Models of Time Travel

I watched Terminator Genisys the other day (only two and some years after it came out, so yeah, I’m behind) and, while I liked it quite a lot, it did make me think about portrayals of time travel in movies and books, and how most of them are nonsense.

One of many egregious examples that comes to mind is Back to the Future, where Marty McFly is on-stage trying desperately to preserve his own personal timeline, and watching members of his family gradually fade out of a photo as things go sideways. There is no coherent model of time travel by which that scenario makes a lick of sense.

So here are some models that I think do make sense, or at least are self-consistent given the initial assumption that time travel is a thing.  And I should perhaps stress that I’m speaking here of models of fictional time travel — I have no opinion on the possibilities or nature of real time travel — and my only criteria is self-consistency; that is, a model that does not contradict itself or result in nonsensical conditions.

That being said, the underlying assertion I’m going to make is this:

The timeline cannot change.

Whatever the overall shape of the timeline — linear, branching, a helix of semi-precious stones — that shape must be static.

This is because when you’re looking at the timeline from outside, you are ipso facto outside time itself, and change is impossible unless you are inside time. Change, by definition, means that something is different from one moment to the next moment; no moments, no change.

This means that we rule out from the start any idea of “changing history.”  The Back to the Future scenario is not self-consistent, nor is that one Red Dwarf episode where they change the past and as a result their timeline begins to dissolve around them.  (Not that Red Dwarf ever prioritized consistency over comedy.)  Also that Bradbury story about stepping on a butterfly.  Also also the “grandfather paradox” and all its variations.

Does this mean that we have to give up all fictional time travel, or that we can’t have stories about what happens when you go back in time and try to kill Hitler?  Not at all.  We certainly can have those stories; we just need to be careful about it.

So given our principle that we can only deal with static timeline structures, what are some of the models that do work?  And how close can we come to classic time travel tropes without giving up self-consistency?

Let’s start with the simplest model: a single timeline, moving linearly from past to future.  Here’s what that looks like:


Within this timeline is depicted the personal timeline of a single person; let’s call her Timothea the time traveler (although she’s not time traveling in Figure 1.) Also on this timeline is a critical event; for the sake of example, we’ll say that a laboratory experiment intended to produce a cure for cancer went horribly wrong and instead turned 95% of all humans into zombies. The world timeline is colored red after this event to indicate that it is a bad future.

Now let’s look at what happens when we add time travel to this model.


After the critical event, Timothea finds or invents a time machine, and travels back in time in an effort to avert the catastrophe. Her personal timeline jumps back to a point in the world timeline before the critical lab experiment, and continues from that point forward, in parallel with her previous timeline (“previous” by her own personal experience.)  In between the time that she arrives in her time machine, and the time she departs, there are two Timothea’s — or more accurately, her personal timeline is running in parallel with itself (these sections of her timeline are designed T1 and T2 — for Timothea 1 and Timothea 2 — on the figure.)

In this model, try as she might, Timothea is unable to avert the catastrophe. Whatever happened the “first” time (by her own timeline, in the section T1) happens exactly the same way the “second” time (again, by her own timeline, in the section T2.)

(In fact, she might find that her attempts to avert the catastrophe are precisely what caused it. This is possible for dramatic irony, but not required by the model.)

Further, let’s say that Timothea, being a careful and methodical sort, decides to do research on the events just before and after the critical point in time. And for the sake of argument, let’s say that she has access to complete video recordings of all relevant events.

At point “R” (for Research) in her personal timeline, then, Timothea looks at recordings of two past points in time, marked as t0 and t1. At time t0, Timothea sees her past self at point A on her own timeline, doing things that she remembers herself doing. The same applies at time t1, at point B on her personal timeline.

She also sees her future self (“future” based on her own timeline, in that she has not yet experienced those points) at points C (t0) and D (t1) doing things that she doesn’t remember because she hasn’t done them yet.  In fact, she may remember, from points A and B, seeing her future self do those things at points C and D.  (It depends on whether, after the time travel journey, Timothea [T2] decides to keep herself hidden from her past self [T1].  For the sake of simplicity, we’ll assume from this point on that Timothea always reveals herself to her past self.  Of course in this model that means that Timothea [T1] is surprised to see her twin suddenly suddenly appear in front of her just before a routine laboratory experiment.)

After she time travels, at times t0 and t1, she may try to do something different than what she has seen herself doing. She will not be able to. She will, inevitably, do exactly the things she saw herself doing, no matter how she tries to change anything. She will have the experience of predestination — of knowing the future but being unable to do anything other than what she knows will happen.

This is a simple and self-consistent model for time travel, but it really only makes for one kind of story, and not a particularly satisfying one:  the story of futility and unavoidable destiny.

Let’s look at another model: a timeline that branches at critical events.


This timeline starts the same way as before, but when it reaches the critical point, the world timeline branches. In one branch, branch α (alpha), the experiment goes wrong and brings about the zombie apocalypse. In the other branch, branch β (beta), the experiment succeeds and all cancer is cured forever. This branch is colored green to indicate that it is a “good” future.

When the world timeline branches, everything in the timeline also branches, including Timothea’s personal timeline. So at the critical point, Timothea’s timeline forks into Timothea-alpha (Tα, in the “bad” branch) and Timothea-beta (Tβ, in the “good” branch.)  Timothea-alpha has to battle to survive hordes of zombies; Timothea-beta is enjoying a cancer-free world.

Now let’s add time travel to this model.


Here, after the fork, Timothea alpha-1 (Tα1) decides to travel back in time to try to avert the zombie apocalypse.  She appears shortly before the critical lab experiment, surprising her past self.  When her personal timeline arrives at the critical point the second time, it — like everything else — forks again, meaning that Timothea’s timeline is now doubled in both branches of the world timeline.

Let’s look at the experience of each of the four Timotheas.

Timothea alpha-1 (Tα1) is our time traveler.  She remembers points A and B in her past, and when she does research at point R, she observes her future self at points D and E (as well as remembering witnessing D and E when she experienced A and B.)

Timothea alpha-2 (Tα2) traveled back in time, attempted to avert the catastrophe, and failed.  She remembers points A, B, R, D, and E, in that order.  Furthermore, she experienced predestination at both t0 and t1 — she was unable to do anything other than what she had seen herself doing.  In fact, her experience is indistinguishable from that of Timothea (T2) in the previous model.

Timothea beta-1 (Tβ1) has never time-traveled.  She remembers points A and C only.  Her experience is that her twin suddenly appeared in front of her, warned her of a potential catastrophe, and together they were able to avert it.  She’s happily living in the good branch of the timeline.

Timothea beta-2 (Tβ2) has time-traveled and, so far as she can tell from her own experience, has changed history.  She remembers points A, B, R, D, and F, in that order; meaning she remembers the zombie timeline but is now living in the cancer-is-cured world.  She experienced predestination at time t0, but not at time t1 — at t1 her research showed point E but she experienced point F.

It’s important to note, however, that despite what both Timothea-betas think, they have not actually changed history.  The zombie apocalypse branch of the timeline still exists; The Tβs are simply experiencing a more congenial branch.

This model is definitely closer to some of the standard time-travel tropes, but in fact we can do better while still maintaining self-consistency. To do so, we have to make two assumptions:

1) In addition to forking at critical points, the timeline also forks whenever a time traveler arrives from the future.

2) The personal timeline of the time traveler continues in only one of the resulting branches.

(Are we allowed to make these assumptions? We’re dealing with fiction; we can make any assumptions we like so long as the results are self-consistent.)

The diagram for this looks complicated at first glance, but bear with me.


The timeline begins the same way at the others. It forks first at the point when Timothea’s time machine arrives from the future, into branches alpha and beta.  At the moment of forking, the only difference between the two branches is that branch alpha contains only one instance of Timothea’s timeline, while branch beta contains two.  Timothea’s original timeline (prior to any time travel) forks into the two branches as Timothea alpha (Tα) and Timothea beta-1 (Tβ1). The timeline of the Timothea that time-traveled continues, per our assumption, only in branch beta, as Timothea beta-2 (Tβ2).

The critical lab experiment occurs in both the alpha and beta branches (although details may be slightly different) and causes both branches to fork again, each one into a “bad” branch (zombie apocalypse) and a “good” branch (cancer cured forever) although again details will be somewhat different. These are branches gamma (γ), delta (δ), epsilon (ε), and zeta (ζ).

Note also that unlike the previous models, Timothea’s timeline is not doubled back upon itself in the alpha/gamma/delta subtree.  Let’s look at the Timotheas in that subtree:

Timothea alpha (Tα) does not see her time-traveling twin suddenly appear in front of her; she has no forewarning that anything bad may be about to happen.  Her timeline continues up to the critical lab experiment, when it forks into Timothea gamma and Timothea delta.

Timothea gamma (Tγ) is our time traveler.  Her timeline (up to that point) is A-B-C-R.  When she does research at point R, she sees no evidence of time travel in the past, at any of points t0 (A), t1 (B), or t2 (C).  Depending on how she thinks time travel works, she might explain this by saying that her time journey “hasn’t happened yet”; but in fact the correct explanation is that everything her future self will do is in a different branch of the world timeline.

Timothea delta (Tδ) is the only Timothea whose timeline is completely untroubled by time travel.  Her timeline is A-B-D.  So far as she is concerned, the lab experiment worked beautifully, cancer was cured, and everything is as it should be.

Now let’s look at the more complicated subtree, beta/epsilon/zeta, which contains the timeline of time-traveling Timothea, continuing from Tγ.

Timothea beta-1 (Tβ1) is startled when, whilst preparing for the lab experiment she hopes will cure cancer, her identical twin suddenly appears and claims she’s come from the future to avert a terrible catastrophe.

Timothea beta-2 (Tβ1) is the timeline of Timothea gamma as it continues after her time journey.  She appears in front of her past self, warns her of the impending apocalypse, and together they begin planning to “change” the outcome.  At time t1, this Timothea remembers point B on her past timeline, but experiences point H, and sees her past self experiencing point E — she sees that things are already different than what she remembers, even though they haven’t gotten to the critical point yet.

At the moment of the critical experiment, the timeline forks and both Timothea’s timelines fork as well, into Timotheas epsilon 1 and 2 (Tε1 and Tε2) in the “bad” branch, and Timotheas zeta 1 and 2 (Tζ1 and Tζ2) in the “good” branch.

Timothea epsilon-1 (Tε1) has never time-traveled, but she saw her future self appear and warn her, and together they attempted to avoid the catastrophe and failed.  Her timeline is A-E-F.

Timothea epsilon-2 (Tε2) traveled back in time, warned her past self, tried to avoid the catastrophe, and failed.  Her timeline is A-B-C-R-H-I.  However, her experience is much different than time-traveling Timothea (T2) from the first model, or Timothea alpha-2 (Tα2) from the second model; she has experienced a different timeline from the moment she stepped out of her time machine.  She never experienced predestination.  As far as her experience shows, she did “change history,” just not enough.

Timothea zeta-1 (Tζ1) has never time-traveled; she saw her future self appear and warn her of the catastrophe, and together the worked successfully to avert it.  Her timeline is A-E-G.

Timothea zeta-2 (Tζ2) traveled back in time, warned her past self, tried to avoid the catastrophe, and succeeded.  Her timeline is A-B-C-R-H-J.  She never experienced predestination, and as far as she knows her time journey was a complete success; she “changed history.”

Of course neither of the Timothea zeta twins changed history; they’re just living in a fork of their timelines that is in a better branch of the world timeline.

See how this model, while remaining consistent according to the basic principle — the timeline cannot change — still supports many of the classic time-travel tropes.  If you write about Timothea zeta-2, her story looks like a good old-fashioned time-travel yarn, complete with past selves and history changing and a happy ending.  The only difference is that all those other branches are still there; nothing any Timothea does affects that, because — say it with me — the timeline cannot change.

This model also unravels the hoary “grandfather paradox” and all its variations. If you travel back in time and kill your grandfather before he can have children (for whatever reason that course of action seems good to you) no paradox results and the universe does not disappear in a puff of logic; in the branch of the timeline in which the murder took place, it’s true that “you” will never be born, but the you that committed the murder came from a different branch. Diagramming this is left as an exercise for the student.

Another interesting exercise would be to use this model to diagram the various Terminator timelines.  Of course the critical point in those timelines is Judgement Day — Skynet either does or does not come online and start a nuclear war.  However, one of the Terminators in Genisys remarks that certain events like Judgement Day “want to happen” — which means that the “good” outcome of any crisis point in the Terminator branching futures only means that there will be another crisis point later on.  There would be many “bad” Judgement Day branches, some starting later than others, and one timeline where Judgement Day keeps getting averted over and over again.

I’ll leave actually drawing that out to someone better acquainted with the franchise than I am.

However,  I think this model provides a way of writing about time travel that still lets authors do most of the things they want to do, but doesn’t do it at the expense of paradox or nonsensical outcomes.

What do you all think?

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