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Decay time of muons: The time dilation formula is = , where T 0 is the proper time of a clock comoving with the muon, corresponding with the mean decay time of the muon in its proper frame. As the muon is at rest in S′, we have γ=1 and its proper time T′ 0 is measured.
Time dilation is the difference in elapsed time as measured by two clocks, ... Taking the muon lifetime at rest as the laboratory value of 2.197 μs, the lifetime of ...
Muon decay almost always produces at least three particles, which must include an electron of the same charge as the muon and two types of neutrinos. Like all elementary particles, the muon has a corresponding antiparticle of opposite charge (+1 e) but equal mass and spin: the antimuon (also called a positive muon). Muons are denoted by μ −
It was possible to confirm velocity time dilation at the 10 −16 level at speeds below 36 km/h. Also, gravitational time dilation was measured from a difference in elevation between two clocks of only 33 cm (13 in). [28] [29]
Length contraction can also be derived from time dilation, [34] according to which the rate of a single "moving" clock (indicating its proper time) is lower with respect to two synchronized "resting" clocks (indicating ). Time dilation was experimentally confirmed multiple times, and is represented by the relation:
Among his scientific publications was a 1963 paper in which he and James H. Smith succeeded in showing objective time dilation in the decay of cosmic muons. A thirty-five-minute movie describing this experiment performed both on the top of Mount Washington in New Hampshire as well as at MIT is available online. [3]
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 classic time dilation experiments such as the Ives–Stilwell experiment, the Moessbauer rotor experiments, and the time dilation of moving particles, have been enhanced by modernized equipment. For example, the Doppler shift of lithium ions traveling at high speeds is evaluated by using saturated spectroscopy in heavy ion storage rings .