![Causal loop billiard ball](https://upload.wikimedia.org/wikipedia/commons/3/37/Causal_loop_billiard_ball.svg)
A causal loop is a theoretical proposition, wherein by means of either
retrocausality
Retrocausality, or backwards causation, is a concept of cause and effect in which an effect precedes its cause in time and so a later event affects an earlier one. In quantum physics, the distinction between cause and effect is not made at the mos ...
or
time travel
Time travel is the concept of movement between certain points in time, analogous to movement between different points in space by an object or a person, typically with the use of a hypothetical device known as a time machine. Time travel is a w ...
, an event (an action, information, object, or person)
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
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
, but their origin cannot be determined.
A hypothetical example of a causality loop is given of a
billiard ball
A billiard ball is a small, hard ball used in cue sports, such as carom billiards, pool, and snooker. The number, type, diameter, color, and pattern of the balls differ depending upon the specific game being played. Various particular ball p ...
striking its past self: 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.
Other terms for "causal loop" are bootstrap paradox, information paradox, ontological paradox, self-sufficient loop, and predestination paradox; see
§ terminology.
Terminology in physics, philosophy, and fiction
Backwards time travel would allow for causal loops involving events, information, people or objects whose histories form a closed loop, and thus seem to "come from nowhere."
The notion of objects or information that are "self-existing" in this way is often viewed as paradoxical,
with several authors referring to a causal loop involving information or objects without origin as a ''bootstrap paradox'',
an ''information paradox'',
or an ''ontological paradox''.
The use of "bootstrap" in this context refers to the expression "
pulling yourself up by your bootstraps" and to
Robert A. Heinlein
Robert Anson Heinlein (; July 7, 1907 – May 8, 1988) was an American science fiction author, aeronautical engineer, and naval officer. Sometimes called the "dean of science fiction writers", he was among the first to emphasize scientific accu ...
's time travel story "
By His Bootstraps
"By His Bootstraps" is a 20,000 word science fiction novella by American writer Robert A. Heinlein. It plays with some of the inherent paradoxes that would be caused by time travel.
The story was published in the October 1941 issue of '' Astoun ...
".
The term "
time loop
The time loop or temporal loop is a plot device in fiction whereby characters re-experience a span of time which is repeated, sometimes more than once, with some hope of breaking out of the cycle of repetition. The term "time loop" is sometimes us ...
" 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.
An example of a causal loop paradox involving information is given by Allan Everett: 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
''Doctor Who'' is a British science fiction television series broadcast by the BBC since 1963. The series depicts the adventures of a Time Lord called the Doctor, an extraterrestrial being who appears to be human. The Doctor explores the u ...
'' 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 – are 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.
A 1992 paper by physicists Andrei Lossev and
Igor Novikov Igor Novikov may refer to:
* Igor Novikov (painter) (born 1961), Russian painter living in Switzerland
* Igor Novikov (pentathlete) (1929–2007), Soviet Olympic modern pentathlete
*Igor Novikov (chess player)
Igor Oleksandrovych Novikov (bor ...
labeled such items without origin as ''Jinn'', with the singular term ''Jinnee''.
This terminology was inspired by the
Jinn
Jinn ( ar, , ') – also Romanization of Arabic, romanized as djinn or Anglicization, anglicized as genies (with the broader meaning of spirit or demon, depending on sources)
– are Invisibility, invisible creatures in early Arabian mytho ...
of the
Quran
The Quran (, ; Standard Arabic: , Classical Arabic, Quranic Arabic: , , 'the recitation'), also romanized Qur'an or Koran, is the central religious text of Islam, believed by Muslims to be a revelation in Islam, revelation from God in Islam, ...
, which are 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 circular passage through time must be identical whenever it is brought back to the past, otherwise it would create an inconsistency; the
second law of thermodynamics
The second law of thermodynamics is a physical law based on universal experience concerning heat and Energy transformation, energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects ( ...
seems to require that the object tends to a lower energy state over the course of 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 entropy to increase in ''closed'' systems, a Jinnee could interact with its environment in such a way as to regain "lost" entropy.
They emphasize that there is no "strict difference" between 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."
The term ''predestination paradox'' is used in the ''
Star Trek
''Star Trek'' is an American science fiction media franchise created by Gene Roddenberry, which began with the eponymous 1960s television series and quickly became a worldwide pop-culture phenomenon. The franchise has expanded into vari ...
'' franchise 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
"Trials and Tribble-ations" is the 104th episode of the American science fiction television series '' Star Trek: Deep Space Nine'', the sixth episode of the fifth season. It was written as a tribute to the original series of '' Star Trek,'' in th ...
", although the phrase had been used previously to refer to belief systems such as
Calvinism
Calvinism (also called the Reformed Tradition, Reformed Protestantism, Reformed Christianity, or simply Reformed) is a major branch of Protestantism that follows the theological tradition and forms of Christian practice set down by John Cal ...
and some forms of
Marxism
Marxism is a Left-wing politics, left-wing to Far-left politics, far-left method of socioeconomic analysis that uses a Materialism, materialist interpretation of historical development, better known as historical materialism, to understand S ...
that encourage followers to strive to produce certain outcomes while at the same time teaching that the outcomes are 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.
Self-fulfilling prophecy
A
self-fulfilling prophecy
A self-fulfilling prophecy is a prediction that comes true at least in part as a result of a person's or group of persons' belief or expectation that said prediction would come true. This suggests that people's beliefs influence their actions. ...
may be a form of causality loop.
Predestination
Predestination, in theology, is the doctrine that all events have been willed by God, usually with reference to the eventual fate of the individual soul. Explanations of predestination often seek to address the paradox of free will, whereby G ...
does not necessarily involve a
supernatural
Supernatural refers to phenomena or entities that are beyond the laws of nature. The term is derived from Medieval Latin , from Latin (above, beyond, or outside of) + (nature) Though the corollary term "nature", has had multiple meanings si ...
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
In philosophy and mathematics, Newcomb's paradox, also known as Newcomb's problem, is a thought experiment involving a game between two players, one of whom is able to predict the future.
Newcomb's paradox was created by William Newcomb of the Uni ...
. A notable fictional example of a self-fulfilling prophecy occurs in the classical play ''
Oedipus Rex
''Oedipus Rex'', also known by its Greek title, ''Oedipus Tyrannus'' ( grc, Οἰδίπους Τύραννος, ), or ''Oedipus the King'', is an Athenian tragedy by Sophocles that was first performed around 429 BC. Originally, to the ancient Gr ...
'', in which
Oedipus
Oedipus (, ; grc-gre, Οἰδίπους "swollen foot") was a mythical Greek king of Thebes. A tragic hero in Greek mythology, Oedipus accidentally fulfilled a prophecy that he would end up killing his father and marrying his mother, thereby ...
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
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
permits some
exact solutions
In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first i ...
that allow for
time travel
Time travel is the concept of movement between certain points in time, analogous to movement between different points in space by an object or a person, typically with the use of a hypothetical device known as a time machine. Time travel is a w ...
. Some of these exact solutions describe universes that contain
closed timelike curves
In mathematical physics, a closed timelike curve (CTC) is a world line in a Lorentzian manifold, of a material particle in spacetime, that is "closed", returning to its starting point. This possibility was first discovered by Willem Jacob van Sto ...
, or
world line
The world line (or worldline) of an object is the path that an object traces in 4-dimensional spacetime. It is an important concept in modern physics, and particularly theoretical physics.
The concept of a "world line" is distinguished from con ...
s that lead back to the same point in spacetime. Physicist
Igor Dmitriyevich Novikov
Igor Dmitriyevich Novikov (russian: И́горь Дми́триевич Но́виков; born November 10, 1935) is a Russian (and former Soviet) theoretical astrophysicist and cosmologist.
Novikov put forward the idea of white holes in 1964. ...
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
Joseph Gerard Polchinski Jr. (; May 16, 1954 – February 2, 2018) was an American theoretical physicist and string theorist.
Biography
Polchinski was born in White Plains, New York, the elder of two children to Joseph Gerard Polchinski Sr. (1929 ...
argued that one could avoid questions of
free will
Free will is the capacity of agents to choose between different possible courses of action unimpeded.
Free will is closely linked to the concepts of moral responsibility, praise, culpability, sin, and other judgements which apply only to actio ...
by considering a potentially paradoxical situation involving a
billiard ball
A billiard ball is a small, hard ball used in cue sports, such as carom billiards, pool, and snooker. The number, type, diameter, color, and pattern of the balls differ depending upon the specific game being played. Various particular ball p ...
sent back in time. In this situation, the ball is fired into a
wormhole
A wormhole (Einstein-Rosen bridge) is a hypothetical structure connecting disparate points in spacetime, and is based on a special Solutions of the Einstein field equations, solution of the Einstein field equations.
A wormhole can be visualize ...
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 from 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
Robert Lull Forward (August 15, 1932 – September 21, 2002) was an American physicist and science fiction writer. His literary work was noted for its scientific credibility and use of ideas developed from his career as an aerospace engineer. He ...
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.
Quantum computation with negative delay
Physicist
David Deutsch
David Elieser Deutsch ( ; born 18 May 1953) is a British physicist at the University of Oxford. He is a Visiting Professor in the Department of Atomic and Laser Physics at the Centre for Quantum Computation (CQC) in the Clarendon Laboratory of ...
shows in a 1991 paper that quantum computation with a negative delay—backwards time travel—could solve NP problems in
polynomial time
In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by ...
,
and
Scott Aaronson
Scott Joel Aaronson (born May 21, 1981) is an American theoretical computer scientist and David J. Bruton Jr. Centennial Professor of Computer Science at the University of Texas at Austin. His primary areas of research are quantum computing an ...
later extended this result to show that the model could also be used to solve
PSPACE
In computational complexity theory, PSPACE is the set of all decision problems that can be solved by a Turing machine using a polynomial amount of space.
Formal definition
If we denote by SPACE(''t''(''n'')), the set of all problems that can b ...
problems in polynomial time. Deutsch shows 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.
Researchers published in 2014 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
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
on spacetimes where CTCs are excluded, casting doubts on whether Deutsch's condition is really characteristic of quantum processes mimicking CTCs in the sense of
general relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
.
In a later article,
the same authors have shown that Deutsch's CTC fixed point condition can also be fulfilled in any system
subject to the laws of classical
statistical mechanics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic be ...
, even if it is not built up by quantum systems. The authors conclude that hence,
Deutsch's condition is not specific to quantum physics, nor does it depend on the quantum nature of a physical system so that it can be fulfilled.
In consequence, Tolksdorf and Verch further conclude that Deutsch's condition isn't sufficiently specific to allow statements about time travel scenarios or their hypothetical realization by quantum physics, and that Deutsch's attempt to explain the possibility of his proposed time-travel scenario using the many-world interpretation of quantum mechanics is misleading.
See also
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References
{{Time travel
Causality
Fiction
Plot (narrative)
Temporal paradoxes