Closed Timelike Curve

Time Travel Classification Pocket-Book for Science Fiction

On this article, I will try to provide a well-defined classification of time traveling of entities, as seen in fiction and as theorized by physicists and philosophers. To have a good categorization, we need strong definitions on the relevant concepts of time traveling, what will be provided based on what I believe to be the “status quo” on the subject.

Definition: Time

First, we need to define time itself. Time could be seen as an ordered dimension (or set) of cause-effect worlds. I mean with that: the world on a given time is the cause of the world on a later time, and an effect caused by the world on a previous time. You can think it as a film: one film frame is a world at one instant, and the next film frame is the world one instant later, which is a direct consequence of the previous frame. The notion that the cause precedes the consequences is very important here. This definition will suffice for the scope of this article, although it is not entirely true in some hypothetical valid situations on modern physics (I am talking about Closed Timelike Curves, but don’t bother with them for now).

Definition: Entity

Entities are the carriers of the cause-effect chain through time, that influences other entities through the mechanical rules of the world. I am aware that it sounds terribly obscure, and I am not even sure if this definition is complete, but what I mean is that an entity can be anything that exists in the world that can influence other things. A ball, a person, a light ray, an atom, a whale, a glass of water. An entity is what we could call a thing. An entity is what can be a time traveler.

Definition: Time Perception

Now what I think to be the most important definition: the time perception. The time perception is, from the point of view of an entity, the order and the rate that cause-effect are chained “around” itself. For around, I mean what the entity can directly influence and be influenced by, including itself. For a human entity, it is the speed that a person perceives the passage of time, or even better, is the speed the time actually passes for that person. It is a very common mistake to assume that time perception is universal in our reality, like thinking that time passes equally to all entities in the universe. Time does not passes equally to all entities in the universe! If you don’t believe me, consult the nearest physicist.

Definition: Time Travel

Given all those names, what is a time travel? An entity is said to have traveled through time when it went to its own future at its ordinary rate according to its own time perception, but arrived at a point in time dimension that would not be possible by the time perception of an important external reference entity (the Earth, in most cases), had them both shared the same time passage duration and rate. In other words: for a time traveler, time passed just as usual: forward, at regular speed. But by the means of his traveling, he will end up in a different position in time as he would if he had experienced this same time ordinarily on Earth.

Notice that in this definition of time travel, we only consider one-way travels. If you want to visit the future and then get back to the time you belong, it would require from you two time travels: one forwards and one backwards, which are, by nature, different beasts. Specifically, backwards time travels may cause paradoxes, while forwards time travels don’t, and have the same direction of the ordinary time passing rate, what could make it somewhat easier. In some sense, one may think that everything is always traveling towards future, but since we defined the time travel in respect to some external reference, if time is passing equally to everything we consider, then nothing is traveling in time, at least not in the sense defined here.

Classification

These were the main terms that must be well understood. Once done, we can dive into classifying time traveling itself. Firstly I want to propose the classification of the travel by continuity of the journey inside the space-time of reality.

Continuous versus Leap

A time travel is continuous if, while traveling, the traveler is in somewhere to be found inside space or somewhen to be found inside history: for instance, it is the case of the famous Twin Paradox, which one twin travels on high-speed through space, and when arrives back at earth, finds that his twin was older than him. Since he was all the time traveling through space and could always be seen from earth, it was a continuous time travel to a future where he found his brother older. On the other hand, we have leap time travels, what is the classical case in fiction, where a dog is placed in a DeLorean and vanishes from reality, to only be found again 5 minutes in future (Back to the Future). Or a war machine is beamed up from a dystopian futuristic world dominated by robots so the next time it would be seen was 45 years in the past (Terminator).

You may have guessed by now that leap time travels are far more common in fiction than the continuous type. It is so because leap travels are much more intuitive and convenient: if I am to travel through time, it is better done instantly, so that I do not have to be anywhen between now and when I want to be. On the other hand, the continuous type is much more technically and theoretically feasible, and fiction targeted to more nerdy audience tend to have more elements of it, like in the movie “Primer”, where the time travelers needed to stay inside the time machine during all the journey, and they would actually be inside it during the time the machine was working. To travel one day to the past, they would need to power on the machine one day before the journey, so the next day, when they get into it and stayed there, the machine would take them to when it was turned on.

Continuous Travel to Future

In the case of continuous time travels, you may have future, past of future and past time travels. Continuous time travel is a mere fact of changing the time perception of the traveler in relation to the reference time perception. In this regard, to send an entity to future, one must make the time perception of that entity slower than the reference. While, in the perception of the entity, one minute have passed, one year have passed in the reference time perception, bringing an entity from past into future. This phenomenon is known as time dilation.

A parody of this time traveling concept can be seen in an episode of The “Powerpuff Girls”, when they raced so fast, making the time slower for them, that when they stopped racing, they where in the future. Accelerating very fast and then de-accelerating back to the initial speed is one method of using time dilation to continuously travel to future. While parodying the physical effect, this same explanation could not be applied to the travel back to past in that same episode, and they only were able to get back home so the episode could have a happy ending.

Continuous Travel to Past of Future

If time perception of a traveler is faster than the reference perception, then he could spend one year in a time machine, get out and find that only one minute have passed in the reference time perception. This is what I called travel to the past of future, because the traveler did not end up in past, but it ended up in a time before he would if he was not traveling.

It seems that there are much more practical issues in using time dilation phenomenon to create this effect than to use it to travel future, although it is not entirely impossible. This kind of time traveling is very well illustrated in “Dragon Ball Z” anime by The Room of Spirit and Time, where one year inside it equals to one day in the outside.

Continuous Travel to Past in the Same Space

The most difficult to understand (and even to think) kind of continuous time travel is the travel to past, where the traveler end up in a time before he started his journey. There is a (maybe a little hard to see) paradox in the “Primer” time machine, where time spent inside it could pass backwards relative to the time outside of it. Imagine you get into the machine to travel past. What would you see? In the moment the machine was powered, would you see yourself undoing what you have done until you have entered the machine? Would you split into two, occupying the same space at the same instant? One for the time going forward and the one for the going backwards? Because, to be able to move into the machine where time passes backwards, your time would need to pass forwards, because the very notion of movement needs time passing forward. It is tricky to even think of this problem, and I can imagine a number of contradictory situations arising from it, both on the entering the machine and exiting from it. The big problem is in the limits, when time passing inverts. There can be no place that at one instant flows one direction and other instant flows another. The time in the machine would be like a one way road, that in the middle of it, the direction inverts, leaving the arriving cars nowhere to go, and leaving no traffic after the inverted part.

What, then, would be a more consistent continuous time travel mechanism that allows travels to past? I will delay this answer until my considerations about leap time travels.

Leap Time Travel

Leap time travels are less physically attainable, at least on non-quantum scale, considering what we currently know about physics. Maybe a fairy can beam you with a magic power and send you through time, but while I try to say one word or two about feasibility, it is not the focus here.

Leap to Future

Suppose you have machine that can instantly send an entity anywhere in space-time. If an entity travels by this mean to future, despite the fact it will no longer exists in reality while it does not arrive to its destination — what itself is bizarre — when it arrives, it will physically behave as it would otherwise, and we would have no further logical problems. If one person disappears to only reappear one year in future, it would walk, talk, tell other how wonderfully he traveled to future, and would influence reality as he always have, with no further consequences.

Leap to Past

The big problem is when someone disappears now and travel to past. Well, past already happened, and already influenced reality so that it would be like it is when then person traveled to past. So what happens if this person kills its former self? It would never be able live to travel past to kill its former self, so it would be alive. Contradiction!

Paradoxes of Traveling to Past

There are three solutions to the travel to past paradox. First: it is impossible to travel past. Well, since this is a time travel discussion, it is fair to discard this solution.

Branching Realities

Second: when the past is altered in a way that would disable the future the traveler knows to happen, the reality is branched, so he would now live in an alternate reality which complies with the new inserted acts of the traveler in the past. This solution is simple, settles the matter, but then arises the question: would the traveler be able to travel back to the reality he left? This fall out of scope of time traveling, into the scope of alternate realities traveling, what may not be so different if this solution to the paradox is to be adopted. Although Marvel stories are not entirely consistent (actually, they are totally inconsistent), it seems that the type of time travel to past the Fantastic Four is often able to perform is the reality branching type.

Self-consistent Realities

The third solution, the most beautiful and astonishing when well orchestrated in science fiction, is the one that estates that reality is self-consistent. If you are able to travel to past, all your actions will inevitably leads to the future you already know. If you think of reality as an system of equations, the travel happens only if there is a solution to the system where there is a travel to the past that leaves the world in a consistent state so that that travel was meant to happen, and the effects caused by a travel led to the travel itself, or at least did not contradicted it. This is the case of time travels as seen in the movie “12 Monkeys” (and by transitivity, in “La Jetée”, which inspired it). Everything though the course of the film leads to what happened in the beginning of it.

The non-contradiction rule have an intimate relationship with Novikov Self-Consistency Principle, created because some solutions to the general relativity equations lead to bizarre things that could be interpreted as time travels to past. At least on this kind of time travel, the principle estates that no contradictory situation could arrive from it.

The biggest problem with this rule has to do with free will. If I want to deliberately kill someone in the past that was alive at my time, somehow I will not succeed, and it may even imply that, if allowing me to travel past will certainly allow me to kill that person, that I may not be able to travel past at all, or only travel with the necessary restriction that would make the present be direct consequence of the past I will be able to influence. This restriction is represented in the “12 Monkeys” movie by the strong stress and mental confusion that were imposed to time travelers, that would influence the travelers to do things they would not do if they were fully aware that they were time travelers.

An amazing effect possible on time travels to past that do not branch reality has to do with causality: what if an effect is its own cause? Suppose I find a sword on a rock. I take the sword and pass on for generations. Then, my grand grandson takes the sword on a travel to past and plant it in the exact same spot I found it, and just leave it there for me to find, then I find it and the story closes. There is no paradox in this story, but where did the sword came from? This situation would break the own definition of time we gave in the beginning of the article. This is the situation depicted in the movie “Predestination” and in one of the time travel situations depicted in movie “Interstellar”.

Swords do rusts, so it is not a very good example. Instead, think that I took a recent edition of the book “Twenty Thousand Leagues Under the Sea”, brought it back to some time it were not written, and gave it to Jules Verne. He takes it, reads it, likes it, and publish it as being his own, so that everybody believes he wrote it, what leads to the reality we know nowdays, so I can take the book back to past, closing the cycle. Who wrote the book? The story just showed up in reality and closed a cycle, it was its own cause. More formal formulations of situations like this, based on general relativity, are called (as I already mentioned), Closed Timelike Curves. It is not a settled matter if closed timelike curves do exists in practice, but what was physically predicted for now is far from allowing a book to travel past.

Continuous Travel Through Space Tunnel

Thus ends the considerations about the paradox and bizarre effects of leap time travels to past. We can now get back to continuous time travels to past. How can it be?

What would somewhat adheres to the definition of continuous time travel is a time tunnel. A time tunnel has two ends and maybe an intermediary space. A more scientifically appealing view would be a wormhole with no intermediate space, and placing your arm inside it would take it to past, as if past was over there, like the next room. The time perception on both ends of the tunnel would be the same to an observer who watched through it, but each end could exist in a different times and space. Observing the other end of the tunnel trough another way besides the tunnel, could reveal that the time perception of one end is different from another, and the difference in time between the two ends is actually increasing, but that would not be observable through the tunnel, since it seamlessly links two different locations of time and space, including their time perception. As a tunnel, it would allow travels in both directions, past and future.

If the branching reality rule applies, the reality is branched at the moment the first entity traverses a tunnel to the past that was not meant to have passed. Since there are zillions of “things” going in every direction in everyplace in space, among light, radiation and all sort of subatomic particle, as long as the tunnel remained open, zillions and zillions of realities would be branching, in a combinatorial explosion of realities and tunnels links between realities. As you can see, the idea of reality branching is not well suited to continuous past time travels. The idea of self consistency seems to be much more appealing in this situation, and it would not be possible to change past through a time tunnel.

A wormhole, that maybe could be used as time tunnel, if somehow they could be created, would look like the one in this video, made by Corvin Zahn:

At first, the wormhole connects just two different places. But if the time of one place is dilated in relation to the other, the time in the ends of the wormhole would also differentiate, turning them time tunnels.

If you find any inconsistency in this article, or any error of any nature, please let me know.