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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 ...
The time the muons need from 1917m to 0m should be about 6.4 μs. Assuming a mean lifetime of 2.2 μs, only 27 muons would reach this location if there were no time dilation. However, approximately 412 muons per hour arrived in Cambridge, resulting in a time dilation factor of 8.8 ± 0.8.
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 .
In addition, the elliptical, rather than perfectly circular, satellite orbits cause the time dilation and gravitational frequency shift effects to vary with time. This eccentricity effect causes the clock rate difference between a GPS satellite and a receiver to increase or decrease depending on the altitude of the satellite.
Equation is a fundamental and much-quoted differential equation for the relation between proper time and coordinate time, i.e. for time dilation. A derivation, starting from the Schwarzschild metric, with further reference sources, is given in Time dilation § Combined effect of velocity and gravitational time dilation.
Time is a slippery thing, as profound thinkers like physicist Albert Einstein and, well, fictional time traveler Dr. Who plainly understood. Scientists made that point anew on Monday in a study ...
Muons, a subatomic particle, travel at a speed such that they have a relatively high Lorentz factor and therefore experience extreme time dilation. Since muons have a mean lifetime of just 2.2 μs, muons generated from cosmic-ray collisions 10 km (6.2 mi) high in Earth's atmosphere should be nondetectable on the ground due to their decay rate ...