time travel types

the eight types of time travel

Time travel is a stable in science fiction. Countless books, comics, movies, and TV shows have used it as their main plot device. Even more have incorporated it into a key moment of the story. Over the years, eight major types of time travel logic emerged. Recently, YouTubers Eric Voss and Héctor Navarro examined all eight types, and looked at which one gets it most correct in term of the real world science behind science fiction.

Type 1 Anything goes

Definition: Characters travel back and forth within their historical timeline.

This approach frees you to have fun and not get lost in the minutiae of how time travel works. Usually, there’s a magical Maguffin that to quote the great Dr. Ememett Brown, “makes time travel possible”. Writers have used a car, a phone booth, and a hot tub, among other options. This approach leads to inconsistent limits on the logic of the time travel, but this doesn’t mean the story is poorly plotted, won’t be enjoyable or won’t be an enormous hit. This approach is more science fantasy than science fiction with no basis in real-world science.

Examples: Back to the Future , Bill and Ted’s Excellent Adventure , Hot Tube Time Machine , Frequency , Austin Powers , Men In Black 3 , Deadpool 2 , The Simpsons , Galaxy Quest , Star Trek TOS , Doctor Who , 11/22/63 by Stephen King.

Type 2 Branch Reality

Definition: Changes to the past don’t rewrite history. They split the timeline into an alternate branch timeline. This action does not change or erase the original timeline.

As authors got more familiar with the science behind time travel in theoretical physics, this type, based upon the many worlds theory in quantum mechanics, emerged. When the character travels back into the past and changes events, they create a new reality. Their original reality is unchanged. Branches themselves can branch leading to a multiverse of possibilities.

Examples: The Disney Plus series, Loki , used this extensively. See also: Back to the Future Part II , Avenger’s Endgame , the DC Comics multiverse, the Marvel Comics multiverse, Rick and Morty , Star Trek (2009), A Wrinkle in Time by Madeleine L’Engle.

Type 3 Time Dilation

Definition: Characters traveling off-world experience time moving more slowly than elsewhere in the universe, allowing them to move forward in time (but not backward).

This type is the based upon our scientific understanding of how time slows down as you approach the speed of the light. This is a forward-only type of time travel. There’s no going backwards.

Examples: Planet of the Apes , Ender’s Game , Flight of the Navigator , Interstellar , Buck Rodgers .

Type 4 This Always Happened

Definition: All of time is fixed on a predestined loop in which the very act of time travel itself sets the events of the story into motion.

This one can confuse and delves closer to the realm of theology than science. It feels gimmicky, and has become something of a trope making it hard to pull this off in a satisfying way for your audience. This type also invites the audience to question if your protagonist ever had free will or agency in the story.

Examples: Terminator , Terminator 2 , Harry Potter and the Prisoner of Azkaban , Game of Thrones -Season 6, Twelve Monkeys , Interstellar , Kate and Leopold , The Butterfly Effect , Predestination , Ricky and Morty -Season 5, Looper .

Type 5 Seeing the Future

Definition: After seeing a vision of their fate, characters choose to change their destiny or embrace their lot.

We’re stretching to call this time travel, but it provides your story with built-in conflict and stakes. Will the hero choose to walk the path knowing how it will end, or will they choose a different path?

Examples: Oedipus Rex , A Christmas Carol , Minority Report , Arrival , Next (Nicolas Cage), Rick and Morty -Season Four. Star Trek:Discovery -Season 2, Avenger’s EndGame with Dr. Strange and the Mind Stone.

Type 6 Time Loop / Groundhog Day

Definition: Characters relive the same day over and over, resetting back to a respawn point once they die or become incapacitated.

This type gained popularity after the movie, Groundhog Day , became a tremendous hit. Most of the other examples take the Groundhog Day idea and put a slight twist on it. Like Type 4 “This Always Happened”, the popularity of this type can make it harder to pull off in a fresh and innovative way.

Examples: Obviously, Groundhog Day with Bill Murray. Edge of Tomorrow , Doctor Strange in the ending battle with Dormammu, Russian Dolls (Netflix), Palm Springs , Star Trek TNG .

Type 7 Unstuck Mind

Definition: Characters consciousness transport through time within his body to his life at different ages.

Nostalgia for the past and dreaming of the future are core parts of the human experience. This type runs more metaphorically than scientific.

Examples: Slaughterhouse 5 by Kurt Vonnegut, X-Men: Days of Future Past , Desmond in the series Lost .

Type 8 Unstuck Body

Definition: A character’s body or object becomes physically detached from the flow of time within the surrounding universe, becoming inverted or younger. Only certain objects or bodies are unstuck from time. Also called Inverted Entropy.

This one will blow your mind if you think about it for too long. Like Type 2 “Branch Reality”, this one comes from the realm of quantum mechanics and theoretical physics. Scientists and mathematicians have all the formulas worked out to make this de-aging a reality, but currently lack the technology to control all the variables in the ways needed. It would like scientists working out than an object could break the speed of the sound in 1890. It would look inconceivable, given the technology of the day, but I wouldn’t put limits on human ingenuity.

Examples: Dr. Strange (the Hong Kong battle). Tenet , briefly in Endgame with Scott Lang and Bruce, Primer .

If you’re writing a time travel story, you’ll need to decide which one of these types you want to deploy. They all have their advantages and disadvantages. In many ways, its similar to designing your magic system, especially if you go with a Type 1 time travel story. The most important thing remains to have relatable characters and to tell a great story while being internally consistent with the rules and logic of your story world.

Ted Atchley  is a freelance writer and professional computer programmer. Whether it’s words or code, he’s always writing. Ted’s love for speculative fiction started early on with Lewis’  Chronicles of Narnia,  and the Star Wars movies. This led to reading Marvel comics and eventually losing himself in Asimov’s Apprentice Adept and the world of Krynn ( Dragonlance Chronicles ). 

After blogging on his own for several years, Blizzard Watch ( blizzardwatch.com ) hired Ted to be a regular columnist in 2016. When the site dropped many of its columns two years later, they retained Ted as a staff writer. 

He lives in beautiful Charleston, SC with his wife and children. When not writing, you’ll find him spending time with his family, and cheering on his beloved Carolina Panthers. He’s currently revising his work-in-progress portal fantasy novel before preparing to query. 

Ted has a quarterly newsletter which  you can join here . You’ll get the latest on his writing and publishing as well as links about writing, Star Wars, and/or Marvel.

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The Four Types of Time Travel (And What They Say About Ourselves and the World Around Us)

A science fiction author breaks down the building blocks of time travel, from seeing into the future to traveling into the past..

Time travel is a genre unto itself, one that spans sci-fi, mystery, fantasy, history and more. But there are distinct categories of time travel narratives, each with its own set of rules—and each with a different baked-in outlook.

Getting to a taxonomy of time travel stories, the first question is—who or what is actually time-traveling? Because while the first stories we think of involve spaceships and Deloreans, the oldest time travel stories are stories about…

1. SEEING THE FUTURE

In these stories, it is actually INFORMATION that travels through time. And this might be the most scientifically plausible form of time travel, one that is already happening all the time on the quantum level.

Visions of the future have shown up in literature and mythology for millennia, it’s just that we used to call them prophecy. But the fundamental storytelling device has changed little, even as it evolved with the times, manifesting in various communication technologies. Characters connect to the future through newspapers (the film It Happened Tomorrow , which inspired the show Early Edition ), letters ( The Lake House ), radio ( Frequency), photography ( Time Lapse ) and now, the Internet (my own recent novel The Future Is Yours , the reason I’m interested in sorting all this out.)

All these stories of peering forward in time differentiate into two categories on the basis of one crucial question: If you see the future, can you change it?

1A: Stories of Inevitable Foresight 

These are stories where the future can be seen—but ultimately, what you see can’t be stopped.

The archetype for this form is one of the oldest works of dramatic literature in the Western canon—Sophocles’ play Oedipus Rex , where the titular king is warned by the seer Tiresias that he will murder his father and wed his mother… and despite his best efforts to the contrary, he ends up inadvertently doing just that (and then gouges his eyes out for good measure).

Stories of inevitable prediction speak to one of our deepest fears: that we have no free will, no agency, no power to control our fate. A glimpse of the future, foreknowledge of what’s to come, only ends up causing the events we aim to prevent.

Sound depressing? Maybe that’s why it’s a theme that spoke to sci-fi author Philip K. Dick, author of Minority Report— which is, for all its superficial differences, a story very similar to Oedipus Rex. It features a trio of precogs who dream of future-murders, and a cop assigned to prevent such killings—until he finds himself accused of one himself.

Dick was a pessimist about the prospect of free will, and in his story (spoiler alert!) his character ends up going through with the predicted murder. But perhaps unsurprisingly, when Steven Spielberg got hold of the same material, the outcome changed, and Tom Cruise’s version of the character was able to alter his destiny. How? Sheer force of movie-star charisma mostly. Which brings us to—

1B: Stories of Preventable Foresight

Other stories of seeing the future treat altering the timeline as quite evitable. In fact, the very act of viewing what’s ahead empowers the individual to change things, and prevent the foreseen events from coming to pass. That’s how Early Edition worked, with Kyla Chandler given the thankless daily task of averting tragedies only he could foresee.

But the prototype for this story form can be traced at least to 1843, in A Christmas Carol . Yes, even Dickens wrote some timey-wimey shenanigans; what else are the Ghosts of Christmas Past and Yet To Come? And when Scrooge beholds the pitiful sight of Tiny Tim dead, and his own neglected grave, he is promised a chance to rewrite the narrative if he can merely change his ways.

Which means that Dickens was much more of an optimist than Sophocles or Philip K. Dick. Being able to see the future and change it, whether through an epiphany or a magical newspaper, is the sort of world most of us want to believe in… whether that’s the way things actually work or not.

But in other types of stories, it’s not only information that travels through time. Many stories concern people getting to do so too—and the way authors treat those journeys says just as much about who they are and how they view the world.

2. TRAVELING TO THE FUTURE

One of the clearest progenitors of the time travel narrative, H.G. Wells’ The Time Machine , is about a man zipping off into the distant future. But the world he encounters—one full of peaceful Eloi and belligerent Morlocks—is so disconnected from our own, it’s hard to know why it’s not simply a story about aliens on another planet.

This points to a problem with time-travel forward. The future feels so unknowable, it often ends up being less interesting than we’d expect. That’s why some “travel into the future” stories make our present the future of the characters—like Time After Time , which features Jack the Ripper fleeing 1890’s London and winding up (via a time-machine that belongs to H.G. Wells) in 1970’s San Francisco (it’s as ridiculous as it sounds, and well worth a watch). But this plot device is really no different from the fish-out-of-water Rip Van Winkle premise, dressed up with technology.

Perhaps this is why “travel into the future” has perhaps been used most effectively as a last-minute twist ending, as in the original Planet of the Apes .

In other words—time-travel into the future is just not that special… maybe because we’re doing it all the time, at a consistent rate of 60 minutes per hour. And given that our own lifetimes have witnessed such seismic changes in technology and society, do we really need to imagine a cosmic leap forward to see things that will blow our minds?

That’s why the most interesting physical-time-travel stories have focused on…

 3. TRAVELING TO THE PAST

Some of these stories are just touristy jaunts that don’t bother with the ramifications of intervening in history (like A Connecticut Yankee in King Arthur’s Court ). Which is fine and well, but more interesting are stories that grapple with the question: Can we alter the past? And by implication… can we alter our own present? Which breaks the category down into two distinct groups…

3A: Changing History

Perhaps the most intuitive mode of time travel is where characters travel to the past, and in doing so, alter the present they left behind. Back to the Future is probably the most popular of all. It’s fun to meet your teenage parents, but if you mess things up, you risk erasing yourself from existence. So then you have to… fight off your mom’s sexual advances and help your dad save her from getting raped? (Yeah, I didn’t really get how messed-up that was as a kid either…) Fix the past, fix the present, life goes on.

Of course, beyond just keeping your parents married and yourself in the family portrait, what people dream of is using time travel to fix history, the easiest go-to being the plot to kill baby Hitler. But in the massive time travel canon, it’s almost exclusively villains who try to rewrite the past. Very few stories feature heroes changing history for the better. Butterfly effects are almost always negative, and even the most well-intentioned time travel plans (like saving Kennedy from assassination in Stephen King’s 11/22/63 ) result in horrible misfortune for the world (catastrophic earthquakes in that case, for, ya know, reasons ).

All of which points to the fact that on some profound level, as much as our minds love playing with the possibilities of altering the timeline, we are deeply attached to the one we have, and innately suspicious of any effort to correct it. Which is why we have…

3B: Immutable Timelines

Stories where characters find themselves fundamentally incapable of altering history,  regardless of their level of intervention. 12 Monkeys ( and the French film it’s based on, La Jetee ) tells the story of a time traveler seeking to prevent an apocalyptic manmade plague. He ultimately fails and realizes, too late, that as a child he witnessed the death of himself, as an older time traveler. The ending is incredibly satisfying—despite the fact that it’s profoundly fatalistic, suggestive of a world in which not even high-tech time-bending can save the human race from killing itself.

A less fatalistic example of this approach to time-rules is found in Avengers:Endgame , in which the characters travel to various moments throughout Marvel history to steal Infinity Stones (think Oceans 11 with a lot of fan-service). Smart Hulk (yes, seriously) gives the stipulation that history will “heal” itself of their interventions, preserving the timeline. On its face, this sounds like a lame gimme of a screenwriting rule — but turns out, it’s actually reasonably well-supported by recent experiments on quantum time travel. Science and sci-fi both point to the same idea: we can’t change the past.

4. TIME LOOPS

Which brings us to the final category—the pinnacle of unalterability—stories where a character is stuck reliving the same day again and again. The prototype here is the 1993 comedy Groundhog Day. The formula it set out brilliantly has been replicated in other genres, including but not limited to YA melodrama ( Before I Fall ), slasher-horror ( Happy Death Day ), sci-fi action with aliens ( Edge of Tomorrow), sci-fi action without aliens ( Source Code, ARQ) , episodic existential-dramedy ( Russian Doll ) and then circling all the way back to comedy again in last year’s Palm Springs.

These films don’t merely share a high-concept, they all have essentially the same theme: life doesn’t change until you change. Which would seem to make them remarkably unoriginal, if not for the surprising fact that they’re ALL good. (Seriously, I’ll go to bat for Before I Fall). No doubt there are some bad time-loop movies that I missed, but the fact that one hyper-specific premise has resulted in so many excellent movies points to the fact that there is a deep, resonant truth to the notion of being trapped in time.

Of course, this is only a partial taxonomy of time travel, but even this incomplete catalogue points to a few key takeaways. Most time travel stories are cautionary tales. Attempting to meddle with history is punished; defying prophecy is futile; the best we can do is pull a Marty McFly and close the Pandora’s box we opened in the first place. These stories, for all their far-flung leaps through space and time, are ultimately about how, if we want to change our lived reality, we need to start with ourselves.

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The Different Types Of Time Travel And How They Work

Have you ever watched a movie or read a book where the characters travel through time? Maybe they go back to prevent a tragedy or forward to see what the world will look like in the future. Time travel is a fascinating concept that has captured our imaginations for centuries. But have you ever wondered about the different types of time travel and how they work?

Let's take the example of Marty McFly from Back to the Future. In this classic film, Marty travels back in time and accidentally changes his parents' meeting, leading to him potentially being erased from existence. This type of time travel is known as a fixed timeline or predestination paradox, where events that occur in the past are predetermined and cannot be changed. However, there are other types of time travel that allow for altering events in history or exploring alternate timelines altogether. Join us as we dive into the different types of time travel and how they work!

Fixed Timeline or Predestination Paradox

Dynamic timeline or multiverse theory, definition and explanation, examples in popular culture, theoretical implications, wormholes and black holes, the philosophy of time travel, the nature of time, the ethics and consequences of time travel, the role of free will and determinism, frequently asked questions, is it possible to travel through time without creating a paradox, what are the ethical implications of time travel, can time travel be used to alter history, how would time travel affect the concept of free will, are there any real-life experiments or technologies that could potentially enable time travel.

The Fixed Timeline, also known as the Predestination Paradox, asserts that events in the past cannot be changed no matter what actions are taken in the present or future. This theory is based on the idea of temporal mechanics, which suggests that time is a fixed and unchangeable entity. In other words, everything that has happened in the past has already been determined and cannot be altered.

However, this does not mean that there are no consequences to our actions. Even though we cannot change the past, our present and future actions can still have an impact on alternate timelines. These alternate timelines may exist alongside our own reality and could potentially lead to different outcomes depending on the choices we make. With this understanding of temporal mechanics and alternate timelines, let's explore another type of time travel: dynamic timeline or multiverse theory.

So, let's talk about the dynamic timeline or multiverse theory. This concept suggests that when someone travels back in time and changes something, they don't actually alter their own timeline but instead create a new universe where those changes have already occurred. In simpler terms, every decision creates a new branching reality where every possibility exists simultaneously. Some examples of this can be seen in popular culture such as Marvel's "What If" series or the movie "The Butterfly Effect." The theoretical implications of this theory are mind-boggling as it suggests that there could be an infinite number of parallel universes with different versions of ourselves living out different realities.

You'll quickly understand the ins and outs of time travel once you grasp how each method takes you on a unique journey through the labyrinth of time. One such method is the dynamic timeline or multiverse theory, which posits that every action taken in the past creates an alternate universe in which those actions had different outcomes. This means that if one were to go back in time and change something, they would not be altering their own history but creating an entirely new reality altogether.

To better understand this concept, consider these emotional responses:

• Fear: The idea that any action taken in the past could potentially lead to disastrous consequences can be overwhelming.
• Fascination: The thought of multiple realities existing simultaneously can spark curiosity and wonder about what other versions of ourselves may exist out there.
• Discomfort: The realization that our actions may not have as much impact on our own lives as we once believed can be unsettling.

Examples in popular culture further illustrate this concept, from Marvel's "What If?" series to Christopher Nolan's "Interstellar." These stories showcase how even small changes made in the past can create vastly different futures, each with their own set of consequences.

Now let's explore some popular culture references that have made time travel a fascinating concept. One of the most iconic examples is the Back to the Future trilogy, where Marty McFly uses a DeLorean time machine to travel between different eras and alter his family's history. This classic film series not only introduced us to the concept of time travel but also explored the idea of changing one's future by altering events in the past.

Another example is Doctor Who, a science fiction television series that has been on air since 1963. The show follows an alien known as The Doctor who travels through time and space in a spaceship called TARDIS. Through this character, we see how different actions can have significant consequences throughout time and how even small changes can lead to drastic outcomes. These pop culture references not only entertain us but also make us question our own understanding of time travel and its implications on our lives.

As we delve further into these examples, it becomes clear that they raise important theoretical implications about the nature of time itself.

As you explore the theoretical implications of time travel, your mind begins to unravel the mysteries of the universe and you feel as though you are floating through a vortex of endless possibilities. One of the most fascinating aspects is the concept of the butterfly effect, where even small actions in the past can have major consequences on future events. This means that if someone were to go back in time and change even one minor detail, it could drastically alter the course of history as we know it.

Another significant theory is The Grandfather Paradox, which poses an interesting dilemma: if someone were to travel back in time and kill their own grandfather before they had children, would they still exist? This paradox highlights one potential consequence of time travel – that any changes made in the past have potentially irreversible effects on future events. These theories are just some examples of how complex and thought-provoking time travel can be. With such profound implications at stake, it's no wonder this topic has captivated audiences for generations.

With so many theories surrounding time travel and its potential impacts on our world and existence, it's clear that there is much more to explore. In fact, some scientists believe that certain types of time loops may actually be possible based on current research into quantum mechanics. As we delve deeper into these topics, we can only hope to uncover more about ourselves and our place within this vast universe.

So, let's talk about time loops. A time loop is when a specific event or sequence of events repeats itself over and over again in a cyclical manner. This concept has been explored in various forms of popular culture such as the movie "Groundhog Day" and the TV show "Supernatural." Not only is it fascinating to think about the possibilities and consequences of being stuck in a time loop, but it also has some profound theoretical implications for our understanding of the nature of time itself.

You probably know by now how time travel actually operates and its various forms. One of these forms is the Time Loop, which occurs when a certain event or series of events repeats itself indefinitely. This means that every action taken by an individual in the loop has already happened before and will continue to happen again and again, creating an endless cycle.

Time Loops have theoretical implications in the sense that they challenge our understanding of causality and free will. If every action we take is predetermined and destined to repeat itself, then do we truly have control over our own lives? Additionally, Time Loops have scientific applications such as studying the effects of repeated actions on physical objects or even exploring alternate timelines.

• A Time Loop can be triggered by a specific event or decision.
• The loop can be broken by making a different choice or taking a different action.
• Time Loops often involve character development as individuals must learn from their past mistakes in order to break the cycle.

Examples in popular culture range from classic films like Groundhog Day to contemporary television shows like Russian Doll. In each instance, characters are forced to confront their own limitations and weaknesses while facing seemingly insurmountable odds. However, through perseverance and self-reflection, they are able to break out of their respective loops and find redemption.

Take a look at how popular culture has tackled the concept of Time Loops, from characters repeating the same day over and over again in Groundhog Day to a woman reliving her death in Russian Doll. Time travel is not just limited to cinema and television shows, but can also be found in video games and literature. In video games, time travel often takes the form of rewinding time or jumping between different points in history. The popular game series Assassin's Creed incorporates this mechanic by allowing players to explore historical events and even alter them through their actions.

In literature, time travel has been explored for centuries with classics like H.G. Wells' The Time Machine and more recently with Audrey Niffenegger's The Time Traveler's Wife. These stories often examine the consequences of changing past events or exploring different timelines. The concept of time travel allows authors to explore philosophical questions about fate, free will, and causality. It raises questions about whether our actions have predetermined outcomes or if we can truly change our future. These theoretical implications make time travel an endlessly fascinating concept to explore across all forms of media.

Exploring the theoretical implications of time travel can lead us to question our understanding of fate and free will, as we grapple with the possibility of altering past events and shaping our own future. The concept of time travel challenges our perception of cause and effect, as we consider the potential consequences of changing even a single event in history. This raises philosophical considerations about whether or not we have control over our destiny, or if our path is predetermined.

Furthermore, time travel forces us to confront ethical dilemmas that arise from manipulating historical events for personal gain. If we are able to change the past, what responsibility do we have to ensure that those changes do not harm others? As we continue to explore the different types of time travel and their possible consequences, it becomes clear that this topic raises complex questions about human nature and morality. With these considerations in mind, let us delve into the fascinating world of wormholes and black holes.

As you approach a black hole or wormhole, you'll feel the intense gravitational pull that could potentially allow you to travel across space and time. This is due to the effects of time dilation caused by extreme gravitational forces near these objects. Time dilation is a phenomenon in which time appears to move slower for an observer who is closer to a stronger gravitational field. This means that as you get closer to a black hole or wormhole, time will appear to slow down for you compared to someone who is far away from these objects.

This effect can be harnessed for interstellar travel and time travel technology, but it comes with significant risks and challenges. The immense gravity of these objects can easily destroy any spacecraft attempting to enter them, making it difficult for us to explore their potential benefits. Additionally, there are still many unknowns about how exactly we could use wormholes and black holes for time travel, leaving this possibility largely in the realm of science fiction at this point. With all of these uncertainties surrounding the practical applications of wormholes and black holes for time travel, it's important to consider the philosophical implications behind this concept as well.

Hey, let's talk about the philosophy of time travel! It's a fascinating subject that raises some big questions about the nature of time itself. We'll explore the ethics and consequences of time travel, as well as the role of free will and determinism in shaping our understanding of this complex topic. So buckle up and get ready for a mind-bending ride through the twists and turns of temporal theory!

Time is a mysterious force that we can never truly control, but as the saying goes, 'time heals all wounds.' The subjective experience of time is something that varies greatly based on our individual perceptions. Some days seem to drag on forever while others fly by in the blink of an eye. Theories of time perception suggest that our brains may alter our sense of time based on external stimuli or internal emotions.

One sub-list suggests that external stimuli like music or movies can make us feel as though time is passing faster or slower than it actually is. Another sub-list proposes that internal emotions such as fear or excitement can also distort our sense of time, making moments seem longer or shorter than they really are. Lastly, some theories suggest that our brain's internal clock may be responsible for how we perceive the passage of time. Understanding these various theories about the nature of time helps us appreciate just how complex and mysterious this concept truly is.

As we delve into the ethics and consequences of time travel, we must consider how actions in one moment can ripple throughout history and change everything that comes after.

You're about to explore the dark and unpredictable consequences of messing with the fabric of reality, and it's going to make your heart race with both fear and excitement. Time travel is an exciting concept, but it comes with a serious set of ethical implications that cannot be ignored. Imagine traveling back in time to prevent a tragedy from happening, only to realize that by doing so, you've inadvertently caused another one. This is known as the butterfly effect - the idea that even the smallest change in the past can have significant repercussions in the present.

The ethical implications of time travel are not limited to accidental outcomes like this either. What if someone were to go back in time and kill Hitler before he rose to power? Would they be justified in doing so? Or would they be altering history in such a way that it ultimately leads to a worse outcome? These are difficult questions without easy answers, and they highlight just how complex time travel can be. With so much at stake, it's no wonder that people are both fascinated by and afraid of this concept.

As we delve deeper into this topic, we will explore another crucial aspect of time travel: its relationship with free will and determinism.

Now, imagine you could go back in time and change a decision you regret; would the outcome still be predetermined or does your free will play a role in altering it? This question brings up the long-standing philosophical debate of determinism vs free will. Determinism is the belief that all events are predetermined and inevitable, while free will asserts that humans have the ability to make choices independent of external factors. Time travel adds another layer to this already complex issue as altering past events can create paradoxes and affect causality.

To understand the role of free will and determinism in time travel, we must first consider the paradoxes that arise when attempting to change past events. The grandfather paradox is one such example where traveling back in time and killing your own grandfather before he has children would mean you were never born, making it impossible for you to travel back in time to commit the act. This paradox highlights how changing past events can lead to contradictions and inconsistencies. Additionally, if we assume that all events are predetermined, then any attempt at altering them through time travel would ultimately fail because those events were always meant to occur. However, if we believe in free will, then it's possible that our actions could alter future outcomes despite their predetermined nature. Ultimately, whether determinism or free will reigns supreme depends on your personal beliefs about fate and choice.

As much as we would love to travel through time without causing any paradoxes, it seems like a tricky business. The idea of alternate timelines comes into play when considering the possibility of avoiding the Grandfather paradox, where traveling back in time and altering something could prevent your own existence. However, even with alternate timelines, there is still the risk of creating new paradoxes and complications that could have unforeseen consequences. While it's fun to imagine the possibilities of time travel, it's important to consider the potential ramifications and embrace the present moment.

When it comes to time travel, there are a lot of ethical considerations to take into account. For starters, what impact will our actions have on the course of history? Will we be altering the past in ways that could negatively affect the future? Additionally, how will our presence in different cultures and time periods impact those around us? It's important to approach time travel with sensitivity and respect for the people and places we encounter. Furthermore, we must consider the cultural impact of introducing modern ideas and technologies into ancient societies. While time travel may seem like an exciting adventure, it's crucial to think about the potential consequences of our actions before jumping headfirst into such an endeavor.

Alternate realities and butterfly effects are two concepts that come to mind when considering the possibility of altering history through time travel. The very idea of changing something in the past can lead to a sense of excitement and curiosity, but it also raises many ethical questions. What if altering one event leads to unintended consequences in the future? Would we be willing to take responsibility for those outcomes? It's easy to get lost in the allure of changing history, but we must remember that every action has a reaction, and even the smallest alteration could have drastic effects on our present-day reality. As intriguing as the idea may be, we must approach it with caution and consider all possible outcomes before making any decisions about altering history.

The philosophical debate surrounding time travel centers on the question of whether or not it would affect the concept of free will. Some argue that if time travel were possible, our past actions would be predetermined and therefore we wouldn't truly have agency over our choices. However, others believe that even with knowledge of the future, individuals would still have the ability to make their own decisions. While there is no scientific evidence to support either side of this argument, it remains a fascinating topic for discussion and speculation.

When it comes to time travel, there are several theories and experiments that have been explored by physicists. Two of the most popular ones are Quantum Entanglement and Wormhole Theories. Quantum Entanglement suggests that two particles can be connected in a way that their states remain correlated, regardless of distance or time. This means that manipulating one particle could potentially affect its entangled counterpart, even if it's light-years away in space or years into the future or past. Wormhole Theories propose the existence of shortcuts through space-time via hypothetical tunnels called wormholes. If these tunnels could be utilized for travel, they could potentially allow us to move through time as well. While these theories have yet to be proven experimentally, the potential for them to enable time travel is certainly exciting and worth continued exploration.

So there you have it - the different types of time travel and how they work. From fixed timelines to dynamic ones, from time loops to wormholes and black holes, each theory offers a unique perspective on the possibility of traveling through time.

But no matter which theory you subscribe to, one thing is certain: time travel remains a fascinating topic that captures our imaginations and challenges our understanding of the universe. As the philosopher Heraclitus once said, "no man ever steps in the same river twice," reminding us that time is constantly moving forward and changing. Whether we will ever be able to manipulate it for our own purposes remains to be seen, but one thing is for sure - we'll keep dreaming about it as long as we live.

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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A Concise Breakdown of How Time Travel Works in Popular Movies, Books & TV Shows

in Film , Literature , Sci Fi | January 24th, 2020 4 Comments

As least since H.G. Wells’ 1895 nov­el  The Time Machine , time trav­el has been a promis­ing sto­ry­telling con­cept. Alas, it has sel­dom deliv­ered on that promise: whether their char­ac­ters jump for­ward into the future, back­ward into the past, or both, the past 125 years of time-trav­el sto­ries have too often suf­fered from inel­e­gance, incon­sis­ten­cy, and implau­si­bil­i­ty. Well, of course they’re implau­si­ble, every­one but Ronald Mal­lett might say — they’re sto­ries about time trav­el. But fic­tion only has to work on its own terms, not real­i­ty’s. The trou­ble is that the fic­tion of time trav­el can all too eas­i­ly stum­ble over the poten­tial­ly infi­nite con­vo­lu­tions and para­dox­es inher­ent in the sub­ject mat­ter.

In the Min­utePhysics video above , Hen­ry Reich sorts out how time-trav­el sto­ries work (and fail to work) using noth­ing but mark­ers and paper. For the time-trav­el enthu­si­ast, the core inter­est of such fic­tions isn’t so much the spec­ta­cle of char­ac­ters hurtling into the future or past but “the dif­fer­ent ways time trav­el can influ­ence causal­i­ty, and thus the plot, with­in the uni­verse of each sto­ry.” As an exam­ple of “100 per­cent real­is­tic trav­el” Reich points to Orson Scott Card’s  Ender’s Game , in which space trav­el­ers at light speed expe­ri­ence only days or months while years pass back on Earth. The same thing hap­pens in Plan­et of the Apes , whose astro­nauts return from space think­ing they’ve land­ed on the wrong plan­et when they’ve actu­al­ly land­ed in the dis­tant future.

But when we think of time trav­el per se, we more often think of sto­ries about how active­ly trav­el­ing to the past, say, can change its future — and thus the sto­ry’s “present.” Reich pos­es two major ques­tions to ask about such sto­ries. The first is “whether or not the time trav­el­er is there when his­to­ry hap­pens the first time around. Was “the time-trav­el­ing ver­sion of you always there to begin with?” Or “does the very act of time trav­el­ing to the past change what hap­pened and force the uni­verse onto a dif­fer­ent tra­jec­to­ry of his­to­ry from the one you expe­ri­enced pri­or to trav­el­ing?” The sec­ond ques­tion is “who has free will when some­body is time trav­el­ing” — that is, “whose actions are allowed to move his­to­ry onto a dif­fer­ent tra­jec­to­ry, and whose aren’t?”

We can all look into our own pasts for exam­ples of how our favorite time-trav­el sto­ries have dealt with those ques­tions. Reich cites such well-known time-trav­el­ers’ tales as A Christ­mas Car­ol , Ground­hog Day , and Bill & Ted’s Excel­lent Adven­ture , as well, of course, as  Back to the Future , the most pop­u­lar drama­ti­za­tion of the the­o­ret­i­cal chang­ing of his­tor­i­cal time­lines caused by trav­el into the past. Rian John­son’s Loop­er treats that phe­nom­e­non more com­plex­ly, allow­ing for more free will and tak­ing into account more of the effects a char­ac­ter in one time peri­od would have on that same char­ac­ter in anoth­er. Con­sult­ing on that film was Shane Car­ruth, whose Primer — my own per­son­al favorite time-trav­el fic­tion — had already tak­en time trav­el “to the extreme, with time trav­el with­in time trav­el with­in time trav­el.”

Har­ry Pot­ter and the Pris­on­er of Azk­a­ban , Reich’s per­son­al favorite time-trav­el fic­tion, exhibits a clar­i­ty and con­sis­ten­cy uncom­mon in the genre. J.K. Rowl­ing accom­plish­es this by fol­low­ing the rule that “while you’re expe­ri­enc­ing your ini­tial pre-time trav­el pas­sage through a par­tic­u­lar point in his­to­ry, your time-trav­el­ing clone is also already there, doing every­thing you’ll even­tu­al­ly do when you time-trav­el your­self.” This sin­gle-time-line ver­sion of time trav­el, in which “you can’t change the past because the past already hap­pened,” gets around prob­lems that have long bedev­iled oth­er time-trav­el fic­tions. But it also demon­strates the impor­tance of self-con­sis­ten­cy in fic­tion of all kinds: “In order to care about the char­ac­ters in a sto­ry,” Reich says, “we have to believe that actions have con­se­quences.” Sto­ries, in oth­er words, must obey their own rules — even, and per­haps espe­cial­ly, sto­ries involv­ing time-trav­el­ing child wiz­ards.

Relat­ed Con­tent:

What’s the Ori­gin of Time Trav­el Fic­tion?: New Video Essay Explains How Time Trav­el Writ­ing Got Its Start with Charles Dar­win & His Lit­er­ary Peers

Pro­fes­sor Ronald Mal­lett Wants to Build a Time Machine in this Cen­tu­ry … and He’s Not Kid­ding

Mark Twain Pre­dicts the Inter­net in 1898: Read His Sci-Fi Crime Sto­ry, “From The ‘Lon­don Times’ in 1904”

What Hap­pened When Stephen Hawk­ing Threw a Cock­tail Par­ty for Time Trav­el­ers (2009)

Pret­ty Much Pop #22 Untan­gles Time-Trav­el Sce­nar­ios in the Ter­mi­na­tor Fran­chise and Oth­er Media

Based in Seoul,  Col­in Mar­shall  writes and broad­casts on cities, lan­guage, and cul­ture. His projects include the book  The State­less City: a Walk through 21st-Cen­tu­ry Los Ange­les  and the video series  The City in Cin­e­ma . Fol­low him on Twit­ter at  @colinmarshall  or on  Face­book .

by Colin Marshall | Permalink | Comments (4) |

Related posts:

Comments (4), 4 comments so far.

The idea of an episode where the time trav­el­er is present and doing his (in this case) thing, as he lives through the episode the first time around, reminds me of one of the great clas­sic sci-fi short sto­ries, but, sor­ry, I can’t remem­ber the author or title. I’ll say there’s a din­er, and a note, involved, but, no spoil­ers! And also check out “The Man in the Emp­ty Suit”.

I real­ly enjoyed this video very much — thanks. Pri­zon­er of Azk­a­ban is my favorite of the HP series in large part because the time-trav­el sequence is so per­fect­ly exe­cut­ed. One thing that occurred to me while watch­ing this though: when you say that the char­ac­ters can “instant­ly jump back in time and can inter­act with your­self, but it does­n’t gen­er­ate new time­lines” — my think­ing is that we don’t know this to be true; only that that the time­line DOESN’T change because. I’m work­ing from mem­o­ry so bear with me, but if I recall Dum­b­le­dore stress­es to Hermione that they must be very care­ful not to be seen while time trav­el­ling — it is because they adhere to this rule that the time­line does not change. One would pre­sume that the rea­son Dum­b­le­dore is so insis­tent on this rule is pre­cise­ly because if they were to inter­act with peo­ple the way Mar­ty does in Back To The Future, the time­line would in fact change. So the con­struct of time trav­el in Pris­on­er of Azk­a­ban and Back To The Future are/may be the same — the dif­fer­ence is that Hermione and Har­ry do not inter­act direct­ly with peo­ple in the past, but Mar­ty does.

Oth­ers: “A Sound of Thun­der”, a 1952 short sto­ry by Ray Brad­bury Dr Who Hitch­hik­er’s Guide to the Galaxy

I know the focus here is film time trav­el, but if you haven’t read Jack Finney’s Time and Again and the sequel, From Time to Time, pos­es some inter­est­ing ideas using Ein­stein’s the­o­ries of par­al­lel time line and time trav­el. I think either or both would make very inter­est­ing films…

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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).

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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5 Bizarre Paradoxes Of Time Travel Explained

December 20, 2014 James Miller Astronomy Lists , Time Travel 58

There is nothing in Einstein’s theories of relativity to rule out time travel , although the very notion of traveling to the past violates one of the most fundamental premises of physics, that of causality. With the laws of cause and effect out the window, there naturally arises a number of inconsistencies associated with time travel, and listed here are some of those paradoxes which have given both scientists and time travel movie buffs alike more than a few sleepless nights over the years.

Types of Temporal Paradoxes

The time travel paradoxes that follow fall into two broad categories:

1) Closed Causal Loops , such as the Predestination Paradox and the Bootstrap Paradox, which involve a self-existing time loop in which cause and effect run in a repeating circle, but is also internally consistent with the timeline’s history.

2) Consistency Paradoxes , such as the Grandfather Paradox and other similar variants such as The Hitler paradox, and Polchinski’s Paradox, which generate a number of timeline inconsistencies related to the possibility of altering the past.

1: Predestination Paradox

A Predestination Paradox occurs when the actions of a person traveling back in time become part of past events, and may ultimately cause the event he is trying to prevent to take place. The result is a ‘temporal causality loop’ in which Event 1 in the past influences Event 2 in the future (time travel to the past) which then causes Event 1 to occur.

This circular loop of events ensures that history is not altered by the time traveler, and that any attempts to stop something from happening in the past will simply lead to the cause itself, instead of stopping it. Predestination paradoxes suggest that things are always destined to turn out the same way and that whatever has happened must happen.

Sound complicated? Imagine that your lover dies in a hit-and-run car accident, and you travel back in time to save her from her fate, only to find that on your way to the accident you are the one who accidentally runs her over. Your attempt to change the past has therefore resulted in a predestination paradox. One way of dealing with this type of paradox is to assume that the version of events you have experienced are already built into a self-consistent version of reality, and that by trying to alter the past you will only end up fulfilling your role in creating an event in history, not altering it.

– Cinema Treatment

In The Time Machine (2002) movie, for instance, Dr. Alexander Hartdegen witnesses his fiancee being killed by a mugger, leading him to build a time machine to travel back in time to save her from her fate. His subsequent attempts to save her fail, though, leading him to conclude that “I could come back a thousand times… and see her die a thousand ways.” After then traveling centuries into the future to see if a solution has been found to the temporal problem, Hartdegen is told by the Über-Morlock:

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

• Movies : Examples of predestination paradoxes in the movies include 12 Monkeys (1995), TimeCrimes (2007), The Time Traveler’s Wife (2009), and Predestination (2014).
• Books : An example of a predestination paradox in a book is Phoebe Fortune and the Pre-destination Paradox by M.S. Crook.

2: Bootstrap Paradox

A Bootstrap Paradox is a type of paradox in which an object, person, or piece of information sent back in time results in an infinite loop where the object has no discernible origin, and exists without ever being created. It is also known as an Ontological Paradox, as ontology is a branch of philosophy concerned with the nature of being or existence.

– Information : George Lucas traveling back in time and giving himself the scripts for the Star War movies which he then goes on to direct and gain great fame for would create a bootstrap paradox involving information, as the scripts have no true point of creation or origin.

– Person : A bootstrap paradox involving a person could be, say, a 20-year-old male time traveler who goes back 21 years, meets a woman, has an affair, and returns home three months later without knowing the woman was pregnant. Her child grows up to be the 20-year-old time traveler, who travels back 21 years through time, meets a woman, and so on. American science fiction writer Robert Heinlein wrote a strange short story involving a sexual paradox in his 1959 classic “All You Zombies.”

These ontological paradoxes imply that the future, present, and past are not defined, thus giving scientists an obvious problem on how to then pinpoint the “origin” of anything, a word customarily referring to the past, but now rendered meaningless. Further questions arise as to how the object/data was created, and by whom. Nevertheless, Einstein’s field equations allow for the possibility of closed time loops, with Kip Thorne the first theoretical physicist to recognize traversable wormholes and backward time travel as being theoretically possible under certain conditions.

• Movies : Examples of bootstrap paradoxes in the movies include Somewhere in Time (1980), Bill and Ted’s Excellent Adventure (1989), the Terminator movies, and Time Lapse (2014). The Netflix series Dark (2017-19) also features a book called ‘A Journey Through Time’ which presents another classic example of a bootstrap paradox.
• Books : Examples of bootstrap paradoxes in books include Michael Moorcock’s ‘Behold The Man’, Tim Powers’ The Anubis Gates, and Heinlein’s “By His Bootstraps”

3: Grandfather Paradox

The Grandfather Paradox concerns ‘self-inconsistent solutions’ to a timeline’s history caused by traveling back in time. For example, if you traveled to the past and killed your grandfather, you would never have been born and would not have been able to travel to the past – a paradox.

Let’s say you did decide to kill your grandfather because he created a dynasty that ruined the world. You figure if you knock him off before he meets your grandmother then the whole family line (including you) will vanish and the world will be a better place. According to theoretical physicists, the situation could play out as follows:

– Timeline protection hypothesis: You pop back in time, walk up to him, and point a revolver at his head. You pull the trigger but the gun fails to fire. Click! Click! Click! The bullets in the chamber have dents in the firing caps. You point the gun elsewhere and pull the trigger. Bang! Point it at your grandfather.. Click! Click! Click! So you try another method to kill him, but that only leads to scars that in later life he attributed to the world’s worst mugger. You can do many things as long as they’re not fatal until you are chased off by a policeman.

– Multiple universes hypothesis: You pop back in time, walk up to him, and point a revolver at his head. You pull the trigger and Boom! The deed is done. You return to the “present,” but you never existed here. Everything about you has been erased, including your family, friends, home, possessions, bank account, and history. You’ve entered a timeline where you never existed. Scientists entertain the possibility that you have now created an alternate timeline or entered a parallel universe.

• Movies : Example of the Grandfather Paradox in movies include Back to the Future (1985), Back to the Future Part II (1989), and Back to the Future Part III (1990).
• Books : Example of the Grandfather Paradox in books include Dr. Quantum in the Grandfather Paradox by Fred Alan Wolf , The Grandfather Paradox by Steven Burgauer, and Future Times Three (1944) by René Barjavel, the very first treatment of a grandfather paradox in a novel.

4: Let’s Kill Hitler Paradox

Similar to the Grandfather Paradox which paradoxically prevents your own birth, the Killing Hitler paradox erases your own reason for going back in time to kill him. Furthermore, while killing Grandpa might have a limited “butterfly effect,” killing Hitler would have far-reaching consequences for everyone in the world, even if only for the fact you studied him in school.

The paradox itself arises from the idea that if you were successful, then there would be no reason to time travel in the first place. If you killed Hitler then none of his actions would trickle down through history and cause you to want to make the attempt.

• Movies/Shows : By far the best treatment for this notion occurred in a Twilight Zone episode called Cradle of Darkness which sums up the difficulties involved in trying to change history, with another being an episode of Dr Who called ‘Let’s Kill Hitler’.
• Books : Examples of the Let’s Kill Hitler Paradox in books include How to Kill Hitler: A Guide For Time Travelers by Andrew Stanek, and the graphic novel I Killed Adolf Hitler by Jason.

5: Polchinski’s Paradox

American theoretical physicist Joseph Polchinski proposed a time paradox scenario in which a billiard ball enters a wormhole, and emerges out the other end in the past just in time to collide with its younger version and stop it from going into the wormhole in the first place.

Polchinski’s paradox is taken seriously by physicists, as there is nothing in Einstein’s General Relativity to rule out the possibility of time travel, closed time-like curves (CTCs), or tunnels through space-time. Furthermore, it has the advantage of being based upon the laws of motion, without having to refer to the indeterministic concept of free will, and so presents a better research method for scientists to think about the paradox. When Joseph Polchinski proposed the paradox, he had Novikov’s Self-Consistency Principle in mind, which basically states that while time travel is possible, time paradoxes are forbidden.

However, a number of solutions have been formulated to avoid the inconsistencies Polchinski suggested, which essentially involves the billiard ball delivering a blow that changes its younger version’s course, but not enough to stop it from entering the wormhole. This solution is related to the ‘timeline-protection hypothesis’ which states that a probability distortion would occur in order to prevent a paradox from happening. This also helps explain why if you tried to time travel and murder your grandfather, something will always happen to make that impossible, thus preserving a consistent version of history.

• Books:  Paradoxes of Time Travel by Ryan Wasserman is a wide-ranging exploration of time and time travel, including Polchinski’s Paradox.

Are Self-Fulfilling Prophecies Paradoxes?

A self-fulfilling prophecy is only a causality loop when the prophecy is truly known to happen and events in the future cause effects in the past, otherwise the phenomenon is not so much a paradox as a case of cause and effect.  Say,  for instance, an authority figure states that something is inevitable, proper, and true, convincing everyone through persuasive style. People, completely convinced through rhetoric, begin to behave as if the prediction were already true, and consequently bring it about through their actions. This might be seen best by an example where someone convincingly states:

“High-speed Magnetic Levitation Trains will dominate as the best form of transportation from the 21st Century onward.”

Jet travel, relying on diminishing fuel supplies, will be reserved for ocean crossing, and local flights will be a thing of the past. People now start planning on building networks of high-speed trains that run on electricity. Infrastructure gears up to supply the needed parts and the prediction becomes true not because it was truly inevitable (though it is a smart idea), but because people behaved as if it were true.

It even works on a smaller scale – the scale of individuals. The basic methodology for all those “self-help” books out in the world is that if you modify your thinking that you are successful (money, career, dating, etc.), then with the strengthening of that belief you start to behave like a successful person. People begin to notice and start to treat you like a successful person; it is a reinforcement/feedback loop and you actually become successful by behaving as if you were.

Are Time Paradoxes Inevitable?

The Butterfly Effect is a reference to Chaos Theory where seemingly trivial changes can have huge cascade reactions over long periods of time. Consequently, the Timeline corruption hypothesis states that time paradoxes are an unavoidable consequence of time travel, and even insignificant changes may be enough to alter history completely.

In one story, a paleontologist, with the help of a time travel device, travels back to the Jurassic Period to get photographs of Stegosaurus, Brachiosaurus, Ceratosaurus, and Allosaurus amongst other dinosaurs. He knows he can’t take samples so he just takes magnificent pictures from the fixed platform that is positioned precisely to not change anything about the environment. His assistant is about to pick a long blade of grass, but he stops him and explains how nothing must change because of their presence. They finish what they are doing and return to the present, but everything is gone. They reappear in a wild world with no humans and no signs that they ever existed. They fall to the floor of their platform, the only man-made thing in the whole world, and lament “Why? We didn’t change anything!” And there on the heel of the scientist’s shoe is a crushed butterfly.

The Butterfly Effect is also a movie, starring Ashton Kutcher as Evan Treborn and Amy Smart as Kayleigh Miller, where a troubled man has had blackouts during his youth, later explained by him traveling back into his own past and taking charge of his younger body briefly. The movie explores the issue of changing the timeline and how unintended consequences can propagate.

Scientists eager to avoid the paradoxes presented by time travel have come up with a number of ingenious ways in which to present a more consistent version of reality, some of which have been touched upon here,  including:

• The Solution: time travel is impossible because of the very paradox it creates.
• Self-healing hypothesis: successfully altering events in the past will set off another set of events which will cause the present to remain the same.
• The Multiverse or “many-worlds” hypothesis: an alternate parallel universe or timeline is created each time an event is altered in the past.
• Erased timeline hypothesis : a person traveling to the past would exist in the new timeline, but have their own timeline erased.

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Methods Of Time Travel In Movies, Ranked By How Much You'd Want To Use Them

The concept of time travel has captivated scientists for centuries, along with theories about different types of time travel. It's no wonder we're so fascinated by time travel - after all, how amazing would it be to go back in time and change the darker parts of your past, or be able to glimpse the future? But as we've learned from various science fiction stories, altering timelines can have dire consequences. Would you time travel if it were real, risking all the potential paradoxes? What would you alter, and what would you leave the same?

This intrigue has permeated the public imagination and pop culture, making its way into countless movies over the years. There are as many different  time travel methods in film as there are movies about time travel . Some have horrific side effects (brain damage among them), while others are as comfortable as hopping into a DeLorean or a hot tub. From mutant powers and quantum realms in the MCU, to time-traveling cars and journals, to invasive inventions in Primer and 12 Monkeys , which methods of time travel would you choose?

Back to the Future

• Universal Pictures

How Do You Travel? In a tricked-out DMC DeLorean.

Are There Unfortunate Side Effects? Not immediately, but if you happen to run into your parents in the past, you may end up erased from existence.

How Comfortable Is It? Some DeLorean models come equipped with leather seats, making this one of the smoother time-traveling options.

Is It One-Way? Only if you run out of fuel.

Star Trek IV: The Voyage Home

• Paramount Pictures

How Do You Travel? By looping a spaceship around the sun. 

Are There Unfortunate Side Effects? No. You just have to survive the whole "getting close to the sun" thing.

How Comfortable Is It? As comfortable as the spaceship being used, and the HMS Bounty looks like it's pretty comfortable. 

Is It One-Way? No, but if you take on extra mass - say, by picking up a few humpback whales and some ocean water - it can make going around the sun more difficult to pull off.

The Time Machine

How Do You Travel? In a stylish steampunk contraption comprised of a couch, gear shift, and spinning things.

Are There Unfortunate Side Effects? No, but if you have a reason for making a time machine, that creates a paradox preventing you from being able to change that event, and something-something... Okay, somehow the paradoxes in this film make less sense than the ones in Hot Tub Time Machine .

How Comfortable Is It? As comfortable as sitting on a leather sofa. It may get a bit windy at times.

Is It One-Way? Only if it breaks - or, say, the owner chooses to destroy it on purpose.

Harry Potter and the Prisoner of Azkaban

• Warner Bros.

How Do You Travel? By twisting a magical charm on a necklace.

Are There Unfortunate Side Effects? No. However, you can only stay in the past for five hours, or you risk harming yourself and/or your timeline.

How Comfortable Is It? As comfortable as wearing a piece of jewelry.

Is It One-Way? No, but time-turners can get caught in time loops that render them useless (see: Battle of the Department of Mysteries ).

• 20th Century Fox

How Do You Travel? A futuristic wristwatch-looking thing. 

Are There Unfortunate Side Effects? You could accidentally cross paths with Deadpool while attempting to avenge your family's slaying.

How Comfortable Is It? It requires only a brief adjustment period and a couple of drinks.

Is It One-Way?  Only if your device runs out of charges.

Avengers: Endgame

• Walt Disney Studios Motion Pictures

How Do You Travel? By hopping about through quantum space-time via a machine built into the back of a Sprinter van.

Are There Unfortunate Side Effects? Only the creation of far too many timelines for viewers to keep up with. Oh, and a baby version of you might pee your pants.

How Comfortable Is It? On par with being an astronaut. 

Is It One-Way?  No, as long as you don't run out of Pym Particles.

Hot Tub Time Machine

How Do You Travel? In a soothing hot tub with your buddies, probably while hammered.

How Comfortable Is It? So long as the water temp stays warm and the bubbles keep bubbling, this may be the most comfortable way to time travel.

Is It One-Way? Only if you run out of “Chernobyl” energy drink.

The Terminator

• Orion Pictures

How Do You Travel? Cyborgs, lightning, and SCIENCE!

Are There Unfortunate Side Effects? No physical toll (aside from arriving in the past sans clothing), but there is  the whole "robot assassins from the future" thing you've got to deal with.

How Comfortable Is It? So comfortable that this franchise sends robots back in time like they're going out of style.

Is It One-Way? You'll be back.

X-Men: Days of Future Past

How Do You Travel? A mutant named Kitty uses her powers to send your consciousness back through time. 

Are There Unfortunate Side Effects? Being forced to work with your worst enemy to save the world, or being fed bad acid. 

How Comfortable Is It? Like waking up from a nap on a waterbed.

Is It One-Way? If Kitty is no longer able to use her powers.

How Do You Travel? In a dark, quiet place, like a closet.

Are There Unfortunate Side Effects? No, but you might accidentally turn your daughter into a son, and back again.

How Comfortable Is It? As comfortable as allowing your sister to get into a near-fatal car wreck while driving under the influence so as to avoid your daughter becoming a son.

Is It One-Way? If you're unable to get to your quiet place.

• TriStar Pictures

How Do You Travel? In a machine comprised of tubing and chicken wire, in a sketchy industrial center manned by de-facto mobsters.

Are There Unfortunate Side Effects? Not physically, but it's against the law, and you may have to eliminate an older version of yourself at some point.

How Comfortable Is It? Looks like it's about as comfortable as crawling inside a washing machine and turning it on.

Is It One-Way? Not unless you off yourself - or get offed by yourself. Time travel is confusing.

The Butterfly Effect

• New Line Cinema

How Do You Travel? Chronic blackouts and avid journaling.

Are There Unfortunate Side Effects? Nosebleeds, brain damage, and endless ill-fated “butterfly effects” from your good intentions. 

How Comfortable Is It? Who doesn’t enjoy blacking out and waking up in strange places?

Is It One-Way? Only if you destroy your journals/memories, or choke yourself while still in the womb.

• Buena Vista Pictures

How Do You Travel? In a controversial and potentially dangerous government experiment.

Are There Unfortunate Side Effects? You might end up detonating in a car underwater.

How Comfortable Is It? Hot and wet at the same time.

Is It One-Way? Yes, but don’t worry - your other self conveniently shows up after you explode.

The Lake House

How Do You Travel? By shoving yourself inside a mailbox.

Are There Unfortunate Side Effects? Falling in love.

How Comfortable Is It? So comfortable you could just expire in your lover's arms.

Is It One-Way? Only if you ignore a letter from two years in the future warning you to avoid stepping in front of a bus on the day you're supposed to perish.

How Do You Travel? Via wormhole and marines, brought to you by ITC Corp.

Are There Unfortunate Side Effects? Permanent DNA and internal organ damage.

How Comfortable Is It? As comfortable as a charging knight. 

Is It One-Way? No, but you’re limited to traveling between only the present day and 1357 in Castlegard, France.

How Do You Travel? In your birthday suit, hooked up to a bunch of electrodes in a clear plastic tube while scientists yell suggestions at you.

Are There Unfortunate Side Effects? Thankfully not, although it seems far too easy to send time-travelers to the wrong year, which can inadvertently get users locked in mental hospitals or take unnecessary fire on historical battlefields. 

How Comfortable Is It? It looks like it's about as comfortable as being a lab rat.

Is It One-Way? No, but this method can certainly use some refinement.

• Magnolia Pictures

How Do You Travel? By accidentally scaring your past self into accidentally finding a time machine in a house in the woods.

Are There Unfortunate Side Effects? There’s a chance you might stab yourself, hit yourself with a car, and attempt to slay your own wife.

How Comfortable Is It? As comfortable as bandages on a disfigured face.

Is It One-Way? If one of your other time-traveling selves succeeds in taking you out.

How Do You Travel? Inside a metal box you and your buddy designed in his garage.

Are There Unfortunate Side Effects? If you get out too late/early, you could go into shock, experience nausea, and even become comatose. After repeated uses, you may experience bleeding from the ears, and your handwriting may suffer. There's also the whole possibly-psycho doubles and triples of yourself to contend with.

How Comfortable Is It? The time machine is dark, cramped, noisy, and flushed with argon, necessitating the use of an oxygen mask. Also, you have to stay inside the box for the duration of time you want to travel. Your claustrophobia may be going off the charts just thinking about it. This is no doubt one of the least comfortable time travel methods ever put on screen.

Is It One-Way? Only if one of your other time-traveling selves shuts off the machine while you're using it.

Slaughterhouse-Five

How Do You Travel? PTSD?

Are There Unfortunate Side Effects? PTSD.

How Comfortable Is It? PTS... Wait, what were we just talking about? Where am I? When am I?

Is It One-Way?  Hello? I have become unstuck in time. Farewell.

The Time Traveler's Wife

How Do You Travel? Without any conscious control over it. Also, your clothes fall off in the process.

Are There Unfortunate Side Effects? Missing out on most of the important things in your life, including the majority of your daughter and wife's lives. Also, losing your clothes.

How Comfortable Is It? As comfortable and natural as appearing unclothed as a 35-year-old man in front of a 6-year-old version of your future wife. Totally not weird at all.

Is It One-Way?  Not physically, but mentally and emotionally, and it might even drive you to drink.

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As they say in well-written scripts, "You mean... like time travel?" + also a few bizarre stories about real people who have claimed, despite every law of physics, they have traveled through time.

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The 23 best time travel movies of all time

From Back to the Future to Looper to Palm Springs, the time travel narrative traverses the film spectrum. Here are EW’s picks for 23 of the best. 

Despite time travel being considered more of a science fiction trope, there is something positively enchanting about the idea of being able to go back to another time or forward into the future, even if just for a moment. While this list deals with a mix of films, some of which consider the hazards of time travel (mostly through time loops), for the most part, these films see time travel as a net positive. Time travel is also a sphere that is mostly occupied by television, thanks to shows like Doctor Who , Quantum Leap , and Lost , even though the number of time travel movies has shot up over the past two decades or so.

Unfortunately, the earliest this list goes is 1962; while there are some time travel movies from the Old Hollywood days, they lack a lot of the imagination and thoughtfulness about the nature of time that the movies on this list bring. This list is a mix of straight dramas, killer action, rollicking comedies, and heartfelt romance — and sometimes, all of those elements exist in a single movie. This list is unranked, and mostly grouped together according to each movie's particular "genre" of time travel: conventional time machines, time loops, magical circumstances, and missions to save the past and the future at the same time. These are 23 of the best time travel movies of all time.

La Jetée (1962)

Kicking off an unranked list of time-travel movies chronologically seems like a good place to start, actually. La Jetée is also probably the most experimental of the films on this list. A French Left Bank short film set in a post-nuclear apocalypse future told through narration and photographs, this is not the first time-travel film by any means, but its impact on the time-travel movies that came after, like 1995's 12 Monkeys , cannot be understated.

A young prisoner (Davos Hanich) is forced to undergo torturous experiments to induce time travel by using impactful memories — and unlike those who came before him, he succeeds, but he ends up discovering a time loop in the process. This is an incredibly stylish telling of what is now a familiar type of story, but in 1962, it was absolutely revolutionary. Honestly, because of its unique technical and visual elements, it still is.

Watch La Jetée on Criterion Channel

Time After Time (1979)

Nicholas Meyer is behind not one, but two brilliant time-travel movies that made this list. For this particular film, he not only wrote the screenplay but also made his directorial debut. The tale of two 19th-century former friends, H.G. Wells ( Malcolm McDowell , unusually wide-eyed and adorable) and John Leslie Stevenson a.k.a. Jack the Ripper ( David Warner , never more menacing yet charming), as they chase each other through 1979 San Francisco thanks to Wells' time machine, Time After Time doesn't spend too much time on the science of time travel, and it's better for it.

This is, in essence, a romantic thriller, as Wells falls for quirky bank clerk Amy ( Mary Steenburgen , delightfully independent) while in search of his old friend turned enemy. It has chase scenes, interrogation sequences, gory murder (courtesy of Jack), and a delightful sense of humor as Wells learns to navigate the future. He thought it would be a utopia; instead, he finds a world in sore need of his idealism, kindness, and dedication to justice.

Where to rent or buy Time After Time

The Back to the Future trilogy (1985, 1989, 1990)

While it's true that the first Back to the Future movie is probably one of the greatest time-travel movies of all time, with its two sequels living in its shadows, all three are essential to understanding the character of Marty McFly ( Michael J. Fox ). The Back to the Future trilogy is an '80s version of a bildungsroman about a teenager who has to learn that there's much more to life than being, well, a teenager. The first film, confidently directed by Robert Zemeckis , is imbued with so much humor and heart, it's all too easy to get sucked into a plot that should be convoluted, but that works so awfully well.

Back to the Future Part II evokes a bit less feeling than the original, and it's significantly grittier, but it's still " another fantastic voyage " as EW's Ira Robbins wrote, flinging Marty and Doc Brown ( Christopher Lloyd ) into a slightly prescient future version of 2015. Back to the Future Part III , meanwhile, restores the heart, but its story is slighter as it wraps up Marty's saga, sending Doc off on a brand new adventure all his own. While the first Back to the Future movie is required viewing for any time travel enthusiast, stick around for the rest of the trilogy, too: Even if this franchise's view of time travel is riddled with potential paradoxes, they are entertaining paradoxes nonetheless.

Watch the Back to the Future trilogy on Tubi

Bill & Ted's Excellent Adventure (1989)

"Be excellent to each other" is the reigning philosophy of Bill & Ted's Excellent Adventure , the adventurous, fun-loving, stoner time-travel comedy that spawned a franchise, including a third installment released in 2020. Alex Winter and Keanu Reeves absolutely triumph in the roles of lackadaisical teenagers Bill and Ted, respectively, as they journey through time to bring back legends in order to pass their history class.

If the film seems silly, that's because it is meant to be. Whereas the Back to the Future franchise intended to craft a legend, Bill & Ted's Excellent Adventure kicks off the journey with George Carlin as the duo's time travel guide and mentor, Rufus, who intends to enlighten the pair on their mission and destiny. In any other film, the two budding legends, with their free-wheeling ideals and misadventures, would bring down the fabric of time and space itself. However, Excellent Adventure is not a time-travel film that forces you to think too hard about its premise; instead, it invites you to just kick back and have a good time.

Watch Bill & Ted's Excellent Adventure on Amazon Prime Video

Meet the Robinsons (2007)

Meet the Robinsons received mixed reviews when it first debuted, but of the 3-D animated movies that came out of Disney Animation in the 2000s, it's probably the most imaginative and outstanding of the bunch. Following a young orphan as he goes on a fantastic voyage into the future with another young boy who is a time traveler (kind of), Robinsons is stylish to a point and is filled with heart. It's probably also the most kid-friendly entry on this list, but its good-natured humor and complicated emotional palette will appeal to adults, too.

It also fits neatly into a more classic genre of time travel, with time machines, eccentric inventors, and kids looking to make an impact — not just on their time, but on the time they find themselves in, be it the near future or the distant past.

Watch Meet the Robinsons on Disney+

Run Lola Run (1998)

This is, in many ways, the time loop movie; debuting in 1998 to rave reviews, Run Lola Run , a German experimental thriller, is one you will not be able to shake, long after you've finished a viewing (or even a second, to catch what you missed the first time). The protagonist, Lola (Franka Potente, in a punishingly physical performance), is forced to relive a scenario, again and again, involving saving her boyfriend Manni (Moritz Bleibtreu) from certain death.

Potente's performance alone is worth the watch, and of the films on this list, Run Lola Run is actually one of the shorter ones, using its 80-minute runtime to its full advantage. The other time loop movies on this list are also worthy viewing experiences in a lot of ways, but for a pure shot of adrenaline, you can't miss the film EW deemed "a masterful pop piece, humming with raw romance, youth, and energy." If you're interested in more of director Tom Tykwer 's work, he also codirected 2012's Cloud Atlas with the Wachowskis , which, while not a pure time-travel movie, certainly plays with the intertwined nature of time and memory.

Where to rent or buy Run Lola Run

Source Code (2011)

Duncan Jones made a splash with his 2009 feature directorial debut Moon , a moody, philosophical insight into possible lunar labor practices in the future. He followed that thoughtful film up with Source Code , which, while not a movie that could always be described as "thoughtful," could certainly be described as moody. Hitchcockian in a sense, Source Code follows the misadventures of a U.S. Army pilot ( Jake Gyllenhaal ), as he attempts to stop a terrorist attack on a Chicago commuter train — repeatedly.

Source Code does have something to say about the commodification of bodies and minds in the service of the so-called "greater good"; while Gyllenhaal's Captain Stevens' services are no doubt helpful, are they necessary, the film asks. Is it really a good idea to force someone to relive an incredibly stressful idea, over and over again? The movie has its funny moments, even in the thick of all the intense chase scenes through the train; EW noted back in 2012, "The director finds moments of humor in unlikely corners of that train of fools." Indeed. If you enjoyed a film like The Commuter (2018), but thought it could use a time loop and the potential of alternate realities, Source Code is your next mandatory viewing.

Watch Source Code on Showtime

Looper (2012)

Before Rian Johnson introduced us to Benoit Blanc or journeyed to a galaxy far, far, away , he made the tangled time-travel film fittingly called Looper . Starring Bruce Willis , Joseph Gordon-Levitt as a younger Bruce Willis, and Emily Blunt , Looper tells the tale of a contract killer sent after his next target: himself. This is a complicated film, and it is imperfect in a lot of ways, but its brutal appraisal of a possible dystopian future, and the efforts one man takes to prevent that future, are worth the amount of head-scratching you might find yourself doing throughout.

That Johnson likes his narratives to be impenetrable Gordian knots that only his designated protagonist can solve can perhaps be frustrating to the audience. However, if there's one thing that the Knives Out franchise seems to have reinforced, it's that not trying to unpack the mysteries of his work might work to your advantage as a viewer, because Johnson will probably have someone explain what just happened by the end, anyway. Like most of his films, Looper has a social conscience lurking within it as well. As EW's Lisa Schwarzbaum noted , "It's time to wipe the drops from our eyes or else get stuck in a loop, an endless cycle, a rut" about Looper 's core tenet back in 2012. It's a worthy takeaway from a film obsessed with self-fulfilling prophecies people find themselves within.

Watch Looper on Freevee

Edge of Tomorrow (2014)

Time loop movies need some incredible editing in order to really succeed, and Doug Liman 's enthralling Edge of Tomorrow certainly does so on that point. While Tom Cruise is the lead as a cowardly lion–turned–near-super soldier, all eyes are on Emily Blunt as Rita Vrataski, who rules this movie as one of the few heroes this dystopian, post-alien invasion world actually has left. While the quest Cruise and Blunt go on may be a bit convoluted, the film is so incredibly entertaining because it's so sharply cut, keeping up the pace even as we see similar things over and over and over again.

A tip of the hat must, of course, go to the action, which is as compelling as you would expect from a mega-star who seems determined these days to do all of his own stunts. In an era of often depressing science fiction, Edge of Tomorrow , as EW's Chris Nashawaty mentioned , is a fun, "deliciously subversive kind of blockbuster" to immerse your senses in for two hours, if nothing else.

Watch Edge of Tomorrow on Max

Interstellar (2014)

While this film might technically be considered more of a space opera than a time-travel movie, there's no reason it can't be both. Christopher Nolan 's Interstellar is a dazzling portrait not just of space travel, but of the love between a father and daughter that stretches over the thin fabric of both time and space. Matthew McConaughey as the astronaut father has never been so serious, but acclaim needs to go to Jessica Chastain and Anne Hathaway as Nolan's strongest women characters to date.

Interstellar varies between being almost too tense to stand, and, at other points, utterly relaxed. As a cinematic experience, it feels all-encompassing, using every possible outstanding special effect to draw its viewers in before the script hits them with emotional truth. While Nolan can certainly be considered " cold and clinical " as EW noted, his space-journeying meditation on the intersection between love and time is anything but.

Watch Interstellar on Paramount+

Palm Springs (2020)

Releasing a time loop movie during a global pandemic where life felt increasingly repetitive and bizarre was certainly a strategy for Hulu and Neon with Palm Springs , but it paid off. While the film was certainly developed long before COVID-19, the scenario of two wedding guests trying to escape the situational loop they've found themselves definitely resonated at the time, and it still does. Palm Springs may seem serious from the above description, but it is actually a fun sci-fi-tinged tale that is largely driven by the comedic skills of leads Andy Samberg and Cristin Milioti .

EW noted that the movie avoids " true discomfort comedy ," and honestly, it's all the better for it. If Palm Springs had been angrier, it wouldn't hit home so hard, and it also wouldn't be nearly as entertaining. Instead, it's an often sweet rom-com that doesn't take itself or its completely made-up time loop physics too seriously. It was a Sundance darling for a reason, never quite letting up on the wild ride it takes its characters or its viewers on over the course of its 90 minutes.

Watch Palm Springs on Hulu

Somewhere in Time (1980)

Somewhere in Time might employ one of the strangest methods of time travel of all the movies on this list: time travel by hypnosis, of all things. (And self-induced hypnosis, for that matter.) Time travel on such shaky ground can't possibly hold up, and it somewhat doesn't, in the end. Science fiction great Richard Matheson adapted his own novel into a lackadaisical screenplay for this film, starring Christopher Reeve in a perfectly tragic role as the young man who gives his all for a woman (Jane Seymour) he can never really have.

In many ways, Somewhere in Time feels like a curio of the era from which it came, serving as a time capsule of how stories were told in the late-'70s and early-'80s. That is actually not a mark against it; this is a film that is just a peak tragic romance in a lot of ways; special nods must also go to Christopher Plummer as the young woman's cynical mentor, who seems to possess a certain foresight about the impossibility of Reeve's character. If you want a time-travel movie that is beautifully romantic, from its iconic score to its grand cinematography, you shouldn't stray from Somewhere in Time .

Watch Somewhere in Time on Tubi

Peggy Sue Got Married (1986)

The tale of a grown, about-to-be-divorced woman forced to relive her high school days and her courtship with a dorky-cool musician, Peggy Sue Got Married might be one of Francis Ford Coppola 's most small-scale movies, but it decidedly has the most soul of his catalog of mostly epics. Peggy Sue ( Kathleen Turner , in an Oscar-nominated performance) just wants to leave Charlie (Nicolas Cage) behind, but her time-traveling coma dream conspires against her to force her to reconsider. (It forces Charlie to become a better person, too.)

The film combines the cynicism of a rightfully embittered '80s housewife with the unbridled idealism of a '60s teenager to make one heck of a sincere cinematic concoction. That the film starts at a high school reunion could mean it becomes awkward very quickly, but instead, it's completely joyful. Whether Peggy Sue Got Married started a tradition of "person has some sort of crisis and subsequently ends up in another time" movies is unclear, but it does have a rather clear descendant in one of our next entries.

Where to rent or buy Peggy Sue Got Married

Kate & Leopold (2001)

Doesn't everyone want a young Hugh Jackman from the 19th century to fall out of the sky and into their lives? Leopold (Jackman) is a foppish and geeky, if not perfect, gentleman who quickly has Kate ( Meg Ryan ) falling for him despite her modern understanding of the world. That so many time-travel movies somehow end up in romantic territory is an interesting phenomenon, but one that does make sense. There is something appealing about falling for someone whose time is not your own.

Kate & Leopold is decidedly not a perfect film, although it is the first of director James Mangold 's and Jackman's collaborations (see 2017's Logan for the much grittier future fruits of their labor). It's fluffy, it's light, and it creates a paradox without even really acknowledging it. Someone looked at the Meg Ryan comedies of the '80s and '90s and asked, "But what if we made them science fiction?" It works in spite of itself, with Jackman's physical comedy as he plays " a doll of a boyfriend " and Ryan's sardonic tone carrying the day.

Watch Kate & Leopold on Paramount+

13 Going on 30 (2004)

When a 13-year-old girl is crushed after being tricked at her own birthday party, she makes a wish to be "30, flirty, and thriving," quickly waking up the next day to find herself just that, in the body of Jennifer Garner . Instead of traveling back to the past à la the protagonist of Peggy Sue Got Married , Jenna (Garner, Christa B. Allen) ends up in a potential future, where she is all the things she wished for, but definitely not as happy as she thought she would be.

The 2004 rom-com is a magical time travel tale — there's literally "magic wishing dust" — but that doesn't take away from the hilarity that comes with a 13-year-old trying to navigate an adult woman's life. Of course, in the end, Jenna learns her lesson — it's okay to just be young, for a little bit longer — but the journey she goes on as she discovers not just herself but also her true love ( Mark Ruffalo ) is worth all the silliness in the end.

Watch 13 Going on 30 on Max

Mirai (2018)

This lovely little gem directed by Japanese animation visionary Mamoru Hosoda tells the story of a little boy who unhappily gets a baby sister and ends up learning a lot of lessons about the past and the future. Kun (Moka Kamishiraishi) gets a chance to meet not only the grown, future version of his sister Mirai (Haru Kuroki) but also members of his family at different points in their lives. Mirai is a delightfully imaginative film with some gorgeous animation that contains some " mind-boggling visuals " as EW's Christian Holub pointed out.

It is also a genuinely heartwarming tearjerker; while all ends well for little Kun, the meditations this film offers on the nature of family bonds over the course of multiple generations might just leave you in a state of reflection on your own ties that bind. While many time-travel movies tell their stories from the perspective of youth, few unveil them through the eyes of a rambunctious preschooler, and gaining that perspective, in this case, allows for a truly precious journey.

Where to rent or buy Mirai

Star Trek IV: The Voyage Home (1986)

If you know anything about Star Trek , you know the fourth film is "the one with the whales," but if you don't know anything about the franchise, you probably also know that this one is "the one with the whales." Star Trek IV: The Voyage Home often gets acclaim as the funny Star Trek movie, but it brings a lot more than just comedy. The original crew of the Enterprise fling themselves back in time to save humpback whales in the past in order to save the future from a strange probe that threatens Earth...and will stop, but only if it hears some natural whalesong.

The crew finds themselves in 1986 San Francisco, so it's great that Time After Time's Nicholas Meyer returned to the franchise not as director (he helmed Star Trek II: The Wrath of Khan ), but as a screenwriter. Watching these characters from a literal utopia navigate a world not designed for them creates not only dynamic humor but great tension as well. As they almost always do, the Enterprise team breaks all the rules in order to save the future as well as the whales. Or, as EW noted in a tribute to the film: "It has heart, and passion — Save the Whales! — and a tremendous sense of fun."

Watch Star Trek IV: The Voyage Home on Max

Star Trek: First Contact (1996)

Star Trek: First Contact doesn't particularly feel as much like a Star Trek movie as Voyage Home does, and EW, in fact, says it harnessed "a sleek, confident style fully independent of its predecessors." As a Trekkie, this may not be the most complimentary way of looking at it, but as a film fan, however, it might be the highest honor someone could bestow upon a movie within this franchise. Captain Jean-Luc Picard ( Patrick Stewart ) turns from a peace-loving diplomat to a Borg-slaying action star while the rest of his crew tries to get the inventor of the Warp Drive (the technology upon which the future relies) to stop drinking so much and actually invent the thing. James Cromwell, as the inventor, Zefram Cochrane, serves as the comedic relief for a remarkably serious and often scary film.

The Borg, '90s Star Trek 's biggest villain, are the main antagonists here, and they do provide some chilling action, even if the introduction that they can easily time travel would really wreck things for some future Trek series. Stewart manages the transition from his mild-mannered diplomat to traumatized warrior well, turning in one of his most ferocious performances. Star Trek: First Contact also gives us a look at a post-apocalyptic world in the midst of a recovery, and in that respect, it makes it both a thoughtful entry in the Trek canon and a time travel action-thriller with a brain.

Watch Star Trek: First Contact on Max

The Terminator (1984) and Terminator 2: Judgment Day (1991)

What would a best time-travel films list be without including at least one of the Terminator movies? While an often brutal franchise with diminishing returns after James Cameron 's first two installments, the misadventures of an evil cyborg-turned-good (played to physical perfection by Arnold Schwarzenegger ) in a consistently dangerous world are always thrilling and entertaining.

Linda Hamilton as Sarah Connor, mother of the future's savior (and much, much more), is also due an acknowledgment; while the films are remembered for Schwarzenegger's portrayal of the T-800, Hamilton is the heart of this franchise a great deal of the time, as she refuses to die or let her son face the same fate, either. The first two Terminator films are so much more than "scary robots take over the world, everybody dies" – they're action-packed, bloody thrillers with startling narratives, pioneering visual effects, and, of course, time travel as the catalyst.

Watch The Terminator on Max

Where to rent or buy Terminator 2: Judgment Day

Safety Not Guaranteed (2012)

"Wanted: Somebody to go back in time with me. This is not a joke...I have only done this once before. SAFETY NOT GUARANTEED": This is part of the joke classified ad from which this movie was inspired. You might inspire a more risky movie from the tone of the ad, but what you get is a light comedy that served as the first leading film role for Aubrey Plaza . This Colin Trevorrow -directed film isn't so much about time travel as it is about the cultural assumptions that surround the concept, and those who think it might be possible.

In that sense, it's a meta-narrative on nearly every time travel story which has come before it, and quite possibly, that will come after it. EW called it " a fable of 'redemption' "; redemption, and the acts of salvaging something, anything, for the benefit of the future, is a regular time travel theme, from all those time machines to all those time loops. Safety Not Guaranteed manages to explore these themes with a lot of irony and a splash of heart.

Where to rent or buy Safety Not Guaranteed

Related content:

• The Terminator movies, ranked
• Back to the Future cast: Where are they now?
• Let's talk about the plot of Interstellar

Related Articles

The 50 All-Time Best Time-Travel Films

1. The Time Machine

2. Back to the Future

3. The Terminator

4. Terminator 2: Judgment Day

5. Time After Time

6. Donnie Darko

7. Planet of the Apes

8. Groundhog Day

9. Run Lola Run

10. Safety Not Guaranteed

11. Doctor Strange

12. Arrival

14. Interstellar

15. 12 Monkeys

16. La Jetée

17. The Girl Who Leapt Through Time

18. Frequency

19. Timecrimes

20. Deja Vu

21. X-Men: Days of Future Past

22. Pleasantville

23. Edge of Tomorrow

24. The Philadelphia Experiment

25. About Time

More to explore, recently viewed.

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:

Time travel: Is it possible?

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

Albert Einstein's theory

• General relativity and GPS
• Wormhole travel
• Alternate theories

Science fiction

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

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

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

Related: The best sci-fi time machines ever

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

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

Related: Controversially, physicist argues that time is real

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

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

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

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

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

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

General relativity and GPS time travel

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

Read more: Can we stop time?

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

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

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

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

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

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

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

Can wormholes take us back in time?

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

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

Related: Best time travel movies

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

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

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

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

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

Alternate time travel theories

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

Infinite cylinder theory

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

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

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

Time donuts

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

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

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

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

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

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

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

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

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

Related: Marvel movies in order: chronological & release order

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

Books about time travel:

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

Movies about time travel:

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

Television about time travel:

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

Games about time travel:

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

Additional resources

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

Join our Space Forums to keep talking space on the latest missions, night sky and more! And if you have a news tip, correction or comment, let us know at: [email protected].

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Vicky Stein is a science writer based in California. She has a bachelor's degree in ecology and evolutionary biology from Dartmouth College and a graduate certificate in science writing from the University of California, Santa Cruz (2018). Afterwards, she worked as a news assistant for PBS NewsHour, and now works as a freelancer covering anything from asteroids to zebras. Follow her most recent work (and most recent pictures of nudibranchs) on Twitter. 

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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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• Wheeler, John Archibald and Richard Phillips Feynman, 1949, “Classical Electrodynamics in Terms of Direct Interparticle Action”, Reviews of Modern Physics , 21(3): 425–433. doi:10.1103/RevModPhys.21.425
• Yurtsever, Ulvi, 1990, “Test Fields on Compact Space‐times”, Journal of Mathematical Physics , 31(12): 3064–3078. doi:10.1063/1.528960

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

• Adlam, Emily, unpublished, “ Is There Causation in Fundamental Physics? New Insights from Process Matrices and Quantum Causal Modelling ”, 2022, arXiv: 2208.02721. doi:10.48550/ARXIV.2208.02721
• Rovelli, Carlo, unpublished, “ Can We Travel to the Past? Irreversible Physics along Closed Timelike Curves ”, arXiv: 1912.04702. doi:10.48550/ARXIV.1912.04702

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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Classic Time Travel Paradoxes (And How To Avoid Them)

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

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

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

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

I’m looking at you, River Song.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

How to Avoid : Watch your step

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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

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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.