A temporal paradox, time paradox, or time travel paradox, is a paradox, an apparent contradiction, or logical contradiction associated with the idea of time travel or other foreknowledge of the future. While the notion of time travel to the future complies with the current understanding of physics via relativistic time dilation, temporal paradoxes arise from circumstances involving hypothetical time travel to the past – and are often used to demonstrate its impossibility.
Temporal paradoxes fall into three broad groups: bootstrap paradoxes, consistency paradoxes, and Newcomb's paradox. [1] Bootstrap paradoxes violate causality by allowing future events to influence the past and cause themselves, or "bootstrapping", which derives from the idiom "pull oneself up by one's bootstraps." [2] [3] Consistency paradoxes, on the other hand, are those where future events influence the past to cause an apparent contradiction, exemplified by the grandfather paradox, where a person travels to the past to prevent the conception of one of their ancestors, thus eliminating all the ancestor's descendants. [4] Newcomb's paradox stems from the apparent contradictions that stem from the assumptions of both free will and foreknowledge of future events. All of these are sometimes referred to individually as "causal loops." The term "time loop" is sometimes referred to as a causal loop, [2] but although they appear similar, causal loops are unchanging and self-originating, whereas time loops are constantly resetting. [5]
A bootstrap paradox, also known as an information loop, an information paradox, [6] an ontological paradox, [7] or a "predestination paradox" is a paradox of time travel that occurs when any event, such as an action, information, an object, or a person, ultimately causes itself, as a consequence of either retrocausality or time travel. [8] [9] [10] [11]
Backward time travel would allow information, people, or objects whose histories seem to "come from nowhere". [8] Such causally looped events then exist in spacetime, but their origin cannot be determined. [8] [9] The notion of objects or information that are "self-existing" in this way is often viewed as paradoxical. [9] [6] [12] A notable example occurs in the 1958 science fiction short story "—All You Zombies—", by Robert A. Heinlein, wherein the main character, an intersex individual, becomes both their own mother and father; it was adapted with great fidelity in the 2014 film Predestination . Allen 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. [6] An example of information which "came from nowhere" is in the movie Star Trek IV: The Voyage Home , in which a 23rd-century engineer travels back in time, and gives the formula for transparent aluminum to the 20th-century engineer who supposedly invented it.
Smeenk uses 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. [7]
The "predestination paradox" is a concept in time travel and temporal mechanics, often explored in science fiction. It occurs when a future event is the cause of a past event, which in turn becomes the cause of the future event, forming a self-sustaining loop in time. This paradox challenges conventional understandings of cause and effect, as the events involved are both the origin and the result of each other. A notable example is found in the TV series Doctor Who, where a character saves her father in the past, fulfilling a memory he had shared with her as a child about a strange woman having saved his life. The predestination paradox raises philosophical questions about free will, determinism, and the nature of time itself. It is commonly used as a narrative device in fiction to highlight the interconnectedness of events and the inevitability of certain outcomes.
The consistency paradox or grandfather paradox occurs when the past is changed in any way that directly negates the conditions required for the time travel to occur in the first place, thus creating a contradiction. A common example given is traveling to the past and intervening with the conception of one's ancestors (such as causing the death of the parent beforehand), thus affecting the conception of oneself. If the time traveler were not born, then it would not be possible for the traveler to undertake such an act in the first place. Therefore, the ancestor lives to conceive the time-traveler's next-generation ancestor, and eventually the time traveler. There is thus no predicted outcome to this. [8] Consistency paradoxes occur whenever changing the past is possible. [9] A possible resolution is that a time traveller can do anything that did happen, but cannot do anything that did not happen. Doing something that did not happen results in a contradiction. [8] This is referred to as the Novikov self-consistency principle.
The grandfather paradox encompasses any change to the past, [13] and it is presented in many variations, including killing one's past self. [14] [15] Both the "retro-suicide paradox" and the "grandfather paradox" appeared in letters written into Amazing Stories in the 1920s. [16] Another variant of the grandfather paradox is the "Hitler paradox" or "Hitler's murder paradox", in which the protagonist travels back in time to murder Adolf Hitler before he can instigate World War II and the Holocaust. Rather than necessarily physically preventing time travel, the action removes any reason for the travel, along with any knowledge that the reason ever existed. [17]
Physicist John Garrison et al. give a variation of the paradox of an electronic circuit that sends a signal through a time machine to shut itself off, and receives the signal before it sends it. [18] [19]
Newcomb's paradox is a thought experiment showing an apparent contradiction between the expected utility principle and the strategic dominance principle. [20] The thought experiment is often extended to explore causality and free will by allowing for "perfect predictors": if perfect predictors of the future exist, for example if time travel exists as a mechanism for making perfect predictions[ how? ], then perfect predictions appear to contradict free will because decisions apparently made with free will are already known to the perfect predictor[ clarification needed ]. [21] [22] Predestination does not necessarily involve a supernatural power, and could be the result of other "infallible foreknowledge" mechanisms. [23] Problems arising from infallibility and influencing the future are explored in Newcomb's paradox. [24]
Even without knowing whether time travel to the past is physically possible, it is possible to show using modal logic that changing the past results in a logical contradiction. If it is necessarily true that the past happened in a certain way, then it is false and impossible for the past to have occurred in any other way. A time traveler would not be able to change the past from the way it is, but would only act in a way that is already consistent with what necessarily happened. [25] [26]
Consideration of the grandfather paradox has led some to the idea that time travel is by its very nature paradoxical and therefore logically impossible. For example, the philosopher Bradley Dowden made this sort of argument in the textbook Logical Reasoning, arguing that the possibility of creating a contradiction rules out time travel to the past entirely. However, some philosophers and scientists believe that time travel into the past need not be logically impossible provided that there is no possibility of changing the past, [13] as suggested, for example, by the Novikov self-consistency principle. Dowden revised his view after being convinced of this in an exchange with the philosopher Norman Swartz. [27]
Consideration of the possibility of backward time travel in a hypothetical universe described by a Gödel metric led famed logician Kurt Gödel to assert that time might itself be a sort of illusion. [28] [29] He suggests something along the lines of the block time view, in which time is just another dimension like space, with all events at all times being fixed within this four-dimensional "block".[ citation needed ]
Sergey 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. [30] : 4 He does not find these paradoxical and attributes problems regarding the validity of time travel to other factors in the interpretation of general relativity. [30] : 14–16
A 1992 paper by physicists Andrei Lossev and Igor Novikov labeled such items without origin as Jinn, with the singular term Jinnee. [31] : 2311–2312 This terminology was inspired by the Jinn of the Quran, which are described as leaving no trace when they disappear. [32] : 200–203 Lossev and Novikov allowed the term "Jinn" to cover both objects and information with the reflexive origin; they called the former "Jinn of the first kind", and the latter "Jinn of the second kind". [6] [31] : 2315–2317 [32] : 208 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 seems to require that the object tends to a lower energy state 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 entropy to increase in closed systems, a Jinnee could interact with its environment in such a way as to regain "lost" entropy. [6] [32] : 200–203 They emphasize that there is no "strict difference" between Jinn of the first and second kind. [31] : 2320 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." [30] : 8–9
The self-consistency principle developed by Igor Dmitriyevich Novikov [33] : p. 42 note 10 expresses one view as to how backward time travel would be possible without the generation of paradoxes. According to this hypothesis, even though general relativity permits some exact solutions that allow for time travel [34] that contain closed timelike curves that lead back to the same point in spacetime, [35] physics in or near closed timelike curves (time machines) can only be consistent with the universal laws of physics, and thus only self-consistent events can occur. Anything a time traveler does in the past must have been part of history all along, and the time traveler can never do anything to prevent the trip back in time from happening, since this would represent an inconsistency. The authors concluded that time travel need not lead to unresolvable paradoxes, regardless of what type of object was sent to the past. [36]
Physicist Joseph Polchinski considered a potentially paradoxical situation involving a billiard ball that is fired into a wormhole at just the right angle such that it will be sent back in time and collides with its earlier self, knocking it off course, which would stop it from entering the wormhole in the first place. Kip Thorne referred to this problem as "Polchinski's paradox". [36] Thorne and two of his students at Caltech, Fernando Echeverria and Gunnar Klinkhammer, went on to find a solution that avoided any inconsistencies, and found that there was more than one self-consistent solution, with slightly different angles for the glancing blow in each case. [37] Later analysis by Thorne and Robert Forward showed that for certain initial trajectories of the billiard ball, there could be an infinite number of self-consistent solutions. [36] It is plausible that there exist self-consistent extensions for every possible initial trajectory, although this has not been proven. [38] : 184 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. [38] : 187–188
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. [39] Krasnikov similarly finds no inherent fault in causal loops but finds other problems with time travel in general relativity. [30] : 14–16 Another conjecture, the cosmic censorship hypothesis, suggests that every closed timelike curve passes through an event horizon, which prevents such causal loops from being observed. [40]
The interacting-multiple-universes approach is a variation of the many-worlds interpretation of quantum mechanics that involves time travelers arriving in a different universe than the one from which they came; it has been argued that, since travelers arrive in a different universe's history and not their history, this is not "genuine" time travel. [41] Stephen Hawking has argued for the chronology protection conjecture, that even if the MWI is correct, we should expect each time traveler to experience a single self-consistent history so that time travelers remain within their world rather than traveling to a different one. [42]
David Deutsch has proposed that quantum computation with a negative delay—backward time travel—produces only self-consistent solutions, and the chronology-violating region imposes constraints that are not apparent through classical reasoning. [43] However Deutsch's self-consistency condition has been demonstrated as capable of being fulfilled to arbitrary precision by any system subject to the laws of classical statistical mechanics, even if it is not built up by quantum systems. [44] Allen Everett has also argued that even if Deutsch's approach is correct, it would imply that any macroscopic object composed of multiple particles would be split apart when traveling back in time, with different particles emerging in different worlds. [45]
Faster-than-light travel and communication are the conjectural propagation of matter or information faster than the speed of light in vacuum. The special theory of relativity implies that only particles with zero rest mass may travel at the speed of light, and that nothing may travel faster.
Time travel is the hypothetical activity of traveling into the past or future. Time travel is a concept in philosophy and fiction, particularly science fiction. In fiction, time travel is typically achieved through the use of a device known as a time machine. The idea of a time machine was popularized by H. G. Wells's 1895 novel The Time Machine.
A wormhole is a hypothetical structure which connects disparate points in spacetime. It may be visualized as a tunnel with two ends at separate points in spacetime. Wormholes are based on a special solution of the Einstein field equations. Specifically, they are a transcendental bijection of the spacetime continuum, an asymptotic projection of the Calabi–Yau manifold manifesting itself in anti-de Sitter space.
The Novikov self-consistency principle, also known as the Novikov self-consistency conjecture and Larry Niven's law of conservation of history, is a principle developed by Russian physicist Igor Dmitriyevich Novikov in the mid-1980s. Novikov intended it to solve the problem of paradoxes in time travel, which is theoretically permitted in certain solutions of general relativity that contain what are known as closed timelike curves. The principle asserts that if an event exists that would cause a paradox or any "change" to the past whatsoever, then the probability of that event is zero. It would thus be impossible to create time paradoxes.
The Alcubierre drive is a speculative warp drive idea according to which a spacecraft could achieve apparent faster-than-light travel by contracting space in front of it and expanding space behind it, under the assumption that a configurable energy-density field lower than that of vacuum could be created. Proposed by theoretical physicist Miguel Alcubierre in 1994, the Alcubierre drive is based on a solution of Einstein's field equations. Since those solutions are metric tensors, the Alcubierre drive is also referred to as Alcubierre metric.
The world line of an object is the path that an object traces in 4-dimensional spacetime. It is an important concept of modern physics, and particularly theoretical physics.
Kip Stephen Thorne is an American theoretical physicist and writer known for his contributions in gravitational physics and astrophysics. Along with Rainer Weiss and Barry C. Barish, he was awarded the 2017 Nobel Prize in Physics for his contributions to the LIGO detector and the observation of gravitational waves.
In theoretical physics, negative mass is a hypothetical type of exotic matter whose mass is of opposite sign to the mass of normal matter, e.g. −1 kg. Such matter would violate one or more energy conditions and exhibit strange properties such as the oppositely oriented acceleration for an applied force orientation. It is used in certain speculative hypothetical technologies such as time travel to the past and future, construction of traversable artificial wormholes, which may also allow for time travel, Krasnikov tubes, the Alcubierre drive, and potentially other types of faster-than-light warp drives. Currently, the closest known real representative of such exotic matter is a region of negative pressure density produced by the Casimir effect.
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 Stockum in 1937 and later confirmed by Kurt Gödel in 1949, who discovered a solution to the equations of general relativity (GR) allowing CTCs known as the Gödel metric; and since then other GR solutions containing CTCs have been found, such as the Tipler cylinder and traversable wormholes. If CTCs exist, their existence would seem to imply at least the theoretical possibility of time travel backwards in time, raising the spectre of the grandfather paradox, although the Novikov self-consistency principle seems to show that such paradoxes could be avoided. Some physicists speculate that the CTCs which appear in certain GR solutions might be ruled out by a future theory of quantum gravity which would replace GR, an idea which Stephen Hawking labeled the chronology protection conjecture. Others note that if every closed timelike curve in a given spacetime passes through an event horizon, a property which can be called chronological censorship, then that spacetime with event horizons excised would still be causally well behaved and an observer might not be able to detect the causal violation.
Joseph Gerard Polchinski Jr. was an American theoretical physicist and string theorist.
The chronology protection conjecture is a hypothesis first proposed by Stephen Hawking that laws of physics beyond those of standard general relativity prevent time travel—even when the latter theory states that it should be possible. The permissibility of time travel is represented mathematically by the existence of closed timelike curves in some solutions to the field equations of general relativity. The chronology protection conjecture should be distinguished from chronological censorship under which every closed timelike curve passes through an event horizon, which might prevent an observer from detecting the causal violation.
A Tipler cylinder, also called a Tipler time machine, is a hypothetical object theorized to be a potential mode of time travel—although results have shown that a Tipler cylinder could only allow time travel if its length were infinite or with the existence of negative energy.
A Krasnikov tube is a speculative mechanism for space travel involving the warping of spacetime into permanent superluminal tunnels. The resulting structure is analogous to a wormhole or an immobile Alcubierre drive with the endpoints displaced in time as well as space. The idea was proposed by Sergey Krasnikov in 1995.
John Richard Gott III is a professor of astrophysical sciences at Princeton University. He is known for his work on time travel and the Doomsday argument.
In the mathematical field of Lorentzian geometry, a Cauchy surface is a certain kind of submanifold of a Lorentzian manifold. In the application of Lorentzian geometry to the physics of general relativity, a Cauchy surface is usually interpreted as defining an "instant of time". In the mathematics of general relativity, Cauchy surfaces provide boundary conditions for the causal structure in which the Einstein equations can be solved
Serguei Vladilenovich Krasnikov is a Russian physicist.
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 most fundamental level and so time-symmetric systems can be viewed as causal or retrocausal. Philosophical considerations of time travel often address the same issues as retrocausality, as do treatments of the subject in fiction, but the two phenomena are distinct.
The causal sets program is an approach to quantum gravity. Its founding principles are that spacetime is fundamentally discrete and that spacetime events are related by a partial order. This partial order has the physical meaning of the causality relations between spacetime events.
The theoretical study of time travel generally follows the laws of general relativity. Quantum mechanics requires physicists to solve equations describing how probabilities behave along closed timelike curves (CTCs), which are theoretical loops in spacetime that might make it possible to travel through time.
A black hole firewall is a hypothetical phenomenon where an observer falling into a black hole encounters high-energy quanta at the event horizon. The "firewall" phenomenon was proposed in 2012 by physicists Ahmed Almheiri, Donald Marolf, Joseph Polchinski, and James Sully as a possible solution to an apparent inconsistency in black hole complementarity. The proposal is sometimes referred to as the AMPS firewall, an acronym for the names of the authors of the 2012 paper. The potential inconsistency pointed out by AMPS had been pointed out earlier by Samir Mathur who used the argument in favour of the fuzzball proposal. The use of a firewall to resolve this inconsistency remains controversial, with physicists divided as to the solution to the paradox.