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This case is sometimes called special relativistic time dilation.
The faster the relative velocity, the greater the time dilation between one another, with the rate of time reaching zero as one approaches the speed of light (299,792,458 m/s).
The worldline of A is the ct-axis, the worldline of B intersecting f is parallel to the ct-axis, and the worldline of C is the ct′-axis.
All events simultaneous with d in S are on the x-axis, in S′ on the x′-axis.
The reciprocity of the phenomenon also leads to the so-called twin paradox where the aging of twins, one staying on Earth and the other embarking on a space travel, is compared, and where the reciprocity suggests that both persons should have the same age when they reunite.
The dilemma posed by the paradox, however, can be explained by the fact that one of twins must accelerate while the other remains inertial.
For GPS satellites to work, they must adjust for similar bending of spacetime to coordinate with systems on Earth.
Upon the trips' completion the clocks were compared to a static, ground based atomic clock.Time dilation explains why two working clocks will report different times after different accelerations.For example, at the ISS time goes slower, lagging 0.007 seconds behind for every six months.As a result of the nature of spacetime, a clock that is moving relative to an observer will be measured to tick slower than a clock that is at rest in the observer's own frame of reference.
A clock that is under the influence of a stronger gravitational field than an observer's will also be measured to tick slower than the observer's own clock.
Such time dilation has been repeatedly demonstrated, for instance by small disparities in a pair of atomic clocks after one of them is sent on a space trip, or by clocks on the Space Shuttle running slightly slower than reference clocks on Earth, or clocks on GPS and Galileo satellites running slightly faster.