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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]].
| | If you compare registry products there are a amount of factors to look out for. Because of the sheer number of for registry cleaners available on the Internet at when it can be quite effortless to be scammed. Something frequently overlooked is that certain of these products can the fact is end up damaging a PC. And the registry they state they have cleaned will simply lead to more difficulties with the computer than the ones we started with.<br><br>So one day my computer suddenly started being weird. I was thus frustrated, because my files were missing, and I cannot open the files that I needed, plus then, suddenly, everything stopped working!<br><br>It doesn't matter whether we are not especially obvious about what rundll32.exe is. But remember that it plays an significant part inside sustaining the stability of the computers plus the integrity of the system. Whenever several software or hardware couldn't reply usually to the system operation, comes the rundll32 exe error, that might be caused by corrupted files or lost information in registry. Usually, error message may shows up at booting or the beginning of running a system.<br><br>Check a Windows taskbar, that is found on the lower appropriate hand corner of your computer screen. This taskbar consist of programs we have running inside the background. If you have too countless of them, they might steal the computer's resources.<br><br>These are the results which the [http://bestregistrycleanerfix.com/tune-up-utilities tuneup utilities 2014] found: 622 incorrect registry entries, 45,810 junk files, 15,643 unprotected privacy files, 8,462 bad Active X items which were not blocked, 16 performance features that have been not optimized, and 4 updates that the computer required.<br><br>We should equally see to it which it is easy to download and install. We must avoid those goods that usually require you a especially complicated set of instructions. Additionally, you should no longer require any additional system requirements.<br><br>Google Chrome is my lifeline plus for this day luckily. My all settings plus analysis related bookmarks were saved in Chrome and stupidly I didn't synchronize them with all the Gmail to store them online. I couldn't afford to install hot adaptation plus sacrifice all my function settings. There was no method to retrieve the aged settings. The just option left for me was to miraculously fix it browser inside a way which all data plus settings stored inside it are recovered.<br><br>Next, there is an easy method to deal with this issue. You can install a registry cleaner that there are it on the internet. This software can help you find out these errors in your computer and clean them. It moreover could figure out these malware and other threats that influence the speed of your computer. So this software will accelerate PC simpler. We can choose one of these methods to accelerate we computer. |
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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]].
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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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If you compare registry products there are a amount of factors to look out for. Because of the sheer number of for registry cleaners available on the Internet at when it can be quite effortless to be scammed. Something frequently overlooked is that certain of these products can the fact is end up damaging a PC. And the registry they state they have cleaned will simply lead to more difficulties with the computer than the ones we started with.
So one day my computer suddenly started being weird. I was thus frustrated, because my files were missing, and I cannot open the files that I needed, plus then, suddenly, everything stopped working!
It doesn't matter whether we are not especially obvious about what rundll32.exe is. But remember that it plays an significant part inside sustaining the stability of the computers plus the integrity of the system. Whenever several software or hardware couldn't reply usually to the system operation, comes the rundll32 exe error, that might be caused by corrupted files or lost information in registry. Usually, error message may shows up at booting or the beginning of running a system.
Check a Windows taskbar, that is found on the lower appropriate hand corner of your computer screen. This taskbar consist of programs we have running inside the background. If you have too countless of them, they might steal the computer's resources.
These are the results which the tuneup utilities 2014 found: 622 incorrect registry entries, 45,810 junk files, 15,643 unprotected privacy files, 8,462 bad Active X items which were not blocked, 16 performance features that have been not optimized, and 4 updates that the computer required.
We should equally see to it which it is easy to download and install. We must avoid those goods that usually require you a especially complicated set of instructions. Additionally, you should no longer require any additional system requirements.
Google Chrome is my lifeline plus for this day luckily. My all settings plus analysis related bookmarks were saved in Chrome and stupidly I didn't synchronize them with all the Gmail to store them online. I couldn't afford to install hot adaptation plus sacrifice all my function settings. There was no method to retrieve the aged settings. The just option left for me was to miraculously fix it browser inside a way which all data plus settings stored inside it are recovered.
Next, there is an easy method to deal with this issue. You can install a registry cleaner that there are it on the internet. This software can help you find out these errors in your computer and clean them. It moreover could figure out these malware and other threats that influence the speed of your computer. So this software will accelerate PC simpler. We can choose one of these methods to accelerate we computer.