; at least, I would rather enjoy a vivid snapshot than read through a day-to-day summary of somebody’s travel journal.

Write About a Trip Using Vivid Descriptions

Take your time. Tell a story. So what if you saw things that were “incredible,” did things that were “amazing,” observed actions that you thought “weird”? These words don’t mean anything to me unless you show me, in a story or a vivid description, the experience that made you want to use those adjectives.

I’d like to see the place, the people, or the journey through your eyes, not someone else’s. Please don’t rewrite someone else’s account of visiting the place. Please don’t try to imitate a travel guide or travelogue or someone’s blog or Facebook entry. You are not writing a real travel essay unless you are describing, as clearly and honestly as possible, yourself in the place you visited. What did you see, hear, taste, say? Don’t worry if your “take” on your experience doesn’t match what everyone else says about it. (I’ve already read what THEY have to say.)

The Importance of Self-Editing Your Trip Essay

Don’t give me your first draft to read. Instead, set it aside and then reread it. Reread it again. Where might I need more explanation? What parts of your account are likely to confuse me? (After all, I wasn’t there.) Where might you be wasting my time by repeating or rambling on about something you’ve already told me?

Make me feel, make me laugh, help me learn something. But don’t overdo it: Please don’t preach to me about broadening my horizons or understanding other cultures. Instead, let me in on your feelings, your change of heart and mind, even your fear and uncertainty, as you confronted something you’d never experienced before. If you can, surprise me with something I didn’t know or couldn’t have suspected.

You Can Do It: Turning Your Trip into a Great Travel Experience Essay

I hope you will take yourself seriously as a traveler and as a writer. Through what—and how—you write about just a small portion of your travel experience, show me that you are an interesting, thoughtful, observant person. I will come back to you, begging for more of your travel essays.

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2 Minute Speech On If Time Travel Were Real In English

Good morning everyone present here, today I am going to give a speech on if time travel were real. The study of time travel has grown quite complicated. Time travel is a popular concept in science fiction media. In his essay “The Paradoxes of Time Travel,” the late philosopher David Lewis characterized it as involving a contradiction between time and space-time. Any traveler sets off and then arrives at his or her destination; the distance traveled is the amount of time between departure and arrival.

Most people typically think of time travel as going back in time or forward to a future location. This is a genuine concern given the idea’s widespread appeal. There are numerous potential solutions to this query, none of which are incompatible. The most straightforward response is that time travel is not feasible because if it were, we’d be doing it by now. It may be argued that it is against the principles of physics, such as relativity or the second law of thermodynamics. Technical difficulties also exist; it might be feasible but would require a significant amount of energy.

Another issue is the time-travel paradoxes, which we can potentially address if free will is a delusion, if there are several worlds, or if the past can only be seen but not felt. Perhaps the reason time must move in a linear fashion and we have no influence over it makes time travel impossible. Alternatively, perhaps time is an illusion, and time travel is meaningless. Thank you. 

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New York Takes Crucial Step Toward Making Congestion Pricing a Reality

The board of the Metropolitan Transportation Authority voted to approve a new $15 toll to drive into Manhattan. The plan still faces challenges from six lawsuits before it can begin in June.

By Winnie Hu and Ana Ley

New York City completed a crucial final step on Wednesday in a decades-long effort to become the first American city to roll out a comprehensive congestion pricing program, one that aims to push motorists out of their cars and onto mass transit by charging new tolls to drive into Midtown and Lower Manhattan.

The program could start as early as mid-June after the board of the Metropolitan Transportation Authority, the state agency that will install and manage the program, voted 11-to-1 to approve the final tolling rates, which will charge most passenger cars $15 a day to enter at 60th Street and below in Manhattan. The program is expected to reduce traffic and raise $1 billion annually for public transit improvements.

It was a historic moment for New York’s leaders and transportation advocates after decades of failed attempts to advance congestion pricing even as other gridlocked cities around the world, including London, Stockholm and Singapore, proved that similar programs could reduce traffic and pollution.

While other American cities have introduced related concepts by establishing toll roads or closing streets to traffic, the plan in New York is unmatched in ambition and scale.

Congestion pricing is expected to reduce the number of vehicles that enter Lower Manhattan by about 17 percent, according to a November study by an advisory committee reporting to the M.T.A. The report also said that the total number of miles driven in 28 counties across the region would be reduced.

“This was the right thing to do,” Janno Lieber, the authority’s chairman and chief executive, said after the vote. “New York has more traffic than any place in the United States, and now we’re doing something about it.”

Congestion pricing has long been a hard sell in New York, where many people commute by car from the boroughs outside of Manhattan and the suburbs, in part because some of them do not have access to public transit.

New York State legislators finally approved congestion pricing in 2019 after Gov. Andrew M. Cuomo helped push it through. A series of recent breakdowns in the city’s subway system had underscored the need for billions of dollars to update its aging infrastructure.

It has taken another five years to reach the starting line. Before the tolling program can begin, it must be reviewed by the Federal Highway Administration, which is expected to approve it.

Congestion pricing also faces legal challenges from six lawsuits that have been brought by elected officials and residents from across the New York region. Opponents have increasingly mobilized against the program in recent months, citing the cost of the tolls and the potential environmental effects from shifting traffic and pollution to other areas as drivers avoid the tolls.

A court hearing is scheduled for April 3 and 4 on a lawsuit brought by the State of New Jersey, which is seen as the most serious legal challenge. The mayor of Fort Lee, N.J., Mark J. Sokolich, has filed a related lawsuit.

Four more lawsuits have been brought in New York: by Ed Day, the Rockland County executive; by Vito Fossella, the Staten Island borough president, and the United Federation of Teachers; and by two separate groups of city residents.

Amid the litigation, M.T.A. officials have suspended some capital construction projects that were to be paid for by the program, and they said at a committee meeting on Monday that crucial work to modernize subway signals on the A and C lines had been delayed.

Nearly all the toll readers have been installed, and will automatically charge drivers for entering the designated congestion zone at 60th Street or below. There is no toll for leaving the zone or driving around in it. Through traffic on Franklin D. Roosevelt Drive and the West Side Highway will not be tolled.

Under the final tolling structure, which was based on recommendations by the advisory panel, most passenger vehicles will be charged $15 a day from 5 a.m. to 9 p.m. on weekdays, and from 9 a.m. to 9 p.m. on weekends. The toll will be $24 for small trucks and charter buses, and will rise to $36 for large trucks and tour buses. It will be $7.50 for motorcycles.

Those tolls will be discounted by 75 percent at night, dropping the cost for a passenger vehicle to $3.75.

Fares will go up by $1.25 for taxis and black car services, and by $2.50 for Uber and Lyft. Passengers will be responsible for paying the new fees, and they will be added to every ride that begins, ends or occurs within the congestion zone. There will be no nighttime discounts. (The new fees come on top of an existing congestion surcharge that was imposed on for-hire vehicles in 2019.)

The tolls will mostly be collected using the E-ZPass system. Electronic detection points have been placed at entrances and exits to the tolling zone. Drivers who do not use an E-ZPass will pay significantly higher fees — for instance, $22.50 instead of $15 during peak hours for passenger vehicles.

Emergency vehicles like fire trucks, ambulances and police cars, as well as vehicles carrying people with disabilities, were exempted from the new tolls under the state’s congestion pricing legislation .

As for discounts, low-income drivers who make less than $50,000 annually can apply to receive half off the daytime toll after their first 10 trips in a calendar month. In addition, low-income residents of the congestion zone who make less than $60,000 a year can apply for a state tax credit.

All drivers entering the zone directly from four tolled tunnels — the Lincoln, Holland, Hugh L. Carey and Queens-Midtown — will receive a “crossing credit” that will be applied against the daytime toll. The credit will be $5 round-trip for passenger vehicles, $12 for small trucks and intercity and charter buses, $20 for large trucks and tour buses, and $2.50 for motorcycles. No credits will be offered at night.

Grace Ashford contributed reporting.

Winnie Hu is a Times reporter covering the people and neighborhoods of New York City. More about Winnie Hu

Ana Ley is a Times reporter covering New York City’s mass transit system and the millions of passengers who use it. More about Ana Ley