Time dilation

Short description: Measured time difference as explained by relativity theory

This page is about a physical concept. For the term used in psychology, see Time perception.

Template:Special relativity sidebar Time dilation is the difference in elapsed time as measured by two clocks, either because of a relative velocity between them (special relativity), or a difference in gravitational potential between their locations (general relativity). When unspecified, "time dilation" usually refers to the effect due to velocity. The dilation compares "wristwatch" clock readings between events measured in different inertial frames and is not observed by visual comparison of clocks across moving frames.

These predictions of the theory of relativity have been repeatedly confirmed by experiment, and they are of practical concern, for instance in the operation of satellite navigation systems such as GPS and Galileo.[1]

## Contents

* 1 Invisibility
* 2 History
* 3 Time dilation caused by a relative velocity
* 3.1 Simple inference
* 3.2 Reciprocity
* 3.3 Experimental testing
* 3.3.1 Moving particles
* 3.3.2 Doppler effect
* 3.4 Proper time and Minkowski diagram
* 3.5 Derivation and formulation
* 3.6 Hyperbolic motion
* 3.7 Clock hypothesis
* 4 Time dilation caused by gravity or acceleration
* 4.1 Experimental testing
* 5 Combined effect of velocity and gravitational time dilation
* 5.1 Experimental testing
* 6 In popular culture
* 6.1 Popular misconception
* 7 In fiction
* 8 See also
* 9 Footnotes
* 10 References
* 11 Further reading
* 12 External links

## Invisibility

Time dilation is a relationship between clock readings. Visually observed clock readings involve delays due to the propagation speed of light from the clock to the observer. Thus there is no direct way to observe time dilation. As an example of time dilation, two experimenters measuring a passing train traveling at .86 light speed may see a 2 second difference on their clocks while on the train the engineer reports only one second elapsed when the experimenters went by. Observations of a clock on the front of the train would give completely different results: the light from the train would not reach the second experimenter only 0.27s before the train passed. This effect of moving objects on observations is associated with the Doppler effect.[2]

## History

Main article: Physics:History of special relativity

Time dilation by the Lorentz factor was predicted by several authors at the turn of the 20th century.[3][4] Joseph Larmor (1897) wrote that, at least for those orbiting a nucleus, individual electrons describe corresponding parts of their orbits in times shorter for the [rest] system in the ratio: 1−v2c2.[5] Emil Cohn (1904) specifically related this formula to the rate of clocks.[6] In the context of special relativity it was shown by Albert Einstein (1905) that this effect concerns the nature of time itself, and he was also the first to point out its reciprocity or symmetry.[7] Subsequently, Hermann Minkowski (1907) introduced the concept of proper time which further clarified the meaning of time dilation.[8]

## Time dilation caused by a relative velocity

From the local frame of reference of the blue clock, the red clock, being in motion, is measured as ticking slower.[9]

Special relativity indicates that, for an observer in an inertial frame of reference, a clock that is moving relative to the observer will be measured to tick more slowly than a clock at rest in the observer's frame of reference. This is sometimes called special relativistic time dilation. The faster the relative velocity, the greater the time dilation between them, with time slowing to a stop as one clock approaches the speed of light (299,792,458 m/s).

In theory, time dilation would make it possible for passengers in a fast-moving vehicle to advance into the future in a short period of their own time. With sufficiently high speeds, the effect would be 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.[10]

With current technology severely limiting the velocity of space travel, the differences experienced in practice are minuscule. After 6 months on the International Space Station (ISS), orbiting Earth at a speed of about 7,700 m/s, an astronaut would have aged about 0.005 seconds less than he would have on Earth.[11] The cosmonauts Sergei Krikalev and Sergey Avdeev both experienced time dilation of about 20 milliseconds compared to time that passed on Earth.[12][13]

### Simple inference

Left: Observer at rest measures time 2L/c between co-local events of light signal generation at A and arrival at A.
Right: Events according to an observer watching as the mirror setup moves to the right: bottom mirror A when signal is generated at time t'=0, top mirror B when signal gets reflected at time t'=D/c, bottom mirror A when signal returns at time t'=2D/c[14]

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.[15][16]

The relativity of time can be illustrated with a thought experiment based on an abstract vertical clock consisting of two mirrors A and B, between which a light pulse is bouncing.[17] The separation of the mirrors is L and the clock ticks once each time the light pulse hits mirror A. 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 2L and the time period between the ticks of the clock Δt is equal to 2L divided by the speed of light c:

Δt=2Lc

From the frame of reference of a moving observer traveling at the speed v relative to the resting frame of the clock (right part of diagram), the light pulse is seen as tracing out a longer, angled path 2D. Keeping the speed of light constant for all inertial observers requires a lengthening (that is dilation) of the time period between the ticks of this clock Δt′ 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 (that is ticking) more slowly, since tick rate equals one over the time period between ticks 1/Δt′.

Straightforward application of the Pythagorean theorem leads to the well-known prediction of special relativity:

The total time for the light pulse to trace its path is given by:

Δt′=2Dc

The length of the half path can be calculated as a function of known quantities as:

D=(12vΔt′)2+L2

Elimination of the variables D and L from these three equations results in:

Time dilation equation

Δt′=Δt1−v2c2=γΔt

which expresses the fact that the moving observer's period of the clock Δt′ is longer than the period Δt in the frame of the clock itself. The Lorentz factor gamma (γ) is defined as[18]

γ=11−v2c2

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 clocks—mechanical, electronic, optical (such as an identical horizontal version of the clock in the example)—should exhibit the same velocity-dependent time dilation.[19]

### Reciprocity

Transversal time dilation. The blue dots represent a pulse of light. Each pair of dots with light "bouncing" between them is a clock. In the frame of each group of clocks, the other group is measured to tick more slowly, because the moving clock's light pulse has to travel a larger distance than the stationary clock's light pulse. That is so, even though the clocks are identical and their relative motion is perfectly reciprocal.

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 measure the other's clock as ticking at a slower rate than their own local clock, due to them both measuring 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.

Time UV of a clock in S is shorter compared to Ux′ in S′, and time UW of a clock in S′ is shorter compared to Ux in S.

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.[20]

The reciprocity of the phenomenon also leads to the so-called twin paradox 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 can be explained by the fact that situation is not symmetric. The twin staying on Earth is in a single inertial frame, and the traveling twin is in two different inertial frames: one on the way out and another on the way back. See also Twin paradox § Role of acceleration.

### Experimental testing

Main article: Experimental testing of time dilation

See also: Tests of special relativity

#### Moving particles

* A comparison of muon 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.[21]
* 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.[22]

#### Doppler effect

Main article: Physics:Ives–Stilwell experiment

* 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 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:f01−v/candf01+v/cThe high and low frequencies of the radiation from the moving sources were measured as:[23]1+v/c1−v/cf0=γ(1+v/c)f0and1−v/c1+v/cf0=γ(1−v/c)f0as deduced by Einstein (1905) from the Lorentz transformation, when the source is running slow by the Lorentz factor.
* Hasselkamp, Mondry, and Scharmann[24] (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:fdetected=frest(1−vccos⁡ϕ)/1−v2/c2as deduced by Einstein (1905).[25] For ϕ = 90° (cos ϕ = 0) this reduces to fdetected = frestγ. This lower frequency from the moving source can be attributed to the time dilation effect and is often called the transverse Doppler effect 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.[26]

### Proper time and Minkowski diagram

Minkowski diagram and twin paradox

Clock C in relative motion between two synchronized clocks A and B. C meets A at d, and B at f.

Twin paradox. One twin has to change frames, leading to different proper times in the twin's world lines.

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.[27] 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.[27]

### Derivation and formulation

Lorentz factor as a function of speed (in natural units where c = 1). Notice that for small speeds (as v tends to zero), γ is approximately 1.

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.[28] Let there be two events at which the moving clock indicates ta and tb, thus:

ta′=ta−vxac21−v2c2, tb′=tb−vxbc21−v2c2

Since the clock remains at rest in its inertial frame, it follows xa=xb, thus the interval Δt′=tb′−ta′ is given by:

Δt′=γΔt=Δt1−v2c2

where Δt 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 or γ) is:

γ=11−v2c2

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, 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. As an approximate threshold, time dilation of 0.5% may become important when an object approaches speeds on the order of 30,000 km/s (1/10 the speed of light).[29]

### Hyperbolic motion

Main article: Physics:Hyperbolic motion (relativity)

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 t = 0 being x = 0 and the velocity being v0 and defining the following abbreviation:

γ0=11−v02/c2

the following formulas hold:[30]

Position:

x(t)=c2g(1+(gt+v0γ0)2c2−γ0)

Velocity:

v(t)=gt+v0γ01+(gt+v0γ0)2c2

Proper time as function of coordinate time:

τ(t)=τ0+∫0t1−(v(t′)c)2dt′

In the case where v(0) = v0 = 0 and τ(0) = τ0 = 0 the integral can be expressed as a logarithmic function or, equivalently, as an inverse hyperbolic function:

τ(t)=cgln⁡(gtc+1+(gtc)2)=cgarsinh⁡(gtc)

As functions of the proper time τ of the ship, the following formulae hold:[31]

Position:

x(τ)=c2g(cosh⁡gτc−1)

Velocity:

v(τ)=ctanh⁡gτc

Coordinate time as function of proper time:

t(τ)=cgsinh⁡gτc

### 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:

τ=∫Pdt2−dx2/c2−dy2/c2−dz2/c2

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 light of experimental verification up to very high accelerations in particle accelerators.[32][33]

## Time dilation caused by gravity or acceleration

Main article: Physics:Gravitational time dilation

Time dilation explains why two working clocks will report different times after different accelerations. For example, time goes slower at the ISS, lagging approximately 0.01 seconds for every 12 Earth months passed. For GPS satellites to work, they must adjust for similar bending of spacetime to coordinate properly with systems on Earth.[1]

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). Unlike 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.[citation needed]

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.[citation needed] Also, a climber's time is theoretically passing slightly faster at the top of a mountain compared to people at sea level.

"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."[34] 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, could yield time-shifting results analogous to those of near-lightspeed space travel.

Richard Feynman suggested in a lecture that, due to time dilation, the core of the Earth is younger than the crust. Subsequent calculations suggest the core is 2.5 years younger, out of 4.5 billion years.[35]

### Experimental testing

Main article: Physics:Experimental testing of time dilation

* In 1959, Robert Pound and Glen Rebka measured the very slight gravitational redshift 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.[36] (See Pound–Rebka experiment)
* In 2010, gravitational time dilation was measured at the Earth's surface with a height difference of only one meter, using optical atomic clocks.[26]

## Combined effect of velocity and gravitational time dilation

Daily time dilation (gain or loss if negative) in microseconds as a function of (circular) orbit radius r = rs/re, where rs is satellite orbit radius and re is the equatorial Earth radius, calculated using the Schwarzschild metric. At r ≈ 1.497[Note 1] there is no time dilation. Here the effects of motion and reduced gravity cancel. ISS astronauts fly below, whereas GPS and geostationary satellites fly above.[1]

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 standard and its relationship with the Barycentric Coordinate Time 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 to the Einstein field equations. In the Schwarzschild metric, the interval dtE is given by:[38][39]

dtE2=(1−2GMiric2)dtc2−(1−2GMiric2)−1dx2+dy2+dz2c2

where:

* dtE is a small increment of proper time tE (an interval that could be recorded on an atomic clock),
* dtc is a small increment in the coordinate tc (coordinate time),
* dx,dy,dz are small increments in the three coordinates x,y,z of the clock's position,
* −GMiri represents the sum of the Newtonian gravitational potentials due to the masses in the neighborhood, based on their distances ri from the clock. This sum includes any tidal potentials.

General relativity

Gμν+Λgμν=κTμν

*     * Introduction
* History

* Mathematical formulation
*     * Tests

Fundamental concepts

* Principle of relativity
* Theory of relativity
* Frame of reference
* Inertial frame of reference
* Rest frame
* Center-of-momentum frame
* Equivalence principle
* Mass–energy equivalence
* Special relativity
* Doubly special relativity
* de Sitter invariant special relativity
* World line
* Riemannian geometry

Phenomena

* Kepler problem
* Gravity
* Gravitational field
* Gravity well
* Gravitational lensing
* Gravitational waves
* Gravitational redshift
* Redshift
* Blueshift
* Time dilation
* Gravitational time dilation
* Shapiro time delay
* Gravitational potential
* Gravitational compression
* Gravitational collapse
* Frame-dragging
* Geodetic effect
* Apparent horizon
* Event horizon
* Gravitational singularity
* Naked singularity
* Black hole
* White hole

Spacetime

* Space
* Time
* Spacetime diagrams
* Minkowski spacetime
* Closed timelike curve (CTC)
* Wormhole
* Ellis wormhole

* v
* t
* e

The coordinate velocity of the clock is given by:

v2=dx2+dy2+dz2dtc2

The coordinate time tc 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 (v=0). 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:

dtEdtc=1+2Uc2−v2c2+(c22U+1)−1v∥2c2=1−(β2+βe2+β∥2βe21−βe2)

where:

* v∥ is the radial velocity,
* ve=2GMiri is the escape speed,
* β=v/c, βe=ve/c and β∥=v∥/c are velocities as a percentage of speed of light c,
* U=−GMiri 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. βe=0. It reduces to gravitational time dilation equation in the absence of motion and presence of gravity, i.e. β=0=β∥.

### Experimental testing

Daily time dilation over circular orbit height split into its components. On this chart, only Gravity Probe A was launched specifically to test general relativity. The other spacecraft on this chart (except for the ISS, whose range of points is marked "theory") carry atomic clocks whose proper operation depend on the validity of general relativity.

* Hafele and Keating, in 1971, flew caesium 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 (cf. Pound–Rebka experiment). 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).[40] In 2005, the National Physical Laboratory in the United Kingdom reported their limited replication of this experiment.[41] 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 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.[42]

## In popular culture

### Popular misconception

The unexpected nature of time dilation makes it a common subject of misconception. One form of misconception claims that time dilation applies only to light-based clocks, such as the “light clock” used in many textbook derivations of the Lorentz transformation, and not to mechanical, atomic, or biological timekeeping devices. This misunderstanding can lead to incorrect conclusions about experimental results, such as the Hafele–Keating experiment, which involved atomic clocks flown around the Earth.[43]

To address this, a thought experiment known as Einstein’s Cat was proposed by physicist Val G. Rousseau.[43] The scenario involves a fictional device—the Sync-or-Die clock—that compares the synchronization of a light clock and a mechanical stopwatch. The life of a cat depends on the precise timing between these two clocks when analyzed in different inertial frames. The paradox arises when time dilation is assumed to apply only to the light pulse but not the mechanical clock. Under this incorrect assumption, the cat would be expected to die only by observers moving relative to the cat. The apparent contradiction is resolved when both clocks are recognized as equally subject to relativistic time dilation. This illustrates the fundamental principle that time dilation is a universal feature of special relativity, independent of the clock’s internal mechanism.

## In fiction

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.[44] In Interstellar, a key plot point involves a planet, which is close to a rotating black hole and on the surface of which one hour is equivalent to seven years on Earth due to time dilation.[45] Physicist Kip Thorne collaborated in making the film and explained its scientific concepts in the book The Science of Interstellar.[46][47]

The Queen song '39 was written by astrophysicist as well as musician Brian May, and is centred around the time dilation effect on spacefarers searching for a new home for mankind, as we gradually ruin planet Earth. They return successful, only to find that all and everything they knew has long since passed away.

Time dilation was used in the Doctor Who 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.[48] Furthermore, the dilation allows the Cybermen 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.[49] 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 at the end of the universe.[50] Other examples in literature, such as Rocannon's World, Hyperion and The Forever War, 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.[51][52]

## See also

* Length contraction
* Mass in special relativity

## Footnotes

1. ↑ Average time dilation has a weak dependence on the orbital inclination angle (Ashby 2003, p.32). The r ≈ 1.497 result corresponds to[37] the orbital inclination of modern GPS satellites, which is 55 degrees.

## References

1. ↑ 1.0 1.1 1.2 Ashby, Neil (2003). "Relativity in the Global Positioning System". Living Reviews in Relativity 6 (1): 16. doi:10.12942/lrr-2003-1. PMID 28163638. Bibcode: 2003LRR.....6....1A.
2. ↑ Hughes, Theo; Kersting, Magdalena (5 January 2021). "The invisibility of time dilation". Physics Education 56 (2): 025011. doi:10.1088/1361-6552/abce02. Bibcode: 2021PhyEd..56b5011H.
3. ↑ Miller, Arthur I. (1981). Albert Einstein's Special Theory of Relativity: Emergence (1905) and Early Interpretation (1905–1911). Reading, Massachusetts: Addison–Wesley. ISBN 978-0-201-04679-3. https://archive.org/details/alberteinsteinss0000mill. .
4. ↑ Darrigol, Olivier (2005). "The Genesis of the Theory of Relativity". Einstein, 1905–2005. 1. pp. 1–22. doi:10.1007/3-7643-7436-5_1. ISBN 978-3-7643-7435-8. http://www.bourbaphy.fr/darrigol2.pdf.
5. ↑ Larmor, Joseph (1897). "On a Dynamical Theory of the Electric and Luminiferous Medium, Part 3, Relations with Material Media". Philosophical Transactions of the Royal Society 190: 205–300. doi:10.1098/rsta.1897.0020. Bibcode: 1897RSPTA.190..205L.
6. ↑ Cohn, Emil (1904), "Zur Elektrodynamik bewegter Systeme II" (in de,en), Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften 1904/2 (43): pp. 1404–1416
7. ↑ Einstein, Albert (1905). "Zur Elektrodynamik bewegter Körper" (in de). Annalen der Physik 322 (10): 891–921. doi:10.1002/andp.19053221004. Bibcode: 1905AnP...322..891E. http://sedici.unlp.edu.ar/handle/10915/2786. . See also: English translation.
8. ↑ Minkowski, Hermann (1908), "Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern" (in de,en), Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse: pp. 53–111
9. ↑ Hraskó, Péter (2011). Basic Relativity: An Introductory Essay (illustrated ed.). Springer Science & Business Media. p. 60. ISBN 978-3-642-17810-8. https://books.google.com/books?id=AEdvt1gc3eMC. Extract of page 60
10. ↑ Calder, Nigel (2006). Magic Universe: A grand tour of modern science. Oxford University Press. p. 378. ISBN 978-0-19-280669-7. https://archive.org/details/magicuniversegra0000cald.
11. ↑ -25 microseconds per day results in 0.00458 seconds per 183 days
12. ↑ Overbye, Dennis (2005-06-28). "A Trip Forward in Time. Your Travel Agent: Einstein.". The New York Times. https://www.nytimes.com/2005/06/28/science/a-trip-forward-in-time-your-travel-agent-einstein.html?_r=0.
13. ↑ Gott, Richard J. (2002). Time Travel in Einstein's Universe. pp. 75.
14. ↑ Cutner, Mark Leslie (2003). Astronomy, A Physical Perspective. Cambridge University Press. p. 128. ISBN 978-0-521-82196-4. https://books.google.com/books?id=2QVmiMW0O0MC&pg=PA128.
15. ↑ Lerner, Lawrence S. (1996). Physics for Scientists and Engineers, Volume 2. Jones and Bartlett. pp. 1051–1052. ISBN 978-0-7637-0460-5. https://books.google.com/books?id=B8K_ym9rS6UC&pg=PA1051.
16. ↑ Ellis, George F. R.; Williams, Ruth M. (2000). Flat and Curved Space-times (2nd ed.). Oxford University Press. pp. 28–29. ISBN 978-0-19-850657-7. https://books.google.com/books?id=Hos31wty5WIC&pg=PA28.
17. ↑ Cassidy, David C.; Holton, Gerald James; Rutherford, Floyd James (2002). Understanding Physics. Springer-Verlag. pp. 422. ISBN 978-0-387-98756-9. https://books.google.com/books?id=rpQo7f9F1xUC&pg=PA422.
18. ↑ Forshaw, Jeffrey; Smith, Gavin (2014). Dynamics and Relativity. John Wiley & Sons. ISBN 978-1-118-93329-9. https://books.google.com/books?id=5TaiAwAAQBAJ.
19. ↑ Galli, J. Ronald; Amiri, Farhang (Apr 2012). "The Square Light Clock and Special Relativity". The Physics Teacher (American Association of Physics Teachers) 50 (4): 212. doi:10.1119/1.3694069. Bibcode: 2012PhTea..50..212G.
20. ↑ Adams, Steve (1997). Relativity: An introduction to space-time physics. CRC Press. p. 54. ISBN 978-0-7484-0621-0. https://books.google.com/books?id=1RV0AysEN4oC&pg=PA54.
21. ↑ Stewart, J. V. (2001). Intermediate electromagnetic theory. World Scientific. p. 705. ISBN 978-981-02-4470-5. https://books.google.com/books?id=93E_vYuCKHYC&pg=PA705.
22. ↑ Bailey, J. (1977). "Measurements of relativistic time dilatation for positive and negative muons in a circular orbit". Nature 268 (5618): 301. doi:10.1038/268301a0. Bibcode: 1977Natur.268..301B.
23. ↑ Blaszczak, Z. (2007). Laser 2006. Springer. p. 59. ISBN 978-3540711131. https://books.google.com/books?id=xbh0iBmDF0AC&pg=PA59.
24. ↑ Hasselkamp, D.; Mondry, E.; Scharmann, A. (1979). "Direct observation of the transversal Doppler-shift". Zeitschrift für Physik A 289 (2): 151–155. doi:10.1007/BF01435932. Bibcode: 1979ZPhyA.289..151H.
25. ↑ Einstein, A. (1905). "On the electrodynamics of moving bodies". Fourmilab. http://www.fourmilab.ch/etexts/einstein/specrel/www/.
26. ↑ 26.0 26.1 Chou, C. W.; Hume, D. B.; Rosenband, T.; Wineland, D. J. (2010). "Optical Clocks and Relativity". Science 329 (5999): 1630–1633. doi:10.1126/science.1192720. PMID 20929843. Bibcode: 2010Sci...329.1630C. https://zenodo.org/record/1230910.
27. ↑ 27.0 27.1 Taylor, Edwin F.; Wheeler, John Archibald (1992). Spacetime Physics: Introduction to Special Relativity. New York: W. H. Freeman. ISBN 978-0-7167-2327-1. https://archive.org/details/spacetimephysics00edwi_0.
28. ↑ Born, Max (1964), Einstein's Theory of Relativity, Dover Publications, ISBN 978-0-486-60769-6, https://archive.org/details/einsteinstheoryo0000born
29. ↑ Petkov, Vesselin (2009). Relativity and the Nature of Spacetime (2nd, illustrated ed.). Springer Science & Business Media. p. 87. ISBN 978-3-642-01962-3. https://books.google.com/books?id=AzfFo6A94WEC. Extract of page 87
30. ↑ See equations 3, 4, 6 and 9 of Iorio, Lorenzo (2005). "An analytical treatment of the Clock Paradox in the framework of the Special and General Theories of Relativity". Foundations of Physics Letters 18 (1): 1–19. doi:10.1007/s10702-005-2466-8. Bibcode: 2005FoPhL..18....1I.
31. ↑ Rindler, W. (1977). Essential Relativity. Springer. pp. 49–50. ISBN 978-3540079705. https://archive.org/details/essentialrelativ00rind_279.
32. ↑ Bailey, H.; Borer, K.; Combley, F.; Drumm, H.; Krienen, F.; Lange, F.; Picasso, E.; von Ruden, W. et al. (1977). "Measurements of relativistic time dilatation for positive and negative muons in a circular orbit". Nature 268 (5618): 301–305. doi:10.1038/268301a0. Bibcode: 1977Natur.268..301B.
33. ↑ Roos, C. E.; Marraffino, J.; Reucroft, S.; Waters, J.; Webster, M. S.; Williams, E. G. H. (1980). "σ+/- lifetimes and longitudinal acceleration". Nature 286 (5770): 244–245. doi:10.1038/286244a0. Bibcode: 1980Natur.286..244R.
34. ↑ Burns, M. Shane; Leveille, Michael D.; Dominguez, Armand R.; Gebhard, Brian B.; Huestis, Samuel E.; Steele, Jeffrey; Patterson, Brian; Sell, Jerry F. et al. (18 September 2017). "Measurement of gravitational time dilation: An undergraduate research project". American Journal of Physics 85 (10): 757–762. doi:10.1119/1.5000802. Bibcode: 2017AmJPh..85..757B.
35. ↑ "New calculations show Earth's core is much younger than thought". Phys.org. 26 May 2016. http://phys.org/news/2016-05-earth-core-younger-thought.html.
36. ↑ Pound, R. V.; Snider J. L. (November 2, 1964). "Effect of Gravity on Nuclear Resonance". Physical Review Letters 13 (18): 539–540. doi:10.1103/PhysRevLett.13.539. Bibcode: 1964PhRvL..13..539P.
37. ↑ Ashby, Neil (2002). "Relativity in the Global Positioning System". Physics Today 55 (5): 45. doi:10.1063/1.1485583. PMID 28163638. PMC 5253894. Bibcode: 2002PhT....55e..41A. http://www.physicstoday.org/resource/1/phtoad/v55/i5/p41_s1.
38. ↑ See equations 2 & 3 (combined here and divided throughout by c2) at pp. 35–36 in Moyer, T. D. (1981). "Transformation from proper time on Earth to coordinate time in solar system barycentric space-time frame of reference". Celestial Mechanics 23 (1): 33–56. doi:10.1007/BF01228543. Bibcode: 1981CeMec..23...33M.
39. ↑ A version of the same relationship can also be seen at equation 2 inAshbey, Neil (2002). "Relativity and the Global Positioning System". Physics Today 55 (5): 45. doi:10.1063/1.1485583. Bibcode: 2002PhT....55e..41A. http://www.ipgp.fr/~tarantola/Files/Professional/GPS/Neil_Ashby_Relativity_GPS.pdf.
40. ↑ Nave, C. R. (22 August 2005). "Hafele and Keating Experiment". http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html.
41. ↑ "Einstein". National Physical Laboratory. 2005. pp. 1–4. http://www.npl.co.uk/upload/pdf/metromnia_issue18.pdf.
42. ↑ Kaplan, Elliott; Hegarty, Christopher (2005). Understanding GPS: Principles and Applications. Artech House. p. 306. ISBN 978-1-58053-895-4. https://books.google.com/books?id=-sPXPuOW7ggC. Extract of page 306
43. ↑ 43.0 43.1 Rousseau, V.G. (2025). "Einstein’s Cat: A Thought Experiment on the Universality of Time Dilation". Physics Education. 60 (4). IOP Publishing. doi:10.1088/1361-6552/adedf1.
44. ↑ Weiner, Adam (30 April 2008). "The Science of Sci-Fi". https://www.popsci.com/entertainment-gaming/article/2008-04/science-sci-fi/.
45. ↑ Luminet, Jean-Pierre (16 January 2016). "The Warped Science of Interstellar (4/6) : Time dilation and Penrose process". https://blogs.futura-sciences.com/e-luminet/2016/01/16/warped-science-interstellar-46-time-dilation-penrose-process/.
46. ↑ Kranking, Carlyn (31 May 2019). "Time travel in movies, explained". in Wagner, Ryan. https://northbynorthwestern.com/time-travel-in-movies-explained/.
47. ↑ Tyson, Neil deGrasse (12 July 2017). "Neil deGrasse Tyson Breaks Down 'Interstellar': Black Holes, Time Dilations, and Massive Waves". The Daily Beast (Interview). Interviewed by Marlow Stern.
48. ↑ Collins, Frank (26 June 2017). "DOCTOR WHO, 10.11 – 'World Enough and Time'". http://www.framerated.co.uk/doctor-who-10x11-world-time/.
49. ↑ Meaney, John (17 December 2003). "Time passages (2)". http://johnmeaney.com/nopub/107169527892588754.html.
50. ↑ Langford, David; Stableford, Brian M (20 August 2018). "Relativity". in Clute, John; Langford, David; Nicholls, Peter et al.. http://sf-encyclopedia.com/entry/relativity.
51. ↑ Cramer, John G. (20 August 1989). "The Twin Paradox Revisited". Analog Science Fiction and Fact (March-1990). https://www.npl.washington.edu/AV/altvw38.html.
52. ↑ Walter, Damien (22 February 2018). "It's about time: how sci-fi has described Einstein's universe". https://www.theguardian.com/books/2016/jan/15/sci-fi-general-relativity-einstein-planet-of-the-apes.

## Further reading

* Callender, C.; Edney, R. (2001). Introducing Time. Icon Books. ISBN 978-1-84046-592-1.
* Einstein, A. (1905). "Zur Elektrodynamik bewegter Körper". Annalen der Physik 322 (10): 891. doi:10.1002/andp.19053221004. Bibcode: 1905AnP...322..891E. http://sedici.unlp.edu.ar/bitstream/handle/10915/2786/Documento_completo__.pdf?sequence=1.
* Einstein, A. (1907). "Über die Möglichkeit einer neuen Prüfung des Relativitätsprinzips". Annalen der Physik 328 (6): 197–198. doi:10.1002/andp.19073280613. Bibcode: 1907AnP...328..197E. https://zenodo.org/record/1424095.
* Hasselkamp, D.; Mondry, E.; Scharmann, A. (1979). "Direct Observation of the Transversal Doppler-Shift". Zeitschrift für Physik A 289 (2): 151–155. doi:10.1007/BF01435932. Bibcode: 1979ZPhyA.289..151H.
* Ives, H. E.; Stilwell, G. R. (1938). "An experimental study of the rate of a moving clock". Journal of the Optical Society of America 28 (7): 215–226. doi:10.1364/JOSA.28.000215. Bibcode: 1938JOSA...28..215I.
* Ives, H. E.; Stilwell, G. R. (1941). "An experimental study of the rate of a moving clock. II". Journal of the Optical Society of America 31 (5): 369–374. doi:10.1364/JOSA.31.000369. Bibcode: 1941JOSA...31..369I.
* Joos, G. (1959). "Bewegte Bezugssysteme in der Akustik. Der Doppler-Effekt". Lehrbuch der Theoretischen Physik, Zweites Buch (11th ed.).
* Larmor, J. (1897). "On a dynamical theory of the electric and luminiferous medium". Philosophical Transactions of the Royal Society 190: 205–300. doi:10.1098/rsta.1897.0020. Bibcode: 1897RSPTA.190..205L. (third and last in a series of papers with the same name).
* Poincaré, H. (1900). "La théorie de Lorentz et le principe de Réaction". Archives Néerlandaises 5: 253–78. http://www.biodiversitylibrary.org/pdf2/003524600031470.pdf.
* Puri, A. (2015). "Einstein versus the simple pendulum formula: does gravity slow all clocks?". Physics Education 50 (4): 431. doi:10.1088/0031-9120/50/4/431. Bibcode: 2015PhyEd..50..431P.
* Reinhardt, S. (2007). "Test of relativistic time dilation with fast optical atomic clocks at different velocities". Nature Physics 3 (12): 861–864. doi:10.1038/nphys778. Bibcode: 2007NatPh...3..861R. http://www.mpq.mpg.de/~haensch/comb/people/thomas/NaturePhysics07.pdf.
* Rossi, B.; Hall, D. B. (1941). "Variation of the Rate of Decay of Mesotrons with Momentum". Physical Review 59 (3): 223. doi:10.1103/PhysRev.59.223. Bibcode: 1941PhRv...59..223R.
* Weiss, M.. "Two way time transfer for satellites". National Institute of Standards and Technology. http://tf.nist.gov/timefreq/time/twoway.htm.
* Voigt, W. (1887). "Über das Doppler'sche princip". Nachrichten von der Königlicher Gesellschaft der Wissenschaften zu Göttingen 2: 41–51.

## External links

* Merrifield, Michael. "Lorentz Factor (and time dilation)". Brady Haran for the University of Nottingham. http://www.sixtysymbols.com/videos/lorentz.htm.

* v
* t
* e

Time measurement and standards

* Chronometry
* Orders of magnitude
* Metrology

International standards|

* Coordinated Universal Time
* offset
* UT
* ΔT
* DUT1
* International Earth Rotation and Reference Systems Service
* ISO 31-1
* ISO 8601
* International Atomic Time
* 6-hour clock (Italian · Thai)
* 12-hour clock
* 24-hour clock
* Barycentric Coordinate Time
* Barycentric Dynamical Time
* Civil time
* Daylight saving time
* Geocentric Coordinate Time
* International Date Line
* Leap second
* Solar time
* Terrestrial Time
* Time zone
* 180th meridian

Obsolete standards|

* Ephemeris time
* Greenwich Mean Time
* Prime meridian

Time in physics|

* Absolute space and time
* Spacetime
* Chronon
* Continuous signal
* Coordinate time
* Cosmological decade
* Discrete time and continuous time
* Planck time
* Proper time
* Theory of relativity
* Time dilation
* Gravitational time dilation
* Time domain
* Time translation symmetry
* T-symmetry

Horology|

* Clock
* Astrarium
* Atomic clock
* Complication
* History of timekeeping devices
* Hourglass
* Marine chronometer
* Marine sandglass
* Radio clock
* Watch
* stopwatch
* Water clock
* Sundial
* Dialing scales
* Equation of time
* History of sundials
* Sundial markup schema

Calendar|

* Astronomical
* Dominical letter
* Epact
* Equinox
* Gregorian
* Hebrew
* Hindu
* Holocene
* Intercalation
* Islamic
* Julian
* Leap year
* Lunar
* Lunisolar
* Solar
* Solstice
* Tropical year
* Weekday determination
* Weekday names

Archaeology and geology|

* Chronological dating
* Geologic time scale
* International Commission on Stratigraphy

Astronomical chronology|

* Galactic year
* Nuclear timescale
* Precession
* Sidereal time

Other units of time|

* Flick
* Shake
* Jiffy
* Second
* Minute
* Moment
* Hour
* Day
* Week
* Fortnight
* Month
* Year
* Olympiad
* Lustrum
* Decade
* Century
* Saeculum
* Millennium

Related topics|

* Chronology
* Duration
* music
* Mental chronometry
* Decimal time
* Metric time
* System time
* Time value of money
* Timekeeper

* v
* t
* e

Relativity

Special
relativity|

| Background|

* Principle of relativity (Galilean relativity
* Galilean transformation)
* Special relativity
* Doubly special relativity

|

Fundamental
concepts|

* Frame of reference
* Speed of light
* Hyperbolic orthogonality
* Rapidity
* Maxwell's equations
* Proper length
* Proper time
* Relativistic mass

Formulation|

* Lorentz transformation

Phenomena|

* Time dilation
* Mass–energy equivalence
* Length contraction
* Relativity of simultaneity
* Relativistic Doppler effect
* Thomas precession
* Ladder paradox
* Twin paradox

Spacetime|

* Light cone
* World line
* Minkowski diagram
* Biquaternions
* Minkowski space

General
relativity|

| Background|

* Introduction
* Mathematical formulation

|

Fundamental
concepts|

* Equivalence principle
* Riemannian geometry
* Penrose diagram
* Geodesics
* Mach's principle

Formulation|

* ADM formalism
* BSSN formalism
* Einstein field equations
* Linearized gravity
* Post-Newtonian formalism
* Raychaudhuri equation
* Hamilton–Jacobi–Einstein equation
* Ernst equation

Phenomena|

* Black hole
* Event horizon
* Singularity
* Two-body problem

* Gravitational waves: astronomy
* detectors (LIGO and collaboration
* Virgo
* LISA Pathfinder
* GEO)
* Hulse–Taylor binary

* Other tests: precession of Mercury
* lensing
* redshift
* Shapiro delay
* frame-dragging / geodetic effect (Lense–Thirring precession)
* pulsar timing arrays

Advanced
theories|

* Brans–Dicke theory
* Kaluza–Klein
* Quantum gravity

Solutions|

* Cosmological: Friedmann–Lemaître–Robertson–Walker (Friedmann equations)
* Kasner
* BKL singularity
* Gödel
* Milne

* Spherical: Schwarzschild (interior
* Tolman–Oppenheimer–Volkoff equation)
* Reissner–Nordström
* Lemaître–Tolman

* Axisymmetric: Kerr (Kerr–Newman)
* Weyl−Lewis−Papapetrou
* Taub–NUT
* van Stockum dust
* discs

* Others: pp-wave
* Ozsváth–Schücking metric

Scientists|

* Poincaré
* Lorentz
* Einstein
* Hilbert
* Schwarzschild
* de Sitter
* Weyl
* Eddington
* Friedmann
* Lemaître
* Milne
* Robertson
* Chandrasekhar
* Zwicky
* Wheeler
* Choquet-Bruhat
* Kerr
* Zel'dovich
* Novikov
* Ehlers
* Geroch
* Penrose
* Hawking
* Taylor
* Hulse
* Bondi
* Misner
* Yau
* Thorne
* Weiss
* others

Categories|

Theory of relativity

* v
* t
* e

Science fiction

Outline|

* Authors
* Definitions
* Hard
* Soft
* History
* Timeline
* The Golden Age
* New Wave
* Anthropological

Subgenres|

| Punk derivatives|

* Biopunk
* Cyberpunk
* Dieselpunk
* Steampunk

|

* Apocalyptic and post-apocalyptic
* Christian
* Climate fiction
* Comedy
* Sitcoms
* Dying Earth
* Feminist
* Gothic
* Libertarian
* Military
* Mundane
* Parallel Worlds
* Planetary romance
* Scientific romance
* Social
* Space opera
* Space Western
* Sword and planet

Culture|

* Conventions
* Fandom
* Fanzines
* Internet Speculative Fiction Database
* Libraries and museums
* Science Fiction Museum
* Studies
* Women in SF
* Worldcon

Region|

* Australian
* Bengali
* Brazilian
* Canadian
* Chilean
* Chinese
* Croatian
* Czech
* Estonian
* French
* Hungarian
* Japanese
* Norwegian
* Polish
* Romanian
* Russian
* Serbian
* Spanish

Awards|

| Multimedia|

* Aurora
* Chandler
* Dragon
* Hugo
* Seiun
* Spectrum

|

Cinematic|

* Jules Verne
* Saturn

Literary/
Art/Audio|

* Astounding
* Aurealis
* BSFA
* Campbell Memorial
* Clarke
* Crook
* Deutscher
* Dick
* Ditmar
* Endeavor
* FantLab
* Galaxy
* Gaughan
* Geffen
* Golden Duck
* Grand Master
* Grand Prix
* Harland
* Heinlein
* Ignotus
* Illustrators of the Future
* Kitschies
* Lambda
* Laßwitz
* Locus
* Nautilus
* Nebula
* Norton
* Parsec
* Prometheus
* Rhysling
* SFERA
* Sidewise
* Skylark
* Sturgeon
* Sunburst
* Tähtivaeltaja
* TBD
* Tiptree
* Tour-Apollo
* Translation
* Urania
* Vogel
* Writers of the Future
* Zajdel

Media|

| Literature|

* Comics
* Magazines
* Novels
* Publishers
* Short stories

|

Stage|

* Opera
* Theatre

Film|

* Film history
* Films
* India

Television|

* TV shows
* Australasian
* British
* Canadian
* European
* Japanese Anime
* Japanese Live-action
* U.S.

Themes|

| Applied|

* Astroengineering
* AI takeover
* Artificial intelligence
* Megastructure
* Space stations and habitats
* Mind uploading
* Nanotechnology
* Organ transplantation
* Prosthetics
* Robots
* Self-replicating machines
* Simulated consciousness
* Simulated reality
* Space warfare
* Terraforming
* Technomancy

|

Formal|

* Fermi paradox
* Grandfather paradox
* Time travel

Life|

* Biological warfare
* Evolution
* Extraterrestrials
* List
* Genetic engineering
* Gender
* Group mind
* Parasites
* Sex and sexuality
* Symbiosis

Physical|

* Faster-than-light
* Heim theory
* Hyperspace
* Jump drive
* Warp drive
* Einstein–Rosen bridge
* Earth
* The multiverse
* Parallel universes
* Planets
* Stars and planetary systems

Social|

* Ancient astronauts
* Alien invasion
* Alien language
* Black
* Cyborgs
* Evil corporation
* Feminist
* First contact
* Frankenstein complex
* Galactic empire
* LGBT
* Libertarian
* Message from space
* Political ideas
* Religious ideas
* Sci horror
* Transhumanism
* Uplifting
* World government
* Xenoarchaeology

Related
topics|

* Alternate history
* Afrofuturism
* Fantasy
* Fictional technology
* Future
* Future history
* Horror
* Magic realism
* Mecha
* Rubber science
* Science and technology studies
* Science fantasy
* Speculative fiction
* Spy-Fi
* Superhero
* Supernatural
* Weird
* Techno-thriller
* Technology and society
* Utopian and dystopian fiction

* Category
* Portal

0.00

(0 votes)

Original source: https://en.wikipedia.org/wiki/Time dilation. Read more

|

Retrieved from "https://handwiki.org/wiki/index.php?title=Physics:Time_dilation&oldid=3841406"
*[v]: View this template
*[t]: Discuss this template
*[e]: Edit this template