Gravitational time dilation
The effects detected in such Earth-bound experiments are extremely small, with differences being measured in nanoseconds.
Gravitational time dilation was first described by Albert Einstein in 1907[3] as a consequence of special relativity in accelerated frames of reference.
Clocks that are far from massive bodies (or at higher gravitational potentials) run more quickly, and clocks close to massive bodies (or at lower gravitational potentials) run more slowly.
For example, considered over the total time-span of Earth (4.6 billion years), a clock set in a geostationary position at an altitude of 9,000 meters above sea level, such as perhaps at the top of Mount Everest (prominence 8,848 m), would be about 39 hours ahead of a clock set at sea level.
[7] According to general relativity, inertial mass and gravitational mass are the same, and all accelerated reference frames (such as a uniformly rotating reference frame with its proper time dilation) are physically equivalent to a gravitational field of the same strength.
[8] Consider a family of observers along a straight "vertical" line, each of whom experiences a distinct constant g-force directed along this line (e.g., a long accelerating spacecraft,[9][10] a skyscraper, a shaft on a planet).
denotes exponentiation by e. For simplicity, in a Rindler's family of observers in a flat spacetime, the dependence would be with constant
See Ehrenfest paradox for application of the same formula to a rotating reference frame in flat spacetime.
A common equation used to determine gravitational time dilation is derived from the Schwarzschild metric, which describes spacetime in the vicinity of a non-rotating massive spherically symmetric object.
The equation is where To illustrate then, without accounting for the effects of rotation, proximity to Earth's gravitational well will cause a clock on the planet's surface to accumulate around 0.0219 fewer seconds over a period of one year than would a distant observer's clock.
In comparison, a clock on the surface of the Sun will accumulate around 66.4 fewer seconds in one year.
Gravitational time dilation has been experimentally measured using atomic clocks on airplanes, such as the Hafele–Keating experiment.
The effect is significant enough that the Global Positioning System's artificial satellites need to have their clocks corrected.
[13] Additionally, time dilations due to height differences of less than one metre have been experimentally verified in the laboratory.
[14] Gravitational time dilation in the form of gravitational redshift has also been confirmed by the Pound–Rebka experiment and observations of the spectra of the white dwarf Sirius B. Gravitational time dilation has been measured in experiments with time signals sent to and from the Viking 1 Mars lander.
