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Time dilation is the difference in elapsed time as measured by two clocks, either because of a relative velocity between them (special relativity), or a difference in gravitational potential between their locations (general relativity). When unspecified, "time dilation" usually refers to the effect due to velocity.
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 ...
Also, the velocities in the directions perpendicular to the frame changes are affected, as shown above. This is due to time dilation, as encapsulated in the dt/dt′ transformation. The V′ y and V′ z equations were both derived by dividing the appropriate space differential (e.g. dy′ or dz′) by the time differential.
Also, gravitational time dilation was measured from a difference in elevation between two clocks of only 33 cm (13 in). [ 28 ] [ 29 ] Presently both gravitational and velocity effects are routinely incorporated, for example, into the calculations used for the Global Positioning System .
The mere curvature of the path of a photon passing near the Sun is too small to have an observable delaying effect (when the round-trip time is compared to the time taken if the photon had followed a straight path), but general relativity predicts a time delay that becomes progressively larger when the photon passes nearer to the Sun due to the ...
The emergence of the muons is caused by the collision of cosmic rays with the upper atmosphere, after which the muons reach Earth. The probability that muons can reach the Earth depends on their half-life, which itself is modified by the relativistic corrections of two quantities: a) the mean lifetime of muons and b) the length between the upper and lower atmosphere (at Earth's surface).
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The measured elapsed time of a light signal in a gravitational field is longer than it would be without the field, and for moderate-strength nearly static fields the difference is directly proportional to the classical gravitational potential, precisely as given by standard gravitational time dilation formulas.