Time dilation of moving particles
Time dilation of moving particles as predicted by special relativity can be measured in particle lifetime experiments. According to special relativity, the rate of clock C traveling between two synchronized laboratory clocks A and B is slowed with respect to the laboratory clock rates. This effect is called time dilation. Since any periodic process can be considered a clock, also the lifetimes of unstable particles such as muons must be affected, so that moving muons should have a longer lifetime than resting ones. Variations of experiments that actually confirmed this effect took place in the atmosphere or in particle accelerators. Other time dilation experiments belong to the group of Ives–Stilwell experiments. See also Tests of special relativity.
Such experiments depend in all inertial frames on the ratio of two quantities: a) the decay time of muons in relative motion to Earth, b) the length between the upper and lower atmosphere (at Earth's surface). This experimental situation allows for a direct application of time dilation and length contraction.
For instance, let there be two rest frames of two muons, with muon-1 moving relative to Earth, muon-2 being at rest at Earth's surface, and v being the relative velocity between the muons:
Distance between upper and lower atmosphere: The contraction formula is given by L = L0 / γ, and is valid in all inertial frames for the computation of this distance. For an observer in the muon-2-system S, it is given with respect to the atmosphere: v = 0 and γ = 1, thus L = L0/γ = L0. So in S, the proper length of the atmosphere is measured. Though for an observer in the muon-1-system S', the atmosphere is in motion: v > 0 and γ > 1, thus L' = L0 / γ < L0. So in S', the contracted length of the atmosphere is measured.
Decay time of muons: The time dilation formula is given by T = T0 · γ, which is valid in all inertial frames for the calculation of the muon decay times. T0 is the identical proper time for the decay of both muons-1 and 2. In S it is given for muon-1: v > 0 and γ > 1, thus T1 = T0 · γ > T0; and for Myon-2: v = 0 and γ = 1, thus T2 = T0 · γ = T0. So in S, muon-1 decays slower than muon-2. However, in S' it is given for muon-1: v = 0 and γ = 1, thus T1' = T0 · γ = T0; and for muon-2: v > 0 und γ > 1, thus T2' = T0 · γ > T0. So in S', muon-2 decays slower than muon-1.
- In S, muon-1 has a longer life time than muon-2. Thus muon-1 has sufficient time to pass the proper length of the atmosphere in order to reach Earth's surface.
- In S', muon-2 has a longer life time than muon-1. But this is no problem, since the atmosphere is in motion here, and thus contracted with respect to its proper length. Therefore even the shorter life time of muon-1 suffices in order to be passed by the moving atmosphere and to be reached by the moving surface of Earth.
In 1940 at Echo Lake and Denver in Colorado, Bruno Rossi and D. B. Hall measured the relativistic decay of muons (which they thought were mesons). They only measured muons in the atmosphere traveling above 99,94% of the speed of light. If no time dilation exists, then those muons should decay in the upper regions of the atmosphere, however, as a consequence of time dilation, they are present in considerable amount also at much lower heights. Rossi and Hall confirmed this in a qualitative manner and also estimated the proper muon lifetime.
A much more precise experiment of this kind was conducted by David H. Frisch and Smith (1963), who measured approximately 563 muons per hour in six runs. The muon's velocity was 0.995 times the speed of light, by which they traversed a difference in height of 1907 m between Mount Washington and Cambridge, Massachusetts in 6.4 µs. Approximately 412 muons per hour arrived in Cambridge, resulting in a time dilation factor of 8.8±0.8 in good agreement with the predicted 8.4±2.
Time dilation and CPT symmetry
Such measurements of particle decays were also made in particle accelerators using different types of particles. Besides the confirmation of time dilation, also CPT symmetry was confirmed by comparing the lifetimes of positive and negative particles. According to this symmetry, the decay rates of particles and their antiparticles have to be the same. A violation of CPT invariance would also lead to violations of Lorentz invariance and thus special relativity.
|Durbin et al. (1952)
Eckhause et al. (1965)
Nordberg et al. (1967)
Greenburg et al. (1969)
Ayres et al. (1971)
|Burrowes et al. (1959)
Boyarski et al. (1962)
Lobkowicz et al. (1969)
Ott et al. (1971)
Skjeggestad et al. (1971)
Geweniger et al. (1974)
Carithers et al. (1975)
Meyer et al. (1963)
Eckhause et al. (1963)
Balandin et al. (1974)
Today, time dilation of particles is routinely confirmed in particle accelerators alongside with tests of relativistic energy and momentum, and its consideration is obligatory in the analysis of particle experiments at relativistic velocities.
Bailey et al. (1977) measured the lifetime of positive and negative muons sent around a loop in the CERN Muon storage ring. This experiment confirmed both time dilation and the twin paradox, i.e. the hypothesis that clocks sent away and coming back to their initial position are retarded with respect to a resting clock. Other measurements of the twin paradox involve gravitational time dilation as well, see for instance the Hafele–Keating experiment and repetitions.
The clock hypothesis states that the extent of acceleration doesn't influence the value of time dilation. In most of the former experiments mentioned above, the decaying particles were in an inertial frame, i.e. unaccelerated. However, in Bailey et al. (1977) the particles were subject to a transverse acceleration of up to ∼1018 g. Since the result was the same, it was shown that acceleration has no impact on time dilation. In addition, Roos et al. (1980) measured the decay of Sigma baryons, which were subject to a longitudinal acceleration between 0.5 and 5.0 × 1015 g. Again, no deviation from ordinary time dilation could be measured.
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