How to Make Time Travel Logical

It’s often assumed that time travel would break the laws of logic. However, according to some philosophers, most famously the late David Lewis, this need not be the case. Scifi is full of time-travel stories that are fun, exciting, and gripping while breaking the laws of logic right and left, so clearly fiction doesn’t always need logic to work. Still, you can construct a logically consistent time-travel story; here’s what to think about.

Changing the Past

If you want to go the logical route, you should give up the idea of “changing the past.” Suppose, for instance, that Bisse, a 29-year-old genius inventor, builds a time machine in the year 2019. Next, he decides to travel back in time to the year 1950. In most scifi stories, we’re supposed to accept the following: It used to be the case, before Bisse started up the time machine, that the year 1950 contained no Bisse. After his trip to the past, however, 1950 was changed; there is now a Bisse in that year.

Often, time-travel stories don’t treat traveling back in time as changing the past; it only counts if the time traveler does something particularly dramatic while there. However, if first there was no Bisse in 1950 and later there was one, that’s a change to the past already.

Now, there is a trivial sense in which the year 1950 might first be Bisse-less and later on contain Bisse. Suppose that Bisse travels back to the summer of 1950. It would be true that first, in the winter and spring of 1950, Bisse didn’t exist, but starting in summer, he does exist. Still, as soon as we zoom in on a particular point in that year, it’s either/or; he either exists or he doesn’t.

According to standard time-travel stories, however, even a single point in time, such as May 15 in 1950, four o’clock sharp in the afternoon – could be first one way (Bisse-less, because Bisse hasn’t made his trip through time yet), and later another way (containing Bisse and his machine). But this contradicts the laws of logic. If we focus on a single point in time, it doesn’t have a “before” and “after.” It cannot first be one way and later on a different way. If you try to construct a logical time travel scenario, this is what you want to avoid.

Single Dimensional Time

The simplest version of logically consistent time travel, and the kind of scenario mostly discussed by David Lewis and present-day philosophers like Kadri Vihvelin, takes place on a single time line. Let’s take a look at that, before moving on to more complicated scenarios.

This graph represents a scenario where time has a single dimension, along which Bisse travels with his time machine. The thick green lines represents Bisse’s existence.

  • A physically (albeit not chronologically) 29-year-old Bisse, along with a time machine, first pops into existence 1950.
  • Both wink out of existence a little later.
  • In the year 1990 Bisse is back – this time, as a new-born baby.
  • In 2019, he builds a time machine, and then, both he and the machine disappear. A little later, they’re back.

This sequence of events is undoubtedly very strange. It might also be impossible, due to how the laws of nature work in our universe. Lewis and other philosophers are not concerned with working out what the laws of nature are or what is against the laws of nature, however. That is not the job of philosophy. What he argued was that as strange as this is, it’s not illogical. But what’s the difference between “against the laws of nature,” “illogical,” and “strange”?

Well, this is not something I can delve too deep into in this post, but very briefly and simply: We must discover laws of nature through scientific investigation. Physics tells us that nothing can move faster than the speed of light, but this is a scientific discovery. Scientific discoveries are either directly based on study, experiment, and observation, or they are based on theories that ultimately go back to those sources. No matter how intelligent you are, you cannot figure out the laws of nature solely from your armchair.

The laws of logic, on the other hand, are more basic than the laws of nature, and we can simply figure them out. Also, the laws of logic cannot be tested scientifically; rather, all science presupposes that you already accept logic. Finally, what’s so-called strange is relative. Something might seem strange at one time, but people later come to accept that this is actually the way things are, and it doesn’t seem strange any longer.

Going back to Bisse’s journeys along a one-dimensional time line, even though it’s not illogical, much is undoubtedly very strange in this scenario:

  • The first thing to note is that Bisse has what Lewis calls a “gappy” existence. At several points in time, he winks out of existence altogether.
  • Not only that, he starts life as a young adult! He pops into existence in 1950, fully formed and in possession of an advanced scifi machine.
  • After some time, both he and his machine wink out of existence. Bisse does not emerge again until the year 1990, and by then, he is a baby.
  • We have to wait an additional 29 years for the time machine to exist again, and this time, it does not simply appear, but is gradually assembled by Bisse.
  • In my example, Bisse didn’t program the machine to return to the exact moment at which he left. So he and his machine wink out of existence in 2019, and pop back 2020. If he programmed the time machine to return to 2018, we’d have two Bisses and two time machines for a while!

All this is very strange – but not strictly illogical.

Time travel means backward causation

Another strange thing about this scenario is what causes what. We are used to thinking of causation as going strictly from the past toward the future. Later events are caused by earlier events and never the other way around. But in this scenario, there are instances of backward causation.

The red arrow in the above picture represents a chain of backward causation. Bisse’s invention of the time machine, setting the dials and starting it up in 2019, causes the appearance of both Bisse and the machine in 1950.

Likewise, all the memories and life experiences he had in 2019 cause Bisse in 1950 to remember a lot of things that haven’t happened yet – to remember the future! All the physical development Bisse’s body has had in the 21st century means that when he first appears in 1950, he’s a young adult.

The blue arrow, which represents forward causation, also shows causation of a strange kind. We’re used to causation running through chains of events, with no gaps in the chain. Normally, if events in 1950 caused someone to have certain memories in 2020, it would have done so through a 70-year-long chain of events, one causing the other. But here, events in 1950 directly cause events in 2020, such as the appearance of Bisse and the time machine. It also causes him to remember events in 1950, which he could not remember just a year earlier.

Because of this weird causation, Bisse’s subjective experience departs radically from what objectively happened. Of course, there are always discrepancies between what actually happened and how we experience things, but this time-travel case is extreme.

In 2019, it seems to Bisse that he hasn’t been in the year 1950 yet. To him, he lives for 29 years in the 21st century, and then he experiences the year 1950 after he’s already experienced the year 2019. This is why Bisse thinks he’s capable of changing the year 1950. That’s an illusion, though. Everything Bisse did in 1950, he did 69 years ago. So while Bisse doesn’t remember 1950, he can’t change it.

What if Bisse goes back in time to shoot his own grandfather?

Bisse is depressed. As a convoluted suicide method, he decides that he’s going to go back in time and shoot his grandfather Venko before Venko had children  – surely, this will result in Bisse disappearing in a puff of logic? Not so fast!

Bisse, as we have established already, does not experience things as they really are when using his time machine. To Bisse, it seems as if he could murder young Venko next week or next month, and he thinks that when he does, he’s going to disappear.

But this is not the case. Say Bisse’s father was conceived in 1965, so that Bisse’s plan hinges on murdering Venko well before that point. Any attempt to murder Venko in 1965 was something he already did, decades ago, and clearly failed at. Bisse doesn’t have any memory of the failed murder attempt yet, and for that reason feels as if the attempt is in the future, and it’s an open question of whether he will succeed or not. But that feeling is illusory; he already attempted it and failed.

Now, to complicate things even further, suppose that lots of time travelers think the same way Bisse does; they’re going to die by suicide via grandfather murder and logic. However, all of them, every single one, failed – they must have, since they’re still here. Isn’t this a weird coincidence? Maybe. Maybe not.

Maybe, it’s no more a strange coincidence than the following:

  • Throughout history, most living organisms die without reproducing.
  • Yet, it’s true of every single living thing today, that all of its ancestors, for billions of years, managed to reproduce before dying.
  • We do not normally think this is a weird coincidence, because it’s in the nature of things. Every single living thing today has an unbroken chain of reproducing ancestors behind it, because if it didn’t, it wouldn’t be here.

Perhaps we can say the same thing about all those death-seeking time travelers; it’s not a weird coincidence that all of them, in one way or another, failed to kill their grandfathers. It is simply the case that had they succeeded, they wouldn’t have been here in the first place; their failure is part of the nature of things.

Two-Dimensional Time

In the above examples, time was one-dimensional. Another logical possibility is that time is two-dimensional. This means that when you go back in time, time branches out. Since this happens every time you go backward, you can never go back to where you started. Too bad! (In this scenario, I allowed for the possibility of going forward in the same time line, but we might also imagine that even forward time travel makes new branches appear.)

In this graph of two-dimensional time, the blue and red arrows once again represent causation. The green thick lines are still Bisse’s life; but there are now two time lines, one next to the other. When Bisse travels back to 1950, he ends up in a different time line than the one in which he started.

In this scenario, by the way, Bisse might very well kill grandfather Venko before his father, Mickey, was conceived. This just ensures that no Bisse will be born in the second time line. Since our Bisse is the descendant of the first time line’s Venko and Mickey, and that Venko wasn’t murdered, there’s no paradox.

Two-dimensional time is unaffected by the time machine’s journeys

Finally, let us move on to a scenario that philosopher David Lewis never talked about, but that is still consistent with the laws of logic. Imagine that time is a two-dimensional grid, but it is unaffected by the time machine. Bisse, however, can travel freely throughout the grid with his time machine; not just backward and forward in time, but also sideways. Look at him go! He’s all over the place now!

Just like before, he’s born in the year 1990 in this diagram, and 29 years old when inventing the time machine.

If we look at his existence from an objective and chronological sense, he first pops into existence in the second time line, as a young adult with a time machine. He disappears again around 1965, and then in 1970, he pops back into existence  as an old man in the first time line. He dies in 1990, but simultaneously in the third timeline, he appears as an adult man in his prime.

However, in the eyes of Bisse himself, he grows up in the first time line, invents a time machine, begins traveling the time grid back and forth and eventually dies an old man. It doesn’t seem to him as if there are any gaps or overlaps in his existence nor as if he bounces back and forth between different ages.

In these graphs, I’ve never drawn Bisse’s existence as “overlapping” in the very same time line. But as I briefly mentioned above, that’s fine too – logic-wise! You could have two versions of Bisse, of different ages, occupying the same time in the same time line for a while.

The Two Basic Rules of Logical Time Travel

If you want to do a time-travel restricted by logic, you should first decide whether time has one or two dimensions. Next, decide whether the time machine makes new time lines every time it moves back or forth or whether the grid of time lines exists independently of the machine. When you have set the basic parameters, there are two rules you need to keep in mind:

  1. Every single point in time, or in the larger grid of time lines, is what it is. It cannot first be one way, and then another.
  2. The time traveler experiences the passage of time in a way that differs radically from reality. Just because it seems to the time traveler that first he’s in the 21st century and later on it’s suddenly 1950, it doesn’t mean that’s the way things really are.

Mythcreants has previously published articles on rational and arbitrary magic systems. I think logical and illogical time travel could be compared to these different versions of magic. Illogical time travel can provide a lot of entertainment value, sense of wonder, and suspense; the latter might even depend on the difficulty the characters have of understanding how time travel actually works.

However, a logical time-travel system could provide the similar benefits as a rational magic system. It could generate suspense that depends on the fact that the characters are more restricted in their options and cannot do just about anything that suits the narrative, and the readers won’t feel like the time machine offers deus ex machina solutions to problems. I believe that the discrepancy between the time traveler’s experiences and the objective reality of time likely holds a lot of potential for stories as well.

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  1. SunlessNick

    Illogical time travel can provide a lot of entertainment value

    Such as the time (in a TimeWatch game) the PC’s threw a bad guy out of the window – then went back in time, procured a truck, filled it with bear traps, and parked it beneath the window in time for him to land.

    • Julia

      Bringing new meaning to the term ‘overkill.’

  2. Cay Reet

    It’s not logical … and not explained in that much detail … but I like the way the Thursday Next series handles time travel. Thursday’s father is a rogue ChronoGuard (to become one, you need the skill to manipulate time). He has been removed from reality (his parents have, essentially, been stopped from having him), but he still exists and so do the children he fathered (well, one is dead, but that has nothing to do with the whole time travel thing). He turns up in Thursday’s life without warning, stopping time to talk to her, mostly about history. He also tries to help her recover her own husband, who has been removed from reality while she’s pregnant with their first child, but the time where the ChronoGuard illegally manipulated things is protected too well. While they’re travelling back in time, he explains to her that they’re actually travelling forward until they come back to the moment they’re looking for.

    • Tifa

      I was actually thinking about re-reading the Thursday Next books just the other day!
      I like the third, fourth, and sixth books best. There’s rumours that there’ll be an eighth book eventually.

      • Cay Reet

        I hope there will be … have you also looked at the two Nursery Crimes books? Since book 3 basically sets everything up? The Big Over Easy and The Fourth Bear are really good, too, if in a more thriller/crime novel way.

        • Tifa

          I haven’t, yet, but they’re on my [huge] list of books to eventually check out.

  3. Colin

    There’s a secret avengers story that does this really well.

    Basically the whole team on black widow’s squad (warmachine, cap and someone else) get killed in action. As he’s dying warmachine hands widow a time device. The whole issue is her travelling back and forth through time, to learn how to change the past: the answer is when an outcome is uncertain and in a way that it doesn’t appear to be changed. From there she has to get the time device built, miniaturized and installed in warmachine’s armor, get the weapons used against the avengers squad weakened in such a way that that they are serious but not fatal, and still take out the enemy forces in the mission.

    It’s quite good and left no paradoxes, highly recommend.

  4. Costin Manda

    Even if the timeline branches into another, it still means we essentially create a way for someone to run a computer for a little while, send the partial result in the past where the same computer will continue the computation until something that would take millions of years is actually achieved instantly. Yet no one I know wrote a story about cryptography broken by time travel. And it would be one of those “easy” time machines that only send information back a few milliseconds.

    Turn that computer into a free thinking AI and you have an infinitely wise machine. How about someone who uses an AI to test a time machine and it turns up fully awakened and having thought of everything that you could ever think of?

    But no, let’s go back into time, change our gender and give birth to ourselves, because that makes more sense to people. Let’s use time travel whenever poor writing backs your show into a wall or when you need to reboot a franchise because contracts expired. AAAARGH! At least go back in time and stop yourself from ranting about the misuse of time travel in popular writing!

  5. Sam Victors

    My time-travel method has one explanation; time-travelers are the godchildren of Father Time, a humanoid personification of time. There are good time-travelers, and there are bad time-travelers. Each trying to change history but ultimately fail or succeed (and Father Time has to clean up their mess so as not to damage time, much to his frustration).

    For example, heroic time-travelers try to kill Hitler, but fail due to villainous time-travelers protecting him. Evil time-travelers try to help Hitler win the war, but fail due to Heroic Time-travelers stopping them.

  6. Richard

    There’s a good treatment of the matter in “Try and Change the Past” by Fritz Leiber (Astounding ScienceFiction ,March 1958).

  7. Erich

    CONTENT NOTICE: On rereading this article before submission, it could be a little disturbing to those who don’t want to think about a murder of a family member, even in a hypothetical way.

    Interesting article. Lots of food for thought. I will have to check out David Lewis.

    The first thing I would like to say is, that I’ve never been a fan of alternate timelines or universes. It is a whole lot of energy expenditure based on what, in the universal scale of things, are extremely insignificant choices or events. Because of this, I am restricting things to a single timeline.

    I’m not sure I agree that, in a single timeline, killing your grandfather, before your father was born, would automatically be a failure. To say that I’ve already failed at something I have yet to try seems to be an attempt to handwave the issue. If someone was to go back in time, they would still be operating within the same physical universe and subject to the same laws of that universe. There should be no reason that, for example, if I were to properly aim a gun at my grandfather and pull the trigger, that he should not die. Whether I am doing it now, 50 years from now, or 50 years prior to now, the physics should still be the same.

    It is the *death* of the grandfather that causes the “disruption” to the timeline. For my father to never be born, for me to never be born, for me to never invent a time machine, for me to never go back in time, and never go to possibly suicidally murder my grandfather: there still has to be a dead grandfather lying on the ground.

    The question then becomes: If I can murder my grandfather, how much housekeeping would the universe do to clean up the mess I’ve made? My guess is, based on the law of the conservation of matter and energy, not much. To me, this is where the real mess of time travel and seeming paradoxes exist. If the universe immediately deletes me, how does it happen? Does my physical body instantly get converted to energy? That could get messy. Does the universe decide that I’m too insignificant to deal with and lets me continue to exist as some sort of time orphan? That would be horrible. Would I even have the memories of my family? I’m guessing that if I return to the original time I left, I would have to rebuild my identity. I wouldn’t exist. No one would remember me.

    Again, interesting article. I liked it a lot. Unfortunately, it is late and trying to handle the ramifications of the question is giving me a headache.

    • SunlessNick

      There should be no reason that, for example, if I were to properly aim a gun at my grandfather and pull the trigger, that he should not die.

      The problem with this is argument is that it presupposes that the failure point must be when you pull the trigger (or the equivalent for whatever other murderous scheme you have in mind.

      “You failed to kill your grandfather” might mean the gun jammed, or it might mean you went after the wrong guy, or it might mean your grandfather was quicker on the draw, or it might mean you didn’t spot your grandmother behind you until it was too late, or it might mean there’s a family secret where your real biological grandfather is someone who assumed the identity of the guy you killed, or it might mean you couldn’t find him, or it might mean you got killed in a freak accident on the way, or it might mean you decided not to go through with it, or it might mean you assumed he was dead but he actually survived, or any other way that a mission to kill someone can fail to be accomplished. None of those depend on physics being different.

      • Erich

        Agreed, all of those things would prevent the murder. However, barring the family secrets and the freak accidents, I am guessing that most of those things are items that would or could be accounted for before you attempt the actual event. (Test fire the gun. Make sure they are alone. Maintain the element of surprise. Etcetera.) Granted, I have zero experience in this regard. I am going under the premise that most people would be able to locate their actual grandparents and would go through with the act if they had seriously put their mind to it. Even if someone failed the first time, there is always another opportunity.

        To say that *something* would automatically and unerringly happen to prevent the event, seems to imbue the universe / cosmos with a lot more intent and attention to detail than I think is possible.

        • Dvärghundspossen

          Time travel IS weird, but no one suggests that the cosmos has intent here. Compare, again, the fact that every single one of your ancestors, as unlikely as that is, managed to reproduce without dying first, even though there were a shitload of fully competent predators around, trying to take them down, and no cosmic will INTENTIONALLY getting in their way.

        • SunlessNick

          It’s not that *would* happen to prevent it, it’s that something *did* happen to prevent it. Making the attempt means you get to find out what it was – the universe needs no intent for that.

          • Rose Embolism

            The end point to that idea is that it is impossible to change history in any way. After all, with a time machine, there’s nothing preventing you from going back and trying to kill your grandfather again. And again. And a thousand times again. Eventually the “reasons why not” have to add up to active intervention.

            Let’s step away from killing one’s grandfather, and go to something different, like preventing the death of Kennedy, or Franz Joseph. Or maybe preventing your grandfather’s death. Or hey, innoculating the American natives against smallpox.
            How do you justify not changing THAT history? How do you prevent a butterfly effect as in “A Sound of Thunder”?

            Now imagine that in all the eternity of future history, all the potential millions of time travellers you have to say none of them have made those changes to history. You quickly reach a point where the end conclusion is that time travel cannot change time at all. Or, more simply, it’s impossible.

            I kind of like Larry Niven’s idea that any timeline where time travel is invented inevitably is altered to the point where time travel is never invented. Its an elegant solution.

          • SunlessNick

            The end point to that idea is that it is impossible to change history in any way.

            It’s the *start* point of that idea.

        • Blackhoof

          In a linear single-dimension conception of timetravel you have to view the entirety of our current history as one in which all the time travelers of the future have already visited the pre-2019 world and left their mark. Every change they will make is a change they have already made in our current world.

          So because you were born, obviously your grandad survived to conceive you. This is set in stone. Going back in time to change this is impossible because it has already happened, so SOMETHING must happen that stops you.

          Maybe you die or are arrested in the attempt and can therefore not try again. It doesn’t matter WHAT happens, but you fail to stop your own birth because you have already been born.

  8. Kenneth Mackay

    One of my long-time favourite time-travel stories is ‘The Technicolour Time Machine’ by Harry Harrison, in which the time travellers are a film production company who need a completed film in the can to stop their creditors foreclosing on them – so they decide to shoot ‘on location’ in the past, as they’ll only need to hire the lights, cameras, etc for one day…!

    More recently, I’ve been following Jodi Taylor’s ‘Chronicles of St Mary’s’ – concerning a group of archeologists who ‘investigate historical events in contemporary time’ – usually with unpredictable results. Fortunately for them, the Director’s secretary is secretly Clio, Muse of History…

  9. Greg S

    I don’t require my time travel to follow any logic other than consistency. For example, in the TV series The Flash, the first couple times Barry Allen travels back in time, he becomes his past self, but with the memories of his future self. But in later episodes where he travels back in time, he encounters his past self as a separate entity.

  10. Thomas Diehl

    Here’s the problem with thinking about time travel: We presupose causality is neccessary. However, there is not a single known mechanism in nature that checks existence against causation.

    So, while causality is one way of making something exist, it might not be the only one. It is very likely that if something happens to exist the universe just treats it as such and does not check if it has any external reason to.
    Meaning, a time traveller killing their grandparent would still exist because their existence does not get double-checked by anything. They’d just happen to be something that popped into existence from a time machine arriving with no history to the universe.

    As any medic can tell you, reality certainly does not care if your knowledge/beliefs/memories of it match reality or not, so that’s not an issue.

    The whole thing does violate the laws of thermodynamics, but those have never been checked against such a thing occuring (for obvious reasons), so it falls squarely into science’s margin of error.

    • Cay Reet

      One other problem is whether you think of time as a long line from beginning to end or are more of the wibbly-wobbly-timey-wimey school.

      If you believe that time moves in a straight line, then changing something along the line will have consequences. If your grandparents die before your parents are born, your parents will not be born, which leads to you never being born.

      For the timey-wimey school, that is not a problem, because for them, such holes get patched up and your parents will somehow exist anyway.

      The question would also be why you would travel back in time when the past is uncertain (or travel so far into the future that you come back the other way, as in the Thursday Next books). A lot of time travel stories are about changing history. If we accept that premise, then time travel only makes sense if changes in the past can change the present. It’s straight line and not timey-wimey. In a straight-line time travel story, killing your grandparents will negate your existence, thereby then negating your grandparents’ death, which leads to a paradox.

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