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Unsolved problem in physics:

Is time travel theoretically and practically possible? If so, how can paradoxes such as the grandfather paradox be avoided?

(more unsolved problems in physics)

Time travel is the concept of moving between different points in time in a manner analogous to moving between different points in space, either sending objects (or in some cases just information) backwards in time to some moment before the present, or sending objects forward from the present to the future without the need to experience the intervening period (at least not at the normal rate).

Although time travel has been a common plot device in fiction since the 19th century, and a form of one-way travel into the future is thought to be possible given the phenomenon of time dilation based on velocity in the theory of special relativity (exemplified by the twin paradox), as well as gravitational time dilation in the theory of general relativity, it is currently unknown whether the laws of physics would allow backwards time travel.

Any technological device, whether fictional or hypothetical, that is used to achieve time travel is commonly known as a time machine.

Some interpretations of time travel also suggest that an attempt to travel backwards in time might take one to a parallel universe whose history would begin to diverge from the traveler's original history after the moment the traveler arrived in the past.^[1]

Origins of the concept

700s BCE to 300s CE – Mahabharata
200s to 400s CE – Talmud

6 century a.c the "Seven Sleepers of Ephesus

720 CE – "Urashima Tarō"
1733 – Samuel Madden’s Memoirs of the Twentieth Century
1771 – Louis-Sébastien Mercier’s L'An 2440, rêve s'il en fût jamais
1781 – Johan Herman Wessel's Anno 7603
1819 – Washington Irving's "Rip Van Winkle"
1824 – Faddey Bulgarin's "Pravdopodobnie Nebylitsi"
1827 – Goethe Faust fragment
1828 – Hans Christian Andersen's Journey on Foot from Holmen's Canal to the East Point of Amager
1832 – Goethe's Faust: The Second Part of the Tragedy
1836 – Alexander Veltman's Predki Kalimerosa
1838 – Hans Christian Andersen's The Goloshes of Fortune
1838 – Missing One's Coach: An Anachronism
1843 – Charles Dickens’ A Christmas Carol
1861 – Pierre Boitard’s Paris avant les hommes
1881 – Edward Page Mitchell’s The Clock That Went Backward
1887 – Enrique Gaspar y Rimbau's El anacronópete
1888 – H. G. Wells' The Chronic Argonauts
1889 – Mark Twain’s A Connecticut Yankee in King Arthur's Court
1895 – H. G. Wells’ The Time Machine

There is no widespread agreement as to which written work should be recognized as the earliest example of a time travel story, since a number of early works feature elements ambiguously suggestive of time travel. Ancient folk tales and myths sometimes involved something akin to travelling forward in time; for example

the Talmud relates that Among the Tannaim, the generations of rabbinic teachers whose work is recorded in the Mishnah, Rabbi Akiba is generally considered the towering personality. Approximately one hundred years after his death, a legend is reported by R. Judah bar Ezekiel (219-299 C.E.), in the name of his teacher and sometime traveling companion, Ray: Rav Judah said in the name of Rav,

God translated Moses in time so that Moses himself attended a lecture given by Rabbi Akiva.  story is told of Rabbi Akiva that when Moses ascended Mount Sinai, he saw that God was putting little taggim (the small 'crowns' on the top of the letters in the Torah scroll) on top of the Torah that was to be presented to the Jews at Mount Sinai. Moses asked God to explain the meaning of these taggim. God explained that in the future a man by the name of Akiva ben Joseph will reveal what these signs mean.

Moses asked God to reveal to him this man and so God replied to Moses to turn around. When Moses turned around he saw a sage surrounded by many rows of students listening eagerly to this man's teaching. The greater students sat in front and the lesser in the rear. Moses, being a very humble man, took a seat in the eighth row and began listening. Rabbi Akiba taught a certain law and the students asked him what is the source, he replied that it came down to us from our great master Moses. At this lecture, Rabbi Akiva stated that all that he was teaching originated with Moses - yet Moses himself heard these matters for the first time! Moses came back and questioned God, if there is such a great man like that why give the Torah through me? God answered, "Be silent, this is my will." (Menachoth 29b)

One can then understand this in this way : Rabbi Akiva indeed originated the material, and then this fact allowed the material to become known to Moses via God prior to Rabbi Akiva's birth, at Mt. Sinai, creating again a non-causal loop.IF so this is the first time paradox story.

               The means by which at Sinai Moses was made aware of all the halachot which would eventually be developed is generally taken to be via direct transmission from God, as was the case with the rest of the Torah. However the means by which Moses is made aware of those matters discovered by Rabbi Akiva may have been by the bringing of Moses forward in time to participate in Rabbi Akiva's lectures.

( see Rabbi Akiba's Crowns: Postmodern Discourse and the Cost of Rabbinic Reading by Laurence L. Edwards http://findarticles.com/p/articles/mi_m0411/is_4_49/ai_68738707/)

, in Hindu mythology, the Mahabharata mentions the story of the King Revaita, who travels to heaven to meet the creator Brahma and is shocked to learn that many ages have passed when he returns to Earth.^[2]^[3] Another one of the earliest known stories to involve traveling forwards in time to a distant future was the Japanese tale of "Urashima Tarō",^[4] first described in the Nihongi (720).^[5] It was about a young fisherman named Urashima Taro who visits an undersea palace and stays there for three days. After returning home to his village, he finds himself three hundred years in the future, where he is long forgotten, his house in ruins, and his family long dead. Another very old example of this type of story can be found in the Talmud with the story of Honi HaM'agel who went to sleep for 70 years and woke up to a world where his grandchildren were grandparents and where all his friends and family were deceased.^[6]

"Seven Sleepers of Ephesus", refers to a group of Christian youths who allegedly hid inside a cave outside the city of Ephesus around 250 AD, to escape a persecution of Christians being conducted during the reign of the Roman emperor Decius. Having fallen asleep inside the cave, they purportedly awoke approximately 150-200 years later during the reign of Theodosius II, following which they were reportedly seen by the people of the now-Christian city before dying. An outline of this tale appears in Gregory of Tours (b. 538, d. 594), and in Paul the Deacon's (b. 720, d. 799) History of the Lombards. The best-known Western version of the story appears in Jacobus de Voragine's Golden Legend.

The story has its highest prominence, however, in the Muslim world; it is told in the Qur'an (Surah 18, verse 9-26). While not giving the number of youths involved, the Quranic rendering of the Seven Sleepers tale largely parallels the Christian account. Unlike the Christian story, the Islamic version includes a dog who allegedly accompanied the youths into the cave, and kept watch at the entrance for the entire time that they were asleep (see Islamic interpretation). In Islam, these youths are referred to as "The People of the Cave". It represents one of the trials of Muhammad by the Jewish elders in Medina; by explaining this mystery to his followers, Muhammad is granted the status of being a prophet.

More recently, Washington Irving's famous 1819 story "Rip Van Winkle" deals with a similar concept, telling the tale of a man named Rip Van Winkle who takes a nap at a mountain and wakes up twenty years in the future, where he has been forgotten, his wife deceased, and his daughter grown up.^[4]

Sleep was also used for time travel in Faddey Bulgarin's story "Pravdopodobnie Nebylitsi" where the protagonist wakes up in the 29th century.

Another more recent story involving travel to the future is Louis-Sébastien Mercier's L'An 2440, rêve s'il en fût jamais ("The Year 2440: A Dream If Ever There Were One"), a utopian novel in which the main character is transported to the year 2440. An extremely popular work (it went through twenty-five editions after its first appearance in 1771), the work describes the adventures of an unnamed man, who, after engaging in a heated discussion with a philosopher friend about the injustices of Paris, falls asleep and finds himself in a Paris of the future. Robert Darnton writes that "despite its self-proclaimed character of fantasy...L'An 2440 demanded to be read as a serious guidebook to the future."^[7]

Backwards time travel seems to be a more modern idea, but the origin of this notion is also somewhat ambiguous. One early story with hints of backwards time travel is Memoirs of the Twentieth Century (1733) by Samuel Madden, which is mainly a series of letters from English ambassadors in various countries to the British Lord High Treasurer, along with a few replies from the British Foreign Office, all purportedly written in 1997 and 1998 and describing the conditions of that era.^[8] However, the framing story is that these letters were actual documents given to the narrator by his guardian angel one night in 1728; for this reason, Paul Alkon suggests in his book Origins of Futuristic Fiction that "the first time-traveler in English literature is a guardian angel who returns with state documents from 1998 to the year 1728",^[9] although the book does not explicitly show how the angel obtained these documents. Alkon later qualifies this by writing, "It would be stretching our generosity to praise Madden for being the first to show a traveler arriving from the future", but also says that Madden "deserves recognition as the first to toy with the rich idea of time-travel in the form of an artifact sent backwards from the future to be discovered in the present."^[8] Hans Christian Andersen Journey on Foot from Holmen's Canal to the East Point of Amager". a journey to the future of 2129. In 1832 ( part appeared in 1827 ) Johann Wolfgang von Goethe had published Faust: The Second Part http://en.wikipedia.org/wiki/Faust:_The_Second_Part_of_the_Tragedy had presented the first known actual time travel to the past thill this time in the story of faust which is taken from Medival Germany to Ancient greece in either time travell or journey to a paralel world.Goethe seems to be the first person which actually had wrote about time travel to the past.

In 1836 Alexander Veltman published Predki Kalimerosa: Aleksandr Filippovich Makedonskii (The forebears of Kalimeros: Alexander, son of Philip of Macedon), which has been called the first original Russian science fiction novel and the first novel to use time travel.^[10] In it the narrator rides to ancient Greece on a hippogriff, meets Aristotle, and goes on a voyage with Alexander the Great before returning to the 19th century. IN MAY 1838 Hans Christian Andersen The Goloshes of Fortune http://hca.gilead.org.il/goloshes.html which is among other things about time travel to the past to Denemark of medieval times.After that the hero make a space journey to the Moon. http://en.wikipedia.org/wiki/The_Galoshes_of_Fortune

In the science fiction anthology Far Boundaries (1951), the editor August Derleth identifies the short story "Missing One's Coach: An Anachronism", written for the Dublin Literary Magazine by an anonymous author in 1838, as a very early time travel story.^[11] In this story, the narrator is waiting under a tree to be picked up by a coach which will take him out of Newcastle, when he suddenly finds himself transported back over a thousand years, where he encounters the Venerable Bede in a monastery, and gives him somewhat ironic explanations of the developments of the coming centuries. It is never entirely clear whether these events actually occurred or were merely a dream—the narrator says that when he initially found a comfortable-looking spot in the roots of the tree, he sat down, "and as my sceptical reader will tell me, nodded and slept", but then says that he is "resolved not to admit" this explanation. A number of dreamlike elements of the story may suggest otherwise to the reader, such as the fact that none of the members of the monastery seem to be able to see him at first, and the abrupt ending where Bede has been delayed talking to the narrator and so the other monks burst in thinking that some harm has come to him, and suddenly the narrator finds himself back under the tree in the present (August 1837), with his coach having just passed his spot on the road, leaving him stranded in Newcastle for another night.^[12]

Charles Dickens' 1843 book A Christmas Carol is considered by some^[13] to be one of the first depictions of time travel, as the main character, Ebenezer Scrooge, is transported to Christmases past, present and yet to come. These might be considered mere visions rather than actual time travel, though, since Scrooge only viewed each time period passively, unable to interact with them.

A clearer example of time travel is found in the popular 1861 book Paris avant les hommes (Paris before Men) by the French botanist and geologist Pierre Boitard, published posthumously. In this story the main character is transported into the prehistoric past by the magic of a "lame demon" (a French pun on Boitard's name), where he encounters such extinct animals as a Plesiosaur, as well as Boitard's imagined version of an apelike human ancestor, and is able to actively interact with some of them.^[14]

Another clear early example of time travel in fiction is the short story Template:PDFlink by Edward Page Mitchell, which appeared in the New York Sun in 1881.

Mark Twain's A Connecticut Yankee in King Arthur's Court (1889), in which the protagonist finds himself in the time of King Arthur after a fight in which he is hit with a sledge hammer, was another early time travel story which helped bring the concept to a wide audience, and was also one of the first stories to show history being changed by the time traveler's actions.

The first time travel story to feature time travel by means of a time machine was Enrique Gaspar y Rimbau's 1887 book El Anacronópete.^[15] This idea gained popularity with the H. G. Wells story The Time Machine, published in 1895 (preceded by a less influential story of time travel Wells wrote in 1888, titled The Chronic Argonauts), which also featured a time machine and which is often seen as an inspiration for all later science fiction stories featuring time travel, using a vehicle that allows an operator to travel purposefully and selectively. The term "time machine", coined by Wells, is now universally used to refer to such a vehicle.

Since that time, both science and fiction (see Time travel in fiction) have expanded on the concept of time travel.

Theory

Some theories, most notably special and general relativity, suggest that suitable geometries of spacetime, or specific types of motion in space, might allow time travel into the past and future if these geometries or motions are possible.^[16] In technical papers, physicists generally avoid the commonplace language of "moving" or "traveling" through time ("movement" normally refers only to a change in spatial position as the time coordinate is varied), and instead discuss the possibility of closed timelike curves, which are worldlines that form closed loops in spacetime, allowing objects to return to their own past. There are known to be solutions to the equations of general relativity that describe spacetimes which contain closed timelike curves (such as Gödel spacetime), but the physical plausibility of these solutions is uncertain.

Relativity predicts that if one were to move away from the Earth at relativistic velocities and return, more time would have passed on Earth than for the traveler, so in this sense it is accepted that relativity allows "travel into the future" (according to relativity there is no single objective answer to how much time has really passed between the departure and the return, but there is an objective answer to how much proper time has been experienced by both the Earth and the traveler, i.e., how much each has aged; see twin paradox). On the other hand, many in the scientific community believe that backwards time travel is highly unlikely. Any theory that would allow time travel would require that problems of causality be resolved. The classic example of a problem involving causality is the "grandfather paradox": what if one were to go back in time and kill one's own grandfather before one's father was conceived? But some scientists believe that paradoxes can be avoided, either by appealing to the Novikov self-consistency principle or to the notion of branching parallel universes (see the 'Paradoxes' section below).

Tourism in time

Stephen Hawking once suggested that the absence of tourists from the future constitutes an argument against the existence of time travel — a variant of the Fermi paradox. Of course this would not prove that time travel is physically impossible, since it might be that time travel is physically possible but that it is never in fact developed (or is cautiously never used); and even if it is developed, Hawking notes elsewhere that time travel might only be possible in a region of spacetime that is warped in the correct way, and that if we cannot create such a region until the future, then time travelers would not be able to travel back before that date, so "This picture would explain why we haven't been over run by tourists from the future."^[17] Carl Sagan also once suggested the possibility that time travelers could be here, but are disguising their existence or are not recognized as time travelers.^[18]

General relativity

However, the theory of general relativity does suggest a scientific basis for the possibility of backwards time travel in certain unusual scenarios, although arguments from semiclassical gravity suggest that when quantum effects are incorporated into general relativity, these loopholes may be closed.^[19] These semiclassical arguments led Hawking to formulate the chronology protection conjecture, suggesting that the fundamental laws of nature prevent time travel,^[20] but physicists cannot come to a definite judgment on the issue without a theory of quantum gravity to join quantum mechanics and general relativity into a completely unified theory.^[21]

In physics

Time travel to the past is theoretically allowed using the following methods:^[22]

Travelling faster than the speed of light
The use of cosmic strings and black holes
Wormholes and Alcubierre drive

Via faster-than-light (FTL) travel

If one were able to move information or matter from one point to another faster than light, then according to special relativity, there would be some inertial frame of reference in which the signal or object was moving backward in time. This is a consequence of the relativity of simultaneity in special relativity, which says that in some cases different reference frames will disagree on whether two events at different locations happened "at the same time" or not, and they can also disagree on the order of the two events (technically, these disagreements occur when the spacetime interval between the events is 'space-like', meaning that neither event lies in the future light cone of the other).^[23] If one of the two events represents the sending of a signal from one location and the second event represents the reception of the same signal at another location, then as long as the signal is moving at the speed of light or slower, the mathematics of simultaneity ensures that all reference frames agree that the transmission-event happened before the reception-event.^[23]

However, in the case of a hypothetical signal moving faster than light, there would always be some frames in which the signal was received before it was sent, so that the signal could be said to have moved backwards in time. And since one of the two fundamental postulates of special relativity says that the laws of physics should work the same way in every inertial frame, then if it is possible for signals to move backwards in time in any one frame, it must be possible in all frames. This means that if observer A sends a signal to observer B which moves FTL (faster than light) in A's frame but backwards in time in B's frame, and then B sends a reply which moves FTL in B's frame but backwards in time in A's frame, it could work out that A receives the reply before sending the original signal, a clear violation of causality in every frame. An illustration of such a scenario using spacetime diagrams can be found here.^[24] The scenario is sometimes referred to as a tachyonic antitelephone.

According to special relativity, it would take an infinite amount of energy to accelerate a slower-than-light object to the speed of light. Although relativity does not forbid the theoretical possibility of tachyons which move faster than light at all times, when analyzed using quantum field theory, it seems that it would not actually be possible to use them to transmit information faster than light,^[25] and that there is no evidence for their existence.

Special spacetime geometries

The general theory of relativity extends the special theory to cover gravity, illustrating it in terms of curvature in spacetime caused by mass-energy and the flow of momentum. General relativity describes the universe under a system of field equations, and there exist solutions to these equations that permit what are called "closed time-like curves," and hence time travel into the past.^[16] The first of these was proposed by Kurt Gödel, a solution known as the Gödel metric, but his (and many others') example requires the universe to have physical characteristics that it does not appear to have.^[16] Whether general relativity forbids closed time-like curves for all realistic conditions is unknown.

Using wormholes

Wormholes are a hypothetical warped spacetime which are also permitted by the Einstein field equations of general relativity,^[26] although it would be impossible to travel through a wormhole unless it were what is known as a traversable wormhole.

A proposed time-travel machine using a traversable wormhole would (hypothetically) work in the following way: One end of the wormhole is accelerated to some significant fraction of the speed of light, perhaps with some advanced propulsion system, and then brought back to the point of origin. Alternatively, another way is to take one entrance of the wormhole and move it to within the gravitational field of an object that has higher gravity than the other entrance, and then return it to a position near the other entrance. For both of these methods, time dilation causes the end of the wormhole that has been moved to have aged less than the stationary end, as seen by an external observer; however, time connects differently through the wormhole than outside it, so that synchronized clocks at either end of the wormhole will always remain synchronized as seen by an observer passing through the wormhole, no matter how the two ends move around.^[27] This means that an observer entering the accelerated end would exit the stationary end when the stationary end was the same age that the accelerated end had been at the moment before entry; for example, if prior to entering the wormhole the observer noted that a clock at the accelerated end read a date of 2007 while a clock at the stationary end read 2012, then the observer would exit the stationary end when its clock also read 2007, a trip backwards in time as seen by other observers outside. One significant limitation of such a time machine is that it is only possible to go as far back in time as the initial creation of the machine;^[28] in essence, it is more of a path through time than it is a device that itself moves through time, and it would not allow the technology itself to be moved backwards in time. This could provide an alternative explanation for Hawking's observation: a time machine will be built someday, but has not yet been built, so the tourists from the future cannot reach this far back in time.

According to current theories on the nature of wormholes, construction of a traversable wormhole would require the existence of a substance with negative energy (often referred to as "exotic matter") . More technically, the wormhole spacetime requires a distribution of energy that violates various energy conditions, such as the null energy condition along with the weak, strong, and dominant energy conditions.^[29] However, it is known that quantum effects can lead to small measurable violations of the null energy condition,^[29] and many physicists believe that the required negative energy may actually be possible due to the Casimir effect in quantum physics.^[30] Although early calculations suggested a very large amount of negative energy would be required, later calculations showed that the amount of negative energy can be made arbitrarily small.^[31]

In 1993, Matt Visser argued that the two mouths of a wormhole with such an induced clock difference could not be brought together without inducing quantum field and gravitational effects that would either make the wormhole collapse or the two mouths repel each other.^[32] Because of this, the two mouths could not be brought close enough for causality violation to take place. However, in a 1997 paper, Visser hypothesized that a complex "Roman ring" (named after Tom Roman) configuration of an N number of wormholes arranged in a symmetric polygon could still act as a time machine, although he concludes that this is more likely a flaw in classical quantum gravity theory rather than proof that causality violation is possible.^[33]

Other approaches based on general relativity

Another approach involves a dense spinning cylinder usually referred to as a Tipler cylinder, a GR solution discovered by Willem Jacob van Stockum^[34] in 1936 and Kornel Lanczos^[35] in 1924, but not recognized as allowing closed timelike curves^[36] until an analysis by Frank Tipler^[37] in 1974. If a cylinder is infinitely long and spins fast enough about its long axis, then a spaceship flying around the cylinder on a spiral path could travel back in time (or forward, depending on the direction of its spiral). However, the density and speed required is so great that ordinary matter is not strong enough to construct it. A similar device might be built from a cosmic string, but none are known to exist, and it does not seem to be possible to create a new cosmic string.

Physicist Robert Forward noted that a naïve application of general relativity to quantum mechanics suggests another way to build a time machine. A heavy atomic nucleus in a strong magnetic field would elongate into a cylinder, whose density and "spin" are enough to build a time machine. Gamma rays projected at it might allow information (not matter) to be sent back in time; however, he pointed out that until we have a single theory combining relativity and quantum mechanics, we will have no idea whether such speculations are nonsense.^{[citation needed]}

A more fundamental objection to time travel schemes based on rotating cylinders or cosmic strings has been put forward by Stephen Hawking, who proved a theorem showing that according to general relativity it is impossible to build a time machine of a special type (a "time machine with the compactly generated Cauchy horizon") in a region where the weak energy condition is satisfied, meaning that the region contains no matter with negative energy density (exotic matter). Solutions such as Tipler's assume cylinders of infinite length, which are easier to analyze mathematically, and although Tipler suggested that a finite cylinder might produce closed timelike curves if the rotation rate were fast enough,^[38] he did not prove this. But Hawking points out that because of his theorem, "it can't be done with positive energy density everywhere! I can prove that to build a finite time machine, you need negative energy."^[39] This result comes from Hawking's 1992 paper on the chronology protection conjecture, where he examines "the case that the causality violations appear in a finite region of spacetime without curvature singularities" and proves that "[t]here will be a Cauchy horizon that is compactly generated and that in general contains one or more closed null geodesics which will be incomplete. One can define geometrical quantities that measure the Lorentz boost and area increase on going round these closed null geodesics. If the causality violation developed from a noncompact initial surface, the averaged weak energy condition must be violated on the Cauchy horizon."^[40] However, this theorem does not rule out the possibility of time travel 1) by means of time machines with the non-compactly generated Cauchy horizons (such as the Deutsch-Politzer time machine) and 2) in regions which contain exotic matter (which would be necessary for traversable wormholes or the Alcubierre drive). Because the theorem is based on general relativity, it is also conceivable a future theory of quantum gravity which replaced general relativity would allow time travel even without exotic matter (though it is also possible such a theory would place even more restrictions on time travel, or rule it out completely as postulated by Hawking's chronology protection conjecture).

Experiments carried out

Certain experiments carried out give the impression of reversed causality but are interpreted in a different way by the scientific community. For example, in the delayed choice quantum eraser experiment performed by Marlan Scully, pairs of entangled photons are divided into "signal photons" and "idler photons", with the signal photons emerging from one of two locations and their position later measured as in the double slit experiment, and depending on how the idler photon is measured, the experimenter can either learn which of the two locations the signal photon emerged from or "erase" that information. Even though the signal photons can be measured before the choice has been made about the idler photons, the choice seems to retroactively determine whether or not an interference pattern is observed when one correlates measurements of idler photons to the corresponding signal photons. However, since interference can only be observed after the idler photons are measured and they are correlated with the signal photons, there is no way for experimenters to tell what choice will be made in advance just by looking at the signal photons, and under most interpretations of quantum mechanics the results can be explained in a way that does not violate causality.

The experiment of Lijun Wang might also show causality violation since it made it possible to send packages of waves through a bulb of caesium gas in such a way that the package appeared to exit the bulb 62 nanoseconds before its entry. But a wave package is not a single well-defined object but rather a sum of multiple waves of different frequencies (see Fourier analysis), and the package can appear to move faster than light or even backwards in time even if none of the pure waves in the sum do so. This effect cannot be used to send any matter, energy, or information faster than light,^[41] so this experiment is understood not to violate causality either.

The physicists Günter Nimtz and Alfons Stahlhofen, of the University of Koblenz, claim to have violated Einstein's theory of relativity by transmitting photons faster than the speed of light. They say they have conducted an experiment in which microwave photons – energetic packets of light – traveled "instantaneously" between a pair of prisms that had been moved up to 3 ft (0.91 m) apart, using a phenomenon known as quantum tunneling. Nimtz told New Scientist magazine: "For the time being, this is the only violation of special relativity that I know of." However, other physicists say that this phenomenon does not allow information to be transmitted faster than light. Aephraim Steinberg, a quantum optics expert at the University of Toronto, Canada, uses the analogy of a train traveling from Chicago to New York, but dropping off train cars at each station along the way, so that the center of the train moves forward at each stop; in this way, the center of the train exceeds the speed of any of the individual cars.^[42]

Some physicists have performed experiments which attempted to show causality violations, but so far without success. The Space-time Twisting by Light (STL) experiment run by physicist Ronald Mallett attempts to observe a violation of causality when a neutron is passed through a circle made up of a laser whose path has been twisted by passing it through a photonic crystal. Mallett has some physical arguments that suggest that closed timelike curves would become possible through the center of a laser which has been twisted into a loop. However, other physicists dispute his arguments (see objections).

Shengwang Du claims in a peer reviewed journal to have observed single photons' precursors, saying that they travel no faster than c in a vacuum. His experiment involved slow light as well as passing light through a vacuum. He generated two single photons, passing one through rubidium atoms that had been cooled with a laser (thus slowing the light) and passing one through a vacuum. Both times, apparently, the precursors preceded the photons' main bodies, and the precursor traveled at c in a vacuum. According to Du, this implies that there is no possibility of light traveling faster than c (and, thus, violating causality).^[43] (Some members of the media took this as an indication of proof that time travel was impossible.^[44]^[45])

Non-physics-based experiments

Several experiments have been carried out to try to entice future humans, who might invent time travel technology, to come back and demonstrate it to people of the present time. Events such as Perth's Destination Day (2005) or MIT's Time Traveler Convention heavily publicized permanent "advertisements" of a meeting time and place for future time travelers to meet. Back in 1982, a group in Baltimore, MD., identifying itself as the Krononauts, hosted an event of this type welcoming visitors from the future.^[46]^[47] These experiments only stood the possibility of generating a positive result demonstrating the existence of time travel, but have failed so far—no time travelers are known to have attended either event. It is hypothetically possible that future humans have traveled back in time, but have traveled back to the meeting time and place in a parallel universe.^[48] Another factor is that for all the time travel devices considered under current physics (such as those that operate using wormholes), it is impossible to travel back to before the time machine was actually made.^[49]^[50]

Time travel to the future in physics

There are various ways in which a person could "travel into the future" in a limited sense: the person could set things up so that in a small amount of his own subjective time, a large amount of subjective time has passed for other people on Earth. For example, an observer might take a trip away from the Earth and back at relativistic velocities, with the trip only lasting a few years according to the observer's own clocks, and return to find that thousands of years had passed on Earth. It should be noted, though, that according to relativity there is no objective answer to the question of how much time "really" passed during the trip; it would be equally valid to say that the trip had lasted only a few years or that the trip had lasted thousands of years, depending on your choice of reference frame.

This form of "travel into the future" is theoretically allowed (and has been demonstrated at very small time scales) using the following methods:^[22]

Using velocity-based time dilation under the theory of special relativity, for instance:
- Traveling at almost the speed of light to a distant star, then slowing down, turning around, and traveling at almost the speed of light back to Earth^[51] (see the Twin paradox)
Using gravitational time dilation under the theory of general relativity, for instance:
- Residing inside of a hollow, high-mass object;
- Residing just outside of the event horizon of a black hole, or sufficiently near an object whose mass or density causes the gravitational time dilation near it to be larger than the time dilation factor on Earth.

Additionally, it might be possible to see the distant future of the Earth using methods which do not involve relativity at all, although it is even more debatable whether these should be deemed a form of "time travel":

Time dilation

Time dilation is permitted by Albert Einstein's special and general theories of relativity. These theories state that, relative to a given observer, time passes more slowly for bodies moving quickly relative to that observer, or bodies that are deeper within a gravity well.^[52] For example, a clock which is moving relative to the observer will be measured to run slow in that observer's rest frame; as a clock approaches the speed of light it will almost slow to a stop, although it can never quite reach light speed so it will never completely stop. For two clocks moving inertially (not accelerating) relative to one another, this effect is reciprocal, with each clock measuring the other to be ticking slower. However, the symmetry is broken if one clock accelerates, as in the twin paradox where one twin stays on Earth while the other travels into space, turns around (which involves acceleration), and returns—in this case both agree the traveling twin has aged less. General relativity states that time dilation effects also occur if one clock is deeper in a gravity well than the other, with the clock deeper in the well ticking more slowly; this effect must be taken into account when calibrating the clocks on the satellites of the Global Positioning System, and it could lead to significant differences in rates of aging for observers at different distances from a black hole.

It has been calculated that, under general relativity, a person could travel forward in time at a rate four times that of distant observers by residing inside a spherical shell with a diameter of 5 meters and the mass of Jupiter.^[22] For such a person, every one second of their "personal" time would correspond to four seconds for distant observers. Of course, squeezing the mass of a large planet into such a structure is not expected to be within our technological capabilities in the near future.

There is a great deal of experimental evidence supporting the validity of equations for velocity-based time dilation in special relativity^[53] and gravitational time dilation in general relativity.^[54]^[55]^[56] However, with current technologies it is only possible to cause a human traveller to age less than companions on Earth by a very small fraction of a second, the current record being about 20 milliseconds for the cosmonaut Sergei Avdeyev.

Time perception

Time perception can be apparently sped up for living organisms through hibernation, where the body temperature and metabolic rate of the creature is reduced. A more extreme version of this is suspended animation, where the rates of chemical processes in the subject would be severely reduced.

Time dilation and suspended animation only allow "travel" to the future, never the past, so they do not violate causality, and it's debatable whether they should be called time travel. However time dilation can be viewed as a better fit for our understanding of the term "time travel" than suspended animation, since with time dilation less time actually does pass for the traveler than for those who remain behind, so the traveler can be said to have reached the future faster than others, whereas with suspended animation this is not the case.

Other ideas from mainstream physics

Paradoxes

The Novikov self-consistency principle and calculations by Kip S. Thorne^{[citation needed]} indicate that simple masses passing through time travel wormholes could never engender paradoxes—there are no initial conditions that lead to paradox once time travel is introduced. If his results can be generalized, they would suggest, curiously, that none of the supposed paradoxes formulated in time travel stories can actually be formulated at a precise physical level: that is, that any situation you can set up in a time travel story turns out to permit many consistent solutions. The circumstances might, however, turn out to be almost unbelievably strange.^{[citation needed]}

Parallel universes might provide a way out of paradoxes. Everett's many-worlds interpretation (MWI) of quantum mechanics suggests that all possible quantum events can occur in mutually exclusive histories.^[57] These alternate, or parallel, histories would form a branching tree symbolizing all possible outcomes of any interaction. If all possibilities exist, any paradoxes could be explained by having the paradoxical events happening in a different universe. This concept is most often used in science-fiction, but some physicists such as David Deutsch have suggested that if time travel is possible and the MWI is correct, then a time traveler should indeed end up in a different history than the one he started from.^[1]^[58] On the other hand, Stephen Hawking has argued 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 own world rather than traveling to a different one.^[17] And the physicist Allen Everett argued that Deutsch's approach "involves modifying fundamental principles of quantum mechanics; it certainly goes beyond simply adopting the MWI." Everett also argues 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 through a wormhole, with different particles emerging in different worlds.^[59]

Daniel Greenberger and Karl Svozil proposed that quantum theory gives a model for time travel without paradoxes.^[60]^[61] In quantum theory observation causes possible states to 'collapse' into one measured state; hence, the past observed from the present is deterministic (it has only one possible state), but the present observed from the past has many possible states until our actions cause it to collapse into one state. Our actions will then be seen to have been inevitable.

Using quantum entanglement

Quantum-mechanical phenomena such as quantum teleportation, the EPR paradox, or quantum entanglement might appear to create a mechanism that allows for faster-than-light (FTL) communication or time travel, and in fact some interpretations of quantum mechanics such as the Bohm interpretation presume that some information is being exchanged between particles instantaneously in order to maintain correlations between particles.^[62] This effect was referred to as "spooky action at a distance" by Einstein.

Nevertheless, the fact that causality is preserved in quantum mechanics is a rigorous result in modern quantum field theories, and therefore modern theories do not allow for time travel or FTL communication. In any specific instance where FTL has been claimed, more detailed analysis has proven that to get a signal, some form of classical communication must also be used.^[63] The no-communication theorem also gives a general proof that quantum entanglement cannot be used to transmit information faster than classical signals. The fact that these quantum phenomena apparently do not allow FTL time travel is often overlooked in popular press coverage of quantum teleportation experiments.^{[citation needed]} How the rules of quantum mechanics work to preserve causality is an active area of research.^{[citation needed]}

Philosophical understandings of time travel

Theories of time travel are riddled with questions about causality and paradoxes. Compared to other fundamental concepts in modern physics, time is still not understood very well. Philosophers have been theorizing about the nature of time since the era of the ancient Greek philosophers and earlier. Some philosophers and physicists who study the nature of time also study the possibility of time travel and its logical implications. The probability of paradoxes and their possible solutions are often considered.

For more information on the philosophical considerations of time travel, consult the work of David Lewis or Ted Sider. For more information on physics-related theories of time travel, consider the work of Kurt Gödel (especially his theorized universe) and Lawrence Sklar.

Presentism vs. eternalism

The relativity of simultaneity in modern physics favors the philosophical view known as eternalism or four-dimensionalism (Sider, 2001), in which physical objects are either temporally extended space-time worms, or space-time worm stages, and this view would be favored further by the possibility of time travel (Sider, 2001). Eternalism, also sometimes known as "block universe theory", builds on a standard method of modeling time as a dimension in physics, to give time a similar ontology to that of space (Sider, 2001). This would mean that time is just another dimension, that future events are "already there", and that there is no objective flow of time. This view is disputed by Tim Maudlin in his The Metaphysics Within Physics.

Presentism is a school of philosophy that holds that neither the future nor the past exist, and there are no non-present objects. In this view, time travel is impossible because there is no future or past to travel to. However, some 21st century presentists have argued that although past and future objects do not exist, there can still be definite truths about past and future events, and thus it is possible that a future truth about a time traveler deciding to travel back to the present date could explain the time traveler's actual appearance in the present.^[64]^[65]

The grandfather paradox

One subject often brought up in philosophical discussion of time is the idea that, if one were to go back in time, paradoxes could ensue if the time traveler were to change things. The best examples of this are the grandfather paradox and the idea of autoinfanticide. The grandfather paradox is a hypothetical situation in which a time traveler goes back in time and attempts to kill his grandfather at a time before his grandfather met his grandmother. If he did so, then his mother or father never would have been born, and neither would the time traveler himself, in which case the time traveler never would have gone back in time to kill his grandfather.

Autoinfanticide works the same way, where a traveler goes back and attempts to kill himself as an infant. If he were to do so, he never would have grown up to go back in time to kill himself as an infant.

This discussion is important to the philosophy of time travel because philosophers question whether these paradoxes make time travel impossible. Some philosophers answer the paradoxes by arguing that it might be the case that backwards time travel could be possible but that it would be impossible to actually change the past in any way,^[66] an idea similar to the proposed Novikov self-consistency principle in physics.

Theory of compossibility

David Lewis's analysis of compossibility and the implications of changing the past is meant to account for the possibilities of time travel in a one-dimensional conception of time without creating logical paradoxes. Consider Lewis’ example of Tim. Tim hates his grandfather and would like nothing more than to kill him. The only problem for Tim is that his grandfather died years ago. Tim wants so badly to kill his grandfather himself that he constructs a time machine to travel back to 1955 when his grandfather was young and kill him then. Assuming that Tim can travel to a time when his grandfather is still alive, the question must then be raised; Can Tim kill his grandfather?

For Lewis, the answer lies within the context of the usage of the word "can". Lewis explains that the word "can" must be viewed against the context of pertinent facts relating to the situation. Suppose that Tim has a rifle, years of rifle training, a straight shot on a clear day and no outside force to restrain Tim’s trigger finger. Can Tim shoot his grandfather? Considering these facts, it would appear that Tim can in fact kill his grandfather. In other words, all of the contextual facts are compossible with Tim killing his grandfather. However, when reflecting on the compossibility of a given situation, we must gather the most inclusive set of facts that we are able to.

Consider now the fact that Tim’s grandfather died in 1993 and not in 1955. This new fact about Tim’s situation reveals that him killing his grandfather is not compossible with the current set of facts. Tim cannot kill his grandfather because his grandfather died in 1993 and not when he was young. Thus, Lewis concludes, the statements "Tim doesn’t but can, because he has what it takes," and, "Tim doesn’t, and can’t, because it is logically impossible to change the past," are not contradictions; they are both true given the relevant set of facts. The usage of the word "can" is equivocal: he "can" and "can not" under different relevant facts. So what must happen to Tim as he takes aim? Lewis believes that his gun will jam, a bird will fly in the way, or Tim simply slips on a banana peel. Either way, there will be some logical force of the universe that will prevent Tim every time from killing his grandfather.^[67]

Ideas from fiction

Rules of time travel

Time travel themes in science fiction and the media can generally be grouped into two general categories (based on effect—methods are extremely varied and numerous), each of which can be further subdivided.^[68]^[69]^[70]^[71] However, there are no formal names for these two categories, so concepts rather than formal names will be used with notes regarding what categories they are placed under (Note: These classifications do not address the method of time travel itself, i.e. how to travel through time, but instead call to attention differing rules of what happens to history.). As used in this section, timeline refers to all physical events in history, so that in time travel stories where events can be changed, the time traveler can create a new or altered timeline. This usage of "timeline" is fairly common in time travel fiction, and is distinct from the usage of "timeline" to refer to a type of chart created by humans to illustrate a particular series of events (see timeline). This concept is also distinct from the concept of a world line, a term from Einstein's theory of relativity which refers to the entire history of a single object (usually idealized as a point particle) that forms a distinct path through through 4-dimensional spacetime.

1. There is a single fixed history, which is self-consistent and unchangeable. In this version, everything happens on a single timeline which does not contradict itself and cannot interact with anything potentially existing outside of it.

A man travelling a few seconds into the past in a single self-consistent timeline. This scenario raises questions about free will, since once the traveller has decided to enter the time machine, then as soon as his own double appears, there is absolutely no way for him to change his mind.

1.1 This can be simply achieved by applying the Novikov self-consistency principle, named after Dr. Igor Dmitrievich Novikov, Professor of Astrophysics at Copenhagen University. The principle states that the timeline is totally fixed, and any actions taken by a time traveler were part of history all along, so it is impossible for the time traveler to "change" history in any way. The time traveler's actions may be the cause of events in their own past though, which leads to the potential for circular causation and the predestination paradox; for examples of circular causation, see Robert A. Heinlein's story "By His Bootstraps". The Novikov self-consistency principle proposes that the local laws of physics in a region of spacetime containing time travelers cannot be any different from the local laws of physics in any other region of spacetime.^[72]

1.2 Alternatively, new physical laws take effect regarding time travel that thwarts attempts to change the past (contradicting the assumption mentioned in 1.1 above that the laws that apply to time travelers are the same ones that apply to everyone else). These new physical laws can be as unsubtle as to reject time travelers who travel to the past to change it by pulling them back to the point from when they came as Michael Moorcock's The Dancers at the End of Time or where the traveler is rendered a noncorporeal phantom unable to physically interact with the past such as in some Pre-Crisis Superman stories and Michael Garrett's "Brief Encounter" in Twilight Zone Magazine May 1981.

2. History is flexible and is subject to change (Plastic Time)

2.1 Changes to history are easy and can impact the traveler, the world, or both

Examples include Doctor Who and the Back to the Future trilogy. In some cases, any resulting paradoxes can be devastating, threatening the very existence of the universe. In other cases the traveler simply cannot return home. The extreme version of this (Chaotic Time) is that history is very sensitive to changes with even small changes having large impacts such as in Ray Bradbury's "A Sound of Thunder".

2.2 History is change resistant in direct relationship to the importance of the event ie. small trivial events can be readily changed but large ones take great effort.

In the Twilight Zone episode "Back There" a traveler tries to prevent the assassination of President Lincoln and fails, but his actions have made subtle changes to the status quo in his own time (e.g. a man who had been the butler of his gentleman's club is now a rich tycoon).

In the 2002 remake of The Time Machine, it is explained via a vision why Hartdegen could not save his sweetheart Emma—doing so would have resulted in his never developing the time machine he used to try and save her.

In The Saga of Darren Shan, major events in the past cannot be changed, but their details can alter while providing the same outcome. Under this model, if a time traveler were to go back in time and kill Hitler, another Nazi would simply take his place and commit his same actions, leaving the broader course of history unchanged.

In the Doctor Who episode The Waters of Mars, Captain Adelaide Brooke's death on Mars is the most singular catalyst of human travel outside the solar system. At first, the Doctor realizes her death is a "fixed point in time" and does not intervene, but later defies this rule and transports her and her crew to Earth. Rather than allow human history to change, Captain Brooke commits suicide on Earth, leaving history mostly unchanged.

Time travel under the parallel universe hypothesis. This scenario has the potential to preserve free will, but breaks symmetry between universes.

3. Alternate timelines. In this version of time travel, there are multiple coexisting alternate histories, so that when the traveler goes back in time, he/she ends up in a new timeline where historical events can differ from the timeline he/she came from, but her original timeline does not cease to exist (this means the grandfather paradox can be avoided since even if the time traveler's grandfather is killed at a young age in the new timeline, he still survived to have children in the original timeline, so there is still a causal explanation for the traveler's existence). Time travel may actually create a new timeline that diverges from the original timeline at the moment the time traveler appears in the past, or the traveler may arrive in an already existing parallel universe (though unless the parallel universe's history was identical to the time traveler's history up until the point where the time traveler appeared, it is questionable whether the latter version qualifies as 'time travel').

James P. Hogan's The Proteus Operation fully explains parallel universe time travel in chapter 20 where it has Einstein explaining that all the outcomes already exist and all time travel does is change which already existing branch you will experience.

Though Star Trek has a long tradition of using the 2.1 mechanic, as seen in "The City on the Edge of Forever", "Tomorrow is Yesterday", "Time and Again", "Future's End", "Before and After", "Endgame" and as late as Enterprise's Temporal Cold War, "Parallels" had an example of what Data called "quantum realities." His exact words on the matter were "But there is a theory in quantum physics that all possibilities that can happen do happen in alternate quantum realities," suggesting the writers were thinking of the many-worlds interpretation of quantum mechanics.

Michael Crichton's novel Timeline takes the approach that all time travel really is travel to an already existing parallel universe where time passes at a slower rate than our own but actions in any of these parallel universes may have already occurred in our past. It is unclear from the novel if any sizable change in events of these parallel universe can be made.

In the Homeline setting of GURPS Infinite Worlds there are echos—parallel universes at an early part of Homeline's history but changes to their history do not affect Homeline's history. However tampering with their history can cause them to shift quanta making access harder if not impossible.

A type of story which could be placed in this category is one where the alternative version of the past lies not in some other dimension, but simply at a distant location in space or a future period of time that replicates conditions in the traveler's past. For example, in a Futurama episode called The Late Philip J. Fry, the professor designed a forward-only time travel device. Trapped in the future, he and two colleagues travel forward all the way to the end of the universe, at which point they witness a new Big Bang which gives rise to a new universe whose history mirrors their own history. Then they continue to go forward until they reach the exact time of their initial departure. Although this journey is not exactly a backward time travel, the final result is the same.

In the Japanese manga, Dragon Ball Z, the character Trunks travels back in time to warn the characters of their deaths soon to come. This does not change his time line, only creates a new one in which they do not die. Soon two of the characters destroy the lab where the monster Cell is being created, stopping him from absorbing the androids, creating a third time line. Later it is revealed that Trunks is killed by Cell in the future, then travels to three years before any of the events occurs, which creates a fourth time line. No matter what any character does in the past, their own original time line is unchanged.

Immutable timelines

Time travel in a type 1 universe does not allow paradoxes such as the grandfather paradox to occur, where one deduces both a conclusion and its opposite (in the case of the grandfather paradox, one can start with the premise of the time traveler killing his grandfather, and reach the conclusion that the time traveler will not be able to kill his grandfather since he was never born) though it can allow other paradoxes to occur.

In 1.1, the Novikov self-consistency principle asserts that the existence of a method of time travel constrains events to remain self-consistent. This will cause any attempt to violate such consistency to fail, even if seemingly extremely improbable events are required.

Example: You have a device that can send a single bit of information back to itself at a precise moment in time. You receive a bit at 10:00:00 p.m., then no bits for thirty seconds after that. If you send a bit back to 10:00:00 p.m., everything works fine. However, if you try to send a bit to 10:00:15 p.m. (a time at which no bit was received), your transmitter will mysteriously fail. Or your dog will distract you for fifteen seconds. Or your transmitter will appear to work, but as it turns out your receiver failed at exactly 10:00:15 p.m., etc. Examples of this kind of universe are found in Robert Forward's novel Timemaster, the Twilight Zone episode "No Time Like the Past", and the 1980 Jeannot Szwarc film Somewhere In Time (based on Richard Matheson's novel Bid Time Return).

In 1.2, time travel is constrained to prevent paradox. How this occurs is dependent on whether interaction with the past is possible.

If interaction with the past is possible and one attempts to make a paradox, one undergoes involuntary or uncontrolled time travel. In the time-travel stories of Connie Willis, time travelers encounter "slippage" which prevents them from either reaching the intended time or translates them a sufficient distance from their destination at the intended time, as to prevent any paradox from occurring.

Example: A man who travels into the past with intentions to kill Hitler finds himself on a Montana farm in late April 1945.

In the The Dancers at the End of Time series, Michael Moorcock invented a plot device called the Morphail Effect. This causes a time traveler to be ejected from the time in which he or she is about to cause a paradox.

Example 1: a man from the End of Time period travels to the past and is executed. Instead of dying (which would cause a paradox), he experiences a return to the End of Time

Example 2: time travelers sometimes visit the End of Time from their own epochs in the past. Those that attempt to return to their own period are likely to reappear inadvertently at the End of Time.

The general consequences are that time travel to the traveler's past is difficult, and many time travelers find themselves adventuring deeper and deeper into their future.

If interaction with the past is not possible then the traveler simply becomes an invisible insubstantial phantom unable to interact with the past as in the case of James Harrigan in Michael Garrett's "Brief Encounter".

While a Type 1 universe will prevent a grandfather paradox it doesn't prevent paradoxes in other aspects of physics such as the predestination paradox and the ontological paradox (GURPS Infinite Worlds calls this "Free Lunch Paradox").

The predestination paradox is where the traveler's actions create some type of causal loop, in which some event A in the future helps cause event B in the past via time travel, and the event B in turn is one of the causes of A. For instance, a time traveler might go back to investigate a specific historical event like the Great Fire of London, and their actions in the past could then inadvertently end up being the original cause of that very event.

Examples of this kind of causal loop are found in Robert Forward's novel Timemaster, the Twilight Zone episode "No Time Like the Past", EC Comics stories like "Man who was Killed in Time" (Weird Science #5), "Why Papa Left Home" (Weird Science #11), "Only Time will Tell" (Weird Fantasy #1), "The Connection" (Weird Fantasy #9), "Skeleton Key" (Weird Fantasy #16), and "Counter Clockwise" (Weird Fantasy #18), the 1980 Jeannot Szwarc film Somewhere In Time (based on Richard Matheson's novel Bid Time Return), the Michael Moorcock novel Behold the Man, and Harry Potter and the Prisoner of Azkaban. It is also featured in 1972's Doctor Who, in the three part The Day of the Daleks, where three freedom fighters from the future attempt to kill a British diplomat they believe responsible for World War Three, and the subsequent easy conquest of Earth by the Daleks. In the future they were taught an explosion at the diplomat's (Sir Reginald Styles) mansion with foreign delegates inside caused the nations of the world to attack each other. The Doctor (Jon Pertwee), figures out that they caused the explosion all along by way of a temporal paradox.

In the 2006 crime thriller Déjà Vu there appears to be causal loops, as Agent Doug Carlin decides to send a message back in time to save his partner's life, but this will eventually cause his death. Later in the movie, tough, Carlin is able to change events and create an alternate reality. This apparent paradox can be explained by multiple previous unseen time travels in a type 3 universe.

In the videogame Escape from Monkey Island there's a section in which the player, controlling Guybrush Threepwood, gets some items from his future self in the Swamp of Time. Soon after that, he will become the future Guybrush and will have to give the items to his past self in the same order. This is an example of causal loop because those items were created purely from the time travel. Anyway if the player doesn't repeat every action properly, will cause a paradox that sends Guybrush back to the entrance of the swamp, implying a type 1.2 universe.

File:Time-travel-causal-loop.gif

A version of the ontological paradox. The appearance of the traveler is the result of his disappearance a few seconds later. In this scenario, the traveler is traveling along a closed timelike curve.

The Novikov self-consistency principle can also result in an ontological paradox (also known as the knowledge or information paradox)^[73] where the very existence of some object or information is a time loop. GURPS Infinite Worlds gives the example (from The Eyre Affair) of a time traveler going to Shakespeare's time with a book of all his works. Shakespeare pressed for time simply copies the information in the book from the future. The paradox is that nobody actually writes the plays.

The philosopher Kelley L. Ross argues in "Time Travel Paradoxes"^[74] that in an ontological paradox scenario involving a physical object, there can be a violation of the second law of thermodynamics. Ross uses Somewhere in Time as an example where Jane Seymour's character gives Christopher Reeve's character a watch she has owned for many years, and when he travels back in time he gives the same watch to Jane Seymour's character 60 years in the past. As Ross states

"The watch is an impossible object. It violates the Second Law of Thermodynamics, the Law of Entropy. If time travel makes that watch possible, then time travel itself is impossible. The watch, indeed, must be absolutely identical to itself in the 19th and 20th centuries, since Reeve carries it with him from the future instantaneously into the past and bestows it on Seymour. The watch, however, cannot be identical to itself, since all the years in which it is in the possession of Seymour and then Reeve it will wear in the normal manner. It's [sic] entropy will increase. The watch carried back by Reeve will be more worn that [sic] the watch that would have been acquired by Seymour."

On the other hand, the second law of thermodynamics is understood by modern physicists to be a statistical law rather than an absolute one, so spontaneous reversals of entropy or failure to increase in entropy are not impossible, just improbable (see for example the fluctuation theorem). In addition, the second law of thermodynamics only states that entropy should increase in systems which are isolated from interactions with the external world, so Igor Novikov (creator of the Novikov self-consistency principle) has argued that in the case of macroscopic objects like the watch whose worldlines form closed loops, the outside world can expend energy to repair wear/entropy that the object acquires over the course of its history, so that it will be back in its original condition when it closes the loop.^[75]

Mutable timelines

Time travel in a Type 2 universe is much more complex. The biggest problem is how to explain changes in the past. One method of explanation is that once the past changes, so do the memories of all observers. This would mean that no observer would ever observe the changing of the past (because they will not remember changing the past). This would make it hard to tell whether you are in a Type 1 universe or a Type 2 universe. You could, however, infer such information by knowing if a) communication with the past were possible or b) it appeared that the time line had never been changed as a result of an action someone remembers taking, although evidence exists that other people are changing their time lines fairly often.

An example of this kind of universe is presented in Thrice Upon a Time, a novel by James P. Hogan. The Back to the Future trilogy films also seem to feature a single mutable timeline (see the "Back to the Future FAQ" for details on how the writers imagined time travel worked in the movies' world). By contrast, the short story "Brooklyn Project" by William Tenn provides a sketch of life in a Type 2 world where no one even notices as the timeline changes repeatedly.

In type 2.1, attempts are being made at changing the timeline, however, all that is accomplished in the first tries is that the method in which decisive events occur is changed; final conclusions in the bigger scheme cannot be brought to a different outcome.

As an example, the movie Déjà Vu depicts a paper note sent to the past with vital information to prevent a terrorist attack. However, the vital information results in the killing of an ATF agent, but does not prevent the terrorist attack; the very same agent died in the previous version of the timeline as well, albeit under different circumstances. Finally, the timeline is changed by sending a human into the past, arguably a "stronger" measure than simply sending back a paper note, which results in preventing both a murder and the terrorist attack. As in the Back to the Future movie trilogy, there seems to be a ripple effect too as changes from the past "propagate" into the present, and people in the present have altered memory of events that occurred after the changes made to the timeline.

The science fiction writer Larry Niven suggests in his essay "The Theory and Practice of Time Travel" that in a type 2.1 universe, the most efficient way for the universe to "correct" a change is for time travel to never be discovered, and that in a type 2.2 universe, the very large (or infinite) number of time travelers from the endless future will cause the timeline to change wildly until it reaches a history in which time travel is never discovered. However, many other "stable" situations might also exist in which time travel occurs but no paradoxes are created; if the changeable-timeline universe finds itself in such a state no further changes will occur, and to the inhabitants of the universe it will appear identical to the type 1.1 scenario.^{[citation needed]} This is sometimes referred to as the "Time Dilution Effect".

Few if any physicists or philosophers have taken seriously the possibility of "changing" the past except in the case of multiple universes, and in fact many have argued that this idea is logically incoherent,^[66] so the mutable timeline idea is rarely considered outside of science fiction.

Also, deciding whether a given universe is of Type 2.1 or 2.2 can not be done objectively, as the categorization of timeline-invasive measures as "strong" or "weak" is arbitrary, and up to interpretation: An observer can disagree about a measure being "weak", and might, in the lack of context, argue instead that simply a mishap occurred which then led to no effective change.

An example would be the paper note sent back to the past in the film Déjà Vu, as described above. Was it a "too weak" change, or was it just a local-time alteration which had no extended effect on the larger timeline? As the universe in Déjà Vu seems not entirely immune to paradoxes (some arguably minute paradoxes do occur), both versions seem to be equally possible.

Alternate histories

In Type 3, any event that appears to have caused a paradox has instead created a new time line. The old time line remains unchanged, with the time traveler or information sent simply having vanished, never to return. A difficulty with this explanation, however, is that conservation of mass-energy would be violated for the origin timeline and the destination timeline. A possible solution to this is to have the mechanics of time travel require that mass-energy be exchanged in precise balance between past and future at the moment of travel, or to simply expand the scope of the conservation law to encompass all timelines.^{[citation needed]} Some examples of this kind of time travel can be found in David Gerrold's book The Man Who Folded Himself and The Time Ships by Stephen Baxter, plus several episodes^[which?] of the TV show Star Trek: The Next Generation^{[citation needed]} and the android saga in the Japanese TV series Dragon Ball Z^{[citation needed]}.

Gradual and instantaneous

In literature, there are two methods of time travel:

File:Time-travel-continuous-version.gif

A gradual time travel, as in the movie Primer. When the time machine is red, everything inside is going through time at normal rate, but backwards. During entry/exit it seems there would have to be fusion/separation between the forward and reversed versions of the traveler.

The most commonly used method of time travel in science fiction is the instantaneous movement from one point in time to another, like using the controls on a CD player to skip to a previous or next song, though in most cases, there is a machine of some sort, and some energy expended in order to make this happen (like the time-traveling De Lorean in Back to the Future or the TARDIS (Time and Relative Dimension in Space) that traveled through time in Doctor Who). In some cases, there is not even the beginning of a scientific explanation for this kind of time travel; it's popular probably because it is more spectacular and makes time travel easier. The "Universal Remote" used by Adam Sandler in the movie Click works in the same manner, although only in one direction, the future. While his character Michael Newman can travel back to a previous point it is merely a playback with which he cannot interact.
In The Time Machine, H.G. Wells explains that we are moving through time with a constant speed. Time travel then is, in Wells' words, "stopping or accelerating one's drift along the time-dimension, or even turning about and traveling the other way." George Pal, director of the 1960 adaptation based on Wells's classic, accordingly chose to depict time travel by employing time-lapse photography. To expand on the audio playback analogy used above, this would be like rewinding or fast forwarding an analogue audio cassette and playing the tape at a chosen point. Perhaps the oldest example of this method of time travel is in Lewis Carroll's Through the Looking-Glass (1871): the White Queen is living backwards, hence her memory is working both ways. Her kind of time travel is uncontrolled: she moves through time with a constant speed of −1 and she cannot change it. T.H. White, in the first part of his Arthurian novel The Once and Future King, The Sword in the Stone (1938) used the same idea: the wizard Merlyn lives backward in time, because he was born "at the wrong end of time" and has to live backwards from the front. "Some people call it having second sight", he says. This method of gradual time travel is not as popular in modern science fiction, though a form of it does occur in the film Primer.

Time travel or space-time travel

An objection that is sometimes raised against the concept of time machines in science fiction is that they ignore the motion of the Earth between the date the time machine departs and the date it returns. The idea that a traveler can go into a machine that sends him or her to 1865 and step out into the exact same spot on Earth might be said to ignore the issue that Earth is moving through space around the Sun, which is moving in the galaxy, and so on, so that advocates of this argument imagine that "realistically" the time machine should actually reappear in space far away from the Earth's position at that date. However, the theory of relativity rejects the idea of absolute time and space; in relativity there can be no universal truth about the spatial distance between events which occur at different times^[76] (such as an event on Earth today and an event on Earth in 1865), and thus no objective truth about which point in space at one time is at the "same position" that the Earth was at another time. In the theory of special relativity, which deals with situations where gravity is negligible, the laws of physics work the same way in every inertial frame of reference and therefore no frame's perspective is physically better than any other frame's, and different frames disagree about whether two events at different times happened at the "same position" or "different positions". In the theory of general relativity, which incorporates the effects of gravity, all coordinate systems are on equal footing because of a feature known as "diffeomorphism invariance".^[77]

Nevertheless, the idea that the Earth moves away from the time traveler when he takes a trip through time has been used in a few science fiction stories, such as the 2000 AD comic Strontium Dog, in which Johnny Alpha uses "Time Bombs" to propel an enemy several seconds into the future, during which time the movement of the Earth causes the unfortunate victim to re-appear in space. Much earlier, Clark Ashton Smith used this form of time travel in several stories such as "The Letter from Mohaun Los" (1932) where the protagonist ends up on a planet millions of years in the future which "happened to occupy the same space through which Earth had passed". Other science fiction stories try to anticipate this objection and offer a rationale for the fact that the traveler remains on Earth, such as the 1957 Robert Heinlein novel The Door into Summer where Heinlein essentially handwaved the issue with a single sentence: "You stay on the world line you were on." In his 1980 novel The Number of the Beast a "continua device" allows the protagonists to dial in the coordinates of space and time and it instantly moves them there—without explaining how such a device might work.

The television series Seven Days also dealt with this problem; when the chrononaut would be 'rewinding', he would also be propelling himself backwards around the Earth's orbit, with the intention of landing at some chosen spatial location, though seldom hitting the mark precisely.^{[citation needed]} In Piers Anthony's Bearing an Hourglass, the potent Hourglass of the Incarnation of Time naturally moves the Incarnation in space according to the numerous movements of the globe through the solar system, the solar system through the galaxy, etc.; but by carefully negating some of the movements he can also travel in space within the limits of the planet. The television series Doctor Who avoided this issue by establishing early on in the series that the Doctor's TARDIS is able to move about in space in addition to traveling in time.

Notes

^ ^a ^b Deutsch, David (1991). "Quantum mechanics near closed timelike curves". Physical Review D. 44 (10): 3197–3217. Bibcode:1991PhRvD..44.3197D. doi:10.1103/PhysRevD.44.3197.
^ Revati, Encyclopedia for Epics of Ancient India
^ Lord Balarama, Sri Mayapur
^ ^a ^b Yorke, Christopher (February 2006). "Malchronia: Cryonics and Bionics as Primitive Weapons in the War on Time". Journal of Evolution and Technology. 15 (1): 73–85. Retrieved 2009-08-29.
^ Rosenberg, Donna (1997). Folklore, myths, and legends: a world perspective. McGraw-Hill. p. 421. ISBN 084425780X.
^ "Choni HaMe'agel". Jewish search. Retrieved November 6, 2009.
^ Robert Darnton, The Forbidden Best-Sellers of Pre-Revolutionary France (New York: W.W. Norton, 1996), 120.
^ ^a ^b Alkon, Paul K. (1987). Origins of Futuristic Fiction. The University of Georgia Press. pp. 95–96. ISBN 0-8203-0932-X.
^ Alkon, Paul K. (1987). Origins of Futuristic Fiction. The University of Georgia Press. p. 85. ISBN 0-8203-0932-X.
^ Yury Akutin, Александр Вельтман и его роман "Странник" (A.V. and his novel Strannik), 1978 (in Russian).
^ Derleth, August (1951). Far Boundaries. Pellegrini & Cudahy. p. 3.
^ Derleth, August (1951). Far Boundaries. Pellegrini & Cudahy. pp. 11–38.
^ Flynn, John L. "Time Travel Literature". Archived from the original on 2006-09-29. Retrieved 2006-10-28.
^ Rudwick, Martin J. S. (1992). Scenes From Deep Time. The University of Chicago Press. pp. 166–169. ISBN 0-226-73105-7.
^ Uribe, Augusto (June 1999). "The First Time Machine: Enrique Gaspar's Anacronópete". The New York Review of Science Fiction. 11, no. 10 (130): 12.
^ ^a ^b ^c Thorne, Kip S. (1994). Black Holes and Time Warps. W. W. Norton. p. 499. ISBN 0-393-31276-3. Cite error: The named reference "Thorne1" was defined multiple times with different content (see the help page).
^ ^a ^b Hawking, Steven. "Space and Time Warps". Retrieved 2010-09-06.
^ "NOVA Online – Sagan on Time Travel". Pbs.org. Retrieved 2010-05-25.
^ Matt Visser (2002). "The quantum physics of chronology protection". arXiv:gr-qc/0204022. {{cite arXiv}}: |class= ignored (help)
^ Hawking, Stephen (1992). "Chronology protection conjecture". Physical Review D. 46 (2): 603. Bibcode:1992PhRvD..46..603H. doi:10.1103/PhysRevD.46.603.
^ Hawking, Stephen (2002). The Future of Spacetime. W. W. Norton. p. 150. ISBN 0-393-02022-3. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
^ ^a ^b ^c Gott, J. Richard (2002). "Time Travel in Einstein's Universe". {{cite journal}}: Cite journal requires |journal= (help) p.33-130 Cite error: The named reference "Gott" was defined multiple times with different content (see the help page).
^ ^a ^b Jarrell, Mark. "The Special Theory of Relativity" (PDF). pp. 7–11. Archived from the original (PDF) on 2006-09-13. Retrieved 2006-10-27.
^ "Sharp Blue: Relativity, FTL and causality – Richard Baker". Theculture.org. Retrieved 2010-05-25.
^ Chase, Scott I. "Tachyons entry from Usenet Physics FAQ". Retrieved 2006-10-27.
^ Visser, Matt (1996). Lorentzian Wormholes. Springer-Verlag. p. 100. ISBN 1-56396-653-0.
^ Thorne, Kip S. (1994). Black Holes and Time Warps. W. W. Norton. p. 502. ISBN 0-393-31276-3.
^ Thorne, Kip S. (1994). Black Holes and Time Warps. W. W. Norton. p. 504. ISBN 0-393-31276-3.
^ ^a ^b Visser, Matt (1996). Lorentzian Wormholes. Springer-Verlag. p. 101. ISBN 1-56396-653-0.
^ Cramer, John G. "NASA Goes FTL Part 1: Wormhole Physics". Archived from the original on 2006-06-27. Retrieved 2006-12-02.
^ Visser, Matt (2003). "Traversable wormholes with arbitrarily small energy condition violations". Physical Review Letters. 90 (20): 201102.1–201102.4. arXiv:gr-qc/0301003. Bibcode:2003PhRvL..90t1102V. doi:10.1103/PhysRevLett.90.201102. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
^ Visser, Matt (1993). "From wormhole to time machine: Comments on Hawking's Chronology Protection Conjecture". Physical Review D. 47 (2): 554–565. arXiv:hep-th/9202090. Bibcode:1993PhRvD..47..554V. doi:10.1103/PhysRevD.47.554.
^ Visser, Matt (1997). "Traversable wormholes: the Roman ring". Physical Review D. 55 (8): 5212–5214. arXiv:gr-qc/9702043. Bibcode:1997PhRvD..55.5212V. doi:10.1103/PhysRevD.55.5212.
^ van Stockum, Willem Jacob (1936). "The Gravitational Field of a Distribution of Particles Rotating about an Axis of Symmetry". Proceedings of the Royal Society of Edinburgh.
^ Lanczos, Kornel (1924, republished in 1997). "On a Stationary Cosmology in the Sense of Einsteins Theory of Gravitation". General Relativity and Gravitation. 29 (3). Springland Netherlands: 363–399. doi:10.1023/A:1010277120072. {{cite journal}}: Check date values in: |year= (help)CS1 maint: year (link)
^ Earman, John (1995). Bangs, Crunches, Whimpers, and Shrieks: Singularities and Acausalities in Relativistic Spacetimes. Oxford University Press. p. 21. ISBN 0-19-509591-X.
^ Tipler, Frank J (1974). "Rotating Cylinders and the Possibility of Global Causality Violation". Physical Review D. 9 (8): 2203. Bibcode:1974PhRvD...9.2203T. doi:10.1103/PhysRevD.9.2203.
^ Earman, John (1995). Bangs, Crunches, Whimpers, and Shrieks: Singularities and Acausalities in Relativistic Spacetimes. Oxford University Press. p. 169. ISBN 0-19-509591-X.
^ Hawking, Stephen (2002). The Future of Spacetime. W. W. Norton. p. 96. ISBN 0-393-02022-3. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
^ Hawking, Stephen (1992). "Chronology protection conjecture". Physical Review D. 46 (2): 603–611. Bibcode:1992PhRvD..46..603H. doi:10.1103/PhysRevD.46.603.
^ Wright, Laura (November 6, 2003). "Score Another Win for Albert Einstein". Discover.
^ Anderson, Mark (August 18–24, 2007). "Light seems to defy its own speed limit". New Scientist. Vol. 195, no. 2617. p. 10.
^ The Hong Kong University of Science & Technology. Ust.hk. Retrieved on 2011-09-05.
^ It's official: Time machines won't work – latimes.com. Latimesblogs.latimes.com (2011-07-25). Retrieved on 2011-09-05.
^ Time travel is sci-fi fantasy: Scientists prove nothing can travel faster than the speed of light | Mail Online. Dailymail.co.uk. Retrieved on 2011-09-05.
^ Franklin, Ben A. (March 11, 1982), "The night the planets were aligned with Baltimore lunacy", New York Times.
^ "Museum of the Future". Lehman.cuny.edu. Retrieved 2010-05-25.
^ Jaume Garriga; Alexander Vilenkin (2001). "[gr-qc/0102010] Many worlds in one". Phys.Rev. D. 64 (4). Arxiv.org: 043511. arXiv:gr-qc/0102010. Bibcode:2001PhRvD..64d3511G. doi:10.1103/PhysRevD.64.043511. {{cite journal}}: |access-date= requires |url= (help)
^ "Taking the Cosmic Shortcut – ABC Science Online". Abc.net.au. 2002-02-21. Retrieved 2010-05-25.
^ "Transcript of interview with Dr. Marc Rayman at "Space Place"". Spaceplace.nasa.gov. 2005-09-08. Retrieved 2010-05-25.
^ "http://www.pbs.org/wgbh/nova/time/thinktime.html". {{cite journal}}: Cite journal requires |journal= (help); External link in |title= (help)
^ Physics for Scientists and Engineers with Modern Physics, Fifth Edition, p.1258.
^ Roberts, Tom (October). "What is the experimental basis of Special Relativity?". Retrieved 4 December 2009. {{cite web}}: Check date values in: |date= and |year= / |date= mismatch (help)
^ "Scout Rocket Experiment". Retrieved 4 December 2009.
^ "Hafele-Keating Experiment". Retrieved 4 December 2009.
^ Pogge, Richard W. (27 April 2009). "GPS and Relativity". Retrieved 4 December 2009.
^ Vaidman, Lev. "Many-Worlds Interpretation of Quantum Mechanics". Retrieved 2006-10-28.
^ See also the discussion in "Quantum Mechanics to the Rescue?" from the Stanford Encyclopedia of Philosophy article "Time travel and Modern Physics".
^ Everett, Allen (2004). "Time travel paradoxes, path integrals, and the many worlds interpretation of quantum mechanics". Physical Review D. 69 (124023). arXiv:gr-qc/0410035. Bibcode:2004PhRvD..69l4023E. doi:10.1103/PhysRevD.69.124023.
^ Greenberger, Daniel M (2005). "Quantum Theory Looks at Time Travel". arXiv:quant-ph/0506027. Bibcode:2005quant.ph..6027G. {{cite journal}}: Cite journal requires |journal= (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)
^ Kettlewell, Julianna (2005-06-17). "New model 'permits time travel'". BBC News. Retrieved 2010-05-25.
^ Goldstein, Sheldon. "Bohmian Mechanics". Retrieved 2006-10-30.
^ Nielsen, Michael; Chuang, Isaac (2000). Quantum Computation and Quantum Information. Cambridge. p. 28. ISBN 0521632358.
^ Keller, Simon (2001). "Presentists should believe in time-travel" (PDF). Australian Journal of Philosophy. 79.3 (3): 333–345. doi:10.1080/713931204. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help); Unknown parameter |month= ignored (help)
^ This view is contested by another contemporary advocate of presentism, Craig Bourne, in his recent book A Future for Presentism, although for substantially different (and more complex) reasons.
^ ^a ^b see this discussion between two philosophers, for example
^ Lewis, David (1976). "The paradoxes of time travel" (PDF). American Philosophical Quarterly. 13: 145–52. arXiv:gr-qc/9603042. Bibcode:1996gr.qc.....3042K.
^ Grey, William (1999). "Troubles with Time Travel". Philosophy. 74 (1). Cambridge University Press: 55–70. doi:10.1017/S0031819199001047.
^ Rickman, Gregg (2004). The Science Fiction Film Reader. Limelight Editions. ISBN 0879109947.
^ Nahin, Paul J. (2001). Time machines: time travel in physics, metaphysics, and science fiction. Springer. ISBN 0387985719.
^ Schneider, Susan (2009). Science Fiction and Philosophy: From Time Travel to Superintelligence. Wiley-Blackwell. ISBN 1405149078.
^ Friedman, John (1990). "Cauchy problem in spacetimes with closed timelike curves". Physical Review D. 42 (6): 1915. Bibcode:1990PhRvD..42.1915F. doi:10.1103/PhysRevD.42.1915. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
^ Sukys, Paul (1999). Lifting the scientific veil: science appreciation for the nonscientist. Ardsley House Publishers. pp. 236–237. ISBN 0847696006.
^ Kelley L. Ross, "Time Travel Paradoxes"
^ Gott, J. Richard (2001). Time Travel in Einstein's Universe. Houghton Mifflin. p. 23. ISBN 0395955637.
^ Geroch, Robert (1978). General Relativity From A to B. The University of Chicago Press. p. 124. ISBN 0226288633.
^ Max Planck Institut für Gravitationsphysik (2005-09-12). "Einstein Online: Actors on a changing stage". Einstein-online.info. Retrieved 2010-05-25.

Bibliography

Davies, Paul (1996). About Time. Pocket Books. ISBN 0-684-81822-1.
Davies, Paul (2002). How to Build a Time Machine. Penguin Books Ltd. ISBN 0-14-100534-3.
Gale, Richard M (1968). The Philosophy of Time. Palgrave Macmillan. ISBN 0-333-00042-0.
Gott, J. Richard (2002). Time Travel in Einstein's Universe: The Physical Possibilities of Travel Through Time. Boston: Mariner Books. ISBN 0-618-25735-7.
Gribbin, John (1985). In Search of Schrödinger's Cat. Corgi Adult. ISBN 0-552-12555-5.
Miller, Kristie (2005). "Time travel and the open future". Disputatio. 1 (19): 223–232.
Nahin, Paul J. (2001). Time Machines: Time Travel in Physics, Metaphysics, and Science Fiction. Springer-Verlag New York Inc. ISBN 0-387-98571-9.
Nahin, Paul J. (1997). Time Travel: A writer's guide to the real science of plausible time travel. Writer's Digest Books. Cincinnati, Ohio. ISBN 0-89879-748-9
Nikolic, H (2006). "Causal paradoxes: a conflict between relativity and the arrow of time". Foundations of Physics Letters. 19 (3): 259. arXiv:gr-qc/0403121. Bibcode:2006FoPhL..19..259N. doi:10.1007/s10702-006-0516-5.
Pagels, Heinz (1985). Perfect Symmetry, the Search for the Beginning of Time. Simon & Schuster. ISBN 0-671-46548-1.
Pickover, Clifford (1999). Time: A Traveler's Guide. Oxford University Press Inc, USA. ISBN 0-19-513096-0.
Randles, Jenny (2005). Breaking the Time Barrier. Simon & Schuster Ltd. ISBN 0-7434-9259-5.
Shore, Graham M (2003). "Constructing Time Machines". Int. J. Mod. Phys. A, Theoretical. 18 (23): 4169. arXiv:gr-qc/0210048. Bibcode:2003IJMPA..18.4169S. doi:10.1142/S0217751X03015118.
Toomey, David (2007). The New Time Travelers: A Journey to the Frontiers of Physics. W.W. Norton & Company. ISBN 978-0-393-06013-3.

External links

Black holes, Wormholes and Time Travel, a Royal Society Lecture
SF Chronophysics, a discussion of Time Travel as it relates to science fiction
On the Net: Time Travel by James Patrick Kelly
How Time Travel Will Work at HowStuffWorks
Time Travel in Flatland?
NOVA Online: Time Travel
Professor Predicts Human Time Travel This Century
Time Traveler Convention at MIT
Time Machines in Physics – almost 200 citations from 1937 through 2001
Time Travel and Modern Physics at the Stanford Encyclopedia of Philosophy
Time Travel at the Internet Encyclopedia of Philosophy
Aparta Krystian: Conventional Models of Time and Their Extensions in Science Fiction
Time travellers from the future 'could be here in weeks'
Time machine on arxiv.org

Template:Link FA Template:Link GA

[deutsch-1] Deutsch, David (1991). "Quantum mechanics near closed timelike curves". Physical Review D. 44 (10): 3197–3217. Bibcode:1991PhRvD..44.3197D. doi:10.1103/PhysRevD.44.3197.

[2] Revati, Encyclopedia for Epics of Ancient India

[3] Lord Balarama, Sri Mayapur

[Yorke-4] Yorke, Christopher (February 2006). "Malchronia: Cryonics and Bionics as Primitive Weapons in the War on Time". Journal of Evolution and Technology. 15 (1): 73–85. Retrieved 2009-08-29.

[5] Rosenberg, Donna (1997). Folklore, myths, and legends: a world perspective. McGraw-Hill. p. 421. ISBN 084425780X.

[6] "Choni HaMe'agel". Jewish search. Retrieved November 6, 2009.

[7] Robert Darnton, The Forbidden Best-Sellers of Pre-Revolutionary France (New York: W.W. Norton, 1996), 120.

[madden1-8] Alkon, Paul K. (1987). Origins of Futuristic Fiction. The University of Georgia Press. pp. 95–96. ISBN 0-8203-0932-X.

[madden2-9] Alkon, Paul K. (1987). Origins of Futuristic Fiction. The University of Georgia Press. p. 85. ISBN 0-8203-0932-X.

[10] Yury Akutin, Александр Вельтман и его роман "Странник" (A.V. and his novel Strannik), 1978 (in Russian).

[derleth-11] Derleth, August (1951). Far Boundaries. Pellegrini & Cudahy. p. 3.

[missingcoach-12] Derleth, August (1951). Far Boundaries. Pellegrini & Cudahy. pp. 11–38.

[Scrooge-13] Flynn, John L. "Time Travel Literature". Archived from the original on 2006-09-29. Retrieved 2006-10-28.

[boitard-14] Rudwick, Martin J. S. (1992). Scenes From Deep Time. The University of Chicago Press. pp. 166–169. ISBN 0-226-73105-7.

[firsttimemachine-15] Uribe, Augusto (June 1999). "The First Time Machine: Enrique Gaspar's Anacronópete". The New York Review of Science Fiction. 11, no. 10 (130): 12.

[Thorne1-16] Thorne, Kip S. (1994). Black Holes and Time Warps. W. W. Norton. p. 499. ISBN 0-393-31276-3. Cite error: The named reference "Thorne1" was defined multiple times with different content (see the help page).

[Hawking_warp-17] Hawking, Steven. "Space and Time Warps". Retrieved 2010-09-06.

[18] "NOVA Online – Sagan on Time Travel". Pbs.org. Retrieved 2010-05-25.

[19] Matt Visser (2002). "The quantum physics of chronology protection". arXiv:gr-qc/0204022. {{cite arXiv}}: |class= ignored (help)

[chronology_protection1-20] Hawking, Stephen (1992). "Chronology protection conjecture". Physical Review D. 46 (2): 603. Bibcode:1992PhRvD..46..603H. doi:10.1103/PhysRevD.46.603.

[futureofspacetime1-21] Hawking, Stephen (2002). The Future of Spacetime. W. W. Norton. p. 150. ISBN 0-393-02022-3. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

[Gott-22] Gott, J. Richard (2002). "Time Travel in Einstein's Universe". {{cite journal}}: Cite journal requires |journal= (help) p.33-130 Cite error: The named reference "Gott" was defined multiple times with different content (see the help page).

[Jarrell-23] Jarrell, Mark. "The Special Theory of Relativity" (PDF). pp. 7–11. Archived from the original (PDF) on 2006-09-13. Retrieved 2006-10-27.

[24] "Sharp Blue: Relativity, FTL and causality – Richard Baker". Theculture.org. Retrieved 2010-05-25.

[tachyon-25] Chase, Scott I. "Tachyons entry from Usenet Physics FAQ". Retrieved 2006-10-27.

[26] Visser, Matt (1996). Lorentzian Wormholes. Springer-Verlag. p. 100. ISBN 1-56396-653-0.

[Thorne2-27] Thorne, Kip S. (1994). Black Holes and Time Warps. W. W. Norton. p. 502. ISBN 0-393-31276-3.

[Thorne3-28] Thorne, Kip S. (1994). Black Holes and Time Warps. W. W. Norton. p. 504. ISBN 0-393-31276-3.

[visserwormholes-29] Visser, Matt (1996). Lorentzian Wormholes. Springer-Verlag. p. 101. ISBN 1-56396-653-0.

[casimir-30] Cramer, John G. "NASA Goes FTL Part 1: Wormhole Physics". Archived from the original on 2006-06-27. Retrieved 2006-12-02.

[negative_energy-31] Visser, Matt (2003). "Traversable wormholes with arbitrarily small energy condition violations". Physical Review Letters. 90 (20): 201102.1–201102.4. arXiv:gr-qc/0301003. Bibcode:2003PhRvL..90t1102V. doi:10.1103/PhysRevLett.90.201102. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

[visser_1-32] Visser, Matt (1993). "From wormhole to time machine: Comments on Hawking's Chronology Protection Conjecture". Physical Review D. 47 (2): 554–565. arXiv:hep-th/9202090. Bibcode:1993PhRvD..47..554V. doi:10.1103/PhysRevD.47.554.

[visser_2-33] Visser, Matt (1997). "Traversable wormholes: the Roman ring". Physical Review D. 55 (8): 5212–5214. arXiv:gr-qc/9702043. Bibcode:1997PhRvD..55.5212V. doi:10.1103/PhysRevD.55.5212.

[stockum-34] van Stockum, Willem Jacob (1936). "The Gravitational Field of a Distribution of Particles Rotating about an Axis of Symmetry". Proceedings of the Royal Society of Edinburgh.

[lanczos-35] Lanczos, Kornel (1924, republished in 1997). "On a Stationary Cosmology in the Sense of Einsteins Theory of Gravitation". General Relativity and Gravitation. 29 (3). Springland Netherlands: 363–399. doi:10.1023/A:1010277120072. {{cite journal}}: Check date values in: |year= (help)CS1 maint: year (link)

[Earman1-36] Earman, John (1995). Bangs, Crunches, Whimpers, and Shrieks: Singularities and Acausalities in Relativistic Spacetimes. Oxford University Press. p. 21. ISBN 0-19-509591-X.

[tipler-37] Tipler, Frank J (1974). "Rotating Cylinders and the Possibility of Global Causality Violation". Physical Review D. 9 (8): 2203. Bibcode:1974PhRvD...9.2203T. doi:10.1103/PhysRevD.9.2203.

[Earman2-38] Earman, John (1995). Bangs, Crunches, Whimpers, and Shrieks: Singularities and Acausalities in Relativistic Spacetimes. Oxford University Press. p. 169. ISBN 0-19-509591-X.

[futureofspacetime2-39] Hawking, Stephen (2002). The Future of Spacetime. W. W. Norton. p. 96. ISBN 0-393-02022-3. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

[chronology_protection2-40] Hawking, Stephen (1992). "Chronology protection conjecture". Physical Review D. 46 (2): 603–611. Bibcode:1992PhRvD..46..603H. doi:10.1103/PhysRevD.46.603.

[gauthier-41] Wright, Laura (November 6, 2003). "Score Another Win for Albert Einstein". Discover.

[nimtz-42] Anderson, Mark (August 18–24, 2007). "Light seems to defy its own speed limit". New Scientist. Vol. 195, no. 2617. p. 10.

[43] The Hong Kong University of Science & Technology. Ust.hk. Retrieved on 2011-09-05.

[44] It's official: Time machines won't work – latimes.com. Latimesblogs.latimes.com (2011-07-25). Retrieved on 2011-09-05.

[45] Time travel is sci-fi fantasy: Scientists prove nothing can travel faster than the speed of light | Mail Online. Dailymail.co.uk. Retrieved on 2011-09-05.

[46] Franklin, Ben A. (March 11, 1982), "The night the planets were aligned with Baltimore lunacy", New York Times.

[47] "Museum of the Future". Lehman.cuny.edu. Retrieved 2010-05-25.

[48] Jaume Garriga; Alexander Vilenkin (2001). "[gr-qc/0102010] Many worlds in one". Phys.Rev. D. 64 (4). Arxiv.org: 043511. arXiv:gr-qc/0102010. Bibcode:2001PhRvD..64d3511G. doi:10.1103/PhysRevD.64.043511. {{cite journal}}: |access-date= requires |url= (help)

[49] "Taking the Cosmic Shortcut – ABC Science Online". Abc.net.au. 2002-02-21. Retrieved 2010-05-25.

[50] "Transcript of interview with Dr. Marc Rayman at "Space Place"". Spaceplace.nasa.gov. 2005-09-08. Retrieved 2010-05-25.

[TimeTravelPBS-51] "http://www.pbs.org/wgbh/nova/time/thinktime.html". {{cite journal}}: Cite journal requires |journal= (help); External link in |title= (help)

[52] Physics for Scientists and Engineers with Modern Physics, Fifth Edition, p.1258.

[tomroberts-53] Roberts, Tom (October). "What is the experimental basis of Special Relativity?". Retrieved 4 December 2009. {{cite web}}: Check date values in: |date= and |year= / |date= mismatch (help)

[scoutrocket-54] "Scout Rocket Experiment". Retrieved 4 December 2009.

[hafelekeating-55] "Hafele-Keating Experiment". Retrieved 4 December 2009.

[GPS-56] Pogge, Richard W. (27 April 2009). "GPS and Relativity". Retrieved 4 December 2009.

[many-worlds-57] Vaidman, Lev. "Many-Worlds Interpretation of Quantum Mechanics". Retrieved 2006-10-28.

[58] See also the discussion in "Quantum Mechanics to the Rescue?" from the Stanford Encyclopedia of Philosophy article "Time travel and Modern Physics".

[59] Everett, Allen (2004). "Time travel paradoxes, path integrals, and the many worlds interpretation of quantum mechanics". Physical Review D. 69 (124023). arXiv:gr-qc/0410035. Bibcode:2004PhRvD..69l4023E. doi:10.1103/PhysRevD.69.124023.

[greenberger-60] Greenberger, Daniel M (2005). "Quantum Theory Looks at Time Travel". arXiv:quant-ph/0506027. Bibcode:2005quant.ph..6027G. {{cite journal}}: Cite journal requires |journal= (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)

[61] Kettlewell, Julianna (2005-06-17). "New model 'permits time travel'". BBC News. Retrieved 2010-05-25.

[Bohm-62] Goldstein, Sheldon. "Bohmian Mechanics". Retrieved 2006-10-30.

[Nielsen_and_Chuang-63] Nielsen, Michael; Chuang, Isaac (2000). Quantum Computation and Quantum Information. Cambridge. p. 28. ISBN 0521632358.

[Presentism-64] Keller, Simon (2001). "Presentists should believe in time-travel" (PDF). Australian Journal of Philosophy. 79.3 (3): 333–345. doi:10.1080/713931204. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help); Unknown parameter |month= ignored (help)

[Bourne-65] This view is contested by another contemporary advocate of presentism, Craig Bourne, in his recent book A Future for Presentism, although for substantially different (and more complex) reasons.

[unchangeable-66] see this discussion between two philosophers, for example

[67] Lewis, David (1976). "The paradoxes of time travel" (PDF). American Philosophical Quarterly. 13: 145–52. arXiv:gr-qc/9603042. Bibcode:1996gr.qc.....3042K.

[68] Grey, William (1999). "Troubles with Time Travel". Philosophy. 74 (1). Cambridge University Press: 55–70. doi:10.1017/S0031819199001047.

[69] Rickman, Gregg (2004). The Science Fiction Film Reader. Limelight Editions. ISBN 0879109947.

[70] Nahin, Paul J. (2001). Time machines: time travel in physics, metaphysics, and science fiction. Springer. ISBN 0387985719.

[71] Schneider, Susan (2009). Science Fiction and Philosophy: From Time Travel to Superintelligence. Wiley-Blackwell. ISBN 1405149078.

[72] Friedman, John (1990). "Cauchy problem in spacetimes with closed timelike curves". Physical Review D. 42 (6): 1915. Bibcode:1990PhRvD..42.1915F. doi:10.1103/PhysRevD.42.1915. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

[73] Sukys, Paul (1999). Lifting the scientific veil: science appreciation for the nonscientist. Ardsley House Publishers. pp. 236–237. ISBN 0847696006.

[74] Kelley L. Ross, "Time Travel Paradoxes"

[Gott2-75] Gott, J. Richard (2001). Time Travel in Einstein's Universe. Houghton Mifflin. p. 23. ISBN 0395955637.

[Geroch-76] Geroch, Robert (1978). General Relativity From A to B. The University of Chicago Press. p. 124. ISBN 0226288633.

[77] Max Planck Institut für Gravitationsphysik (2005-09-12). "Einstein Online: Actors on a changing stage". Einstein-online.info. Retrieved 2010-05-25.

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v t e Time travel
General terms and concepts	Chronology protection conjecture Closed timelike curve Novikov self-consistency principle Self-fulfilling prophecy Quantum mechanics of time travel
Time travel in fiction	Timelines in fiction in science fiction Time loop in film
Temporal paradoxes	Grandfather paradox Causal loop
Parallel timelines	Alternative future Alternate history Many-worlds interpretation Multiverse Parallel universes in fiction
Philosophy of space and time	Butterfly effect Determinism Eternalism Fatalism Free will Predestination
Spacetimes in general relativity that can contain closed timelike curves	Alcubierre metric BTZ black hole Gödel metric Kerr metric Krasnikov tube Misner space Tipler cylinder van Stockum dust Traversable wormholes