Time dilation
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.
This article is about a physical concept. For the term used in psychology, see Time perception.
After compensating for varying signal delays resulting from the changing distance between an observer and a moving clock (i.e. Doppler effect), the observer will measure the moving clock as ticking more slowly than a clock at rest in the observer's own reference frame. 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 farther from the same massive body (and which is at a higher gravitational potential).
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]
is a small increment of proper time (an interval that could be recorded on an atomic clock),
is a small increment in the coordinate (),
coordinate time
are small increments in the three coordinates of the clock's position,
represents the sum of the Newtonian gravitational potentials due to the masses in the neighborhood, based on their distances from the clock. This sum includes any tidal potentials.
In popular culture[edit]
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.[42] 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.[43] Physicist Kip Thorne collaborated in making the film and explained its scientific concepts in the book The Science of Interstellar.[44][45]
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.[46] 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.[47] 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.[48] 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.[49][50]
