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physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...
and relativity, time dilation is the difference in the elapsed
time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...
as measured by two clocks. It is either due to a relative
velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity i ...
between them ( special relativistic "kinetic" time dilation) or to a difference in
gravitational potential In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that would be needed to move an object to that location from a fixed reference location. It is analogous to the electric ...
between their locations ( general relativistic gravitational time dilation). When unspecified, "time dilation" usually refers to the effect due to velocity. After compensating for varying signal delays due to the changing distance between an observer and a moving clock (i.e.
Doppler effect The Doppler effect or Doppler shift (or simply Doppler, when in context) is the change in frequency of a wave in relation to an observer who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who ...
), the observer will measure the moving clock as ticking slower than a clock that is at rest in the observer's own
reference frame In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system whose origin, orientation, and scale are specified by a set of reference points― geometric points whose position is identified both math ...
. In addition, a clock that is close to a massive body (and which therefore is at lower gravitational potential) will record less elapsed time than a clock situated further from the said massive body (and which is at a higher gravitational potential). These predictions of the
theory of relativity The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in ...
have been repeatedly confirmed by experiment, and they are of practical concern, for instance in the operation of
satellite navigation A satellite navigation or satnav system is a system that uses satellites to provide autonomous geo-spatial positioning. It allows satellite navigation devices to determine their location ( longitude, latitude, and altitude/ elevation) to hig ...
systems such as GPS and
Galileo Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...
. Time dilation has also been the subject of science fiction works.


History

Time dilation by the Lorentz factor was predicted by several authors at the turn of the 20th century.
Joseph Larmor Sir Joseph Larmor (11 July 1857 – 19 May 1942) was an Irish and British physicist and mathematician who made breakthroughs in the understanding of electricity, dynamics, thermodynamics, and the electron theory of matter. His most influen ...
(1897), at least for electrons orbiting a nucleus, wrote "... individual electrons describe corresponding parts of their orbits in times shorter for the estsystem in the ratio: \sqrt". Emil Cohn (1904) specifically related this formula to the rate of clocks. In the context of
special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The law ...
it was shown by
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theor ...
(1905) that this effect concerns the nature of time itself, and he was also the first to point out its reciprocity or symmetry. Subsequently,
Hermann Minkowski Hermann Minkowski (; ; 22 June 1864 – 12 January 1909) was a German mathematician and professor at Königsberg, Zürich and Göttingen. He created and developed the geometry of numbers and used geometrical methods to solve problems in number t ...
(1907) introduced the concept of proper time which further clarified the meaning of time dilation.


Time dilation caused by a relative velocity

Special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The law ...
indicates that, for an observer in an
inertial frame of reference In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any acceleration. ...
, a clock that is moving relative to them will be measured to tick slower than a clock that is at rest in their frame of reference. This case is sometimes called special relativistic time dilation. The faster the relative velocity, the greater the time dilation between one another, with time slowing to a stop as one approaches the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit fo ...
(299,792,458 m/s). Theoretically, time dilation would make it possible for passengers in a fast-moving vehicle to advance further into the future in a short period of their own time. For sufficiently high speeds, the effect is dramatic. For example, one year of travel might correspond to ten years on Earth. Indeed, a constant 1  g acceleration would permit humans to travel through the entire known Universe in one human lifetime. With current technology severely limiting the velocity of space travel, however, the differences experienced in practice are minuscule: after 6 months on the
International Space Station The International Space Station (ISS) is the largest Modular design, modular space station currently in low Earth orbit. It is a multinational collaborative project involving five participating space agencies: NASA (United States), Roscosmos ( ...
(ISS), orbiting Earth at a speed of about 7,700 m/s, an astronaut would have aged about 0.005 seconds less than those on Earth. The cosmonauts Sergei Krikalev and Sergei Avdeyev both experienced time dilation of about 20 milliseconds compared to time that passed on Earth.


Simple inference

Time dilation can be inferred from the observed constancy of the speed of light in all reference frames dictated by the second postulate of special relativity. This constancy of the speed of light means that, counter to intuition, the speeds of material objects and light are not additive. It is not possible to make the speed of light appear greater by moving towards or away from the light source. Consider then, a simple vertical clock consisting of two mirrors and , between which a light pulse is bouncing. The separation of the mirrors is and the clock ticks once each time the light pulse hits mirror . In the frame in which the clock is at rest (see left part of the diagram), the light pulse traces out a path of length and the period of the clock is divided by the speed of light: :\Delta t = \frac From the frame of reference of a moving observer traveling at the speed relative to the resting frame of the clock (right part of diagram), the light pulse is seen as tracing out a longer, angled path. Keeping the speed of light constant for all inertial observers requires a lengthening of the period of this clock from the moving observer's perspective. That is to say, as measured in a frame moving relative to the local clock, this clock will be running more slowly. Straightforward application of the
Pythagorean theorem In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposit ...
leads to the well-known prediction of special relativity: The total time for the light pulse to trace its path is given by: :\Delta t' = \frac The length of the half path can be calculated as a function of known quantities as: :D = \sqrt Elimination of the variables and from these three equations results in: :\Delta t' = \frac which expresses the fact that the moving observer's period of the clock \Delta t' is longer than the period \Delta t in the frame of the clock itself. Because all clocks that have a common period in the resting frame should have a common period when observed from the moving frame, all other clocksmechanical, electronic, optical (such as an identical horizontal version of the clock in the example)should exhibit the same velocity-dependent time dilation.


Reciprocity

Given a certain frame of reference, and the "stationary" observer described earlier, if a second observer accompanied the "moving" clock, each of the observers would perceive the other's clock as ticking at a ''slower'' rate than their own local clock, due to them both perceiving the other to be the one that is in motion relative to their own stationary frame of reference. Common sense would dictate that, if the passage of time has slowed for a moving object, said object would observe the external world's time to be correspondingly sped up. Counterintuitively, special relativity predicts the opposite. When two observers are in motion relative to each other, each will measure the other's clock slowing down, in concordance with them being in motion relative to the observer's frame of reference. While this seems self-contradictory, a similar oddity occurs in everyday life. If two persons A and B observe each other from a distance, B will appear small to A, but at the same time, A will appear small to B. Being familiar with the effects of perspective, there is no contradiction or paradox in this situation. The reciprocity of the phenomenon also leads to the so-called
twin paradox In physics, the twin paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more. T ...
where the aging of twins, one staying on Earth and the other embarking on space travel, is compared, and where the reciprocity suggests that both persons should have the same age when they reunite. On the contrary, at the end of the round-trip, the traveling twin will be younger than the sibling on Earth. The dilemma posed by the paradox, however, can be explained by the fact that the traveling twin must markedly accelerate in at least three phases of the trip (beginning, direction change, and end), while the other will only experience negligible acceleration, due to rotation and revolution of Earth. During the acceleration phases of space travel, time dilation is not symmetric.


Experimental testing


Doppler effect

* The stated purpose by Ives and Stilwell (1938, 1941) of these experiments was to verify the time dilation effect, predicted by Larmor–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 The Doppler effect or Doppler shift (or simply Doppler, when in context) is the change in frequency of a wave in relation to an observer who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who ...
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 classically predicted values:\frac \qquad \text \qquad \frac The high and low frequencies of the radiation from the moving sources were measured as:\sqrt f_0 = \gamma \left(1 + v/c\right) f_0 \qquad \text \qquad \sqrt f_0 = \gamma \left(1 - v/c\right) f_0 \,as deduced by Einstein (1905) from the Lorentz transformation, when the source is running slow by the Lorentz factor. * Hasselkamp, Mondry, and Scharmann (1979) measured the Doppler shift from a source moving at right angles to the line of sight. The most general relationship between frequencies of the radiation from the moving sources is given by:f_\mathrm = f_\mathrmas deduced by Einstein (1905). For () this reduces to . This lower frequency from the moving source can be attributed to the time dilation effect and is often called the
transverse Doppler effect The relativistic Doppler effect is the change in frequency (and wavelength) of light, caused by the relative motion of the source and the observer (as in the classical Doppler effect), when taking into account effects described by the special the ...
and was predicted by relativity. * In 2010 time dilation was observed at speeds of less than 10 metres per second using optical atomic clocks connected by 75 metres of optical fiber.


Moving particles

*A comparison of
muon A muon ( ; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with an electric charge of −1 '' e'' and a spin of , but with a much greater mass. It is classified as a lepton. As w ...
lifetimes at different speeds is possible. In the laboratory, slow muons are produced; and in the atmosphere, very fast-moving muons are introduced by cosmic rays. Taking the muon lifetime at rest as the laboratory value of 2.197 μs, the lifetime of a cosmic-ray-produced muon traveling at 98% of the speed of light is about five times longer, in agreement with observations. An example is Rossi and Hall (1941), who compared the population of cosmic-ray-produced muons at the top of a mountain to that observed at sea level. *The lifetime of particles produced in particle accelerators are longer due to time dilation. In such experiments, the "clock" is the time taken by processes leading to muon decay, and these processes take place in the moving muon at its own "clock rate", which is much slower than the laboratory clock. This is routinely taken into account in particle physics, and many dedicated measurements have been performed. For instance, in the muon storage ring at CERN the lifetime of muons circulating with γ = 29.327 was found to be dilated to 64.378 μs, confirming time dilation to an accuracy of 0.9 ± 0.4 parts per thousand.


Proper time and Minkowski diagram

In the Minkowski diagram from the first image on the right, clock C resting in inertial frame S′ meets clock A at ''d'' and clock B at ''f'' (both resting in S). All three clocks simultaneously start to tick in S. The worldline of A is the ct-axis, the worldline of B intersecting ''f'' is parallel to the ct-axis, and the worldline of C is the ct′-axis. All events simultaneous with ''d'' in S are on the x-axis, in S′ on the x′-axis. The proper time between two events is indicated by a clock present at both events. It is invariant, i.e., in all inertial frames it is agreed that this time is indicated by that clock. Interval ''df'' is, therefore, the proper time of clock C, and is shorter with respect to the coordinate times ''ef=dg'' of clocks B and A in S. Conversely, also proper time ''ef'' of B is shorter with respect to time ''if'' in S′, because event ''e'' was measured in S′ already at time ''i'' due to relativity of simultaneity, long before C started to tick. From that it can be seen, that the proper time between two events indicated by an unaccelerated clock present at both events, compared with the synchronized coordinate time measured in all other inertial frames, is always the ''minimal'' time interval between those events. However, the interval between two events can also correspond to the proper time of accelerated clocks present at both events. Under all possible proper times between two events, the proper time of the unaccelerated clock is ''maximal'', which is the solution to the
twin paradox In physics, the twin paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more. T ...
.


Derivation and formulation

In addition to the light clock used above, the formula for time dilation can be more generally derived from the temporal part of the Lorentz transformation. Let there be two events at which the moving clock indicates t_ and t_, thus: :t_^=\frac,\ t_^=\frac Since the clock remains at rest in its inertial frame, it follows x_=x_, thus the interval \Delta t^=t_^-t_^ is given by: : \Delta t' = \gamma \, \Delta t = \frac \, where Δ''t'' is the time interval between ''two co-local events'' (i.e. happening at the same place) for an observer in some inertial frame (e.g. ticks on their clock), known as the '' proper time'', Δt′ 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 the Lorentz factor (conventionally denoted by the Greek letter
gamma Gamma (uppercase , lowercase ; ''gámma'') is the third letter of the Greek alphabet. In the system of Greek numerals it has a value of 3. In Ancient Greek, the letter gamma represented a voiced velar stop . In Modern Greek, this letter r ...
or γ) is: : \gamma = \frac \, 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 even considering space travel, are not great enough to produce easily detectable time dilation effects and such vanishingly small effects can be safely ignored for most purposes. It is only when an object approaches speeds on the order of 30,000 km/s (1/10 the speed of light) that time dilation becomes important.


Hyperbolic motion

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 which is applied with a force per unit mass, relative to some reference object in uniform (i.e. constant velocity) motion, equal to ''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 being and the velocity being ''v''0 and defining the following abbreviation: :\gamma_0 = \frac the following formulas hold: Position: :x(t) = \frac \left( \sqrt -\gamma_0 \right) Velocity: :v(t) =\frac Proper time as function of coordinate time: :\tau(t) = \tau_0 + \int_0^t \sqrt dt' In the case where ''v''(0) = ''v''0 = 0 and ''τ''(0) = ''τ''0 = 0 the integral can be expressed as a logarithmic function or, equivalently, as an inverse hyperbolic function: :\tau(t) = \frac \ln \left( \frac + \sqrt \right) = \frac \operatorname \left( \frac \right) As functions of the proper time \tau of the ship, the following formulae hold: Position: :x(\tau) = \frac \left( \cosh \frac-1 \right) Velocity: :v(\tau) = c \tanh \frac Coordinate time as function of proper time: :t(\tau) = \frac \sinh \frac


Clock hypothesis

The clock hypothesis is the assumption that the rate at which a clock is affected by time dilation does not depend on its acceleration but only on its instantaneous velocity. This is equivalent to stating that a clock moving along a path P measures the proper time, defined by: : \tau = \int_P \sqrt The clock hypothesis was implicitly (but not explicitly) included in Einstein's original 1905 formulation of special relativity. Since then, it has become a standard assumption and is usually included in the axioms of special relativity, especially in the light of experimental verification up to very high accelerations in particle accelerators.


Time dilation caused by gravity or acceleration

Gravitational time dilation is experienced by an observer that, at a certain altitude within a gravitational potential well, finds that their local clocks measure less elapsed time than identical clocks situated at higher altitude (and which are therefore at higher gravitational potential). Gravitational time dilation is at play e.g. for ISS astronauts. While the astronauts' relative velocity slows down their time, the reduced gravitational influence at their location speeds it up, although to a lesser degree. Also, a climber's time is theoretically passing slightly faster at the top of a mountain compared to people at sea level. It has also been calculated that due to time dilation, the core of the Earth is 2.5 years younger than the crust. "A clock used to time a full rotation of the Earth will measure the day to be approximately an extra 10 ns/day longer for every km of altitude above the reference geoid." Travel to regions of space where extreme gravitational time dilation is taking place, such as near (but not beyond the event horizon of) a
black hole A black hole is a region of spacetime where gravity is so strong that nothing, including light or other electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts that a sufficiently compact mass can def ...
, could yield time-shifting results analogous to those of near-lightspeed space travel. Contrarily to velocity time dilation, in which both observers measure the other as aging slower (a reciprocal effect), gravitational time dilation is not reciprocal. This means that with gravitational time dilation both observers agree that the clock nearer the center of the gravitational field is slower in rate, and they agree on the ratio of the difference.


Experimental testing

* In 1959, Robert Pound and Glen A. Rebka measured the very slight
gravitational redshift In physics and general relativity, gravitational redshift (known as Einstein shift in older literature) is the phenomenon that electromagnetic waves or photons travelling out of a gravitational well (seem to) lose energy. This loss of energy ...
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. In 1964, Pound and J. L. Snider measured a result within 1% of the value predicted by gravitational time dilation. (See
Pound–Rebka experiment The Pound–Rebka experiment was an experiment in which gamma rays were emitted from the top of a tower and measured by a receiver at the bottom of the tower. The purpose of the experiment was to test Albert Einstein's theory of general relativit ...
) * In 2010, gravitational time dilation was measured at the Earth's surface with a height difference of only one meter, using optical atomic clocks.


Combined effect of velocity and gravitational time dilation

High-accuracy timekeeping, low-Earth-orbit satellite tracking, and pulsar timing are applications that require the consideration of the combined effects of mass and motion in producing time dilation. Practical examples include the
International Atomic Time International Atomic Time (abbreviated TAI, from its French name ) is a high-precision atomic coordinate time standard based on the notional passage of proper time on Earth's geoid. TAI is a weighted average of the time kept by over 450 ato ...
standard and its relationship with the
Barycentric Coordinate Time Barycentric Coordinate Time (TCB, from the French Temps-coordonnée barycentrique) is a coordinate time standard intended to be used as the independent variable of time for all calculations pertaining to orbits of planets, asteroids, comets, and ...
standard used for interplanetary objects. Relativistic time dilation effects for the solar system and the Earth can be modeled very precisely by the
Schwarzschild solution In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assu ...
to the Einstein field equations. In the Schwarzschild metric, the interval dt_\text is given by:A version of the same relationship can also be seen at equation 2 in : dt_\text^2 = \left( 1-\frac \right) dt_\text^2 - \left( 1-\frac \right)^ \frac where: *dt_\text is a small increment of proper time t_\text (an interval that could be recorded on an atomic clock), *dt_\text is a small increment in the coordinate t_\text (
coordinate time In the theory of relativity, it is convenient to express results in terms of a spacetime coordinate system relative to an implied observer. In many (but not all) coordinate systems, an event is specified by one time coordinate and three spat ...
), *dx, dy, dz are small increments in the three coordinates x, y, z of the clock's position, *\frac represents the sum of the Newtonian gravitational potentials due to the masses in the neighborhood, based on their distances r_i from the clock. This sum includes any tidal potentials. The coordinate velocity of the clock is given by: :v^2 = \frac The coordinate time t_c is the time that would be read on a hypothetical "coordinate clock" situated infinitely far from all gravitational masses (U=0), and stationary in the system of coordinates (). The exact relation between the rate of proper time and the rate of coordinate time for a clock with a radial component of velocity is: :\frac = \sqrt = \sqrt where: *v_\shortparallel is the radial velocity, *v_e = \sqrt is the escape speed, *\beta = v/c, \beta_e = v_e/c and \beta_\shortparallel = v_\shortparallel/c are velocities as a percentage of speed of light ''c'', *U = \frac is the Newtonian potential; hence -U equals half the square of the escape speed. The above equation is exact under the assumptions of the Schwarzschild solution. It reduces to velocity time dilation equation in the presence of motion and absence of gravity, i.e. \beta_e = 0. It reduces to gravitational time dilation equation in the absence of motion and presence of gravity, i.e. \beta = 0 = \beta_\shortparallel.


Experimental testing

* Hafele and Keating, in 1971, flew
caesium Caesium (IUPAC spelling) (or cesium in American English) is a chemical element with the symbol Cs and atomic number 55. It is a soft, silvery-golden alkali metal with a melting point of , which makes it one of only five elemental metals that a ...
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 U.S. Naval Observatory. Two opposite effects came into 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 experiment The Pound–Rebka experiment was an experiment in which gamma rays were emitted from the top of a tower and measured by a receiver at the bottom of the tower. The purpose of the experiment was to test Albert Einstein's theory of general relativit ...
). But also, contrastingly, the moving clocks were expected to age more slowly because of the speed of their travel. From the actual flight paths of each trip, the theory predicted that the flying clocks, compared with reference clocks at the U.S. Naval Observatory, should have lost 40±23 nanoseconds during the eastward trip and should have gained 275±21 nanoseconds during the westward trip. Relative to the atomic time scale of the U.S. Naval Observatory, the flying clocks lost 59±10 nanoseconds during the eastward trip and gained 273±7 nanoseconds during the westward trip (where the error bars represent standard deviation). In 2005, the National Physical Laboratory in the United Kingdom reported their limited replication of this experiment. The NPL experiment differed from the original in that the caesium clocks were sent on a shorter trip (London–Washington, D.C. return), but the clocks were more accurate. The reported results are within 4% of the predictions of relativity, within the uncertainty of the measurements. * The
Global Positioning System The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of the global navigation satellite ...
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 as described above, so that (as observed from the Earth's surface) they run at the same rate as clocks on the surface of the Earth.


In popular culture

Velocity and gravitational time dilation have been the subject of science fiction works in a variety of media. Some examples in film are the movies '' Interstellar'' and ''
Planet of the Apes ''Planet of the Apes'' is an American science fiction media franchise consisting of films, books, television series, comics, and other media about a world in which humans and intelligent apes clash for control. The franchise is based on Frenc ...
''. In ''Interstellar'', a key plot point involves a planet, which is close to a
rotating black hole A rotating black hole is a black hole that possesses angular momentum. In particular, it rotates about one of its axes of symmetry. All celestial objects – planets, stars (Sun), galaxies, black holes – spin. Types of black holes Ther ...
and on the surface of which one hour is equivalent to seven years on Earth due to time dilation. Physicist Kip Thorne collaborated in making the film and explained its scientific concepts in the book '' The Science of Interstellar''. Time dilation was used in the
Doctor Who ''Doctor Who'' is a British science fiction television series broadcast by the BBC since 1963. The series depicts the adventures of a Time Lord called the Doctor, an extraterrestrial being who appears to be human. The Doctor explores the ...
episodes World Enough and Time and The Doctor Falls, which take place on a spaceship in the vicinity of a black hole. Due to the immense gravitational pull of the black hole and the ship's length (400 miles), time moves faster at one end than the other. When The Doctor's companion, Bill, gets taken away to the other end of the ship, she waits years for him to rescue her; in his time, only minutes pass. Furthermore, the dilation allows the
Cybermen The Cybermen are a fictional race of cyborgs principally portrayed in the British science fiction television programme ''Doctor Who''. The Cybermen are a species of space-faring cyborgs who often forcefully and painfully convert human beings ( ...
to evolve at a "faster" rate than previously seen in the show. '' Tau Zero'', a novel by Poul Anderson, is an early example of the concept in science fiction literature. In the novel, a spacecraft uses a Bussard ramjet to accelerate to high enough speeds that the crew spends five years on board, but thirty-three years pass on the Earth before they arrive at their destination. The velocity time dilation is explained by Anderson in terms of the tau factor which decreases closer and closer to zero as the ship approaches the speed of light—hence the title of the novel. Due to an accident, the crew is unable to stop accelerating the spacecraft, causing such extreme time dilation that the crew experiences the
Big Crunch The Big Crunch is a hypothetical scenario for the ultimate fate of the universe, in which the expansion of the universe eventually reverses and the universe recollapses, ultimately causing the cosmic scale factor to reach zero, an event potentia ...
at the end of the universe. Other examples in literature, such as '' Rocannon's World'' and ''
The Forever War ''The Forever War'' (1974) is a military science fiction novel by American author Joe Haldeman, telling the contemplative story about human soldiers fighting an interstellar war against an alien civilization known as the Taurans. It won the Nebul ...
'', similarly make use of relativistic time dilation as a scientifically plausible literary device to have certain characters age slower than the rest of the universe.


See also

*
Length contraction Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame. It is also known as Lorentz contraction or Lorentz–FitzGera ...
*
Mass in special relativity The word " mass" has two meanings in special relativity: '' invariant mass'' (also called rest mass) is an invariant quantity which is the same for all observers in all reference frames, while the relativistic mass is dependent on the velocity ...


Footnotes


References


Further reading

* * * * * * * * (third and last in a series of papers with the same name). * * * * * *


External links

* {{Authority control Special relativity
Dilatation Dilation (or dilatation) may refer to: Physiology or medicine * Cervical dilation, the widening of the cervix in childbirth, miscarriage etc. * Coronary dilation, or coronary reflex * Dilation and curettage, the opening of the cervix and surgi ...
Physical phenomena