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Encyclopedia > Time dilation

Time dilation is the phenomenon whereby an observer finds that another's clock which is physically identical to their own is ticking at a slower rate as measured by their own clock. This is often taken to mean that time has "slowed down" for the other clock, but that is only true in the context of the observer's frame of reference. Locally, time is always passing at the same rate. The time dilation phenomenon applies to any process that manifests change over time.


In Albert Einstein's theories of relativity time dilation is manifested in two circumstances: “Einstein” redirects here. ... Two-dimensional analogy of space-time curvature described in General Relativity. ...

In special relativity, the time dilation effect is reciprocal: as observed from the point of view of any two clocks which are in motion with respect to each other, it will be the other party's clocks that is time dilated. (This presumes that the relative motion of both parties is uniform; that is, they do not accelerate with respect to one another during the course of the observations.) The special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. Some three centuries earlier, Galileos principle of relativity had stated that all uniform motion was relative, and that there was no absolute and well-defined state of rest... In physics, an inertial frame of reference, or inertial frame for short (also descibed as absolute frame of reference), is a frame of reference in which the observers move without the influence of any accelerating or decelerating force. ... A Lorentz transformation (LT) is a linear transformation that preserves the spacetime interval between any two events in Minkowski space, while leaving the origin fixed (=rotation of Minkowski space). ... An illustration of a rotating black hole at the center of a galaxy General relativity (GR) (aka general theory of relativity (GTR)) is the geometrical theory of gravitation published by Albert Einstein in 1915/16. ... A gravitational field is a model used within physics to explain how gravity exists in the universe. ... Gravitational time dilation is a consequence of Albert Einsteins theories of relativity and related theories which causes time to pass at different rates in regions of a different gravitational potential; the higher the local distortion of spacetime due to gravity, the slower time passes. ... For other topics related to Einstein see Einstein (disambig) In the general theory of relativity by Albert Einstein, the gravitational redshift or Einstein shift is the effect that clocks in a gravitational field tick slower when observed by a distant observer. ...


In contrast, gravitational time dilation (as treated in General Relativity) is not reciprocal: an observer at the top of a tower will observe that clocks at ground level tick slower, and observers on the ground will agree. Thus gravitational time dilation is agreed upon by all stationary observers, independent of their altitude.

Contents

Overview

The formula for determining time dilation in special relativity is:

 Delta t = gamma  Delta t_0 = frac{Delta t_0}{sqrt{1-v^2/c^2}} ,

where

 Delta t_0 , is the time interval between two colocal events (i.e. happening at the same place) for an observer in some inertial frame (e.g. ticks on his clock),
 Delta t , is the time interval between those same events, as measured by another observer, inertially moving with velocity v with respect to the former observer,
 v , is the relative velocity between the observer and the moving clock,
 c , is the speed of light, and
 gamma = frac{1}{sqrt{1-v^2/c^2}} , is the Lorentz factor.

Thus the duration of the clock cycle of a moving clock is found to be increased: it is measured to be "running slow." The range of such variances in ordinary life, where v / c < < 1 even considering space travel, are not great enough to produce easily detectable time dilation effects, and such vanishingly small effects can be safely ignored. It is only when an object approaches speeds on the order of 30,000 km/s (1/10 of the speed of light) that time dilation becomes important. A line showing the speed of light on a scale model of Earth and the Moon, about 1. ... It has been suggested that Lorentz term be merged into this article or section. ... km redirects here. ... Look up second in Wiktionary, the free dictionary. ... A line showing the speed of light on a scale model of Earth and the Moon, about 1. ...


Time dilation by the Lorentz factor was predicted by Joseph Larmor (1897), at least for electrons orbiting a nucleus. Thus "... individual electrons describe corresponding parts of their orbits in times shorter for the [rest] system in the ratio :sqrt{1 - frac{v^2}{c^2}}" (Larmor 1897). Time dilation of magnitude corresponding to this (Lorentz) factor has been experimentally confirmed, as described below. Sir Joseph Larmor (11 July 1857 – 19 May 1942), an Northern Irish physicist, mathematician and politician, researched electricity, dynamics, and thermodynamics. ...


==Experimental confirmation== Time dilation has been tested a number of times. The routine work carried on in particle accelerators since the 1950s, such as those at CERN, is a continuously running test of the time dilation of special relativity. The specific experiments include: CERN logo The European Organization for Nuclear Research (French: ), commonly known as CERN (see Naming), pronounced (or in French), is the worlds largest particle physics laboratory, situated just northwest of Geneva on the border between France and Switzerland. ...


Velocity time dilation tests

  • Ives and Stilwell (1938, 1941), “An experimental study of the rate of a moving clock”, in two parts. The stated purpose of these experiments was to verify the time dilation effect, predicted by Lamor-Lorentz ether theory, due to motion through the ether using Einstein's suggestion that Doppler effect in canal rays would provide a suitable experiment. These experiments measured the Doppler shift of the radiation emitted from cathode rays, when viewed from directly in front and from directly behind. The high and low frequencies detected were not the classical values predicted.
f_mathrm{detected} = frac{f_mathrm{moving}}{1 - v/c} and frac{f_mathrm{moving}}{1+v/c} =frac{f_mathrm{rest}}{1 - v/c} and frac{f_mathrm{rest}}{1+v/c}
i.e. for sources with invariant frequencies f_mathrm{moving}, = f_mathrm{rest} The high and low frequencies of the radiation from the moving sources were measured as
f_mathrm{detected} = f_mathrm{rest}sqrt{left(1 + frac{v}{c}right)/left(1 - frac{v}{c}right) } and f_mathrm{rest}sqrt{left(1 - frac{v}{c}right)/left(1 + frac{v}{c}right)}
as deduced by Einstein (1905) from the Lorentz transformation, when the source is running slow by the Lorentz factor.
  • Rossi and Hall (1941) compared the population of cosmic-ray produced muons at the top of a mountain to that observed at sea level. Although the travel time for the muons from the top of the mountain to the base is several muon half-lives, the muon sample at the base was only moderately reduced. This is explained by the time dilation attributed to their high speed relative to the experimenters. That is to say, the muons are decaying about 10 times slower than they would in a rest frame (that is, for "stationary observers").
  • Hasselkamp, Mondry, and Scharmann (1979) measured the Doppler shift from a source moving at right angles to the line of sight (the transverse Doppler shift). The most general relationship between frequencies of the radiation from the moving sources is given by:
f_mathrm{detected} = f_mathrm{rest}{left(1 - frac{v}{c} cosphiright)/sqrt{1 - {v^2}/{c^2}} }
as deduced by Einstein (1905)[1]. For phi = 90^circ (cosphi = 0,) this reduces to fdetected = frestγ. Thus there is no transverse Doppler shift, and the lower frequency of the moving source can be attributed to the time dilation effect alone.

The Doppler effect is the apparent change in frequency or wavelength of a wave that is perceived by an observer moving relative to the source of the waves. ... Performed in 1941 at echo lake in Colorado, the Rossi-Hall experiment measured the relatavistic decay of mesotrons(mesons, they happened to be measuring muon decay)and found it to be in good agreement with the predicitions of Special Relativity. ... The muon (from the letter mu (μ)--used to represent it) is an elementary particle with negative electric charge and a spin of 1/2. ... In special relativity, the transverse Doppler effect is the nominal redshift component associated with transverse (i. ...

Gravitational time dilation tests

  • Pound, Rebka in 1959 measured the very slight gravitational red shift in the frequency of light emitted at a lower height, where Earth's gravitational field is relatively more intense. The results were within 10% of the predictions of general relativity. Later Pound and Snider (in 1964) derived an even closer result of 1%. This effect is as predicted by gravitational time dilation.

The Pound-Rebka experiment is a well known experiment in general relativity. ... For other topics related to Einstein see Einstein (disambig) In the general theory of relativity by Albert Einstein, the gravitational redshift or Einstein shift is the effect that clocks in a gravitational field tick slower when observed by a distant observer. ...

Velocity and gravitational time dilation combined-effect tests

  • Hafele and Keating, in 1971, flew cesium atomic clocks east and west around the Earth in commercial airliners, to compare the elapsed time against that of a clock that remained at the US Naval Observatory. Two opposite effects came in to play. The clocks were expected to age more quickly (show a larger elapsed time) than the reference clock, since they were in a higher (weaker) gravitational potential for most of the trip (c.f. Pound, Rebka). But also, contrastingly, the moving clocks were expected to age more slowly because of the speed of their travel. The gravitational effect was the larger, and the clocks suffered a net gain in elapsed time. To within experimental error, the net gain was consistent with the difference between the predicted gravitational gain and the predicted velocity time loss. In 2005, the National Physical Laboratory in the United Kingdom reported their limited replication of this experiment[1]. The NPL experiment differed from the original in that the cesium clocks were sent on a shorter trip (London-Washingon D. C. return), but the clocks were more accurate. The reported results are within 4% of the predictions of relativity.
  • The Global Positioning System can be considered a continuously operating experiment in both special and general relativity. The in-orbit clocks are corrected for both special and general relativistic time-dilation effects so they run at the same (average) rate as clocks at the surface of the Earth. In addition, but not directly time-dilation related, general relativistic correction terms are built into the model of motion that the satellites broadcast to receivers — uncorrected, these effects would result in an approximately 7-metre oscillation in the pseudo-ranges measured by a receiver over a cycle of 12 hours.

The Hafele-Keating experiment was a test of the theory of relativity. ... General Name, Symbol, Number Caesium, Cs, 55 Series Alkali metals Group, Period, Block 1(IA), 6, s Density, Hardness 1879 kg/m3, 0. ... Aerial view of USNO. The United States Naval Observatory (USNO) is one of the oldest scientific agencies in the United States. ... The Pound-Rebka experiment is a well known experiment in general relativity. ... The National Physical Laboratory (NPL) is the national measurement standards laboratory for the United Kingdom, based at Bushy Park in Teddington in the London Borough of Richmond upon Thames. ... The Global Positioning System (GPS) is the only fully functional Global Navigation Satellite System (GNSS). ...

Time dilation and space flight

Time dilation would make it possible for passengers in a fast moving vehicle to travel further into the future while aging very little, in that their great speed retards the rate of passage of onboard time. That is, the ship's clock (and according to relativity, any human travelling with it) shows less elapsed time than stationary clocks. For sufficiently high speeds the effect is dramatic. For example, one year of travel might correspond to ten years at home. Indeed, a constant 1 g acceleration would permit humans to travel as far as light has been able to since the big bang (some 13.7 billion light years) in one human lifetime. The space-travellers could return to earth billions of years in the future (provided the Universe hadn't collapsed and our solar system was still around, of course). A scenario based on this idea was presented in the novel Planet of the Apes by Pierre Boulle. According to the Big Bang model, the universe developed from an extremely dense and hot state. ... A light-year or lightyear (symbol: ly) is a unit of measurement of length, specifically the distance light travels in vacuum in one year. ... This article is about the book. ... Pierre Boulle (20 February 1912 – 30 January 1994) was a French novelist. ...


A more likely use of this effect would be to enable humans to travel to nearby stars without spending their entire lives aboard the ship. However, any such application of time dilation would require the use of some new, advanced method of propulsion. A further problem with relativistic travel is that at such velocities dispersed particles in the rarefied interstellar medium would turn into a stream of high-energy cosmic rays that would destroy the ship unless extraordinary radiation protection measures were taken. Strong electromagnetic fields that could ionize and deflect any interstellar matter has been suggested as one way to avoid these potentially disastrous consequences. A remote camera captures a close-up view of a Space Shuttle Main Engine during a test firing at the John C. Stennis Space Center in Hancock County, Mississippi Propulsion means to add speed or acceleration to an object, by an engine or other similar device. ...


Current space flight technology has fundamental theoretical limits based on the practical problem that an increasing amount of energy is required for propulsion as a craft approaches the speed of light. The likelihood of collision with small space debris and other particulate material is another practical limitation. At the velocities presently attained, however, time dilation is not a factor in space travel. Travel to regions of spacetime where gravitational time dilation is taking place, such as within the gravitational field of a black hole but outside the event horizon (perhaps on a hyperbolic trajectory exiting the field), could also yield results consistent with present theory. A line showing the speed of light on a scale model of Earth and the Moon, about 1. ... Space debris or orbital debris, also called space junk and space waste, are the objects in orbit around Earth created by man that no longer serve any useful purpose. ... For the science fiction film, see Event Horizon (film). ...


Time dilation at constant acceleration

In Special Relativity, time dilation is most simply described in circumstances where relative velocity is unchanging. Nevertheless, the Lorentz equations allow one to calculate proper time and movement in space for the simple case of a spaceship whose acceleration, relative to some referent object in uniform (ie, unaccelerating) motion, equals g throughout the period of measurement.


Let t be the time in an inertial frame subsequently called the rest frame. Let x be a spatial coordinate, and let the direction of the constant acceleration as well as the spaceship's velocity (relative to the rest frame) be parallel to the x-axis. Assuming the spaceship's position at time t = 0 being x = 0 and the velocity being v0, the following formulas hold [2]:


Position:

x = left( sqrt{1 + frac{(g cdot t + frac{v_0}{sqrt{1-frac{v_0^2}{c^2}}})^2}{c^2}} -frac{1}{ sqrt{1 - frac{v_0^2}{c^2}}} right) cdot frac {c^2}{g}

Velocity:

v=frac{g cdot t + frac{v_0}{sqrt{1-frac{v_0^2}{c^2}}}}{sqrt{1 + frac{ left(g cdot t + frac{v_0 }{sqrt{1-frac{v_0^2}{c^2}}}right)^2}{c^2}}}

Proper time:

t^*=frac{c}{g} cdot ln left( left(sqrt{c^2 + v_0^2} - frac{v_0}{sqrt{1-frac{v_0^2}{c^2}}} right) cdot frac{sqrt{c^2 + (g cdot t + v_0/sqrt{1-frac{v_0^2}{c^2}})^2} + g cdot t + v_0/sqrt{1-frac{v_0^2}{c^2}}}{c^2} right)

Time in the rest frame as a function of x:

t=frac{1}{g} cdot left(-v_0 + frac{1}{c} cdot sqrt{v_0^2 cdot c^2 + x^2 cdot g^2 + 2 cdot x cdot g cdot c cdot sqrt{c^2 + v_0^2}} right)

Simple inference of time dilation

Observer at rest sees time 2L/c
Observer at rest sees time 2L/c
Observer moving left relative to setup, sees longer path, time > 2L/c, same speed c
Observer moving left relative to setup, sees longer path, time > 2L/c, same speed c

Time dilation can be inferred from the constancy of the speed of light in all reference frames as follows: Image File history File links Time-dilation-001. ... Image File history File links Time-dilation-001. ... Image File history File links Time-dilation-002. ... Image File history File links Time-dilation-002. ...


Consider a simple clock consisting of two mirrors A and B, between which a photon is bouncing. The separation of the mirrors is L, and the clock ticks once each time it hits a given mirror.


In the frame where the clock is at rest (diagram at right), the photon traces out a path of length 2L and the period of the clock is 2L divided by the speed of light.


From the frame of reference of a moving observer (diagram at lower right), the photon traces out a longer, angled, path. The second postulate of special relativity states that the speed of light is constant in all frames, which implies a lengthening of the period of this clock from the moving observer's perspective. That is to say, in a frame moving relative to the clock, the clock appears to be running slower. Straightforward application of the Pythagorean theorem leads to the well-known prediction of special relativity. In mathematics, the Pythagorean theorem or Pythagoras theorem is a relation in Euclidean geometry among the three sides of a right triangle. ...

t = frac{2Delta}{c}
Delta = sqrt{left (frac{1}{2}vtright )^2+L^2}
ct = 2sqrt{left (frac{1}{2}vtright )^2+L^2}
c^2t^2 = v^2t^2+4L^2
t^2 = frac{4L^2}{c^2-v^2}
t = frac{2L/c}{sqrt{1-(v/c)^2}}

Time dilation is symmetric between two inertial observers

One assumes, naturally enough, that if time-passage has slowed for a moving object, the moving object would find the external world to be correspondingly "sped up." But counterintuitively, Einsteinian relativity predicts the opposite, a situation difficult to visualize. This is based on an essential principle of the overall theory: if one object is moving with respect to another (at an unchanging velocity), the other is equally moving with respect to it.


We're accustomed to this notion of relativity with respect to distance: the distance from Los Angeles to New York is, and must be, the same as the distance from New York to Los Angeles. But when we consider speeds, we think of an object as "really" moving, overlooking that its motion is always relative to something else — to oneself, the ground, the stars, etc. A camera dollying along with a moving object against a blank background would reveal no motion.


The Einsteinian takes seriously the thesis that all motion is indeed relative to some actual (if specified only by implication) "benchmark" that is regarded as stationary, setting aside any issue as to whether what is treated as stationary "really is". You regard it as stationary, and are justified in so treating it, if you yourself are maintaining a fixed distance from it. And this is true even if, for someone else, both you and the benchmark are moving along side-by-side.


But if motion is thus understood as purely relative, it can be divided-up between "mover" and "benchmark" in any way one pleases, even allowing them to completely switch roles. All that matters is the rate at which they are approaching, or departing from, one another, a grand total which re-distributing the speed-contribution of each one doesn't change. And if that is true, the consequences of relative motion predicted by the theory must also "add up" to an unchanging total effect. If A finds that B has undergone a slowdown-in-time during the period of relative motion, it must work out that B will also find that A has a relatively slower "clock." It seems an inconceivable situation: yet the math works out, and actual tests confirm it.


With respect to constant relative motion between two "clocks", a measurement of relative time must choose one clock as being "stationary" in spacetime, and that clock is the basis of a temporal coordinate system where time throughout is treated as synchronized with the stationary clock. The other "moving" clock is in motion with respect to this treated-as-stationary coordinated system, and its relative motion is the velocity value used in the applicable equations. Stationary can mean: Look up stationary in Wiktionary, the free dictionary. ... In physics, spacetime is any mathematical model that combines space and time into a single construct called the space-time continuum. ...


In the Special Theory of Relativity, the moving clock is found to be ticking slow with respect to the temporal coordinate system of the stationary clock. And as indicated, this effect is symmetrical: In a coordinate system synchronized, by contrast, with the "moving" clock, it is the "stationary" clocks that is found (by all methods of measurement) to be running slow. (Neglecting this principle of symmetry leads to the so-called twin paradox being regarded as paradoxical.) In his famous work on Special Relativity in 1905, Albert Einstein predicted that when two clocks were brought together and synchronised, and then one was moved away and brought back, the clock which had undergone the traveling would be found to be lagging behind the clock which had stayed put. ...


Note that in all such attempts to establish "synchronization" within the reference system, the question of whether something happening at one location is in fact happening simultaneously with something happening elsewhere, is of key importance. Calculations are ultimately based on determining what is simultaneous with what.


It is a natural and legitimate question to ask how, in detail, Special Relativity can be self-consistent if clock A is time-dilated with respect to clock B and clock B is also time-dilated with respect to clock A. It is by challenging the assumptions we build into the common notion of simultaneity that logical consistency can be restored. Within the framework of the theory and its terminology, the short answer is that there is a relativity of simultaneity that affects how the specified "benchmark" moments of "simultaneous" events are aligned with respect to each other by observers who are in motion with respect to one other. Because the pairs of putatively simultaneous moments are differently identified by the different observers (as illustrated in the twin paradox article), each can treat the other clock as being the slow one without Relativity being self-contradictory. For those seeking a more explicit account, this can be explained in many ways, some of which follow. The relativity of simultaneity is the dependence of the notion of simultaneity on the observer. ... In his famous work on Special Relativity in 1905, Albert Einstein predicted that when two clocks were brought together and synchronised, and then one was moved away and brought back, the clock which had undergone the traveling would be found to be lagging behind the clock which had stayed put. ...


Temporal coordinate systems and clock synchronization

In Relativity, temporal coordinate systems are set up using a procedure for synchronizing clocks, discussed by Poincaré (1900) in relation to Lorentz's local time (see relativity of simultaneity). It is now usually called the Einstein synchronization procedure, since it appeared in his 1905 paper. The relativity of simultaneity is the dependence of the notion of simultaneity on the observer. ...


An observer with a clock sends a light signal out at time t1 according to his clock. At a distant event, that light signal is reflected back to, and arrives back to the observer at time t2 according to his clock. Since the light travels the same path at the same rate going both out and back for the observer in this scenario, the coordinate time of the event of the photon being reflected for the observer tE is tE = (t1 + t2) / 2. In this way, a single observer's clock can be used to define temporal coordinates which are good anywhere in the universe.


Symmetric time dilation occurs with respect to temporal coordinate systems set up in this manner. It is an effect where another clock is being viewed as running slow by an observer. Observers in rest in their coordinate system do not consider their own clock time to be time-dilated, but may find that it is understood to be time-dilated in another coordinate system.


The spacetime geometry of velocity time dilation

Time dilation in transversal motion.

The green dots and red dots in the animation represent spaceships. The ships of the green fleet have no velocity relative to each other, so for the clocks onboard the individual ships the same amount of time elapses relative to each other, and they can set up a procedure to maintain a synchronized standard fleet time. The ships of the "red fleet" are moving with a velocity of 0.866 of the speed of light with respect to the green fleet. Image File history File links This animated GIF is meant to be used as an illustration for the time dilation article. ...


The blue dots represent pulses of light. One cycle of light-pulses between two green ships takes two seconds of "green time", one second for each leg.


As seen from the perspective of the reds, the transit time of the light pulses they exchange among each other is one second of "red time" for each leg. As seen from the perspective of the greens, the red ships' cycle of exchanging light pulses travels a diagonal path that is two light-seconds long. (As seen from the green perspective the reds travel 1.73 (sqrt{3}) light-seconds of distance for every two seconds of green time.)


One of the red ships emits a light pulse towards the greens every second of red time. These pulses are received by ships of the green fleet with two-second intervals as measured in green time. Not shown in the animation is that all aspects of physics are proportionally involved. The lightpulses that are emitted by the reds at a particular frequency as measured in red time are received at a lower frequency as measured by the detectors of the green fleet that measure against green time, and vice versa.


The animation cycles between the green perspective and the red perspective, to emphasize the symmetry. As there is no such thing as absolute motion in relativity (as is also the case for Newtonian mechanics), both the green and the red fleet are entitled to consider themselves as "non-moving" in their own frame of reference. It has been suggested that this article or section be merged with Classical mechanics. ...


Again, it is vital to understand that the results of these interactions and calculations reflect the real state of the ships as it emerges from their situation of relative motion. It is not a mere quirk of the method of measurement or communication.


Time dilation in popular culture

  • Time dilation underlies the theme song of the cult movie Dark Star, "Benson, Arizona". The lyrics are a lament of a space traveler separated from his lover by space and time.
  • Relativistic time dilation is used in Flight of the Navigator as the central plot conflict solved by a time travel jump to restore David to his proper time.
  • Time dilation is a theme in the song "'39" by Queen.
  • Mostly in Japan, time dilation is commonly called the Urashima effect, after Urashima Tarō.
  • In the series Stargate SG-1, a time dilation device is used by the Asgard aliens to try to contain the robotic Replicators. The Replicators then use the device to strengthen their own forces, advancing by centuries in what is months to the rest of the universe.
  • Another episode of Stargate SG-1 has a time dilation effect being created when a stargate connection is made to a planet being devoured by a black hole.
  • In the final episode of Stargate SG-1, the time dilation device created by the Asgard is used to encompass the Odyssey to prevent an Ori energy beam from destroying the ship. As the beam is about hit, time outside the ship seems to stop, while time seems to pass normally for the passengers inside. This gives them more time to come up with a way to somehow escape the beam.
  • Time dilation was also put into use in the Original Video Animation, Aim for the Top! Gunbuster. As a result of traveling at the speed of light during the struggle against the space monsters, the two heroines of the show barely age at all while several years pass on Earth.
  • Time dilation plays an integral part of the story in the short anime film Voices of a Distant Star. Young lovers are separated when one decides to enlist in a six month tour of the galaxy and the other ages many years.
  • Time dilation is shown in Planet of the Apes (1968 film). During the introduction, Taylor mentions that because his ship is going near the speed of light, he has aged only months and everyone he knew on Earth is now long dead.
  • Time dilation is shown in Andromeda (TV series). In the first episode of the series, Captain Dylan Hunt and his artificially intelligent ship, the Andromeda Ascendant, are trapped in time at the event horizon of a black hole. Due to the artificial gravity used on the ship reacting with the gravity of the singularity, time dilation occurs, visible as sections of action [a fight scene] slowing down. (Erroneously, the characters are aware of the time dilation, which shouldn't actually happen: time would flow consistantly in their perception.)
  • Time dilation is the main plot element in Poul Anderson's novel, Tau Zero. A group of human scientists enroute to a local star system experience numerous engine problems with their starcraft. They are stuck accelerating toward the speed of light as they traverse the cosmos, aging only a few years while Earth is billions of years long dead.

Lafayette Ronald Hubbard (13 March 1911 – 24 January 1986), better known as L. Ron Hubbard, was an American science fiction writer,[1][2][3] creator of Dianetics, and founder of the Church of Scientology. ... Joseph William Haldeman is an American science fiction author. ... 1977 Orbit paperback edition. ... The tone or style of this article or section may not be appropriate for Wikipedia. ... The Enders Game Series (or simply Ender Series) is a series of science fiction books by Orson Scott Card, started with the short story Enders Game, which was later expanded into the novel Enders Game. ... Andrew Ender Wiggin is a fictional character from Orson Scott Cards science fiction story Enders Game and its sequels (Speaker for the Dead, Xenocide, Children of the Mind), as well as in the first part of the spin-off series, Enders Shadow. ... The terms Dark Star or Darkstar may refer to: Dark star, a theoretical star whose gravity is strong enough to trap light, mostly superseded by the concept of black holes. RQ-3 Dark Star, a military drone developed by the United States Dark Star (band), an English rock band Dark... This article is about the film; for the a definition of the UFO related phenomenon, see Close encounter. ... Flight of the Navigator is a 1986 Disney science fiction film about a boy, David, who is somehow transported in time eight years into the future without aging. ... 39 is a song by the English rock band Queen. ... Queen are an English rock band formed in 1970 in London by guitarist Brian May, singer Freddie Mercury and drummer Roger Taylor, with bassist John Deacon joining the following year. ... Urashima Tarō ) is a Japanese fairy tale about a fisherman who rescues a turtle and is rewarded with a visit to the Ryūgū-jō, the Dragon Palace. ... Stargate SG-1 (often abbreviated as SG-1) is a science fiction television series, part of the Stargate franchise. ... In the science fiction series Stargate SG-1, the Asgard are a benevolent, highly advanced and evolved race from another galaxy, called Ida, who have visited Earth on many occasions, giving rise to the Norse legends. ... In the science fiction series Stargate SG-1, the Replicators are a race of self-replicating machines, and arguably one of the most advanced races in the Stargate universe. ... A Matter of Time is an episode of the science fiction television series Stargate SG-1. ... Simulated view of a black hole in front of the Milky Way. ... Episode chronology Unending is the twentieth episode of season ten of the science fiction television series Stargate SG-1, as well as the series finale. ... The Daedalus-class battlecruiser is a fictional starship in the science fiction television series Stargate SG-1 and Stargate Atlantis. ... The Ori (pronounced OR-eye) are characters on the fictional Stargate SG-1 television program. ... Original Video Animation ), abbreviated OVA ), is a term used for anime titles that are released direct-to-video, without prior showings on TV or in theaters. ... Gunbuster, known in Japan as Aim for the Top! ) is a six episode anime OVA series created by Gainax in 1988. ... Hoshi no Koe redirects here. ... Planet of the Apes is a 1968 science fiction film about an astronaut (Charlton Heston) who finds himself stranded on an Earth-like planet two thousand years in the future. ... Gene Roddenberrys Andromeda is an American science fiction television series, based on unused material by Gene Roddenberry developed by Robert Hewitt Wolfe, and produced posthumously by his widow, Majel Roddenberry. ... The Andromeda Ascendant is a fictional starship in the television series Gene Roddenberrys Andromeda. ... Poul William Anderson (November 25, 1926–July 31, 2001) was an American science fiction author of the genres Golden Age. ... Tau Zero is a science fiction novel by Poul Anderson. ...

References

Wikibooks
Wikibooks has a book on the topic of
  • Callender, Craig & Edney, Ralph (2001). Introducing Time. Icon. ISBN 1-84046-592-1. 
  • Einstein, A. (1905) "Zur Elektrodynamik bewegter Körper", Annalen der Physik, 17, 891. English translation: On the electrodynamics of moving bodies
  • Einstein, A. (1907) "Über eine Möglichkeit einer Prüfung des Relativitätsprinzips", Annalen der Physik.
  • Hasselkamp, D., Mondry, E. and Scharmann, A. (1979) "Direct Observation of the Transversal Doppler-Shift", Z. Physik A 289, 151-155
  • Ives, H. E. and Stilwell, G. R. (1938), “An experimental study of the rate of a moving clock”, J. Opt. Soc. Am, 28, 215-226
  • Ives, H. E. and Stilwell, G. R. (1941), “An experimental study of the rate of a moving clock. II”, J. Opt. Soc. Am, 31, 369-374
  • Joos, G. (1959) Lehrbuch der Theoretischen Physik, 11. Auflage, Leipzig; Zweites Buch, Sechstes Kapitel, § 4: Bewegte Bezugssysteme in der Akustik. Der Doppler-Effekt.
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  • Poincaré, H. (1900) "La theorie de Lorentz et la Principe de Reaction", Archives Neerlandaies, V, 253-78.
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  • NIST Two way time transfer for satellites
  • Voigt, W. "Ueber das Doppler'sche princip" Nachrichten von der Königlicher Gesellschaft der Wissenschaften zu Göttingen, 2, 41-51.

Image File history File links Wikibooks-logo-en. ... Wikibooks logo Wikibooks, previously called Wikimedia Free Textbook Project and Wikimedia-Textbooks, is a wiki for the creation of books. ...

See also

In relativity, a four-vector is a vector in a four-dimensional real vector space, whose components transform like the space and time coordinates (ct, x, y, z) under spatial rotations and boosts (a change by a constant velocity to another inertial reference frame). ... An illustration of a rotating black hole at the center of a galaxy General relativity (GR) (aka general theory of relativity (GTR)) is the geometrical theory of gravitation published by Albert Einstein in 1915/16. ... Gravitational time dilation is a consequence of Albert Einsteins theories of relativity and related theories which causes time to pass at different rates in regions of a different gravitational potential; the higher the local distortion of spacetime due to gravity, the slower time passes. ... The Hafele-Keating experiment was a test of the theory of relativity. ... Herbert Dingle (1890 – 1978) was an English astronomer and president of the Royal Astronomical Society. ... The Ives-Stilwell experiment exploits the Transverse Doppler effect (TDE) described by Albert Einstein in his 1905 paper. ... The Trouton-Rankine Experiment was an experiment designed to test the Lorentz-FitzGerald contraction hypothesis. ... Length contraction, according to Albert Einsteins special theory of relativity, is the decrease in length experienced by people or objects traveling at a substantial fraction of the speed of light. ... The Lorentz-FitzGerald contraction hypothesis was proposed by George FitzGerald and independently proposed and extended by Hendrik Lorentz to explain the negative result of the Michelson-Morley experiment, which attempted to detect Earths motion relative to the luminiferous aether. ... A Lorentz transformation (LT) is a linear transformation that preserves the spacetime interval between any two events in Minkowski space, while leaving the origin fixed (=rotation of Minkowski space). ... In physics and mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einsteins theory of special relativity is most conveniently formulated. ... The Pound-Rebka experiment is a well known experiment in general relativity. ... In relativity, proper time is time measured by a single clock between events that occur at the same place as the clock. ... A source of light waves moving to the right with velocity 0. ... In special relativity, the transverse Doppler effect is the nominal redshift component associated with transverse (i. ... The relativity of simultaneity is the dependence of the notion of simultaneity on the observer. ... The special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. Some three centuries earlier, Galileos principle of relativity had stated that all uniform motion was relative, and that there was no absolute and well-defined state of rest... In his famous work on Special Relativity in 1905, Albert Einstein predicted that when two clocks were brought together and synchronised, and then one was moved away and brought back, the clock which had undergone the traveling would be found to be lagging behind the clock which had stayed put. ...

External links


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