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Daily time dilation (gain or loss if negative) in microseconds as a function of (circular) orbit radius r = rs/re, where rs is satellite orbit radius and re is the equatorial Earth radius, calculated using the Schwarzschild metric. At r ≈ 1.497 [Note 1] there is no time dilation. Here the effects of motion and reduced gravity cancel.
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 ...
This is the formula for time dilation: t ′ = γ t {\displaystyle t'=\gamma t} In this example the time measured in the frame on the vehicle, t , is known as the proper time .
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 ...
Fig 4–2. Relativistic time dilation, as depicted in a single Loedel spacetime diagram. Both observers consider the clock of the other as running slower. Relativistic time dilation refers to the fact that a clock (indicating its proper time in its rest frame) that moves relative to an observer is observed to run slower. The situation is ...
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.
The time difference was observable during the flight, before later analysis. An overall difference of 47.1 ns was measured, which consisted of the velocity effect of −5.7 ns and a gravitational effect of 52.8 ns. This agrees with the relativistic predictions to a precision of about 1.6%. [16] [17]
In a 1964 article entitled Fourth Test of General Relativity, Irwin Shapiro wrote: [1] Because, according to the general theory, the speed of a light wave depends on the strength of the gravitational potential along its path, these time delays should thereby be increased by almost 2 × 10 −4 sec when the radar pulses pass near the sun. Such a ...