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IF WE HAD TIME TRAVEL WE COULD EAT CHEESE THEN GO BACK AND EAT IT AGAIN THEN AGSIN AND AGAIN AND NEVER GET FAT. OR WE COULD KEEP IT FROM GOING BAD

This article details time travel itself. For other uses, see Time Traveler (disambiguation)[original research?]
Unsolved problem in physics:
Is time travel theoretically and practically possible? Will such travel invoke paradoxes, such as often used in fiction?
(more unsolved problems in physics)

Time travel is the concept of moving backward or forward to different points in time, in a manner analogous to moving through space. Additionally, some interpretations of time travel suggest the possibility of travel between parallel realities or universes.[1]

Origins of the concept

Charles Dickens' 1843 book A Christmas Carol is considered by some[2] 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 more clear example of time travel is found in the popular 1861 book Paris avant les hommes (Paris before Men), published posthumously by the French botanist and geologist Pierre Boitard. In this story the main character is transported into the prehistoric past by the magic of a "lame demon", where he encountered such extinct animals as a Plesiosaur, as well as Boitard's imagined version of an apelike human ancestor, and was able to actively interact with some of them. Another early example of time travel in fiction is the short story The Clock That Went Backward by Edward Page Mitchell, which appeared in the New York Sun in 1881.

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. This idea gained popularity with the H. G. Wells story The Time Machine, published in 1895, which is often seen as an inspiration for all later science fiction stories featuring time travel.

Since that time, both science and fiction (see Time travel in fiction) have expanded on the concept of time travel, but whether it could be possible in reality is still an open question.

Time travel in theory

Some theories, most notably special and general relativity, suggest that suitable geometries of spacetime, or specific types of motion in space, may allow time travel into the past and future if these geometries or motions are possible.[3] Concepts that aid such understanding include the closed timelike curve.

Although the possibility of traveling to the future by moving at relativistic velocities is taken for granted by physicists, many in the scientific community believe that backwards time travel is highly unlikely. Any theory which would allow time travel would require that issues of causality be resolved. What if one were to go back in time and kill one's own grandfather? Additionally, Stephen Hawking once suggested that the absence of tourists from the future constitutes a strong argument against the existence of time travel—a variant of the Fermi paradox, with time travelers instead of alien visitors. However, the theory of general relativity does suggest scientific grounds for thinking backwards time travel could be possible in certain unusual scenarios, although arguments from semiclassical gravity suggest that when quantum effects are incorporated into general relativity, these loopholes may be closed. These semiclassical arguments led Stephen Hawking to formulate the chronology protection conjecture, suggesting that the fundamental laws of nature prevent time travel, 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.

The "presentist" view

Main article: Presentism (philosophy of time)

Presentism holds that neither the future nor the past exist; that the matter of the universe only exists in the present moment, that time is merely a concept of man used to describe what is going on around him. This could be interpreted to mean that there is nowhere for a time traveller to go, thus rendering the whole topic of time travel null and void. However, some presentists argue that although past and future objects do not exist, there can still be definite truths about past and future events, and that it is possible that a future truth about the time traveler deciding to return to the present date could explain the time traveler's actual presence in the present.[4] In any case, the relativity of simultaneity in modern physics is generally understood to cast serious doubt on presentism and to favor the view known as four dimensionalism (closely related to the idea of block time) in which past, present and future events all coexist in a single spacetime.

Time travel to the past

Time travel to the past is theoretically allowed using the following methods[5]:

The equivalence of time travel and faster-than-light 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 backwards 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 spacetime interval between the events is 'space-like', meaning that neither event lies in the future light cone of the other).[6] 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.[6] 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 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 recieves 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.

It should be noted that according to relativity it would take an infinite amount of energy to accelerate a slower-than-light object to faster-than-light speeds, and 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[7], and 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. [8]The first of these was proposed by Kurt Gödel, a solution known as the Gödel metric, but his (and many others') example require the universe to have physical characteristics that it does not appear to have.[8] Whether general relativity forbids closed time-like curves for all realistic conditions is unknown.

Using wormholes

File:Worm3.jpg
A wormhole

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

A proposed time-travel machine using a traversable wormhole would (hypothetically) work something like this. A wormhole is created somehow. One end of the wormhole is accelerated to nearly the speed of light, perhaps with an advanced spaceship, and then brought back to the point of origin. Due to time dilation, the accelerated end of the wormhole has now 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. 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 2005 while a clock at the stationary end read 2010, then the observer would exit the stationary end when its clock also read 2005, 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[9]; 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, creating a wormhole of a size useful for a person or spacecraft, keeping it stable, and moving one end of it around would require significant energy, many orders of magnitude more than the Sun can produce in its lifetime. Construction of a traversable wormhole would also require the existence of a substance known as "exotic matter", which, while not known to be impossible, is also not known to exist in forms useful for wormhole construction (but see for example the Casimir effect). Therefore it is unlikely such a device will ever be constructed, even with highly advanced technology. On the other hand, microscopic wormholes could still be useful for sending information back in time.

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. [10] 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 than not a flaw in classical quantum gravity theory rather than proof that causality violation is possible. [11]

Another approach — attributed to Frank Tipler, [12] but invented independently by Willem Jacob van Stockum [13] in 1936 and Kornel Lanczos [14] in 1924 — involves a spinning cylinder. If a cylinder is long, and dense, 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]

Time travel and the anthropic principle

It has been suggested by physicists such as Max Tegmark that the absence of time travel and the existence of causality may be due to the anthropic principle. The argument is that a universe which allows for time travel and closed time-like loops is one in which intelligence could not evolve because it would be impossible for a being to sort events into a past and future or to make predictions or comprehend the world around them (at least, not if the time travel occurs in such a way that it disrupts that evolutionary process).[citation needed]

Time travel to the future

Twin paradox diagram
Transversal Time dilation

Time travel to the future is theoretically allowed using the following methods[5]:

Time dilation

Main article: Time dilation

Time dilation is permitted by Albert Einstein's special theory of relativity. These theories state that, relative to a stationary observer, time appears to pass more slowly for faster-moving bodies, or bodies that are within a deep gravity well. [16] For example, a moving clock will appear to run slow; as a clock approaches the speed of light it will appear to slow to a stop. This has given rise to the popular twin paradox. General relativity states that a similar effect would occur if the clock were to be close to a black hole.

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 arguably should not be considered time travel.

Curved spacetime shell

This method of travelling to the future is unique in that it does not require travelling in space. However, it is impractical because it requires a mass on the order of the planet Jupiter. If a clump of distorted spacetime as massive as Jupiter is squeezed to be 5 meters tall and forms a funnel shape, a person who went into the bottom of it would not have to move anywhere to travel. The traveller inside the funnel would be moving 4 times faster than everything else, and the traveller would be able to see through the distorted spacetime like a window and see objects moving fast outside as if the world were in fast forward[5]. To observers on the outside, the time traveller would appear to be moving more slowly.

Small travel

Today, the only way to "travel" to the future cannot be used to travel over long periods of time -- only less than a single second. It is so insignificant that it is usually not mentioned at all. And the only people that have used this method have been astronauts. Basically, the longer a person is in orbit around the Earth, the younger the astronaut will be in relation to observers on Earth. So far, the record for traveling farthest in the future using this method is held by Sergei Avdeyev[5]. He was in orbit 748 days (total) and traveling approximately 17,000 mph, resulting in him traveling 0.02 seconds (20 milliseconds) into the future[17]. That means that for Sergei Avdeyev to time travel just one whole second into the future, he would need to orbit for approximately 102.47 years. A common misconception was that the Apollo astronauts traveled faster, so they held the record -- they did travel faster, but not long enough (only a few days).

Other theories

The possibility of paradoxes

The Novikov self-consistency principle and recent 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 generalised, 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 of quantum mechanics suggests that all possible quantum events can occur in mutually exclusive histories.[18] 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 many-worlds interpretation is correct, then a time traveler should indeed end up in a different history than the one he started from. [1]

Daniel Greenberger and Karl Svozil proposed that quantum theory gives a model for time travel without paradoxes. [19] 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.

The science fiction writer Larry Niven made his own suggestion about paradox avoidance in his essay The Theory and Practice of Time Travel. He argued that as long as time travel exists, history will change, and will only become static when a timeline is reached in which no time travel exists and thus no further changes can be made (unless it is on a course that is repetitive or will never become static, but there is no evidence of this). Assuming there is only a single dimension of time, the timeline we perceive must be the one that exists after all changes (if any) are made, and thus we will never perceive the invention of time travel, since it will have already destabilised itself out of the timeline by the 'time' we would have reached it.[citation needed] However, 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 (see this discussion between two philosophers, for example), so this idea is not usually seen outside of science fiction.

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.[citation needed] This effect was referred to as "spooky action at a distance" by Einstein.

Nevertheless, the rules of quantum mechanics curiously appear to prevent an outsider from using these methods to actually transmit useful information, and therefore do not appear to allow for time travel or FTL communication. The fact that these quantum phenomena apparently do not allow FTL/time travel is often overlooked in popular press coverage of quantum teleportation experiments. How the rules of quantum mechanics work to preserve causality is an active area of research.

Time travel in fiction

Main article: Time travel in fiction

[original research?]

Types of time travel

Time travel themes in science fiction and the media can generally be grouped into two main types and a third, less common type (based on effect—methods are extremely varied and numerous), each of which is further subdivided. These type classifications do not address the issue of time travel itself, i.e. how to travel through time, but instead call to attention differing rules of the time line.

1. The time line is consistent and can never be changed.
1.1 One does not have full control of the time travel. One example of this is The Morphail Effect. This concept of time can be referred to as circular causation. For exampes of circular causation, see Robert A. Heinlein's story By His Bootstraps.
1.2 The Novikov self-consistency principle applies (named after Dr. Igor Dmitrievich Novikov, Professor of Astrophysics at Copenhagen University). The principle states that if you travel in time, you cannot act in such a way so as to create a paradox.
1.3 Any event that appears to have changed a time line has instead created a new one. It has been suggested that travel to the past would create an entire new parallel universe where the traveler would be free from paradoxes since he/she is not from that universe[citation needed]
1.3.1 Such an event can be the life line existence of a human (or other intelligence) such that manipulation of history ends up with there being more than one of the same individual, sometimes called time clones.
1.3.2 The new time line may be a copy of the old one with changes caused by the time traveler. For example there is the Accumulative Audience Paradox where multitudes of time traveler tourists wish to attend some event in the life of Jesus or some other historical figure, where history tells us there were no such multitudes. Each tourist arrives in a reality that is a copy of the original with the added people, and no way for the tourist to travel back to the original time line.
2. The time line is flexible and is subject to change.
2.1 The time line is extremely change resistant and requires great effort to change it. Small changes will only alter the immediate future and events will conspire to maintain constant events in the far future; only large changes will alter events in the distant future.
2.2 The time line is easily changed (example: Doctor Who, where the time line is fluid and changes often naturally).
3. The time line is consistent, but only insofar as its consistency can be verified.
3.1 The Novikov self-consistency principle applies, but if and only if it is verified to apply. Attempts to travel into the past to change events are possible, but provided that:
-They do not interfere with the occurrence of such an attempt in the present (as would be the case in the Grandfather Paradox), and
-The change is never ultimately verified to occur by the traveller (e.g. there is no possibility of returning to the present to witness the change).

There are also numerous science fiction stories allegedly about time travel that are not internally consistent, where the traveler makes all kinds of changes to some historical time, but we do not get to see any consequences of this in our present day.[citation needed]

Immutable timelines

Time travel in a type 1 universe does not allow any paradoxes, although in 1.3, events can appear to be paradoxical.

In 1.1, time travel is constrained to prevent paradox. If one attempts to make a paradox, one undergoes involuntary or uncontrolled time travel. Michael Moorcock uses a form of this principle and calls it The Morphail Effect. 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 and attempts to kill Hitler finds himself in Montana in 1945.

In 1.2, the Novikov self-consistency principle asserts that the existence of a method of time travel constrains events to remain self-consistent (i.e. no paradoxes). This will cause any attempt to violate such consistency to fail, even if 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. Two examples of this kind of universe is found in Timemaster, a novel by Dr. Robert Forward, and the 1980 Jeannot Szwarc film Somewhere In Time (based on Richard Matheson's novel Bid Time Return).
An example which could conceivably fall into either 1.1 or 1.2 can be seen in book and film versions of Harry Potter and the Prisoner of Azkaban. Harry went back in time with Hermione to change history. As they do so it becomes apparent that they are simply performing actions that were previously seen in the story, although neither the characters nor the reader were aware of the causes of those actions at the time. This is another example of the predestination paradox. It is arguable, however, that the mechanics of time travel actually prevented any paradoxes, firstly, by preventing them from realizing a priori that time travel was occurring and secondly, by enabling them to recall the precise action to take at the precise time and keep history consistent.

In 1.3, 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 traveller 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. Some examples of this kind of time travel can be found in David Gerrold's book The Man Who Folded Himself, The Time Ships by Stephen Baxter and the (1994) film Star Trek: Generations.

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 too 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. In film, the Back to the Future trilogy also seems to feature a single mutable timeline.

Larry Niven suggests 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 may 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 1.2 scenario.[citation needed] This is sometimes referred to as the "Time Dilution Effect."

Gradual and instantaneous

In literature, there are two methods of time travel:

1. 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 DeLorean in Back to the Future or the phonebooth and the circuits of time in Bill and Ted's Excellent Adventure). 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.

2. 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." 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. This method of gradual time travel fits best in quantum physics, but is not as popular in modern science fiction. 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. This would make Lewis Carroll the inventor of time travel. 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: CHEESE IS GOOD.

Time travel, or space-time travel?

An objection that is sometimes raised against the concept of "time travel ships" in science fiction is that they often assume that the time traveler will remain in the same spatial position in the Earth's frame of reference, as opposed to some other frame. The idea that a traveller 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. However, this argument is somewhat confused according to special relativity, since relativity rejects the notion of absolute time and space, meaning that the speed of the Earth and Sun would themselves depend on your frame of reference, so that there is no single point in space today that is objectively the "same place" that the Earth was at some point in the past. It would always be possible to find at least one frame where the Earth's position today is the same as the Earth's position at the past or future date that is the time traveler's destination, and this frame cannot be considered any more or less valid than any other according to relativity. Also, since there is no basis in physics for the notion of a time traveler disappearing from one location in spacetime and reappearing in another (all the time travel schemes proposed in physics involve the traveler's world line remaining continuous and unbroken, as with time travel via a trip through a wormhole), there cannot be any basis in physics for saying a fictional time traveler "should" reappear at any particular location in space.

Still, 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-materialize in space. 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 six (not four!) co-ordinates 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 in the same place (in space) that he originated.[citation needed]

References

  1. ^ a b Deutsch, David (1991). "Quantum mechanics near closed timelike curves". Physical Review D. 44: 3197–3217. {{cite journal}}: Check date values in: |date= (help)
  2. ^ Flynn, John L. "Time Travel Literature". Retrieved 2006-10-28.
  3. ^ Kip S., Thorne. "Black Holes and Time Warps". {{cite journal}}: Cite has empty unknown parameter: |1= (help); Cite journal requires |journal= (help) p. 499
  4. ^ Keller, Simon (2001). "Presentists should believe in time-travel" (PDF). Australian Journal of Philosophy. 79.3: 333–345. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help); Unknown parameter |month= ignored (help)
  5. ^ a b c d Gott, J. Richard (2002). "Time Travel in Einstein's Universe". {{cite journal}}: Cite has empty unknown parameter: |1= (help); 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).
  6. ^ a b Jarrell, Mark. "The Special Theory of Relativity" (pdf). pp. 7–11. Retrieved 2006-10-27.
  7. ^ Chase, Scott I. "Tachyons entry from Usenet Physics FAQ". Retrieved 2006-10-27.
  8. ^ a b Kip S., Thorne. "Black Holes and Time Warps". {{cite journal}}: Cite has empty unknown parameter: |1= (help); Cite journal requires |journal= (help) p. 499 Cite error: The named reference "Thorne1" was defined multiple times with different content (see the help page).
  9. ^ Black Holes and Time Warps by Kip S. Thorne p.504
  10. ^ Visser, Matt (1993). "From wormhole to time machine: Comments on Hawking's Chronology Protection Conjecture". Physical Review D. 47: 554–565. arXiv:hep-th/9202090
  11. ^ Visser, Matt (1997). "Traversable wormholes: the Roman ring". Physical Review D. 55: 5212–5214. arXiv:gr-qc/9702043
  12. ^ Tipler, Frank J (1974). "Rotating Cylinders and the Possibility of Global Causality Violation". Physical Review D. 9: 2203.
  13. ^ 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.
  14. ^ 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)
  15. ^ "http://www.pbs.org/wgbh/nova/time/thinktime.html". {{cite journal}}: Cite has empty unknown parameter: |1= (help); Cite journal requires |journal= (help); External link in |title= (help)
  16. ^ Physics for Scientists and Engineers with Modern Physics, Fifth Edition, p.1258.
  17. ^ "http://www.amnh.org/exhibitions/einstein/time/exploring.php". {{cite journal}}: Cite has empty unknown parameter: |1= (help); Cite journal requires |journal= (help); External link in |title= (help)
  18. ^ Vaidman, Lev. "Many-Worlds Interpretation of Quantum Mechanics". Retrieved 2006-10-28.
  19. ^ Greenberger, Daniel M (2005). "Quantum Theory Looks at Time Travel". {{cite journal}}: Cite journal requires |journal= (help); Unknown parameter |coauthors= ignored (|author= suggested) (help) arXiv:quant-ph/0506027

Further reading

  • 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. Time Travel in Einstein's Universe: The Physical Possibilities of Travel Through Time. 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.
  • Nikolic, H. "Causal paradoxes: a conflict between relativity and the arrow of time". {{cite journal}}: Cite journal requires |journal= (help) arXiv:gr-qc/0403121
  • 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. "Constructing Time Machines". Int. J. Mod. Phys. A, Theoretical. arXiv:gr-qc/0210048

See also

Speculations

Claims of time travel

Fiction, humor

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