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[35] Travel to regions of space where extreme gravitational time dilation is taking place, such as near (but not beyond the event horizon of) a black hole, could yield time-shifting results analogous to those of near-lightspeed space travel. Contrarily to velocity time dilation, in which both observers measure the other as aging slower (a ...
An observer at rest observing an object travelling very close to the speed of light would observe the length of the object in the direction of motion as very near zero. Then, at a speed of 13 400 000 m/s (30 million mph, 0.0447 c) contracted length is 99.9% of the length at rest; at a speed of 42 300 000 m/s (95 million mph, 0.141 c), the ...
(For comparison's sake, another muon at rest on Earth can be considered, called muon-S. Therefore, its decay time in S is shorter than that of muon-S′, while it is longer in S′.) In S, muon-S′ has a longer decay time than muon-S. Therefore, muon-S' has sufficient time to pass the proper length of the atmosphere in order to reach Earth.
Satellite clocks are slowed by their orbital speed, but accelerated by their distance out of Earth's gravitational well. 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.
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.
The time it takes light to traverse back-and-forth along the Lorentz–contracted length of the longitudinal arm is given by: = + = / + / + = / = where T 1 is the travel time in direction of motion, T 2 in the opposite direction, v is the velocity component with respect to the luminiferous aether, c is the speed of light, and L L the length of the longitudinal interferometer arm.
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Consider a space ship traveling from Earth to the nearest star system: a distance d = 4 light years away, at a speed v = 0.8c (i.e., 80% of the speed of light). To make the numbers easy, the ship is assumed to attain full speed in a negligible time upon departure (even though it would actually take about 9 months accelerating at 1 g to get up ...