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In the context of special relativity it was shown by Albert Einstein (1905) that this effect concerns the nature of time itself, and he was also the first to point out its reciprocity or symmetry. [7] Subsequently, Hermann Minkowski (1907) introduced the concept of proper time which further clarified the meaning of time dilation. [8]
Today, special relativity is proven to be the most accurate model of motion at any speed when gravitational and quantum effects are negligible. [3] [4] Even so, the Newtonian model is still valid as a simple and accurate approximation at low velocities (relative to the speed of light), for example, everyday motions on Earth.
Gravitational time dilation has been experimentally measured using atomic clocks on airplanes, such as the Hafele–Keating experiment. The clocks aboard the airplanes were slightly faster than clocks on the ground. The effect is significant enough that the Global Positioning System's artificial satellites need to have their clocks corrected. [13]
The mathematics of general relativity is complicated. In Newton 's theories of motion, an object's length and the rate at which time passes remain constant while the object accelerates , meaning that many problems in Newtonian mechanics may be solved by algebra alone.
Roundtrip radar-time isocontours. The Lorentz-transform calculation above uses a definition of extended-simultaneity (i.e. of when and where events occur at which you were not present) that might be referred to as the co-moving or "tangent free-float-frame" definition. This definition is naturally extrapolated to events in gravitationally ...
Speed is a scalar, being the magnitude of the velocity vector which in relativity is the four-velocity and in three-dimension Euclidean space a three-velocity. Speed is empirically measured as average speed, although current devices in common use can estimate speed over very small intervals and closely approximate instantaneous speed.
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By measuring their kinetic energy, mean muon velocities between 0.995 c and 0.9954 c were determined. Another measurement was taken in Cambridge, Massachusetts at sea-level. 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.