Disclaimer
Although in this article I aim to be as scientific as possible, I have no idea how well (if at all) the mathematical model of timetravel that I will try to construct is representative of reality, although being representative of reality is an intention of mine. But don't fear if you are not mathematically minded: we won't get to heavy into the calculus of general relativity. Very basic algebra is all you need, although you will have to throw away one of the very basic principles of boolean logic.
Introduction: Timetravel in Literature
No matter how you spin it, humans are only familiar with one dimension of time, and moving through it only one way at that. Because of this, timetravel often makes the plot of a story difficult to follow, and thus most writers choose to avoid the topic like the plague.
Making a realistic story with time travel is tricky. Since humankind has never achieved timetravel, we can't yet empirically test what would happen. This means that all timetravel mechanics are left up to the imagination of the writer(s). But barring the scenario in which timetravel is physically impossible (in which case all imaginings are equally valid, since all are vacuously true), someone has to be wrong.
But when it comes to time travel, we can (probably) due better than a brute force guessing approach by making models that are mathematically sound. And while physicists have made a good number of models for timetravel, all of them seem to have problems. The Trigamon Model of Timetravel (TMoT) attempts to reconcile these models, and while I think the TMoT is consistent, it does have some strange implications, including something akin to the "Doom Factor" from Futurama, albeit not quite that silly.
Visualizing Time
Just about everyone is familiar with the concept of a timeline: a timeline is a map of time over a fixed interval. In this way, a timeline is akin to any map of space. But as maps of space are 2, or sometimes 3-dimensional, maps of time are 1D, which is why it's a line.
But while there is no difference between forwards and backwards in space, time only (at least naturally) goes in one direction, which we will call the "
The reason that it's important to define Automatic Direction for maps of time is because Automatic Direction does not exist for maps of space. In space, objects, when left alone, can be pushed in all directions. Not the case with maps of time.
From this, if we let timelines be maps of time, then we can look at two maps of time at once the same way we look at two maps of space at once. I make this point to introduce the concept of "
The spatial version of this is a map of Earth and a map of the Moon.
| Planet Earth | Earth's Moon |
|---|---|
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Assuming you start on the surface of the Earth, no matter how far you travel along the surface of the Earth, you will never reach the moon. In order to go from the Earth to the moon, one must use a new direction (up/down), which is effectively perpendicular to the surface of the Earth. (Or at least perpendicular to one point on the surface of the Earth). Of course, surface of the Earth and the surface of the moon are curved, but the same rules still apply whether the surface is curved or flat.
Temporal Geometry
These mathematical properties bring us to how we view time in Trigamon: not as a line, but as a 2-dimensional surface. For the Trigamon Multiverse specifically, time is technically conically shaped (line a cone), but for our purposes we can just view time as a flat plane. (Thing of it in terms of the Earth's surface: it's curved, but because it's so big it appears flat)
In this model, the automatic direction is downwards: so all timelines run in parallel downwards. Each timeline in this plane of timeline then is a line (not necessarily straight) on the surface of the cone.
Timeline Branching and Fusion
At first glance, this may seem like re-inventing the wheel: why remodel the geometry of time? The trouble is that using timetravel with the classical line model creates paradoxes. Two famous ones are the Grandfather Paradox in which an object negates it's own existence and the Bootstrap Paradox (AKA Causal Loop) in which an object causes it's own existence. These cause huge problems in science fiction, and although some writers simply ignore the illogical implications, a scientist cannot allow a plothole to exist in the equations.
Timeline Branching
On it's own, timeline branching isn't something new, but by itself it ultimately undermines the existence of true time travel when used as a mechanism of paradox resolution. The idea originates from quantum mechanics, but can be also applied on an everyday scale. This concept is what the story of Shrodinger's Cat was designed to illustrate. (If we ignore the fact that the cat counts as an observer.)
The idea behind branching is that probability is an illusion. Let A be an event with a 50% chance of occurring. In this model, the universe would be unable to decide, and as a result, split into two. One universe where the event happened and one where it didn't. Thus, both results happen at once. In the story of Shrodinger's Cat, this means that the cat is alive in one universe and dead in the other.
In order to use this concept to resolve the Grandfather Paradox, we have to replace the random event with a conscious actor making a decision. In this version of the Grandfather Paradox, someone discovers a robot factory that was supposed to be dismantled ages ago, and decides to make a robot to go back in time and dismantle the factory, so the factory will be dismantled by the deadline.
The paradox here is fairly obvious: a dismantled factory could not have created the robot to dismantle it. (Also it would have already been dismantled, so such a robot would be unnecessary).
However we can resolve this paradox fairly easily by splitting the universe.
| Unresolved | Resolved With Split |
|---|---|
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Problems with Branching
The problem with splitting the entire universe is conservation of energy. The energy to create an entirely new universe has to come from somewhere[1]. While in physics, we can "borrow" energy from nothing, however that leads to instability, as things want to go back to the ground state as quickly as possible, which means a single universe[2].
Of course if possible, the universe would like to avoid the red timeline altogether. A robot coming from the future to dismantle a factory doesn't have to create a paradox. In this scenario the universe would have to ensure that the time-traveling robot got created some point in the future of the blue timeline. Trigamon has a mechanism for this, called The Smart Universe.
Normally, this would know the future, and thus negate the entire concept of free will, which makes for a bad story. But The Smart Universe makes this entirely unnecessary. Instead, the universe can calculate an arbitrarily large number of possible futures until it finds one that works. As it turns out, the number of variables which conscious actors control is absolutely minuscule compared to all of the variables that are completely random. The universe can then choose values for random variables until the paradox is avoided, even if it needs to create a Boltzmann Brain, or perhaps a Boltzmann Robot. (This is a karmic process)
Timeline Fusion
But The Smart Universe can't help when a paradox is unavoidable, or can it? Is it even possible to create an unavoidable paradox anyway? Maybe in theory. But this is very difficult in practice with a universe able to create Boltzmann-Type entities as needed. But unless we can rule an event out in theory, our theoretical model should be able to handle it.
With an unresolvable paradox, The Smart Universe, by definition, won't be able to reduce the number of timelines down to 1 immediately. But just because the timeline is split, doesn't mean it has to stay split indefinitely. And by this, we mean that the effect of karma will employed to force the events that were different in the red and blue universes to become completely "moot". This is the process that is most akin to Futurama's "Doom Factor". An observer will see a string of extremely unlikely events that often will appear to have an intent of messing something up. However, there is zero malice behind this process, it's just how karma fixes the universe.
Before we get too far ahead, we need to define "moot" in a quantum sense. Moot is a term coined by humans to mean an event no longer matters, so one could say that an event is "moot" to the universe if it is no longer affecting the state of the universe. This is not what we mean, as everything that has ever happened obviously affects the state of the universe. For an event to be moot in our sense, it means that even though the event happened, it did not "need to" happen in order for the universe to arrive in it's current state.
Definition: It is impossible to tell if a moot event occurred in a universe by observing the universe at sometime AFTER the event. Mathematically there exists a time "t" for universe "u" when it is possible for moot event "me" to have occurred, and for moot event "me" to NOT have occurred.Making a universe splitting event(s) moot is important, because it will ultimately allow the universes to fuse back together. By definition, if an event(s) can be made moot in one universe, then it can be made moot in the same way in the other universe. (By contradiction, otherwise, the state of the universe would determine whether or not the event occurred, which would mean that the event would not be moot.)
Once the event is made to be moot, the final step occurs of merging the timelines back together. This occurs when every red timeline particle in the red universe is in the same location as it's blue timeline counterpart in the blue universe. The timelines merge and the paradox is resolved.
Aftermath
Just because in the merged universe it is impossible to tell whether or not a moot event happened, it is very possible (at least with high probability) to tell whether the timeline was split and then merged back together. Extreme coincidences and mass data corruption highlight these scenarios like beacons in the night. Conscious decision of intelligent life forms are not affected, but memories are. People may be left with multiple memories of an incident or no memory of it at all. Mechanical records will be tainted by unrealistic levels of bit-rot and extremely improbable quantum tunneling. The signs of a large scale event being rendered moot are extremely hard to miss.
People unfamiliar with quantum mechanics may wonder which path actually happened, but both paths are equally valid. In what is perhaps the most brazen violation of boolean logic: the event happened and did not happen. In other words, Shrodinger's cat is both dead and alive, and someone who committed a crime and then prevented it would be found both innocent and guilty.
TL:DR
I admit, this article was confusing, and it violated the law of the excluded middle, which all boolean logic is founded upon. Basically, if you create a paradox, karma will resolve it as soon as physically possible and cause all sorts of extremely unlikely coincidences in doing so. Once the whole thing is over, the event will have both happened AND not happened, much like the death of Shrodinger's cat.
(Although Shrodinger's cat is a metaphor to aid in understanding quantum mechanics, it also works for karmic paradox resolution)
Next: Fenyran Mathematics[1] Technically, the new universes could have a fraction of the energy of the old one, but I'm not going to go into that here.
[2] One might think, rather than creating an entirely new universe, it would just make more sense to convert the red universe into the blue universe, which would mean the red universe changing into the blue one. However this is impossible.