Time dilation

[1] 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.

[2] Time dilation by the Lorentz factor was predicted by several authors at the turn of the 20th century.

[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.

[10] With current technology severely limiting the velocity of space travel, the differences experienced in practice are minuscule.

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.

is equal to 2L divided by the speed of light c: 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

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: The length of the half path can be calculated as a function of known quantities as: Elimination of the variables D and L from these three equations results in:

The Lorentz factor gamma (γ) is defined as[18] 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.

[27] 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.

is given by: 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: Thus the duration of the clock cycle of a moving clock is found to be increased: it is measured to be "running slow".

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 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.

measures the proper time, defined by: The clock hypothesis was implicitly (but not explicitly) included in Einstein's original 1905 formulation of special relativity.

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.

[34] "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.

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.

is the time that would be read on a hypothetical "coordinate clock" situated infinitely far from all gravitational masses (

It reduces to velocity time dilation equation in the presence of motion and absence of gravity, i.e.

It reduces to gravitational time dilation equation in the absence of motion and presence of gravity, i.e.

Velocity and gravitational time dilation have been the subject of science fiction works in a variety of media.

[43] 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.

[44] Physicist Kip Thorne collaborated in making the film and explained its scientific concepts in the book The Science of Interstellar.

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.

Tau Zero, a novel by Poul Anderson, is an early example of the concept in science fiction literature.

[49] 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.

From the local frame of reference of the blue clock, the red clock, being in motion, is measured as ticking slower. [ 9 ]
Left : Observer at rest measures time 2 L / c between co-local events of light signal generation at A and arrival at A.
Right : Events according to an observer moving to the left of the setup: 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
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.
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.
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.
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. [ 2 ]
Time passes more quickly further from a center of gravity, as is witnessed with massive objects (like the Earth).
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. [ 2 ]
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.