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Gravitational time dilation is a form of time dilation, an actual difference of elapsed time between two events, as measured by observers situated at varying distances from a gravitating mass. The lower the gravitational potential (the closer the clock is to the source of gravitation), the slower time passes, speeding up as the gravitational ...
In 1964, Pound and J. L. Snider measured a result within 1% of the value predicted by gravitational time dilation. [36] (See Pound–Rebka experiment) In 2010, gravitational time dilation was measured at the Earth's surface with a height difference of only one meter, using optical atomic clocks. [26]
A small mass has an extremely small Schwarzschild radius. A black hole of mass similar to that of Mount Everest [19] [note 2] would have a Schwarzschild radius much smaller than a nanometre. [note 3] Its average density at that size would be so high that no known mechanism could form such extremely compact objects.
The distance traveled, under constant proper acceleration, from the point of view of Earth as a function of the traveler's time is expressed by the coordinate distance x as a function of proper time τ at constant proper acceleration a. It is given by: [8] [9]
To calculate the changes in frequency in a nearly static gravitational field, only the time component of the metric tensor is important, and the lowest order approximation is accurate enough for ordinary stars and planets, which are much bigger than their Schwarzschild radius.
From a theoretical standpoint, however, the status of gravitational redshift/time dilation is quite different. It is widely recognized that general relativity, despite accounting for all data gathered to date, cannot represent a final theory of nature. [11] The equivalence principle (EP) lies at the heart of the general theory of relativity ...
But time is weird, and there's another phenomenon called relative velocity time dilation that usurps gravity's effect. Why astronauts age slower Relative velocity time dilation is where time moves ...
where the numerator is the gravitational, and the denominator is the kinematic component of the time dilation. For a particle falling in from infinity the left factor equals the right factor, since the in-falling velocity v {\textstyle v} matches the escape velocity c r s r {\textstyle c{\sqrt {\frac {r_{\text{s}}}{r}}}} in this case.