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3 Popular Time Travel Theory Concepts Explained

Time travel theory. It’s one of the most popular themes in fiction. But every plotline falls into one of these three Time Travel Theories.

Time travel is one of the most popular themes in cinema . Although most time travel movies are in the sci-fi genre, every genre, even comedy, horror, and drama, have tackled complicated storylines involving time travel theory. Chances are, you’ve seen at least a few of the movies listed below:

• But what about...

The Possibility Of Time Travel

Time travel theory.

• Bill & Ted’s Excellent Adventure (1989)
• The Time Machine  (2002)
• Timeline (2003)
• Time Cop (2004)
• Back to the Future  (1985)
• 12 Monkeys  (1995)
• Terminator Series (1984)
• Star Trek (2009)
• Harry Potter and the Prisoner of Azkaban (2004)
• Freejack (1992)
• Looper (2012)

But one thing you might not have realized, even if you’ve seen hundreds of time travel-related films, is that there are only  3 different theories of time travel. That’s it. Every time travel movie or book that you’ve ever enjoyed falls into one of these time travel theories.

Fixed Timeline: Time Travel Theory

Want to change the future on Earth by modifying the past or present? Don’t even bother according to this time travel theory. In a fixed timeline, there’s a single history that is unchangeable. Whatever you are attempting to change by time-traveling is what created the problems in the present that you’re trying to fix ( 12 Monkeys ). Or you’re just wasting your time because the events you are trying to prevent will happen anyway ( Donnie Darko ).

Dynamic Timeline: Time Travel Theory

History is fragile and even the smallest changes can have a huge impact. After traveling back in time, your actions may impact your own timeline. The result is a paradox. Your changes to the past might result in you never being born, like in Back to the Future (1985), or never traveling in time in the first place. In The Time Machine (2002), Hartdegen goes back in time to save his sweetheart Emma but can’t. Doing so would have resulted in his never developing the time machine that he used to try and save her.

One common way to explore this paradox theory is by killing your own grandfather. The grandfather paradox is when a time traveler attempts to kill their grandfather before the grandfather meets their grandmother. This prevents the time travel’s parents from being born and thus the time traveler himself from being born. But if the time traveler was never born, then the traveler would never have traveled back in time, therefore erasing his or her actions involving the death of their grandfather.

Multiverse: Time Travel Theory

Travel all over time and do whatever you want. It doesn’t matter because there are multiple universes and your actions only create new timelines. This is a common theory used by the science fiction TV series, Doctor Who . Using the multiverse theory of time travel, it’s assumed that there are multiple coexisting alternate timelines.

Therefore, when the traveler goes back in time, they end up in a new timeline where historical events can differ from the timeline they came from, but their original timeline does not cease to exist. This means the grandfather paradox can be avoided. Even if the time traveler’s grandparent is killed at a young age in the new timeline, he/she still survived to have children in the original timeline, so there is still a causal explanation for the traveler’s existence.

Time travel may actually create a new timeline that diverges from the original timeline at the moment the time traveler appears in the past, or the traveler may arrive in an already existing parallel universe. There’s just one problem… you can’t go back ( The One , 2002).

But what about…

Some may argue that people who are “trapped” in time are time travelers as well. This happens in countless time travel movies including Robin Williams ‘ character in the 1995 film Jumanji who gets trapped inside a board game. The list of “people who are cryogenically frozen and then successfully thawed out in the future” is even longer and includes Austin Powers: The Spy Who Shagged Me  (1999), Planet of the Apes (1968) and so on.

Although these characters are “moving” through time, they are doing so by pausing and then rejoining the current timeline. The lack of a time machine device disqualifies them from technically being “time travelers” and included in this list of theories on time travel.

So will time travel ever be possible? All we know for sure is that the experts don’t agree. According to the Albert Einstein theory of relativity, time is relative, not constant and the bending of spacetime could be possible. But according to  Stephen Hawking , time travel is not possible. The Stephen Hawking time travel theory suggests that the absence of present-day time travelers from the future is an argument against the existence of time travel — a variant of the Fermi paradox (aka where the hell is everybody?). But it’s fun to think about.

NERD NOTE:  What happens to time in a black hole? We don’t know for sure, but according to both Stephen Hawking and Albert Einstein’s theory, time near a black hole slows down. This is because a black hole’s gravitational pull is so strong that even light can’t escape. Since gravity also affects light, time would also slow down.

If you could successfully travel into the future, or back in time, what would you do? Warn people about natural disasters? Buy a winning lottery ticket ? Try to prevent your own death? What do you think about these time travel theory ideas or the time travel movies that we included in this article? Please tell us in the comments below.

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Frank Wilson is a retired teacher with over 30 years of combined experience in the education, small business technology, and real estate business. He now blogs as a hobby and spends most days tinkering with old computers. Wilson is passionate about tech, enjoys fishing, and loves drinking beer.

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Mar 24, 2015 at 11:24 PM

are there really only 3 theories? i feel like there are more but i cant think of any besides the movies listed here. hummmmmmmmm

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In This Article Expand or collapse the "in this article" section Time Travel

Introduction, general overviews.

• David Lewis’s Analysis, Its Forerunners and Critics
• Gödel and the Ideality of Time
• Models and Issues from Relativity
• Models and Issues from Quantum Theory
• Causal Loops and Probability
• Time Travel in Many Worlds and the Autonomy Principle
• Travel in Dynamic Time and Multi-Dimensional Time
• General Metaphysical Issues

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Time Travel by Alasdair Richmond LAST REVIEWED: 26 October 2015 LAST MODIFIED: 26 October 2015 DOI: 10.1093/obo/9780195396577-0295

Time travel is a philosophical growth industry, with many issues in metaphysics and elsewhere recently transformed by consideration of time travel possibilities. The debate has gradually shifted from focusing on time travel’s logical possibility (which possibility is now generally although not universally granted) to sundry topics including persistence, causation, personal identity, freedom, composition, and natural laws, to name but a few. Besides metaphysical discussions, some time travel works draw on the philosophies of science, spacetime, and computation. Some interesting forerunners notwithstanding, serious physical interest in time travel begins with Gödel’s 1949a demonstration that general relativity permits space-times that are riddled with closed timelike curves (“CTCs” henceforth). A key philosophical text on time travel is Lewis 1976 and its argument for the logical possibility of certain backward time travel journeys and even for the possibility of casual loops. Lewis concludes that time travel could occur in a possible world, albeit perhaps a strange world that would feature (or seem to feature) strange restrictions on actions. In Lewis’s analysis, a traveler can arrive in the past of the same history they come from provided that the traveler’s actions on arrival are consistent with the history that they come from. So other worlds or multiple temporal dimensions are not necessary to make time travel consistent. Granted, the physics, persistence conditions, agency, and epistemology of agents in such worlds might look weird indeed. Since Lewis, philosophical time travel questions include the following: given that a traveler into the past cannot create any paradoxical outcomes on arrival, what then would stay their hand? Are the constraints on a traveler’s actions admissible within our ordinary understanding of physical law or human agency? Is time travel compatible with dynamic time or even with the existence of time itself? Can backward time travel be physically possible within a single history? If a time traveler meets another stage of him- or herself, is the traveler in two places at once, and what theory of persistence can cope with this puzzling multiplication? Can time-travel spacetimes resolve otherwise intractable computational problems?

Despite several hundred philosophical and scientific articles, book chapters, and Internet resources devoted to philosophical problems posed by time travel, there is currently no full-length monograph or anthology on the subject. The best introduction to the topic in general so far is chapter 8 of Dainton (second edition 2010), Dainton 2010 being the best general philosophical resource available on time and space. The key work is Lewis 1976 , a defense of the logical possibility of backward time travel, from which a large number of subsequent treatments take their cue. A useful overview, albeit largely from a physical science perspective, is Nahin 1999 . Also largely physical in emphasis but comprehensive and thorough is Earman 1995 . Richmond 2003 surveys philosophical work on time travel to date. Arntzenius 2006 details the problems of free action and nomological constraint posed by backward time travel. Arntzenius and Maudlin 2005 is helpful on (especially) problems of physical law. Carroll 2008 is perhaps the best single online resource available on any aspect of time travel. Le Poidevin 2003 is a highly commendable introduction to the philosophy of time in general but especially good on problems of time travel. Bourne 2006 offers some useful arguments and clarifications centered on Gödel’s arguments about time travel and the relations between time travel and the status of times themselves. Earman and Wüthrich 2006 offers scientifically well informed but approachable and philosophically cogent discussions of what physics might, and might not, allow by way of time travel.

Arntzenius, Frank. “Time Travel: Double Your Fun.” Philosophy Compass 6 (2006): 599–616.

DOI: 10.1111/j.1747-9991.2006.00045.x

Entertaining survey of the philosophical terrain around time travel that concentrates particularly on the constraints on action likely to be suffered by travelers in the past. An excellent introduction to the nomological contrivance problem and more. Available online for purchase or by subscription.

Arntzenius, Frank, and Tim Maudlin. “ Time Travel and Modern Physics .” In Stanford Encyclopedia of Philosophy . Edited by Edward N. Zalta. 2005.

Notably acute survey of physical possibilities for time travel, including detailed arguments that backward time travel threatens to create correlations that conflict with standard quantum predictions.

Bourne, C. A Future for Presentism . Oxford: Oxford University Press, 2006.

DOI: 10.1093/acprof:oso/9780199212804.001.0001

Although primarily devoted to defending presentism, chapter 8 offers one of the best treatments of Gödel’s ideality argument around and pp. 132–134 offer some interesting sidelights on the possible compatability of time travel and presentism.

Carroll, John W. A Time Travel Website . 2008–.

Extremely thorough, engagingly-written, well-designed, and continually evolving online resource that offers helpful discussions, well-chosen readings, and helpful animations to boot.

Dainton, Barry. Time and Space . 2d ed. Durham, NC: Acumen, 2010.

Revised and expanded edition of Dainton’s classic 2001 introduction to the philosophy of space and time. Can be highly recommended but notable here for its extensive, essential treatments of time travel, relativity, and Gödel’s “ideality” argument.

Earman, John. “Recent Work on Time Travel.” In Time’s Arrows Today . Edited by Steven F. Savitt, 268–310. Cambridge, UK: Cambridge University Press, 1995.

DOI: 10.1017/CBO9780511622861

Thorough discussion of the then-current state of play in the philosophical and physical literature on time travel. This is still a valuable resource.

Earman, John, and Christian Wüthrich. “ Time Machines .” In Stanford Encyclopedia of Philosophy . Edited by Edward N. Zalta. 2006.

Comprehensive discussion of physical resources for time travel, among other intriguing suggestions, develops the view that physically realistic time machines might be uncontrollable even if they become a possiblility.

Le Poidevin, Robin. Travels in Four Dimensions: The Enigmas of Space and Time . Oxford: Oxford University Press, 2003.

Engaging and clearly written introduction to the philosophy of space and time. Often offers problems and discussions that lend themselves to time travel interpretation. An excellent introductory and pedagogical resource.

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

The philosophical time travel work. Includes Lewis’s discrepancy definition of time travel: the most useful by far. Invokes the notion of compossibility to disambiguate “Grandfather paradox” arguments and argues that backward time travel and causal loops can occur in (nonbranching) possible worlds. Usefully distinguishes between replacement change and counterfactual change. (This is often cited and sometimes rebutted but never refuted.)

Nahin, Paul. Time Machines: Time Travel in Physics, Metaphysics and Science Fiction . 1st ed. New York: American Institute of Physics, 1999.

DOI: 10.1007/978-1-4757-3088-3

Engaging and comprehensive attempt at surveying all the scientific, philosophical, and fictional literature on time travel. Perhaps slightly more at ease with physics and fiction than with philosophy, but this is a detailed and thorough treatment.

Richmond, Alasdair. “Recent Work: Time Travel.” Philosophical Books 44 (2003): 297–309.

DOI: 10.1111/1468-0149.00308

Survey of the time travel debate from Lewis 1976 onward, sketching links with debates in persistence, philosophy of spacetime and temporal topology. Available online by subscription.

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Can we time travel? A theoretical physicist provides some answers

Emeritus professor, Physics, Carleton University

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Peter Watson received funding from NSERC. He is affiliated with Carleton University and a member of the Canadian Association of Physicists.

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Time travel makes regular appearances in popular culture, with innumerable time travel storylines in movies, television and literature. But it is a surprisingly old idea: one can argue that the Greek tragedy Oedipus Rex , written by Sophocles over 2,500 years ago, is the first time travel story .

But is time travel in fact possible? Given the popularity of the concept, this is a legitimate question. As a theoretical physicist, I find that there are several possible answers to this question, not all of which are contradictory.

The simplest answer is that time travel cannot be possible because if it was, we would already be doing it. One can argue that it is forbidden by the laws of physics, like the second law of thermodynamics or relativity . There are also technical challenges: it might be possible but would involve vast amounts of energy.

There is also the matter of time-travel paradoxes; we can — hypothetically — resolve these if free will is an illusion, if many worlds exist or if the past can only be witnessed but not experienced. Perhaps time travel is impossible simply because time must flow in a linear manner and we have no control over it, or perhaps time is an illusion and time travel is irrelevant.

Laws of physics

Since Albert Einstein’s theory of relativity — which describes the nature of time, space and gravity — is our most profound theory of time, we would like to think that time travel is forbidden by relativity. Unfortunately, one of his colleagues from the Institute for Advanced Study, Kurt Gödel, invented a universe in which time travel was not just possible, but the past and future were inextricably tangled.

We can actually design time machines , but most of these (in principle) successful proposals require negative energy , or negative mass, which does not seem to exist in our universe. If you drop a tennis ball of negative mass, it will fall upwards. This argument is rather unsatisfactory, since it explains why we cannot time travel in practice only by involving another idea — that of negative energy or mass — that we do not really understand.

Mathematical physicist Frank Tipler conceptualized a time machine that does not involve negative mass, but requires more energy than exists in the universe .

Time travel also violates the second law of thermodynamics , which states that entropy or randomness must always increase. Time can only move in one direction — in other words, you cannot unscramble an egg. More specifically, by travelling into the past we are going from now (a high entropy state) into the past, which must have lower entropy.

This argument originated with the English cosmologist Arthur Eddington , and is at best incomplete. Perhaps it stops you travelling into the past, but it says nothing about time travel into the future. In practice, it is just as hard for me to travel to next Thursday as it is to travel to last Thursday.

Resolving paradoxes

There is no doubt that if we could time travel freely, we run into the paradoxes. The best known is the “ grandfather paradox ”: one could hypothetically use a time machine to travel to the past and murder their grandfather before their father’s conception, thereby eliminating the possibility of their own birth. Logically, you cannot both exist and not exist.

Read more: Time travel could be possible, but only with parallel timelines

Kurt Vonnegut’s anti-war novel Slaughterhouse-Five , published in 1969, describes how to evade the grandfather paradox. If free will simply does not exist, it is not possible to kill one’s grandfather in the past, since he was not killed in the past. The novel’s protagonist, Billy Pilgrim, can only travel to other points on his world line (the timeline he exists in), but not to any other point in space-time, so he could not even contemplate killing his grandfather.

The universe in Slaughterhouse-Five is consistent with everything we know. The second law of thermodynamics works perfectly well within it and there is no conflict with relativity. But it is inconsistent with some things we believe in, like free will — you can observe the past, like watching a movie, but you cannot interfere with the actions of people in it.

Could we allow for actual modifications of the past, so that we could go back and murder our grandfather — or Hitler ? There are several multiverse theories that suppose that there are many timelines for different universes. This is also an old idea: in Charles Dickens’ A Christmas Carol , Ebeneezer Scrooge experiences two alternative timelines, one of which leads to a shameful death and the other to happiness.

Time is a river

Roman emperor Marcus Aurelius wrote that:

“ Time is like a river made up of the events which happen , and a violent stream; for as soon as a thing has been seen, it is carried away, and another comes in its place, and this will be carried away too.”

We can imagine that time does flow past every point in the universe, like a river around a rock. But it is difficult to make the idea precise. A flow is a rate of change — the flow of a river is the amount of water that passes a specific length in a given time. Hence if time is a flow, it is at the rate of one second per second, which is not a very useful insight.

Theoretical physicist Stephen Hawking suggested that a “ chronology protection conjecture ” must exist, an as-yet-unknown physical principle that forbids time travel. Hawking’s concept originates from the idea that we cannot know what goes on inside a black hole, because we cannot get information out of it. But this argument is redundant: we cannot time travel because we cannot time travel!

Researchers are investigating a more fundamental theory, where time and space “emerge” from something else. This is referred to as quantum gravity , but unfortunately it does not exist yet.

So is time travel possible? Probably not, but we don’t know for sure!

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Internet Encyclopedia of Philosophy

Time travel.

Before the twentieth century, scientists and philosophers rarely investigated time travel, but now it is an exciting and deeply studied topic. There are investigations into travel to the future and travel to the past, although travel to the past is more problematical and receives more attention.   There are also investigations of the logical possibility of time travel, the physical possibility of time travel, and the technological practicality of time travel. The most attention is paid to time travel that is consistent with current physical theory such as Einstein’s general theory of relativity. In science, different models of the cosmos and the laws of nature governing the universe imply different possibilities for time travel. So, theories about time travel have changed radically as the dominant cosmological theories have evolved from classical, Newtonian conceptions to modern, relativistic and quantum mechanical conceptions. Philosophers were quick to note some of the implications of the new physics for venerable issues in metaphysics: the nature of time, causation and personal identity, to name just a few. The subject continues to produce a fruitful cross-fertilization of ideas between scientists and philosophers as theorists in both fields struggle to resolve confounding paradoxes that emerge when time travel is pondered seriously. This article discusses both the scientific and philosophical issues relevant to time travel.

Table of Contents

• Introduction
• Time in Philosophy
• Newtonian Cosmology
• Special Relativity
• General Relativity
• Quantum Interpretations
• The Grandfather Paradox
• Causal Loops
• Personal Identity
• References and Further Reading

1. Introduction

Time travel stories have been a staple of the science fiction genre for the past century. Good science fiction stories often pay homage to the fundamentals of scientific knowledge of the time. Thus, we see time travel stories of the variety typified by H. G. Wells as set within the context of a Newtonian universe: a three-dimensional Euclidean spatial manifold that changes along an inexorable arrow of time. By the early to mid-twentieth century, time travel stories evolved to take into account the features of an Einsteinian universe: a four-dimensional spacetime continuum that curves and in which time has the character of a spatial dimension (that is, there can be local variations or “warps”). More recently, time travel stories have incorporated features of quantum theory: phenomena such as superposition and entanglement suggest the possibility of parallel or many universes, many minds, or many histories. Indeed, the sometimes counter-intuitive principles and effects of quantum theory have invigorated time travel stories. Bizarre phenomena like negative energy density (the Casimir effect) lend their strangeness to the already odd character of time travel stories.

In this article, we make a distinction between time travel stories that might be possible within the canon of known physical laws and those stories that contravene or go beyond known laws. The former type of stories, which we shall call natural time travel, exploit the features or natural topology of spacetime regions. Natural time travel tends to severely constrain the activities of a time traveler and entails immense technological challenges. The latter type of stories, which we shall call Wellsian time travel, enable the time traveler more freedom and simplify the technological challenges, but at the expense of the physics. For example, in H. G. Wells’ story, the narrator is a time traveler who constructs a machine that transports him through time. The time traveler’s journey, as he experiences it, occurs over some nonzero duration of time. Also, the journey is through some different nonzero duration of time in the world. It is the latter condition that distinguishes the natural time travel story from the Wellsian time travel story. Our laws of physics do not allow travel through a nonzero duration of time in the world (in a sense that will be made clearer below). Wellsian time travel stories are mortgaged on our hope or presumption that more fundamental laws of nature are yet to be discovered beyond the current horizon of scientific knowledge. Natural time travel stories can be analyzed for consistency with known physics while Wellsian time travel stories can be analyzed for consistency with logic. Finally, time travel stories implicate themselves in a constellation of common philosophical problems. Among these philosophically related issues we will address in this article are the metaphysics of time, causality, and personal identity.

2. Definition

What is time travel? One standard definition is that of David Lewis’s: an object time travels iff the difference between its departure and arrival times in the surrounding world does not equal the duration of the journey undergone by the object. This definition applies to both natural and Wellsian time travel. For example, Jane might be a time traveler if she travels for one hour but arrives two hours later in the future (or two hours earlier in the past). In both types of time travel, the times experienced by a time traveler are different from the time undergone by their surrounding world.

But what do we mean by the “time” in time travel? And what do we mean by “travel” in time travel? As the definition for time travel presently stands, we need to clarify what we mean by the word “time” (see the next section). While philosophical analysis of time travel has attended mostly to the difficult issue of time, might there also be vagueness in the word “travel”? Our use of the word “travel” implies two places: an origin and a destination. “I’m going to Morocco,” means “I’m departing from my origination point here and I plan to arrive eventually in Morocco.” But when we are speaking of time travel, where exactly does a time traveler go? The time of origin is plain enough: the time of the time traveler and the time traveler’s surrounding world coincide at the beginning of the journey. But “where” does the time traveler arrive? Are we equivocating in our use of the word ‘travel’ by simply substituting a when for a where? In truth, how do we conceive of a “when”—as a place, a locale, or a region? Different scientific ontologies result in different ideas of what travel through time might be like. Also, different metaphysical concepts of time result in different ideas of what kinds of time travel are possible. It is to the issue of time in philosophy that we now turn.

3. Time in Philosophy

How is time related to existence? Philosophy offers three primary answers to this metaphysical question: eternalism, possibilism, and presentism. The names of these views indicate the ontological status given to time. The eternalist thinks that time, correctly understood, is a fourth dimension essentially constitutive of reality together with space. All times, past, present and future, are actual times just like all points distributed in space are actual points in space. One cannot privilege any one moment in the dimension of time as “more” real than any other moment just like one cannot privilege any point in space as “more” real than any other point. The universe is thus a spacetime “block,” a view that has philosophical roots at least as far back as Parmenides . Everything is one; the appearance of things coming to be and ceasing to be, of time passing or flowing, is simply phenomenal, not real. Objects from the past and future have equal ontological status with present objects. Thus, a presently extinct individual dodo bird exists as equably as a presently existing individual house finch, and the dodo bird and the house finch exist as equably as an individual baby sparrow hatched next Saturday. Whether or not the dodo bird and the baby sparrow are present is irrelevant ontologically; they simply aren’t in our spacetime region right now. The physicist typically views the relation of time to existence in the way that the eternalist does. The life of an object in the universe can be properly shown as:

This diagram shows the spatial movement (in one dimension) of an object through time. The standard depiction of an object’s spacetime “worldline” in Special Relativity, the Minkowski diagram (see below), privileges this block view of the universe. Many Wellsian time travel stories assume the standpoint of eternalism. For example, in Wells’ The Time Machine, the narrator (the time traveler) explains: “There is no difference between Time and any of the three dimensions of Space except that our consciousness moves along it.” Eternalism fits easily into the metaphysics of time travel.

The second view is possibilism, also known as the “growing block” or “growing universe” view. The possibilist thinks that the eternalist’s picture of the universe is correct except for the status of the future. The past and the present are fixed and actual; the future is only possible. Or more precisely, the future of an object holds the possibility of many different worldlines, only one of which will become actual for the object. If eternalism seems overly deterministic, eliminating indeterminacies and human free choice, then possibilism seems to retain some indeterminacy and free choice, at least as far as the future is concerned. For the possibilist, the present takes on a special significance that it does not have for the eternalist. The life of an object according to possibilism might be shown as:

This diagram shows that the object’s worldline is not yet fixed or complete. (It should be pointed out that the necessity of illustrating the time axis with a beginning and end should not be construed as an implicit claim that time itself has a beginning and end.) Some Wellsian time travel stories make use of possibilism. Stories like Back to the Future and Terminator suggest that we can change the outcome of historical events in our world, including our own personal future, through time travel. The many different possible histories of an object introduce other philosophical problems of causation and personal identity, issues that we will consider in greater depth in later sections of the article.

The third view is presentism. The presentist thinks that only temporally present objects are real. Whatever is, exists now. The past was, but exists no longer; the future will be, but does not exist yet. Objects are scattered throughout space but they are not scattered throughout time. Presentists do not think that time is a dimension in the same sense as the three spatial dimensions; they say the block universe view of the eternalists (and the intermediate view of the possibilists) gets the metaphysics of time wrong. If eternalism has its philosophical roots in Parmenides, then presentism can be understood as having its philosophical roots in Heraclitus. Presently existing things are the only actuality and only what is now is real. Each “now” is unique: “You cannot step twice into the same river; for fresh waters are ever flowing in upon you.” The life of an object according to presentism might be shown as:

Many presentists account for the continuity of time, the timelike connection of one moment to the next moment, by appealing to the present intrinsic properties of the world (Bigelow). To fully describe some of these present intrinsic properties of the world, you need past- and future-tensed truths to supervene on those properties. For example, in ordinary language we might make the claim that “George Washington camped at Valley Forge.” This sentence has an implicit claim to a timeless truth, that is, it was true 500 years ago, it was true when it was happening, it is true now, and it will be true next month. But, according to presentism, only presently existing things are real. Thus, the proper way to understand the truth of this sentence is to translate it into a more primitive form, where the tense is captured by an operator. So in our example, the truth of the sentence supervenes on the present according to the formulation “WAS(George Washington camps at Valley Forge).” In this way, presentists can describe events in the past and future as truths that supervene on the present. It is the basis for their account of persistence through time in issues like causality and personal identity.

4. Time in Physics

Since the use of the term ‘time’ in our definition of time travel remains ambiguous, we may further distinguish external, or physical time from personal, or inner time (again, following Lewis). In the ordinary world, external time and one’s personal time coincide with one another. In the world of the time traveler, they do not. So, with these two senses of time, we may further clarify time travel to occur when the duration of the journey according to the personal time of the time traveler does not equal the duration of the journey in external time. Most (but not all) philosophy of time concerns external time (see the encyclopedia entry Time ). For the purpose of natural time travel, we need to examine the scientific understanding of external time and how it has changed.

a. Newtonian Cosmology

Newton argued that space, time and motion were absolute, that is, that the entire universe was a single, uniform inertial frame and that time passed equably throughout it according to an eternally fixed, immutable and inexorable rate, without relation to anything external. Natural time travel in the Newtonian universe is impossible; there are no attributes or topography of space or time that can be exploited for natural time travel stories. Only time travel stories that exceed the bounds of Newtonian physics are possible and scenarios described by some Wellsian time travel stories (most notably like the one Wells himself wrote) are examples of such unscientific time travel.

Several philosophers and scientists objected to the notion of absolute space, time and motion, most notably Leibniz, Berkeley and Mach. Mach rejected Newton’s implication that there was anything substantive about time: “It is utterly beyond our power to measure the changes of things by time. Quite the contrary, time is an abstraction, at which we arrive by means of the changes of things” (The Science of Mechanics, 1883). For Mach, change was more fundamental than the concept of time. We talk about time “passing” but what we’re really noticing is that things move and change around us. We find it convenient to talk as if there were some underlying flowing substance like the water of a river that carries these changes along with it. We abstract time to have a standard measuring tool by which we can quantify change. These views of Mach’s were influential for the young Albert Einstein. In 1905, Einstein published his famous paper on Special Relativity. This theory began the transformation of our understanding of space, time and motion.

b. Special Relativity

The theory of Special Relativity has two defining principles: the principle of relativity and the invariance of the speed of light. Briefly, the principle of relativity states that the laws of physics are the same for any inertial observer. An observer is an inertial observer if the observer’s trajectory has a constant velocity and therefore is not under the influence of any force. The second principle is the invariance of the speed of light. All inertial observers measure the speed c of light in a vacuum as 3 x 10 8 m/s, regardless of their velocities relative to one another. This principle was implied in Maxwell’s equations of electromagnetism (1873) and the constancy of c was verified by the Michelson-Morley interferometer experiment (1887).

This second principle profoundly affected the model of the cosmos: the constancy of c was inconsistent with Newtonian physics. The invariance of the speed of light according to Special Relativity replaces the invariance of time and distance in the Newtonian universe. Intervals of space, like length, and intervals of time (and hence, motion) are no longer absolute quantities. Instead of speaking of an object in a particular position independently of a particular time, we now speak of an event in which position and time are inseparable. We can relate two events with a new quantity, the spacetime interval. For any pair of events, the spacetime interval is an absolute quantity (that is, has the same value) for all inertial observers. To visualize this new quantity, one constructs spacetime diagrams (Minkowski diagrams) in which an event is defined by its spatial position (usually restricted to one dimension, x) and its time (ct). Thus, a spacetime interval might be null (parallel to the trajectory of light, which, because of the y-axis units, is shown at a 45° angle), spacelike (little or no variation in time), or timelike (little or no variation in spatial position). The following figure shows a Minkowski diagram depicting the flat spacetime of Special Relativity and three different spacetime intervals, or worldlines .

What are the consequences of Special Relativity for time travel? First, we lose the common sense meaning of simultaneity. For example, the same event happens at two different times if one observer’s inertial frame is stationary relative to another observer’s inertial frame moving at some velocity. Furthermore, an observer in the stationary inertial frame may determine two events to have happened simultaneously, but an observer in the second moving inertial frame would see the same two events happening at different times. Thus, there is no universal or absolute external time; we can only speak of external time within one’s own frame of reference. The lack of simultaneity across frames of reference means that we might experience the phenomenon of time dilation. If your frame of reference is moving at some fraction of the speed of light, your external time passes more slowly than the external time in a frame of reference that is stationary relative to yours. If we imagine that someone in the stationary frame of reference could peek at a clock in your frame of reference, they would see your clock run very slowly. So in Special Relativity, we can find a kind of natural time travel. An example of Special Relativity time travel is of an astronaut who travels some distance in the universe at a velocity near the speed of light. The astronaut’s personal time elapses at the same rate it always has. He travels to his destination and then returns home to find that external time has passed there quite differently. Everyone he knew has aged more than he, or perhaps has even been dead for hundreds or thousands of years.

Such stories are physically consistent with the Einsteinian universe of Special Relativity, but of course they remain technologically beyond our present capability. Nevertheless, they are an example of a natural time travel story—adhering to the known laws of physics—which do not require exceptions to fundamental scientific principles (for example, the invariant and inviolable speed of light). But as a time travel story, they require that the time traveler also be an ordinary traveler, too, that is, that he travel some distance through space at extraordinary speeds. Furthermore, this sort of natural time traveler can only time travel into the future. (Conversely, from the perspective of those in the originating frame of reference, when the astronaut returns, they witness the effects of time travel to the past perhaps because they have a person present among them who was alive in their distant past.) So natural time travel according to Special Relativity is perhaps too limited for what we normally mean by time travel since it requires (considerable) spatial travel in order to work.

In addition, there are other limitations, not least of which is mass-energy equivalence. This principle was published by Einstein in his second paper of 1905, entitled “Does the Inertia of a Body Depend Upon Its Energy Content?” Mass-energy equivalence was implied by certain consequences of Special Relativity (other theorists later discovered that it was suggested by Maxwell’s electromagnetism theory). Mass-energy equivalence is expressed by the famous formula, E = mc 2 . It means that there is an energy equivalent to the mass of a particle at rest. When we harmonize mass-energy equivalence with the conservation law of energy, we find that if a mass ceases to exist, its equivalent amount of energy must appear in some form. Mass is interchangeable with energy. Now only mass-less objects, like photons, can actually move at the speed of light. They have kinetic energy but no mass energy. Indeed, all objects with mass at rest, like people and spaceships cannot, in principle, attain the speed of light. They would require an infinite amount of energy.

c. General Relativity

In Special Relativity, all inertial frames are equivalent, and while this is a useful approximation, it does not yet suggest how inertial frames are to be explained. Mach had stated that the distribution of matter determines space and time. But how? This was the question answered by Einstein in his theory of General Relativity (1916). Special Relativity is actually a subset of General Relativity. General Relativity takes into account accelerating frames of reference (that is, non-inertial frames) and thus, the phenomenon of gravity. The topography of spacetime is created by the distribution of mass. Spacetime is dynamic, it curves, and matter “tells” a region of spacetime how to curve. Likewise, the resultant geometry of a spacetime region determines the motion of matter in it.

The fundamental principle in General Relativity is the equivalence principle, which states that gravity and acceleration are two names designating the same phenomenon. If you are accelerating upwards at a rate g in an elevator located in a region of spacetime without a gravitational field, the force you would feel and the motion of objects in the elevator with you would be indistinguishable from an elevator that is stationary within a downward uniform gravitational field of magnitude g. To be more precise, there is no “force” of gravity. When we observe astronauts who are in orbit over the Earth, it is not true to say that they are in an environment with no gravity. Rather, they are in free fall within the Earth’s gravitational field. They are in a local inertial frame and thus do not feel the weight of their own mass.

One curious effect of General Relativity is that light bends when it travels near objects. This may seem strange when we remember that light has no mass. How can light be affected by gravity? Light always travels in straight lines. Light bends because the geometry of spacetime is non-Euclidean in the vicinity of any mass. The curved path of light around a massive body is only apparent; it is simply traveling a geodesic straight line. If we draw the path of an airplane traveling the shortest international route in only two dimensions (like on a flat map), the path appears curved; however, because the earth itself is curved and not flat, the shortest distance, a straight line, must always follow a geodesic path. Light travels along the straight path through the various contours of spacetime. Another curious effect of General Relativity is that gravity affects time. Imagine a uniformly accelerating frame, like a rocket during an engine burn. General Relativity predicts that, depending on one’s location in the rocket, one will measure time differently. To an observer at the bottom or back of the rocket (depending on how you want to visualize its motion), a clock at the top or front of the rocket will appear to run faster. According to the principle of equivalence, then, a clock at sea level on the Earth runs a little slower than a clock at the top of Mount Everest because the strength of the field is weaker the further you are from the center of mass.

Are natural time travel stories possible in General Relativity? Yes, they are, and some of them are quite curious. While most of spacetime seems to be flat or gently rolling contours, physicists are aware of spacetime regions with unusual and severe topologies such as rotating black holes. Black holes are entities that remain from the complete collapse of stars. Black holes are the triumph of gravity over all other forces and are predicted by a solution to Einstein’s General Relativity equations (Kerr, 1963). When they rotate, the singularity of the black hole creates a ring or torus, which might be traversable (unlike the static black hole, whose singularity would be an impenetrable point). If an intrepid astronaut were to position herself near the horizon of the rapidly spinning center of a black hole (without falling into its center and possibly being annihilated), she would be treated to a most remarkable form of time travel. In a brief period of her personal time she would witness an immensely long time span in the universe beyond the black hole horizon; her spacetime region would be so far removed from the external time of the surrounding cosmos that she conceivably could witness thousands, millions, or billions of years elapse. This is a kind of natural time travel; however, it severely restricts the activity of the astronaut/time traveler and she is limited to “travel” into the future. Are there solutions to General Relativity that allow natural time travel into the past? Yes, but unlike rotating black holes, they remain only theoretical possibilities.

Einstein’s neighbor in Princeton, Kurt Gödel, developed one such solution. In 1949, Gödel discovered that some worldlines in closed spacetime could curve so severely that they curved back onto themselves, forming a loop in spacetime. These loops are known as closed timelike curves (CTCs). If you were an object on a CTC worldline, you would eventually arrive at the same spacetime position from which you started, that is, your older self would appear at one of its own earlier spacetime points. Gödel’s CTC spacetime describes a rotating universe; thus, it is an extreme case for a CTC because it is globally intrinsic to the structure of the universe. It is not considered a realistic solution since current cosmological theory states that the universe is expanding, not rotating.

One type of spacetime region that a natural time traveler might exploit is a wormhole : two black holes whose throats are linked by a tunnel. Wormholes would connect two regions of space and two regions of time as well. Physicist Kip Thorne speculated that if one could trap one of the black holes that comprise the mouths of the wormhole it would be conceivable to transport it, preferably at speeds near the speed of light. The moving black hole would age more slowly than the stationary black hole at the other end of the wormhole because of time dilation. Eventually, the two black holes would become unsynchronized and exist in different external times. The natural time traveler could then enter the stationary black hole and emerge from the wormhole some years earlier than when he departed. Unfortunately for our time traveler, if wormholes exist naturally many scientists think that they are probably quite unstable (particularly if quantum effects are taken into account). So, any natural wormhole would require augmentation from exotic phenomena like negative energy in order to be useful as a time machine.

Another type of CTC suggested by Gott (1991) employs two infinitely long and very fast moving cosmic “strings” of extremely dense material. The atom-width strings would have to travel parallel to one another in opposite directions. As they rush past one another, they would create severely curved spacetime such that spacetime curved back on itself. The natural time traveler would be prepared to exploit these conditions at just the right moment and fly her spaceship around the two strings. If executed properly, she would return to her starting point in space but at an earlier time.

One common feature of all CTCs, whether it is the global Gödelian rotating universe or the local regions of rolled-up spacetime around a wormhole or cosmic strings, is that they are solutions to General Relativity that would describe CTCs as already built into the universe. The natural time traveler would have to seek out these structures through ordinary travel and then exploit them. So far, we are not aware of any solution to General Relativity that describes the evolution of a CTC in a spacetime region where time travel had not been possible previously; however, it is usually assumed that there are such solutions to the equations. These solutions would entail particular physical constraints. One constraint would be the creation of a singularity in a finite region of spacetime. To enter the region where time travel might be possible, one would have to cross the Cauchy horizon, the hourglass-shaped (for two crossing cosmic strings) boundary of the singularity in which the laws of physics are unknown. Were such a CTC constructed, a second constraint would limit the external time that would be accessible to the time traveler. You could not travel to a time prior to the inception date of the CTC. (For more on this sort of time travel, see Earman, Smeenk, and Wüthrich, 2002.)

Natural time travel according to General Relativity faces daunting technological challenges especially if you want to have some control over the trajectory of your worldline. One problem already mentioned is that of stability. But equally imposing is the problem of energy. Fantastic amounts of exotic matter (or structures and conditions similar to the early moments of the Big Bang, like membranes with negative tension boundary layers, or gravitational vacuum polarization) would be needed to construct and manage a usable wormhole; infinitely long tubes of hyperdense matter would be needed for cosmic strings. Despite these technological challenges, it should be pointed out that the possibility of natural time travel into the past is consistent with General Relativity. But Hawking and other physicists recognize another problem with actual time travel into the past along CTCs: maintaining a physically consistent history within causal loops (see Causation below). One advantage of some interpretations of relativistic quantum theory is that the logical requirement for a consistent history in a time travel story is seemingly avoided by postulating alternative histories (or worlds) instead of one history of the universe.

d. Quantum Interpretations

Certain aspects of quantum theory are relevant to time travel, in particular the field of quantum gravity. The fundamental forces of nature (strong nuclear force, electromagnetic force, weak nuclear force, and gravitation) have relativistic quantum descriptions; however, attempts to incorporate gravity in quantum theory have been unsuccessful to date. On the current standard model of the atom, all forces are carried by “virtual” particles called gauge bosons (corresponding to the order given above for the forces: mesons and gluons, photons, massive W and Z particles, and the hypothetical graviton). A physicist might say that the photon “carries” electromagnetic force between “real” particles. The graviton, which has eluded attempts to detect it, “carries” gravity. This particle-characterization of gravity in quantum theory is very different from Einstein’s geometrical characterization in General Relativity. Reconciling these two descriptions is a robust area of research and many hope that gravity can be understood in the same way as the other fundamental forces. This might eventually lead to the formulation of a “theory of everything.”

Scientists have proposed several interpretations of quantum theory. The central issue in interpretations of quantum theory is entanglement. When two quantum systems enter into temporary physical interaction, mutually influencing one another through known forces, and then separate, the two systems cannot be described again in the same way as when they were first brought together. Microstate and macrostate entanglement occurs when an observer measures some physical property, like spin, with some instrumentation. The rule, according to the orthodox (or Copenhagen) interpretation, is that when observed the state vector (the equation describing the entangled system) reduces or jumps from a state of superposition to one of the actually observed states. But what happens when an entangled state “collapses?” The orthodox interpretation states that we don’t know; all we can say about it is to describe the observed effects, which is what the wave equation or state vector does.

Other interpretations claim that that the state vector does not “collapse” at all. Instead, some no-collapse interpretations claim that all possible outcomes of the superposition of states become real outcomes in one way or another. In the many-worlds version of this interpretation (Everett, 1957), at each such event the universe that involves the entangled state exfoliates into identical copies of the universe, save for the values of the properties included in the formerly entangled state vector. Thus, at any given moment of “collapse” there exist two or more nearly identical universes, mutually unobservable yet equally real, that then each divide further as more and more entangled events evolve. On this view, it is conceivable that you were both born and not born, depending on which world we’re referring to; indeed, the meaning of ‘world’ becomes problematic. The many universes are collectively designated as the multiverse. There are other variations on the many-worlds interpretation, including the many minds version (Albert and Loewer, 1988) and the many histories version (Gell-Mann and Hartle, 1989); however, they all share the central claim that the state vector does not “collapse.”

Many natural time travel stories make use of these many-worlds conceptions. Some scientists and storytellers speculate that if we were able to travel through a wormhole that we would not be traversing a spacetime interval in our own universe, but instead we would be hopping from “our” universe to an alternative universe. A natural time traveler in a many-worlds universe would, upon their return trip, enter a different world history. This possibility has become quite common in Wellsian time travel stories, for example, in Back to the Future and Terminator. These types of stories suggest that through time travel we can change the outcome of historical events in our world. The idea that the history of the universe can be changed is why many of the inconsistencies with causation and personal identity arise. We now turn to these topics to examine the philosophical implications of time travel stories.

5. Causation

Inconsistencies and incoherence in time travel stories often result from spurious applications of causation. Causation describes the connected continuity of events that change. The nature of this relation between events, for example, whether it is objective or subjective, is a subject of debate in philosophy. But for our purposes, we need only notice that events generally appear to have causes. The distinction made between external and personal time is crucial now for the difficulties of causation in some time travel stories.

Imagine Heloise is a time traveler who travels 80 years in the past to visit Harold. They have a fight and Heloise knocks out one of Harold’s teeth. If we follow the progression of Heloise’s personal time (or of Harold’s), the story is consistent; indeed, time travel seems to have little effect upon the events described. The difficulty arises when we test the consistency of the story in external time, because it involves an earlier event being affected by a later event. The ordinary forward progress of events related to Harold 80 years ago requires a schism in the connectivity and continuity of those events to allow the entry of a later event, namely, Heloise’s time travel journey. The activity of Heloise is causally continuous with respect to her personal time but not with respect to external time (assuming that the continuity of her personal identity is not in question, as we shall discuss in the next section). With respect to external time, this story describes reversed causation, for later events produce changes in earlier events. How does the story change if Heloise is homicidal and encounters her own grandfather 80 years ago? This is a scenario many think show that time travel into the past is inconsistent and thus impossible.

a. The Grandfather Paradox

Heloise despises her paternal grandfather. Heloise is homicidal and has been trained in various lethal combat techniques. Despite her relish at the thought of murdering her grandfather, time has conspired against her, for her grandfather has been dead for 30 years. As a crime investigator might say, she has motive and means, but lacks the opportunity; that is, until she fortuitously comes into the possession of a time machine. Now Heloise has the opportunity to fulfill her desire. She makes the necessary settings on the machine and plunges back into time 80 years. She emerges from the machine and begins to stalk her grandfather. He suspects nothing. She waits for the perfect moment and place to strike so that she can enjoy the full satisfaction of her hatred. At this point, we might pause to observe: “If Heloise murders her grandfather, she will have prevented him from fathering any children. That means that Heloise’s own father will not be born. And that means that Heloise will not be born. But if she never comes into existence, then how is she able to return…?” And so we have the infamous grandfather paradox. Before we examine what happens next, let’s consider the possible outcomes of her impending action.

First, let’s assume that the many-worlds hypothesis correctly describes the universe. If so, then we avoid the paradox. If Heloise succeeds in killing her grandfather before her father is conceived, then the state of the world includes quantum entanglement of the events involved in Heloise’s mind, body, surrounding objects, etc., such that when she succeeds in killing her grandfather (or willing his death just prior to the physical accomplishment of it), the universe at that moment divides into one universe in which she succeeded and a second universe in which she did not. So the paradox of causal continuity in external time does not arise; causation presumably connects events in the different universes without any inconsistency. But as we shall see in the next section this quantum interpretation trades-off a causation paradox for a personal identity paradox.

Next, let’s assume that we do not have the many-worlds quantum interpretation available to us, nor for that matter, any theory of different worlds. Can Heloise murder her grandfather? As David Lewis famously remarked, in one sense she can, and in another sense she can’t. The sense in which she can murder her grandfather refers to her ability, her willingness, and her opportunity to do so. But the sense in which she cannot murder her grandfather trumps the sense in which she can. In fact, she does not murder her grandfather because the moments of external time that have already passed are no longer separable. Assuming that events 80 years ago did not include Heloise murdering her grandfather, she cannot create another moment 80 years ago that does. A set of facts is arranged such that it is perfectly appropriate to say that, in one sense, Heloise can murder her grandfather. However, this set of facts is enclosed by the larger set of facts that include the survival of her grandfather. Were Heloise to actually succeed in carrying out her murderous desire, this larger set of facts would contain a contradiction (that her grandfather both is murdered and is not murdered 80 years ago), which is impossible. History remains consistent.

This is also related to Stephen Hawking’s view (1992). According to his so-called Chronology Protection Conjecture, he claims that the laws of physics conspire to prevent macroscopic inconsistencies like the grandfather paradox. A “Chronology Protection Agency” works through events like vacuum fluctuations or virtual particles to prevent closed trajectories of spacetime curvature in the negative direction (CTCs). If Hawking is right and many-worlds quantum interpretations are not available, then is time travel to the past still possible? Hawking’s view about consistent history then takes us to the special case of causation paradoxes: the causal loop.

b. Causal Loops

A causal loop is a chain of causes that closes back on itself. A causes B, which causes C,…which causes X, which causes A, which causes B…and so on ad infinitum. This sequence of events is exploited in some natural and Wellsian time travel stories. It is a point of debate whether all time travel stories involving travel to the past include causal loops. As we have seen, causal loops can occur when extraordinary cosmic structures curve spacetime in a negative direction. Wellsian time travel stories with causal loops describe scenarios like the following one by Keller and Nelson (2001).

Jennifer, a young teenager, is visited by an old woman who materializes in her bedroom. The old woman describes intimate details that only Jennifer would know and thus convinces Jennifer to pursue a professional tennis career. Jennifer does exactly as the old woman suggested and eventually retires, successful and happy. One day she comes into the possession of a time machine and decides to use it to travel back in time so that she might try to make her teenage years happier. Jennifer travels back into the past and stands before a person she recognizes as her younger self. Jennifer begins to talk to the teenager about her hidden talents and the bright future before her as a tennis professional. At the end of their conversation, Jennifer activates the time machine and returns to her original time. We can describe the causal loop in Keller and Nelson’s story as follows. The story contained within in the causal loop is presented on the left side. At event C, the story splits, with the causal loop continuing along C1, and the exit from the loop beginning at C2. At C2, the worldline of Jennifer continues outside the causal loop events. Thus:

The events of Jennifer’s life include a causal loop: some of those events have no beginning and no end. What is the problem with the story? Each moment of the causal sequence is explicable in terms of the prior events. But where (or when) did the crucial information that Jennifer would have a successful tennis career come from originally? While each part of the causal sequence makes sense, the causal loop as a whole is surprising because it includes information ex nihilo . It is controversial whether such uncaused causes are possible. Some philosophers (for example, Mellor, 1998) think that causal loop time travel stories are impossible because causal loops are themselves impossible. They argue that time and causality must progress in the same direction. Other philosophers (for example, Horwich, 1987) argue that while causal loops are not impossible, they are highly implausible, and thus spacetime does not permit time travel into the “local” past (like one’s own life) because fantastic amounts of energy would be required. Still other philosophers (for example, Lewis) think that causal loops are possible because at least some events, like the Big Bang, appear to be events without causes, introducing information ex nihilo .

According to Hawking, causal loop stories that employ CTCs are like grandfather paradox stories. While backwards causation might be logically possible, it is not physically possible. The “Chronology Protection Agency” actively prevents them from occurring. The laws of physics conspire such that natural time travel into the past thwarts backwards or reverse causation. In closed spacetime, the Cauchy horizon of a CTC acts as an impenetrable barrier to a timelike worldline for objects. If a time traveler could travel to the past, whether or not that past included their younger self, they are prevented from interacting with the events of the past.

If causal loops are possible, then the objects may interact with the events of the past, but only in a consistent way, that is, only in a way that preserves the already established events of the past. Perhaps we could call it the CTC prime directive (see Ray Bradbury’s short story “A Sound of Thunder”). Causal loops, like any other aporia of uncaused causes, occupy the inexplicable perimeter of philosophical thought about causation. Nevertheless, causal loop stories like that of Jennifer raise another issue: personal identity .

6. Personal Identity

The old Jennifer travels back in time to talk with her younger self. Are there two Jennifers or just one Jennifer at event A? At the same moment in external time, a young Jennifer and an old Jennifer are separated by a distance of a few feet. At that moment, is there one person or two? Identity theory involves the relationships between the mind and the body that attempts to show the connection between mental states and physical states (see the entry Personal Identity ). It tries, for example, to describe and explain the connection (if any) between mind and the brain. For Lewis, the mental/physical distinction is crucial for explaining how a time traveler like Jennifer is one person, even when she travels back to talk with her younger self. Our cognitions change according to the requirement of causal continuity. These mental states occur in personal time. For everyday purposes, we can ignore the distinction between personal time and external time; personal time and external time coincide. But for a time traveler like Jennifer, identity is maintained only by virtue of the traveler’s personal time; their mental states continue like anyone else’s and at any given point in personal time, later mental states do not cause earlier ones.

In the case of Jennifer, it is therefore proper to say that at event A in her life, there is only one person, even though it is also true to say from an external perspective, that she has two different bodies present at event A. Lewis’s distinction between the sense in which you can and the sense in which you can’t has its coda in the subject of personal identity. In the sense of personal time, Jennifer is one person who is perceiving another person (from either Jennifer’s perspective). The older Jennifer’s materialization into the presence of the younger Jennifer is strange, to be sure, but in a time travel story, it is explicable. Regardless, in her personal time, the causal continuity of her perception (and thus mental states) is consistent. In the sense of external time, from the perspective of their surrounding world, there are two Jennifers at event A. The mental state of the younger Jennifer is not identical to the mental state of the older Jennifer. But these mental states, these stages of Jennifer’s life are not duplicates of the same stage; rather, two moments of personal time overlap at one moment of external time. So is it still proper to say that there are two of her? Lewis argues no, it is not. In the strange case of a time traveler like Jennifer, her stages are scattered in such a way that they do not connect in a continuously forward direction through external time, but they do connect continuously forward through her personal time. The time traveler who meets up with her younger self gives the appearance to an outside observer that she is two different people, but in reality, there is only one person.

The question of how objects persist through time is the subject of the endurance and perdurance debate in philosophy. An endurantist is someone who thinks that objects are wholly present at each moment of an interval of time. A perdurantist is someone who thinks that objects only have a temporal part present at each moment of an interval of time. The perdurantist claims that the identity of the whole object is identified as the sum of these temporal parts over the lifetime of the object. It seems that it is impossible for an endurantist to believe the story about Jennifer because she would have to be wholly present in two different spatial locations at the same time. The endurantist can avoid this problem by appealing to the distinction between personal time and external time. If Jennifer is wholly present at different locations “at the same time,” which kind of time do we mean? We mean external time. The endurantist can claim that two different temporal stages in her personal time just so happen to coincide because she is a time traveler at different locations at a single moment of external time. For those of us who are not time travelers, our different temporal stages are also distinct moments in external time. But in either case, whether time traveler or not, a person is wholly present at any moment of their personal time.

The perdurantist seems to have an easier way with the problem of personal identity in time travel stories. Since a person is only partially present at each moment of external time, it is readily conceivable that different temporal parts might coincide, but we still need to appeal to the distinction between personal time and external time. The two temporal parts of Jennifer’s life that occur when the young and old Jennifer meet and have a conversation are each elements among many others that in toto form the whole person.

Personal identity is especially problematic in a many-worlds hypothesis. Consider the case of Heloise and her desire to murder her grandfather. According to the many-worlds hypothesis, she travels back in time but by doing so also skips into another universe. Heloise is free to kill her grandfather because she would not be killing “her” grandfather, that is, the same grandfather that she knew about before her time travel journey. Indeed, Heloise herself may have split into two different persons. Whatever she does after she travels into the past would be consistent with the history of the alternative universe. But the question of who exactly Heloise or her grandfather is becomes problematic, especially if we assume that her actions in the different universes are physically distinct. Is Heloise the sum of her appearances in the many worlds? Or is each appearance of Heloise a unique person?

Also, see the related article Time in this Encyclopedia.

7. References and Further Reading

• Albert, David and Barry Loewer. 1988. Interpreting the many worlds interpretation. Synthese 77:195-213.
• Bigelow, John. Time travel fiction. In Gerhard Preyer and Frank Siebelt, eds., Reality and Humean Supervenience. Lanham, MD: Rowan & Littlefield, 2001. 58-91.
• Bigelow, John. Presentism and properties. In James E. Tomberlin, ed., Philosophical Perspectives 10. Cambridge, MA: Blackwell Publishers, 1996. 35-52.
• Bradbury, Ray. 1952. A Sound of Thunder. In R is for Rocket. New York: Doubleday.
• Earman, John. 1995. Outlawing Time Machines: chronology protection theorems. Erkenntnis 42(2):125-139.
• Earman, John, Smeenk, Christopher and Wüthrich, Christian. 2002. Take a ride on a time machine. In R. Jones and P. Ehrlich, eds., Reverberations of the Shaky Game: Festschrift for Arthur Fine. Oxford: Oxford University Press.
• Everett, Hugh. 1957. Relative state formulation of quantum mechanics. Review of Modern Physics 29:454-62.
• Gell-Mann, Murray and James B. Hartle. 1989. Quantum mechanics in the light of quantum cosmology. In Proceedings of the 3rd International Symposium on the Foundations of Quantum Mechanics. Tokyo, Japan. 321-43.
• Gott, J. Richard. Time Travel in Einstein’s Universe: The Physical Possibilities of Travel Through Time. Boston: Houghton Mifflin, 2001.
• Hawking, S. W. 1992. Chronology protection conjecture. Physical Review D 46(2):603-11.
• Horwich, Paul. 1987. Asymmetries in Time: Problems in the Philosophy of Science. Cambridge, MA: MIT Press.
• Keller, Simon and Michael Nelson. 2001. Presentists should believe in time-travel. Australasian Journal of Philosophy 79:333-45.
• Lewis, David. 1976. The paradoxes of time travel. American Philosophical Quarterly 13:145-52.
• Mellor, D. H. Real Time II. London: Routledge, 1998.
• Monton, Bradley. 2003. Presentists can believe in closed timelike curves. Analysis 63(3).
• Smith, Nicholas J. J. 1997. Bananas enough for time travel? British Journal of Philosophy 48:363-389.

Author Information

Joel Hunter Email: [email protected] Truckee Meadows Community College U. S. A.

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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.

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causation: backward | determinism: causal | quantum mechanics | quantum mechanics: retrocausality | space and time: being and becoming in modern physics | time machines | time travel

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Time Travel

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This chapter departs from the way in which time travel has been conceptualized in modern and theoretical physics, to show how the trope of time travel was refracted and developed in cultural productions from a variety of different cultural and temporal contexts.

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Hawking, Stephen J. 1988. A short history of time: From the big bang to black holes . New York: Bantam Press.

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6 Is Time Travel Possible?

• Published: July 2013
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The static theory of time treats temporal location a lot like spatial location. In accordance with contemporary physics, spacetime is treated in this theory as an unchanging four-dimensional block. Each temporal slice of the continuum is just as real as any other, just as any part of space is just as real as any other. Some might suggest that this means that travel to other parts of time should be possible, at least in theory, just as travel to other parts of space is possible. Thus an investigation of the possibility of time travel is at the same time an investigation of the implications of the static theory of time .

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April 26, 2023

Is Time Travel Possible?

The laws of physics allow time travel. So why haven’t people become chronological hoppers?

By Sarah Scoles

yuanyuan yan/Getty Images

In the movies, time travelers typically step inside a machine and—poof—disappear. They then reappear instantaneously among cowboys, knights or dinosaurs. What these films show is basically time teleportation .

Scientists don’t think this conception is likely in the real world, but they also don’t relegate time travel to the crackpot realm. In fact, the laws of physics might allow chronological hopping, but the devil is in the details.

Time traveling to the near future is easy: you’re doing it right now at a rate of one second per second, and physicists say that rate can change. According to Einstein’s special theory of relativity, time’s flow depends on how fast you’re moving. The quicker you travel, the slower seconds pass. And according to Einstein’s general theory of relativity , gravity also affects clocks: the more forceful the gravity nearby, the slower time goes.

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“Near massive bodies—near the surface of neutron stars or even at the surface of the Earth, although it’s a tiny effect—time runs slower than it does far away,” says Dave Goldberg, a cosmologist at Drexel University.

If a person were to hang out near the edge of a black hole , where gravity is prodigious, Goldberg says, only a few hours might pass for them while 1,000 years went by for someone on Earth. If the person who was near the black hole returned to this planet, they would have effectively traveled to the future. “That is a real effect,” he says. “That is completely uncontroversial.”

Going backward in time gets thorny, though (thornier than getting ripped to shreds inside a black hole). Scientists have come up with a few ways it might be possible, and they have been aware of time travel paradoxes in general relativity for decades. Fabio Costa, a physicist at the Nordic Institute for Theoretical Physics, notes that an early solution with time travel began with a scenario written in the 1920s. That idea involved massive long cylinder that spun fast in the manner of straw rolled between your palms and that twisted spacetime along with it. The understanding that this object could act as a time machine allowing one to travel to the past only happened in the 1970s, a few decades after scientists had discovered a phenomenon called “closed timelike curves.”

“A closed timelike curve describes the trajectory of a hypothetical observer that, while always traveling forward in time from their own perspective, at some point finds themselves at the same place and time where they started, creating a loop,” Costa says. “This is possible in a region of spacetime that, warped by gravity, loops into itself.”

“Einstein read [about closed timelike curves] and was very disturbed by this idea,” he adds. The phenomenon nevertheless spurred later research.

Science began to take time travel seriously in the 1980s. In 1990, for instance, Russian physicist Igor Novikov and American physicist Kip Thorne collaborated on a research paper about closed time-like curves. “They started to study not only how one could try to build a time machine but also how it would work,” Costa says.

Just as importantly, though, they investigated the problems with time travel. What if, for instance, you tossed a billiard ball into a time machine, and it traveled to the past and then collided with its past self in a way that meant its present self could never enter the time machine? “That looks like a paradox,” Costa says.

Since the 1990s, he says, there’s been on-and-off interest in the topic yet no big breakthrough. The field isn’t very active today, in part because every proposed model of a time machine has problems. “It has some attractive features, possibly some potential, but then when one starts to sort of unravel the details, there ends up being some kind of a roadblock,” says Gaurav Khanna of the University of Rhode Island.

For instance, most time travel models require negative mass —and hence negative energy because, as Albert Einstein revealed when he discovered E = mc 2 , mass and energy are one and the same. In theory, at least, just as an electric charge can be positive or negative, so can mass—though no one’s ever found an example of negative mass. Why does time travel depend on such exotic matter? In many cases, it is needed to hold open a wormhole—a tunnel in spacetime predicted by general relativity that connects one point in the cosmos to another.

Without negative mass, gravity would cause this tunnel to collapse. “You can think of it as counteracting the positive mass or energy that wants to traverse the wormhole,” Goldberg says.

Khanna and Goldberg concur that it’s unlikely matter with negative mass even exists, although Khanna notes that some quantum phenomena show promise, for instance, for negative energy on very small scales. But that would be “nowhere close to the scale that would be needed” for a realistic time machine, he says.

These challenges explain why Khanna initially discouraged Caroline Mallary, then his graduate student at the University of Massachusetts Dartmouth, from doing a time travel project. Mallary and Khanna went forward anyway and came up with a theoretical time machine that didn’t require negative mass. In its simplistic form, Mallary’s idea involves two parallel cars, each made of regular matter. If you leave one parked and zoom the other with extreme acceleration, a closed timelike curve will form between them.

Easy, right? But while Mallary’s model gets rid of the need for negative matter, it adds another hurdle: it requires infinite density inside the cars for them to affect spacetime in a way that would be useful for time travel. Infinite density can be found inside a black hole, where gravity is so intense that it squishes matter into a mind-bogglingly small space called a singularity. In the model, each of the cars needs to contain such a singularity. “One of the reasons that there's not a lot of active research on this sort of thing is because of these constraints,” Mallary says.

Other researchers have created models of time travel that involve a wormhole, or a tunnel in spacetime from one point in the cosmos to another. “It's sort of a shortcut through the universe,” Goldberg says. Imagine accelerating one end of the wormhole to near the speed of light and then sending it back to where it came from. “Those two sides are no longer synced,” he says. “One is in the past; one is in the future.” Walk between them, and you’re time traveling.

You could accomplish something similar by moving one end of the wormhole near a big gravitational field—such as a black hole—while keeping the other end near a smaller gravitational force. In that way, time would slow down on the big gravity side, essentially allowing a particle or some other chunk of mass to reside in the past relative to the other side of the wormhole.

Making a wormhole requires pesky negative mass and energy, however. A wormhole created from normal mass would collapse because of gravity. “Most designs tend to have some similar sorts of issues,” Goldberg says. They’re theoretically possible, but there’s currently no feasible way to make them, kind of like a good-tasting pizza with no calories.

And maybe the problem is not just that we don’t know how to make time travel machines but also that it’s not possible to do so except on microscopic scales—a belief held by the late physicist Stephen Hawking. He proposed the chronology protection conjecture: The universe doesn’t allow time travel because it doesn’t allow alterations to the past. “It seems there is a chronology protection agency, which prevents the appearance of closed timelike curves and so makes the universe safe for historians,” Hawking wrote in a 1992 paper in Physical Review D .

Part of his reasoning involved the paradoxes time travel would create such as the aforementioned situation with a billiard ball and its more famous counterpart, the grandfather paradox : If you go back in time and kill your grandfather before he has children, you can’t be born, and therefore you can’t time travel, and therefore you couldn’t have killed your grandfather. And yet there you are.

Those complications are what interests Massachusetts Institute of Technology philosopher Agustin Rayo, however, because the paradoxes don’t just call causality and chronology into question. They also make free will seem suspect. If physics says you can go back in time, then why can’t you kill your grandfather? “What stops you?” he says. Are you not free?

Rayo suspects that time travel is consistent with free will, though. “What’s past is past,” he says. “So if, in fact, my grandfather survived long enough to have children, traveling back in time isn’t going to change that. Why will I fail if I try? I don’t know because I don’t have enough information about the past. What I do know is that I’ll fail somehow.”

If you went to kill your grandfather, in other words, you’d perhaps slip on a banana en route or miss the bus. “It's not like you would find some special force compelling you not to do it,” Costa says. “You would fail to do it for perfectly mundane reasons.”

In 2020 Costa worked with Germain Tobar, then his undergraduate student at the University of Queensland in Australia, on the math that would underlie a similar idea: that time travel is possible without paradoxes and with freedom of choice.

Goldberg agrees with them in a way. “I definitely fall into the category of [thinking that] if there is time travel, it will be constructed in such a way that it produces one self-consistent view of history,” he says. “Because that seems to be the way that all the rest of our physical laws are constructed.”

No one knows what the future of time travel to the past will hold. And so far, no time travelers have come to tell us about it.

Is Time Travel Possible?

We all travel in time! We travel one year in time between birthdays, for example. And we are all traveling in time at approximately the same speed: 1 second per second.

We typically experience time at one second per second. Credit: NASA/JPL-Caltech

NASA's space telescopes also give us a way to look back in time. Telescopes help us see stars and galaxies that are very far away . It takes a long time for the light from faraway galaxies to reach us. So, when we look into the sky with a telescope, we are seeing what those stars and galaxies looked like a very long time ago.

However, when we think of the phrase "time travel," we are usually thinking of traveling faster than 1 second per second. That kind of time travel sounds like something you'd only see in movies or science fiction books. Could it be real? Science says yes!

This image from the Hubble Space Telescope shows galaxies that are very far away as they existed a very long time ago. Credit: NASA, ESA and R. Thompson (Univ. Arizona)

How do we know that time travel is possible?

More than 100 years ago, a famous scientist named Albert Einstein came up with an idea about how time works. He called it relativity. This theory says that time and space are linked together. Einstein also said our universe has a speed limit: nothing can travel faster than the speed of light (186,000 miles per second).

Einstein's theory of relativity says that space and time are linked together. Credit: NASA/JPL-Caltech

What does this mean for time travel? Well, according to this theory, the faster you travel, the slower you experience time. Scientists have done some experiments to show that this is true.

For example, there was an experiment that used two clocks set to the exact same time. One clock stayed on Earth, while the other flew in an airplane (going in the same direction Earth rotates).

After the airplane flew around the world, scientists compared the two clocks. The clock on the fast-moving airplane was slightly behind the clock on the ground. So, the clock on the airplane was traveling slightly slower in time than 1 second per second.

Credit: NASA/JPL-Caltech

Can we use time travel in everyday life?

We can't use a time machine to travel hundreds of years into the past or future. That kind of time travel only happens in books and movies. But the math of time travel does affect the things we use every day.

For example, we use GPS satellites to help us figure out how to get to new places. (Check out our video about how GPS satellites work .) NASA scientists also use a high-accuracy version of GPS to keep track of where satellites are in space. But did you know that GPS relies on time-travel calculations to help you get around town?

GPS satellites orbit around Earth very quickly at about 8,700 miles (14,000 kilometers) per hour. This slows down GPS satellite clocks by a small fraction of a second (similar to the airplane example above).

GPS satellites orbit around Earth at about 8,700 miles (14,000 kilometers) per hour. Credit: GPS.gov

However, the satellites are also orbiting Earth about 12,550 miles (20,200 km) above the surface. This actually speeds up GPS satellite clocks by a slighter larger fraction of a second.

Here's how: Einstein's theory also says that gravity curves space and time, causing the passage of time to slow down. High up where the satellites orbit, Earth's gravity is much weaker. This causes the clocks on GPS satellites to run faster than clocks on the ground.

The combined result is that the clocks on GPS satellites experience time at a rate slightly faster than 1 second per second. Luckily, scientists can use math to correct these differences in time.

If scientists didn't correct the GPS clocks, there would be big problems. GPS satellites wouldn't be able to correctly calculate their position or yours. The errors would add up to a few miles each day, which is a big deal. GPS maps might think your home is nowhere near where it actually is!

In Summary:

Yes, time travel is indeed a real thing. But it's not quite what you've probably seen in the movies. Under certain conditions, it is possible to experience time passing at a different rate than 1 second per second. And there are important reasons why we need to understand this real-world form of time travel.

If you liked this, you may like:

The Dynamic Theory of Time and Time Travel to the Past

• Articles in this Issue

Published Online : Dec 08, 2020

Page range: 137 - 165, doi: https://doi.org/10.2478/disp-2020-0006, keywords time travel , dynamic theory of time , static theory of time , backward causation , presentism, © 2020 ned markosian, published by sciendo, this work is licensed under the creative commons attribution-noncommercial-noderivatives 3.0 license..

I argue that time travel to the past is impossible, given a certain metaphysical theory, namely, The Dynamic Theory of Time. I first spell out my particular way of capturing the difference between The Dynamic Theory of Time and its rival, The Static Theory of Time. Next I offer four different arguments for the conclusion that The Dynamic Theory is inconsistent with the possibility of time travel to the past. Then I argue that, even if I am wrong about this, it will still be true that The Dynamic Theory entails that you should not want to travel back to the past. Finally, I conclude by considering a puzzle that arises for those who believe that time travel to the past is metaphysically impossible: What exactly are we thinking about when we seem to be thinking about traveling back in time? For it certainly does not feel like we are thinking about something that is metaphysically impossible.

A beginner's guide to time travel

Learn exactly how Einstein's theory of relativity works, and discover how there's nothing in science that says time travel is impossible.

Everyone can travel in time . You do it whether you want to or not, at a steady rate of one second per second. You may think there's no similarity to traveling in one of the three spatial dimensions at, say, one foot per second. But according to Einstein 's theory of relativity , we live in a four-dimensional continuum — space-time — in which space and time are interchangeable.

Einstein found that the faster you move through space, the slower you move through time — you age more slowly, in other words. One of the key ideas in relativity is that nothing can travel faster than the speed of light — about 186,000 miles per second (300,000 kilometers per second), or one light-year per year). But you can get very close to it. If a spaceship were to fly at 99% of the speed of light, you'd see it travel a light-year of distance in just over a year of time. 

That's obvious enough, but now comes the weird part. For astronauts onboard that spaceship, the journey would take a mere seven weeks. It's a consequence of relativity called time dilation , and in effect, it means the astronauts have jumped about 10 months into the future. 

Traveling at high speed isn't the only way to produce time dilation. Einstein showed that gravitational fields produce a similar effect — even the relatively weak field here on the surface of Earth . We don't notice it, because we spend all our lives here, but more than 12,400 miles (20,000 kilometers) higher up gravity is measurably weaker— and time passes more quickly, by about 45 microseconds per day. That's more significant than you might think, because it's the altitude at which GPS satellites orbit Earth, and their clocks need to be precisely synchronized with ground-based ones for the system to work properly. 

The satellites have to compensate for time dilation effects due both to their higher altitude and their faster speed. So whenever you use the GPS feature on your smartphone or your car's satnav, there's a tiny element of time travel involved. You and the satellites are traveling into the future at very slightly different rates.

But for more dramatic effects, we need to look at much stronger gravitational fields, such as those around black holes , which can distort space-time so much that it folds back on itself. The result is a so-called wormhole, a concept that's familiar from sci-fi movies, but actually originates in Einstein's theory of relativity. In effect, a wormhole is a shortcut from one point in space-time to another. You enter one black hole, and emerge from another one somewhere else. Unfortunately, it's not as practical a means of transport as Hollywood makes it look. That's because the black hole's gravity would tear you to pieces as you approached it, but it really is possible in theory. And because we're talking about space-time, not just space, the wormhole's exit could be at an earlier time than its entrance; that means you would end up in the past rather than the future.

Trajectories in space-time that loop back into the past are given the technical name "closed timelike curves." If you search through serious academic journals, you'll find plenty of references to them — far more than you'll find to "time travel." But in effect, that's exactly what closed timelike curves are all about — time travel

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There's another way to produce a closed timelike curve that doesn't involve anything quite so exotic as a black hole or wormhole: You just need a simple rotating cylinder made of super-dense material. This so-called Tipler cylinder is the closest that real-world physics can get to an actual, genuine time machine. But it will likely never be built in the real world, so like a wormhole, it's more of an academic curiosity than a viable engineering design.

Yet as far-fetched as these things are in practical terms, there's no fundamental scientific reason — that we currently know of — that says they are impossible. That's a thought-provoking situation, because as the physicist Michio Kaku is fond of saying, "Everything not forbidden is compulsory" (borrowed from T.H. White's novel, "The Once And Future King"). He doesn't mean time travel has to happen everywhere all the time, but Kaku is suggesting that the universe is so vast it ought to happen somewhere at least occasionally. Maybe some super-advanced civilization in another galaxy knows how to build a working time machine, or perhaps closed timelike curves can even occur naturally under certain rare conditions.

This raises problems of a different kind — not in science or engineering, but in basic logic. If time travel is allowed by the laws of physics, then it's possible to envision a whole range of paradoxical scenarios . Some of these appear so illogical that it's difficult to imagine that they could ever occur. But if they can't, what's stopping them? 

Thoughts like these prompted Stephen Hawking , who was always skeptical about the idea of time travel into the past, to come up with his "chronology protection conjecture" — the notion that some as-yet-unknown law of physics prevents closed timelike curves from happening. But that conjecture is only an educated guess, and until it is supported by hard evidence, we can come to only one conclusion: Time travel is possible.

A party for time travelers 

Hawking was skeptical about the feasibility of time travel into the past, not because he had disproved it, but because he was bothered by the logical paradoxes it created. In his chronology protection conjecture, he surmised that physicists would eventually discover a flaw in the theory of closed timelike curves that made them impossible. 

In 2009, he came up with an amusing way to test this conjecture. Hawking held a champagne party (shown in his Discovery Channel program), but he only advertised it after it had happened. His reasoning was that, if time machines eventually become practical, someone in the future might read about the party and travel back to attend it. But no one did — Hawking sat through the whole evening on his own. This doesn't prove time travel is impossible, but it does suggest that it never becomes a commonplace occurrence here on Earth.

The arrow of time 

One of the distinctive things about time is that it has a direction — from past to future. A cup of hot coffee left at room temperature always cools down; it never heats up. Your cellphone loses battery charge when you use it; it never gains charge. These are examples of entropy , essentially a measure of the amount of "useless" as opposed to "useful" energy. The entropy of a closed system always increases, and it's the key factor determining the arrow of time.

It turns out that entropy is the only thing that makes a distinction between past and future. In other branches of physics, like relativity or quantum theory, time doesn't have a preferred direction. No one knows where time's arrow comes from. It may be that it only applies to large, complex systems, in which case subatomic particles may not experience the arrow of time.

Time travel paradox 

If it's possible to travel back into the past — even theoretically — it raises a number of brain-twisting paradoxes — such as the grandfather paradox — that even scientists and philosophers find extremely perplexing.

Killing Hitler

A time traveler might decide to go back and kill him in his infancy. If they succeeded, future history books wouldn't even mention Hitler — so what motivation would the time traveler have for going back in time and killing him?

Killing your grandfather

Instead of killing a young Hitler, you might, by accident, kill one of your own ancestors when they were very young. But then you would never be born, so you couldn't travel back in time to kill them, so you would be born after all, and so on … 

A closed loop

Suppose the plans for a time machine suddenly appear from thin air on your desk. You spend a few days building it, then use it to send the plans back to your earlier self. But where did those plans originate? Nowhere — they are just looping round and round in time.

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

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The dynamic theory of time and time travel to the past.

Ned Markosian , University of Massachusetts Amherst

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I argue that time travel to the past is impossible, given a certain metaphysical theory, namely, The Dynamic Theory of Time. I first spell out my particular way of capturing the difference between The Dynamic Theory of Time and its rival, The Static Theory of Time. Next I offer four different arguments for the conclusion that The Dynamic Theory is inconsistent with the possibility of time travel to the past. Then I argue that, even if I am wrong about this, it will still be true that The Dynamic Theory entails that you should not want to travel back to the past. Finally, I conclude by considering a puzzle that arises for those who believe that time travel to the past is metaphysically impossible: What exactly are we thinking about when we seem to be thinking about traveling back in time? For it certainly does not feel like we are thinking about something that is metaphysically impossible.

https://doi.org/10.2478/disp-2020-0006

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Markosian, Ned, "The Dynamic Theory of Time and Time Travel to the Past" (2020). Disputatio . 229. https://doi.org/10.2478/disp-2020-0006

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Exploring Time Travel Rules in Time Travel Films

• Jarvis Tyrell Curry University of the Cumberlands http://orcid.org/0000-0001-9464-3792

Throughout film history, time travel has been an intriguing concept revisited time and again by film productions, creating a universe of time travel principles and becoming a discipline of scientific import. With some of the greatest minds and thinkers of our time contributing to the living discourse, time travel has gained global significance and has developed several rules films attempt to follow. Time travel theory postulates several theories concerning the effect of an individual traveling through time and coming into contact with themselves; some benign, some many catastrophic. This study reviews time travel films to determine the cinematic consistency of three of these rules; the grandfather paradox, time-traveling for self-benefit, and meeting oneself in an alternate time.

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Audissino, E. (2014). Bicycles, airplanes and Peter Pans: flying scenes in Steven Spielberg's films. CINEJ Cinema Journal, 3(2), 104-120.

Bacon, T. (2020, August 21). Star Trek: How time travel works in each TV show & movie. Screen Rant. Retrieved May 26, 2022, from https://screenrant.com/star-trek-time-travel-tos-tng-ds9-discovery-movies/

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the future. Journal of Science Fiction, 2(1), 1-12.

Markosian, N. (2020). The dynamic theory of time and time travel to the past. Disputatio: International Journal of Philosophy, 12(57), 137–165. https://doi.org/10.2478/disp-2020-0006 .

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Inconceivable Paradoxes: 3 Theories of Time Travel

Time travel is one of those things that seems like it should be possible. After all, it’s been a plot device in countless works of fiction and pop culture . But serious physicists have never been able to come up with a way to do it. These theories explain why we’re not zipping around through time as much as we’d like to—and why you shouldn’t get your hopes up about ever going on a Star Trek-style adventure through history.

The Fixed Timeline

The Fixed Timeline is the theory of time travel where you can only travel to a point in your own future. It’s like time is like a train track and everything that happens has always happened and will always happen. The train cannot go backwards, it cannot go off the track and if you’re on the train you can only move forward with it. This means that if we were to travel back in time then our actions would already have been done before they could even happen in front of us again! This theory also suggests that there are parallel universes out there where every single event that ever happened or will ever happen has already happened somewhere else (and probably more than once).

The Dynamic Timeline

The Dynamic Timeline is a theory that says that the timeline is dynamic and can be changed. The theory is that the timeline is not fixed and can be changed by time travelers or other events in one’s life. This means that it’s possible for you to change your past, present and future if you travel back in time like in Back to the Future or 12 Monkeys.

The Multiverse

The multiverse theory , also known as the many-worlds interpretation (MWI), is a theory that states that our universe is just one of many universes. In this model, all possible alternative histories and futures actually exist; it’s just that we can’t see most of them. The MWI suggests that time travel is possible because we are constantly traveling through time—just in different directions than we normally experience in our everyday lives. The MWI has its roots in quantum mechanics, where it was first developed by Hugh Everett III during his PhD work at Princeton University. Basically, according to this theory you could go back in time if there were infinite universes: You’d simply hop across one of these other universes—and therefore a different timeline—when you tried to change something about your life or world line. It sounds confusing but it makes sense when explained more clearly:

Time travel is possible . You’ve probably heard of three different theories about time travel: the fixed timeline, dynamic timeline and multiverse. The first theory is that time travel isn’t possible. The second theory states that it is possible, but only in one direction (from future to past). The third says you can go back and forth between past and future in both directions. In the end, I think we’re going to have to accept that time travel is possible in some form. Whether it’s in the future or right now, the question isn’t whether there are people who can get around through time. It’s how they do it and why we haven’t seen them yet. They may have been there all along without us noticing—or maybe they’re still working on figuring out their own theories about what time really means in order for us humans (and our brains) to understand!

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The Dynamic Theory of Time and Time Travel to the Past

I argue that time travel to the past is impossible, given a certain metaphysical theory, namely, The Dynamic Theory of Time. I first spell out my particular way of capturing the difference between The Dynamic Theory of Time and its rival, The Static Theory of Time. Next I offer four different arguments for the conclusion that The Dynamic Theory is inconsistent with the possibility of time travel to the past. Then I argue that, even if I am wrong about this, it will still be true that The Dynamic Theory entails that you should not want to travel back to the past. Finally, I conclude by considering a puzzle that arises for those who believe that time travel to the past is metaphysically impossible: What exactly are we thinking about when we seem to be thinking about traveling back in time? For it certainly does not feel like we are thinking about something that is metaphysically impossible.

Related Papers

Adrian Nita

Abstract: we examine the arguments for time travel, in order to appreciate the force of these arguments. We arrive at the conclusion that the arguments for are weaker than the arguments against of the conceptual possibility of the time travel. Away to be a strange world, the world in which took place the travel in time is an impossible world. The basic idea on which is based the rejection of the conceptual possibility of time travel is the violation of the law of identity regarding the world: the world from which the time-traveller goes is not the same with the world in which he arrive. In other words, he cannot travel in the local past or in the local future of the one and the same world.

Daniel Burkett

Ordinarily, philosophers arguing for the possibility of time travel restrict themselves to defending time travel against allegations of inconsistency and contradiction. These objections are usually based on particular theories about time and causality. I believe, however, that this way of arguing can be turned on its head. By using the conceivability thesis – that is, the thesis that if something is conceivable, then it is also possible – we can put forward a positive argument for the possibility of time travel, and then consider how this should inform our metaphysical views. I do this by assuming the truth of the conceivability thesis and then presenting a simple piece of time travel fiction. I argue for the conceivability of this story and, in doing so, attempt to show that the time travel journey it describes is logically possible. I then develop this argument by considering other more controversial cases of time travel. I make minor alterations to the original time travel story in order to show that there are a number of different kinds of time travel journeys (including cases of both forwards and backwards time travel) which are conceivable and, therefore, logically possible. Finally, I ask how the conceivability of different types of time travel should affect the metaphysical views we choose to adopt. I argue that since the conceivability of time travel entails the logical possibility of journeys to other times, any plausible theory of time must be able to accommodate such journeys. I also explain how the conceivability of time travel entails the logical possibility of two particularly unusual cases of causation. I argue that the conceivability of instantaneous time travel entails the logical possibility of causation at a distance, and that the conceivability of backwards time travel entails the logical possibility of backwards causation. Any plausible theory of causation must therefore be able to account for the possibility of these two types of causation. I consider one particular theory of causation which does not (namely, that put forward by D.H. Mellor), and then attempt to establish where it goes wrong.

Alexandros Schismenos

The concept of time-travel is a modern idea which combines the imaginary signification of rational domination, the imaginary signification of technological omnipotence, the imaginary concept of eternity and the imaginary desire for immortality. It is a synthesis of central conceptual schemata of techno-science, such as the linearity and homogeneity of time, the radical separation of subjectivity from the world, the radical separation of the individual from his/her social-historical environment. The emergence of this idea, its spread during the 20 th century as a major theme of science fiction literature alongside its dissemination as a scientific hypothesis, its popularity with both the public and the scientific community, are indications of the religious role of techno-science. It is my opinion, finally, that, as a chimera, time-travel is non-feasible and impossible. In order to support my claims, I will briefly outline the origins of the time-travel concept and its epistemological and metaphysical/ontological conditions. If these conditions prove to be absurd, the logical impossibility of time-travel will have been demonstrated.

Heather Dyke

Dan Mellamphy

Time: A Philosophical Treatment

Keith Seddon

Exploring the metaphysics of time, this book examines key questions about the nature of time. It begins by examining the distinction between the two main theories of time, the static view and the tensed view, arguing that the temporal properties of 'past', 'present' and 'future' are not in fact properties of events. Other topics also discussed include fatalism, the 'open' future, death and dying, whether there are logical impediments to travelling in time, and the metaphysical implications of precognition.

European Journal of Analytic Philosophy

Dennis Dieks

Scientific American

Physics Time

In Search of a New Humanism

Mauro Dorato

The Agonist

Juliano C S Neves

Time machines are predictions of Einstein's theory of general relativity and provide a myriad of unsolved paradoxes. Convincing and general arguments against time machines and their paradoxes are missing in physics and philosophy so far. In this article, a philosophical argument against time machines is given. When thought of as a process, individuation refuses the idea of time machines, in particular travels into the past. With the aid of Nietzsche-Heraclitus' philosophy of becoming and Simondon's notion of process of individuation, I propose that time machines are modern fables, created by the man of ressentiment. In the amor fati formula of Nietzsche, I suggest the antipode to time machines.

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