Gravitational time dilation is a consequence of Albert Einstein's theories of relativity and related theories which causes time to pass at different rates in regions of a different gravitational potential; the higher the local distortion of spacetime due to gravity, the slower time passes. Albert Einstein( ) (March 14, 1879 – April 18, 1955) was a German-born theoretical physicist who is widely considered to have been one of the greatest physicists of all time. ... Two-dimensional analogy of space-time curvature described in General Relativity. ... In theoretical physics, the current Gold Standard Theory of Gravitation is the general theory of relativity. ... In physics, gravitational potential is the measure of potential energy an object possesses due to its position in a gravitational field. ...

This has been demonstrated by noting that atomic clocks at differing altitudes (and thus different gravitational potential) will eventually show different times. The effects detected in such experiments are extremely small, with differences being measured in nanoseconds. A nanosecond is an SI derived unit of time equal to 10-9 of a second. ...

Gravitational time dilation was first described by Albert Einstein in 1907 as a consequence of special relativity in accelerated frames of reference. In general relativity, it is considered to be difference in the passage of proper time at different positions as described by a metric tensor of spacetime. The existence of gravitational time dilation was first confirmed directly by the Pound-Rebka experiment. Albert Einstein( ) (March 14, 1879 – April 18, 1955) was a German-born theoretical physicist who is widely considered to have been one of the greatest physicists of all time. ... The special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. Some three centuries earlier, Galileos principle of relativity had stated that all uniform motion was relative, and that there was no absolute and well-defined state of rest... General relativity (GR) [also called the general theory of relativity (GTR) and general relativity theory (GRT)] is the geometrical theory of gravitation published by Albert Einstein in 1915/16. ... In relativity, proper time is time measured by a single clock between events that occur at the same place as the clock. ... In general relativity, the metric tensor (or simply the metric) is the fundamental object of study. ... In physics, spacetime is a mathematical model that combines space and time into a single construct called the space-time continuum. ... The Pound-Rebka experiment is a well known experiment in general relativity. ...

Definition

Background knowledge the reader may need to learn: What is a gravitational field? What is time dilation? What is spacetime? The reader may also research gravitational redshift or ordinary redshift. In addition, the much more fundamental, but crucial question: What really is Time itself? The gravitational field is a field (physics), generated by massive objects, that determines the magnitude and direction of gravitation experienced by other massive objects. ... Time dilation is the phenomenon whereby an observer finds that anothers clock which is physically identical to their own is ticking at a slower rate as measured by their own clock. ... In physics, spacetime is a mathematical model that combines space and time into a single construct called the space-time continuum. ... This article or section is in need of attention from an expert on the subject. ... Redshift of spectral lines in the optical spectrum of a supercluster of distant galaxies (right), as compared with that of the Sun (left). ... A pocket watch, a device used to tell time Look up time in Wiktionary, the free dictionary. ...

Gravitational time dilation is manifested in accelerated frames of reference or, by virtue of the equivalence principle, in the gravitational field of massive objects. In more simple terms, clocks which are far from massive bodies (or at higher gravitational potentials) run faster, and clocks close to massive bodies (or at lower gravitational potentials) run slower. A wrist watch A clock (from the Latin cloca, bell) is an instrument for measuring time. ... In physics, gravitational potential is the measure of potential energy an object possesses due to its position in a gravitational field. ...

It can also be manifested by any other kind of accelerated reference frame such as a dragster or space shuttle. Spinning objects such as merry-go-rounds and ferris wheels are subjected to gravitation time dilation as an effect of their angular spin. Drag racing is a form of auto racing in which cars attempt to complete a fairly short, straight and level course in the shortest amount of time. ... NASAs Space Shuttle, officially called Space Transportation System (STS), is the United States governments current manned launch vehicle. ... This article is about the fairground ride. ... A Ferris wheel on the boardwalk in Ocean City, New Jersey, USA. A Ferris wheel (or, more commonly in the UK, big wheel) is a nonbuilding structure consisting of an upright wheel with passenger gondolas suspended from the rim. ...

This is supported by General Relativity due to the equivalence principle that states all accelerated reference frames possess a gravitational field. According to General Relativity, inertial mass and gravitational mass are the same. Not all gravitational fields are "curved" or "spherical", some are flat as in the case of an accelerating dragster or space shuttle. Any kind of g-load contributes to gravitational time dilation. In relativity, the equivalence principle is applied to several related concepts dealing with gravitation and the uniformity of physical measurements in different frames of reference. ... Drag racing is a form of auto racing in which cars attempt to complete a fairly short, straight and level course in the shortest amount of time. ... NASAs Space Shuttle, officially called Space Transportation System (STS), is the United States governments current manned launch vehicle. ...

• In an accelerated box, the equation with respect to an arbitrary base observer is T_d = 1 − gh / c², where
  • T_d is the total time dilation at a distant position,
  • g is the acceleration of the box as measured by the base observer, and
  • h is the "vertical" distance between the observers.
• On a rotating disk when the base observer is located at the center of the disk and co-rotating with it (which makes their view of spacetime non-inertial), the equation is , where
  • r is the distance from the center of the disk (which is the location of the base observer), and
  • ω is the angular velocity of the disk.

(It is no accident that in an inertial frame of reference this becomes the familiar velocity time dilation ).

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: It has been suggested that Deriving the Schwarzschild solution be merged into this article or section. ... In physics, spacetime is a mathematical model that combines space and time into a single construct called the space-time continuum. ...

, where

• t₀ is the proper time between events A and B for a slow-ticking observer within the gravitational field,
• t_f is the proper time between events A and B for a fast-ticking observer distant from the massive object (and therefore outside of the gravitational field),
• G is the gravitational constant,
• M is the mass of the object creating the gravitational field,
• r is the radial coordinate of the observer (which is analogous to the classical distance from the center of the object, but is actually a Schwarzschild coordinate),
• c is the speed of light, and
• r₀ = 2GM / c² is the called the Schwarzschild Radius of M. If a mass collapses so that its surface lies at less than this radial coordinate (or in other words covers an area of less than 16πG²M² / c⁴), then the object exists within a black hole.

In relativity, proper time is time measured by a single clock between events that occur at the same place as the clock. ... In relativity, proper time is time measured by a single clock between events that occur at the same place as the clock. ... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ... Unsolved problems in physics: What causes anything to have mass? The U.S. National Prototype Kilogram, which currently serves as the primary standard for measuring mass in the U.S. Mass is the property of a physical object that quantifies the amount of matter and energy it is equivalent to. ... In General Relativity, Schwarzschild coordinates refers to the coordinate system of the Schwarzschild metric. ... A line showing the speed of light on a scale model of Earth and the Moon The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness. It is the speed of all electromagnetic radiation... The Schwarzschild radius (sometimes inappropriately referred to as the gravitational radius[1]) is a characteristic radius associated with every mass. ... A black hole is an object with a gravitational field so powerful that no form of matter or radiation (including light) can escape once it is less than a certain distance from the center. ...

Circular orbits

In the Schwarzschild metric, free-falling objects can be in circular orbits if the orbital radius is larger than . The formula for a clock at rest is given above; for a clock in a circular orbit, the formula is instead

Important things to stress

• According to General Relativity, gravitational time dilation is copresent with the existence of an accelerated reference frame.

• The speed of light in a locale is always equal to c according to the observer who is there. The stationary observer's perspective corresponds to the local proper time. Every infinitesimal region of space time may have its own proper time that corresponds to the gravitational time dilation there, where electromagnetic radiation and matter may be equally affected, since they are made of the same essence (as shown in many tests involving the famous equation E = mc²). Such regions are significant whether or not they are occupied by an observer. A time delay is measured for signals that bend near the sun, headed towards Venus, and bounce back to earth along more or less a similar path. There is no violation of the speed of light in this sense, as long as an observer is forced to observe only the photons which intercept the observing faculties and not the ones that go passing by in the depths of more (or even less) gravitational time dilation.

If a distant observer is able to track the light in a remote, distant locale which intercepts a time dilated observer nearer to a more massive body, he sees that both the distant light and that distant time dilated observer have a slower proper time clock than other light which is coming nearby him, which intercept him, at c, like all other light he really can observe. When the other, distant light intercepts the distant observer, it will come at c from the distant observer's perspective.

In theoretical physics, an accelerated reference frame is usually a coordinate system or frame of reference, that undergoes a constant and continual change in velocity over time as judged from an inertial frame. ... In relativity, proper time is time measured by a single clock between events that occur at the same place as the clock. ... In relativity, proper time is time measured by a single clock between events that occur at the same place as the clock. ... In General relativity, the Shapiro effect, or gravitational time delay, is one of the four classic solar system tests of general relativity. ...

Experimental confirmation

Gravitational time dilation has been experimentally measured using atomic clocks on airplanes. The clocks that traveled aboard the airplanes upon return were slightly fast with respect to clocks on the ground. The effect is significant enough that the Global Positioning System needs to correct for its effect on clocks aboard artificial satellites, providing a further experimental confirmation of the effect. Chip-Scale Atomic Clock Unveiled by NIST An atomic clock is a type of clock that uses an atomic resonance frequency standard to feed its counter. ... The Global Positioning System (GPS) is currently the only fully functional Global Navigation Satellite System (GNSS). ... An Earth observation satellite, ERS 2 For other uses, see Satellite (disambiguation). ...

Gravitational time dilation has also been confirmed by the Pound-Rebka experiment, observations of the spectra of the white dwarf Sirius B and experiments with time signals sent to and from Viking 1 mars lander. The Pound-Rebka experiment is a well known experiment in general relativity. ... This article or section does not adequately cite its references or sources. ... This article is about the star. ... The Viking 1 was the first of two spacecraft sent to Mars as part of NASAs Viking program. ...

References

• Einstein, Albert. "Relativity : the Special and General Theory by Albert Einstein." Project Gutenberg. <http://www.gutenberg.org/etext/5001.>
• Einstein, Albert. "The effect of gravity on light" (1911), translated and reprinted in The Principle of Relativity
• Nave, C.R. "Gravity and the Photon." Hyperphysics. <http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/blahol.html#c2.>