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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.
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.
Statistical tests are used to test the fit between a hypothesis and the data. [1] [2] Choosing the right statistical test is not a trivial task. [1]The choice of the test depends on many properties of the research question.
In physics, the Ives–Stilwell experiment tested the contribution of relativistic time dilation to the Doppler shift of light. [1] [2] The result was in agreement with the formula for the transverse Doppler effect and was the first direct, quantitative confirmation of the time dilation factor. Since then many Ives–Stilwell type experiments ...
However, one can often account for most of the discrepancy by the introduction of gravitational time dilation, the slowing down of time near gravitating bodies. In case of the GPS, the receivers are closer to Earth than the satellites, causing the clocks at the altitude of the satellite to be faster by a factor of 5×10 −10 , or about +45.8 ...
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. [30]
The transverse Doppler effect and consequently time dilation was directly observed for the first time in the Ives–Stilwell experiment (1938). In modern Ives-Stilwell experiments in heavy ion storage rings using saturated spectroscopy, the maximum measured deviation of time dilation from the relativistic prediction has been limited to ≤ 10 −8.
The Shapiro time delay effect, or gravitational time delay effect, is one of the four classic Solar System tests of general relativity. Radar signals passing near a massive object take slightly longer to travel to a target and longer to return than they would if the mass of the object were not present.