It turns out that as an object moves with relativistic speeds a "strange" thing seems to happen to its time as observed by "us" the stationary observer (observer in an inertial reference frame). What we see happen is that the "clock" in motion slows down according to our clock, therefore we read two different times. The length of any object in a moving frame will appear foreshortened in the direction of motion, or contracted. The amount of contraction can be calculated from the Lorentz transformation.
A clock at rest with respect to one observer may be measured to tick at a different rate when compared to a second observer's clock. This effect arises neither from technical aspects of the clocks nor from the propagation time of signals, but from the nature of spacetime.
Time dilation could affect planned meetings for astronauts with advanced technologies and greater travel speeds. The astronauts would have to set their clocks to count exactly 80 years, whereas mission control – back on Earth – might need to count 81 years. The astronauts would return to Earth, after their mission, having aged one year less than the people staying on Earth. What is more, the local experience of time passing never actually changes for anyone. In other words, the astronauts on the ship as well as the mission control crew on Earth each feel normal, despite the effects of time dilation .
t = t0/(1-v2/c2)1/2
where: t = time observed in the other reference frame
t0 = time in observers own frame of reference (rest time)
v = the speed of the moving object
c = the speed of light in a vacuum
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