Artistic Illustration Of Time Travel
Image 1: Artistic Illustration Of Time Travel | © Unrevealed Files

Imagine, A time traveler in the present time steals a time machine from a museum to make his time trip and travel back in time, he travels back in time and reaches in the past then at the end of the trip he donates the time machine to the same museum from where he stole it. In this case, the time machine itself is never built by anyone; it simply exists.

Thus, time traveling in the past would allow for the possibility of causal loops, in which things come from nowhere means arrive or emerge unexpectedly. Things here might be events, information, people, or objects. In this article, we have briefly discussed What are the Causal loops in time travel?

What is a Causal loop?

Causal loop is a theoretical proposition of either retro-causality or time travel in which a sequence of events (actions, information, objects, people) is among the causes of another event, which is in turn among the causes of the first-mentioned event. Such causally looped events then exist in Spacetime, but their origin cannot be determined.

A most popular hypothetical example of a causality loop is given of a billiard ball striking its past self:

Example of causal loop by Causal loop billiard ball time travel.
Figure 1: This is the diagram of a causal loop illustrated with a billiard ball. Top: original billiard ball trajectory. Middle: the billiard ball emerges from the future at a different angle than the original, and delivers its past self a glancing blow. Bottom: the billiard ball changed its trajectory in just the right way so that it will travel back in time with the angle required to deliver its younger self the glancing blow.
Source: Derivative work of content under free licenses.
Author: BrightRoundCircle.

The billiard ball moves in a path towards a time machine, and the future self of the billiard ball emerges from the time machine before its past self enters it, giving its past self a glancing blow, altering the past ball’s path and causing it to enter the time machine at an angle that would cause its future self to strike its past self the very glancing blow that altered its path. In this sequence of events, the change in the ball’s path is its own cause, which might appear paradoxical.

Thus we can say that the causal loop is a sequence of events e1, … , en. Each event in the loop is one of the causes of the next event. The last event en is one of the causes of the first event e1. If a causal loop has no external (outside-the-loop) causes or effects, then that causal loop is a closed causal loop; otherwise, it is an open causal loop. Think of closed causal loops as causally isolated. Think of open causal loops as causally embedded. See the diagram below.

Two kinds of Casual loops

Open and Closed Causal loop
Figure 2: Open and Closed Causal loop | © Unrevealed Files

Examples of a Causal loop Paradox

Allan Everett has given an example of a causal loop paradox involving information: suppose a time traveler copies a mathematical proof from a textbook, then travels back in time to meet the mathematician who first published the proof, at a date prior to publication, and allows the mathematician to simply copy the proof. In this case, the information in the proof has no origin.

A similar example is given in the television series “Doctor Who” of a hypothetical time-traveler who copies Beethoven’s music from the future and publishes it in Beethoven’s time in Beethoven’s name. Everett gives the movie Somewhere in Time as an example involving an object with no origin: an old woman gives a watch to a playwright who later travels back in time and meets the same woman when she was young, and gives her the same watch that she will later give to him.

Krasnikov writes that these bootstrap paradoxes – information or an object looping through time – is the same; the primary apparent paradox is a physical system evolving into a state in a way that is not governed by its laws. He does not find this paradoxical, and attributes problems regarding the validity of time travel to other factors in the interpretation of general relativity.

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Nomenclature Causal loop

Traveling back in time would allow for causal loops which includes events, information, people, or objects whose histories form a closed loop, and thus seem to arrive or emerge unexpectedly. The notion of objects or information that are “self-existing” in this way is often viewed as paradoxical, and several authors refer this a Causal loop which involves information or objects without origin as a Bootstrap paradox, an information paradox, or an ontological paradox (Ontology means the branch of metaphysics dealing with the study of being and existence) The term time loop is sometimes referred to as a causal loop, but although they appear similar, causal loops are unchanging and self-originating, whereas time loops are constantly resetting.

The term “bootstrap” here refers to the expression “pulling yourself up by your bootstraps”. Learn more about Bootstrap Paradox here: Bootstrap Paradox, a theoretical paradox of time travel. You can also read Robert A. Heinlein’s time travel story By His Bootstraps(PDF).

The term Causal loop in Science fiction movies, books and philosophies

In a 1992 paper Physicists Andrei Lossev and Igor Novikov labeled such sequence of events (actions, information, objects, people) without origin as Jinn, with the singular term Jinnee. This terminology was inspired by the Jinn of the Quran, which is described as leaving no trace when they disappear. Lossev and Novikov allowed the term “Jinn” to cover both objects and information with reflexive origin; they called the former “Jinn of the first kind”, and the latter “Jinn of the second kind”.

They point out that an object making a circular path through time must be identical whenever it is brought back to the past, otherwise it would create an inconsistency; the second law of thermodynamics seems to require that the object become more disordered throughout its history, and such objects that are identical in repeating points in their history seem to contradict this, but Lossev and Novikov argued that since the second law only requires disorder to increase in closed systems, a Jinnee could interact with its environment in such a way as to regain lost order. They emphasize that there is no “strict difference” between the Jinn of the first and second kind. Krasnikov equivocates between “Jinn”, “self-sufficient loops”, and “self-existing objects”, calling them “lions” or “looping or intruding objects”, and asserts that they are no less physical than conventional objects, “which, after all, also could appear only from either infinity or a singularity.”

An example of a Jinni is Swann’s necklace from a 1982 film Timerider: The Adventure of Lyle Swann.

In a 1982 film Timerider: The Adventure of Lyle Swann., Swann is accidentally sent back in time and meets a woman named Claire, who eventually attracts him. After a series of spectacular events, the people who accidentally transported him back in time rescue Swann. Just before he is saved, Claire snatches the necklace that was handed down to Swann from his great-great-grandmother who stole it from his great-great-grandfather. The necklace is a jinni because Swann receives the necklace from his great-great-grandmother who stole the same necklace from him years earlier. You might think here that, Claire is Swann’s great-great-grandma. Swann himself is his own great-great-grandpa.

Here this problem raising many questions presented by the necklace, and most jinn, is the source of their existence. How can a physical object like a necklace just exist? Who designed the necklace? What explains why it is a necklace rather than a bracelet? There must be some explanation for why the necklace is the way it is. These questions might come into our mind.

There are explanations for stages of the necklace’s existence. The necklace has causes. Swann’s receiving the necklace from his grandmother is a cause of him taking it with him back in time. The necklace’s going back in time is a cause of Claire being able to steal the necklace, and so on. In addition, one could argue that the universe and natural laws must have a specific structure in order for causal loops to exist. These laws would also be a source of useful explanations.

Some facts, though, seem bound to go unexplained, facts like that the necklace is a necklace and not a bracelet. In addition, why is there a causal loop rather than no causal loop? Does our inability to explain these facts show that there is something incoherent about causal loops? No; the problem with this reasoning is that similar issues arise regarding normal objects. You can see the causes of a chair because you can see the carpenter build the chair from wood, but what made the wood? Even more so, what made the atoms that compose the wood? One can keep asking these questions, but a fully sufficient and complete explanation may be all but impossible to advance in normal conditions. There are many facts and objects for which we may never find a good explanation.

Here also in the case of the necklace consider the origin of the artistic design of the necklace. The necklace appeared to be a normal necklace, one that had been crafted with intent and artistry. This begs the question of where the artistry came from. Who’s (or what’s) skill and knowledge went into creating this necklace? Storrs McCall (2010) says that there is no solution to this problem. Perhaps, some facts simply do not have explanations. Insisting that everything must have an explanation is unwarranted.

Predestination paradox

Another example from the Star Trek, where the predestination paradox is used to mean “a time loop in which a time traveler who has gone into the past causes an event that ultimately causes the original future version of the person to go back into the past.” This use of the phrase was created for a sequence in a 1996 episode of Star Trek: Deep Space Nine titled “Trials and Tribble-ations”. This phrase had been also used previously to refer to belief systems such as Calvinism and some forms of Marxism that encouraged followers to strive to produce certain outcomes while at the same time teaching that the outcomes were predetermined. Smeenk and Morgenstern use the term “predestination paradox” to refer specifically to situations in which a time traveler goes back in time to try to prevent some event in the past, but ends up helping to cause that same event.

The term Causal loop in Physics

To introduce some theoretical causal loops in the context of physics, let us consider the idea of a time-like curve. A time-like curve is an object’s path through space-time where the object persists locally forward in time with time-like connections between each interval. A causal loop occurs when an object’s time-like curve loops back on itself.

One way of introducing a causal loop is with the idea that the universe has a rolled-up space-time. The best analogy for this idea is a cylinder where the dimensions that make up space are the axis of the cylinder. This structure allows an object’s time-like curve to loop around the cylinder and meet up with itself.

Curved Space-Time
Figure 3: Curved Space-Time | © Unrevealed Files
Spacetime is curve
Figure 4: In 1916, Einstein addressed these two contradictions (the instant propagation problem and the equivalence of gravity and acceleration) by reconstructing the theory of gravity. Einstein presented the world with a new understanding of the world- his theory of general relativity. In this theory, space is not an empty void, but an invisible structure called spacetime. Nor is space simply a three-dimensional grid through which matter and energy moves. It is a four-dimensional structure whose shape is determined by the presence of matter and energy. Around any mass (or energy), spacetime is curved. The presence of planets, stars, and galaxies deforms the fabric of spacetime like a large ball deforms a bedsheet. (This deformation occurs in four dimensions, so the two-dimensional bedsheet is a limited model. Try visualizing these depressions on all sides of a planet to build a more accurate image of this concept.) When a smaller mass passes near a larger mass, it curves toward the larger mass because spacetime itself is curved toward the larger mass. The smaller mass is not “attracted” to the larger mass by any force. The smaller mass simply follows the structure of curved spacetime near the larger mass. For example, the massive Sun curves spacetime around it, a curvature that reaches out to the edges of the solar system and beyond. The planets orbiting the Sun are not being pulled by the Sun; they are following the curved spacetime deformed by the Sun.

Wormhole-based time travel also allows for closed time-like curves, Physics poses some serious problems for the possibility of jinn(discussed above). According to the second law of thermodynamics, entropy (or disorder) always increases with time. Consider the example of the necklace in Timerider. 

According to thermodynamics

In normal conditions, the entropy of the necklace(discussed above) would increase from the moment that Claire steals the necklace to when the necklace is being passed down to Swann and until Swann travels back in time. Now, most understandings of time travel do not alter the state of objects as they travel back in time. However, since the entropy of the necklace right before Swann goes back should have the same amount of entropy as when Swann arrives in the past, this would produce a contradiction. A contradiction arises because the necklace’s entropy just before Swann leaves both equals and is greater than the entropy when Swann arrives in the past. This contradiction means that in order for jinn to exist time travel models must in some way account for reducing the entropy for its return to the past.

Rather than originating from a big bang, the universe began as a space-time ‘doughnut’

Another interesting example of causal loops in physics is the hypothesis that, rather than originating from a big bang, the universe began as a space-time ‘doughnut’ from which the rest of the universe branched. The authors of this theory, J. Richard Gott and Li-Xin Li, formulated this theory based on an alternative solution to Einstein’s field equations. The space-time doughnut is essentially a causal loop with both closed and open paths around the loop. So, some paths through space-time exist as a loop, but there are others that branch off to make the rest of the universe and its contents.

Causal Loops and Multi-Dimensional Time

Multi-Dimensional time is sometimes called to be the structure of time with branching of timelines and which removes most of the interesting features of causal loops. It is sometimes introduced to keep causal loops out. Time-traveling causes timelines to split with multi-dimensional time, so an event cannot cause an event along its past branch. This unwraps the loops and all that is left is a series of split causal chains. A result of this is, if multi-dimensional time were to be true, then the answer to the question of whether time travel to the past always involves a causal loop would be a no. A time traveler creates branches instead of loops.

Quantum computation with negative delay

In a 1991 paper Physicist David Deutsch showed that quantum computation with a negative delay—backward time travel—could solve NP problems in polynomial time. Later Scott Aaronson extended this result to show that the model could also be used to solve PSPACE problems in polynomial time. Deutsch showed that quantum computation with a negative delay produces only self-consistent solutions, and the chronology-violating region imposes constraints that are not apparent through classical reasoning. In 2014 Researchers published a simulation validating Deutsch’s model with photons, However, it was shown in an article by Tolksdorf and Verch that Deutsch’s CTC (closed timelike curve, or a causal loop) fixed-point condition can be fulfilled to arbitrary precision in any quantum system described according to relativistic quantum field theory on spacetimes where CTCs are excluded, casting doubts on whether Deutsch’s condition is characteristic of quantum processes mimicking CTCs in the sense of general relativity.

Self-fulfilling prophecy

A self-fulfilling prophecy is a process in which an originally false expectation leads to its confirmation. In a self-fulfilling prophecy, an individual’s expectations about another person or entity eventually result in the other person or entity acting in ways that confirm the expectations.

Thus self-fulfilling prophecy may be a form of causality loop. Predestination does not necessarily involve a supernatural power, and could be the result of other “infallible foreknowledge” mechanisms. Problems arising from infallibility and influencing the future are explored in Newcomb’s paradox. A notable fictional example of a self-fulfilling prophecy occurs in the classical play Oedipus Rex, in which Oedipus becomes the king of Thebes and in the process unwittingly fulfills a prophecy that he would kill his father and marry his mother. The prophecy itself serves as the impetus for his actions, and thus it is self-fulfilling. The movie 12 Monkeys heavily deals with themes of predestination and the Cassandra complex, where the protagonist who travels back in time explains that he can’t change the past.

Novikov self-consistency principle

General relativity permits some exact solutions that allow for time travel. Some of these exact solutions describe universes that contain closed timelike curves, or world lines that lead back to the same point in spacetime. Physicist Igor Dmitriyevich Novikov discussed the possibility of closed timelike curves in his books in 1975 and 1983, offering the opinion that only self-consistent trips back in time would be permitted. In a 1990 paper by Novikov and several others, “Cauchy problem in spacetimes with closed timelike curves”, the authors suggested the principle of self-consistency, which states that the only solutions to the laws of physics that can occur locally in the real Universe are those which are globally self-consistent. The authors later concluded that time travel need not lead to unresolvable paradoxes, regardless of what type of object was sent to the past.

Physicist Joseph Polchinski argued that one could avoid questions of free will by considering a potentially paradoxical situation involving a billiard ball sent back in time. In this situation, the ball is fired into a wormhole at an angle such that, if it continues along its course, it will exit in the past at just the right angle to hit its earlier self, knocking it off course, which would stop it from entering the wormhole in the first place. Thorne referred to this problem as “Polchinski’s paradox”. Two students at Caltech, Fernando Echeverria, and Gunnar Klinkhammer, went on to find a solution that avoided any inconsistencies.

In the revised scenario, the ball would emerge from the future at a different angle than the one that had generated the paradox, and delivers its past self a glancing blow instead of knocking it completely away from the wormhole. This blow changes its trajectory by just the right degree, meaning it will travel back in time with the angle required to deliver its younger self the necessary glancing blow. Echeverria and Klinkhammer actually found that there was more than one self-consistent solution, with slightly different angles for the glancing blow in each case. Later analysis by Thorne and Robert Forward showed that for certain initial trajectories of the billiard ball, there could actually be an infinite number of self-consistent solutions.

Echeverria, Klinkhammer, and Thorne published a paper discussing these results in 1991, in addition, they reported that they had tried to see if they could find any initial conditions for the billiard ball for which there were no self-consistent extensions, but were unable to do so. Thus it is plausible that there exist self-consistent extensions for every possible initial trajectory, although this has not been proven. The lack of constraints on initial conditions only applies to spacetime outside of the chronology-violating region of spacetime; the constraints on the chronology-violating region might prove to be paradoxical, but this is not yet known.

Novikov’s views are not widely accepted. Visser views causal loops and Novikov’s self-consistency principle as an ad hoc solution and supposes that there are far more damaging implications of time travel. Krasnikov similarly finds no inherent fault in causal loops, but finds other problems with time travel in general relativity.

Conclusion and Final thoughts

At the beginning of this article we have discussed about a time traveler who steals a time machine from a museum to make his time trip, he travels back in time and reaches in the past then at the end of the trip he donates the time machine to the same museum from where he stole it. Here we can examine some aspects of this Paradox strongly, but we may have many questions too, so the discussion is always open. Despite these questions, did you thereby can find out where did the time machine came from? You can’t and we too can’t because here the time machine itself is never built by anyone – it simply exists. Thus time traveling in the past would allow for the possibility of Causal loops, in which things come from nowhere means arrive or emerge unexpectedly.


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