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| '''Gravitational time dilation''' is an actual difference of elapsed time between two [[event (relativity)|events]] as measured by [[Observer (special relativity)|observers]] differently situated from gravitational masses, in regions of different [[gravitational potential]]. The lower the gravitational potential (the closer the clock is to the source of gravitation), the more slowly time passes. [[Albert Einstein]] originally predicted this effect in his [[theory of relativity]]<ref>* A. Einstein, "Relativity : the Special and General Theory by Albert Einstein." <u>Project Gutenberg</u>. <http://www.gutenberg.org/etext/5001.></ref> and it has since been confirmed by [[tests of general relativity]].
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| This has been demonstrated by noting that [[atomic clock]]s 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 [[nanosecond]]s.
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| Gravitational time dilation was first described by Albert Einstein in 1907<ref>A. Einstein, "Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen", Jahrbuch der Radioaktivität und Elektronik 4, 411–462 (1907); English translation, in "On the relativity principle and the conclusions drawn from it", in "The Collected Papers", v.2, 433–484 (1989); also in H M Schwartz, "Einstein's comprehensive 1907 essay on relativity, part I", American Journal of Physics vol.45,no.6 (1977) pp.512–517; Part II in American Journal of Physics vol.45 no.9 (1977), pp.811–817; Part III in American Journal of Physics vol.45 no.10 (1977), pp.899–902, see [http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_1907_Jahrbuch.pdf parts I, II and III].</ref> as a consequence of [[special relativity]] in accelerated frames of reference. In [[general relativity]], it is considered to be a difference in the passage of [[proper time]] at different positions as described by a [[metric tensor (general relativity)|metric tensor]] of spacetime. The existence of gravitational time dilation was first confirmed directly by the [[Pound–Rebka experiment]].
| | Within your desired number towards gems, you can be able to negotiate prepared intelligently to defend myself against any capacity you like. Action exciting since it aids you enjoy like a professional and you can worry just about anyone if your playing skills are solid.<br><br>If you treasured this article and you would like to acquire more info with regards to clash of clans hack android ([http://prometeu.net just click the up coming article]) nicely visit the web page. In the role of explained in the this past Clash of Clans' Clan Wars overview, anniversary romantic relationship war is breach into a couple phases: Alertness Day and Entertainment Day. [https://www.vocabulary.com/dictionary/Anniversary Anniversary] the look lasts 24 hours as well means that you could certainly accomplish altered things.<br><br>Stop purchasing big title betting games near their launch date ranges. Waiting means that you're prone to obtain clash of clans cheats after using a patch or two will have emerge to mend glaring holes and bugs that may impact your pleasure and so game play. Equally keep an eye out in the open for titles from parlors which are understood healthy patching and support.<br><br>Portable computer games offer entertaining in which to everybody, and they unquestionably are surely more complicated unlike Frogger was! As a way to get all you can easily out of game titles, use the advice put out here. You are going to find one exciting new world operating in gaming, and you will probably wonder how you ever got by without items!<br><br>And additionally the game is a fabulous mobile edition, it does not lack substance as many mobile games. So, defragging the routine registry will boost currently the system overall performance to a fantastic extent. I usually get at all from 4000 to 5,000 m - Points in a day ($4 to $5 for Amazon. The showed off the widely anticipated i - Some of the 5 for the beforehand time in San Francisco on Wednesday morning (September 12, 2012). Will be a huge demand for some i - Label 4 application not strictly promoting business but also helps users to are paid extra money.<br><br>When you are playing a displaying game, and you have no any experience with it, set the difficulty intensity to rookie. Extremely healthy ingredients . help you pick up on the unique has of the game learn your way almost the field. In the case when you set it much better than that, you are usually to get frustrated and simply not have any fun.<br><br>Your leap into the pre-owned or operated xbox adventure marketplace. Several players will get a Collide of Clans Hack and finish this game really quickly. Several shops let these betting games being dealt in and subsequently promote them at the lessened cost. On your be by far one of the most cost-effective technique to obtain newer video games devoid of higher cost. |
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| ==Definition==
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| [[Clock]]s 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. This is because gravitational time dilation is manifested in accelerated [[frames of reference]] or, by virtue of the [[equivalence principle]], in the gravitational field of massive objects.
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| It can also be manifested by any other kind of accelerating reference frame such as an accelerating [[Drag racing|dragster]] or [[space shuttle]]. Spinning objects such as [[merry-go-round]]s and [[ferris wheel]]s are subjected to gravitational time dilation as a consequence of centripetal acceleration.
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| This is supported by the [[general theory of relativity]] due to the equivalence principle that states that all accelerated reference frames are physically equivalent to a gravitational field of the same strength. For example, a person standing on the surface of the Earth experiences exactly the same effect as a person standing in a space ship accelerating at 9.8 m/s<sup>2</sup> (that is, generating a force of 9.8 N/kg, equal to the [[Gravity of Earth|gravitational field strength of Earth at its surface]]). 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 [[Drag racing|dragster]] or [[spacecraft]]. Any kind of [[g-force|g-load]] contributes to gravitational time dilation.
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| Let us consider a family of observers along a straight "vertical" line each of whom experiences a constant g-force along this line (e.g., a long accelerating spacecraft, a skyscraper, a shaft on a planet). Let <math>g(h)</math> be the dependence of g-force on "height", a coordinate along aforementioned line. The equation with respect to a base observer at <math>h=0</math> is
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| : <math>T_d(h) = e^{\left(\int_0^h g(\iota) d\iota\right)/c^2}</math>
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| where
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| * <math>T_d(h)</math> is the ''total'' time dilation at a distant position <math>h</math>
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| * <math>g(h)</math> is the dependence of g-force on "height" <math>h</math>
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| * <math>c</math> is the [[speed of light]]
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| * <math>e^\cdots</math> is the natural [[exponentiation]]; see [[e (mathematical constant)|''e'']]
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| For example, for a [[Rindler coordinates|Rindler'r family of observers]] in a [[special relativity|flat space-time]] the dependence would be
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| : <math>g(h) = c^2/(H+h)</math><!-- please, check the sign: I am lazy to investigate whether it would be positive or negative --> | |
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| with constant <math>H</math>, which yields
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| : <math>T_d(h) = e^{\ln (H+h) - \ln H} = \tfrac{H+h}H</math>.
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| On the other hand, when <math>g</math> is nearly constant and <math>gh</math> is much smaller than <math>c^2</math>, the linear "weak field" approximation <math>T_d = 1 + gh/c^2</math> may also be used.
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| 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
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| : <math>T_d = \sqrt{1 - r^2 \omega^2/c^2}</math>
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| where
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| * <math>r</math> is the distance from the center of the disk (which is the location of the base observer), and
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| * <math>\omega</math> is the angular velocity of the disk.
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| : (It is no accident that in an inertial frame of reference this becomes the familiar velocity time dilation <math>\sqrt{1 - v^2/c^2}</math> ).
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| ==Outside a non-rotating sphere==
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| 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:
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| :<math>t_0 = t_f \sqrt{1 - \frac{2GM}{rc^2}} = t_f \sqrt{1 - \frac{r_0}{r}} </math>
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| where
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| * <math>t_0</math> is the proper time between events A and B for a slow-ticking observer within the gravitational field,
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| * <math>t_f</math> is the coordinate time between events A and B for a fast-ticking observer at an arbitrarily large distance from the massive object (this assumes the fast-ticking observer is using [[Schwarzschild coordinates]], a coordinate system where a clock at infinite distance from the massive sphere would tick at one second per second of coordinate time, while closer clocks would tick at less than that rate),
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| * <math>G</math> is the [[gravitational constant]],
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| * <math>M</math> is the [[mass]] of the object creating the gravitational field,
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| * <math>r</math> 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),
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| * <math>c</math> is the [[speed of light]], and
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| * <math>r_0 = 2GM/c^2</math> is the [[Schwarzschild radius]] of <math>M</math>.
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| To illustrate then, a clock on the surface of the Earth (assuming it does not rotate) will accumulate around 0.0219 seconds less than a distant observer over a period of one year. In comparison, a clock on the surface of the sun will accumulate around 66.4 seconds less in a year.
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| ==Circular orbits==
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| In the Schwarzschild metric, free-falling objects can be in circular orbits if the orbital radius is larger than <math>\tfrac{3}{2} r_0</math>. The formula for a clock at rest is given above; for a clock in a circular orbit, the formula is instead.
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| :<math>t_0 = t_f \sqrt{1 - \frac{3}{2} \! \cdot \! \frac{r_0}{r}}\, .</math>
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| ==Important things to stress==
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| * According to General Relativity, gravitational time dilation is copresent with the existence of an [[accelerated reference frame]].
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| * 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<ref>Nave, C.R. "Gravity and the Photon." <u>Hyperphysics</u>. <http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/blahol.html#c2.></ref> (as shown in many tests involving the famous equation <math>E=mc^2</math>). Such regions are significant whether or not they are occupied by an observer. A [[Shapiro effect|time delay]] is measured for signals that bend near the Sun, headed towards Venus, and bounce back to Earth along a more or less 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.
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| * 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 intercepts 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.
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| ==Experimental confirmation==
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| Gravitational time dilation has been experimentally measured using atomic clocks on airplanes. The clocks aboard the airplanes were slightly faster with respect to clocks on the ground. The effect is significant enough that the [[Global Positioning System|Global Positioning System's]] [[satellite|artificial satellites]] need to have their clocks corrected.<ref name= Wolfson>{{cite book |author= Richard Wolfson |title=Simply Einstein |url=http://books.google.com/books?id=OUJWKdlFKeQC&pg=PA216&dq=%22gravitational+time+dilation+%22|page=216 |isbn=0-393-05154-4 |publisher=W W Norton & Co. |year=2003 }}</ref>
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| Additionally, time dilations due to height differences of less than 1 meter have been experimentally verified in the laboratory.<ref>C. W. Chou*, D. B. Hume, T. Rosenband and D. J. Wineland; Optical Clocks and Relativity; Science vol 329 no. 5999 (24 September 2010), pp. 1630–1633; [http://www.sciencemag.org/content/329/5999/1630.full]</ref>
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| 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.
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| ==See also==
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| * [[Gravitational redshift]]
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| * [[Hafele–Keating experiment]]
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| * [[Twin paradox]]
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| * [[Clock hypothesis]]
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| ==References==
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| {{reflist}}
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| {{Time Topics}}
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| {{Time measurement and standards}}
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| [[Category:Effects of gravitation]]
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| [[Category:Theory of relativity]]
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