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.
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:
- 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.
- 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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