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Keeping the speed of light constant for all inertial observers, requires a lengthening of the period of this clock from the moving observer's perspective.

That is to say, in a frame moving relative to the local clock, this clock will appear to be running more slowly.

Straightforward application of the Pythagorean theorem leads to the well-known prediction of special relativity: The total time for the light pulse to trace its path is given by Given a certain frame of reference, and the "stationary" observer described earlier, if a second observer accompanied the "moving" clock, each of the observers would perceive the other's clock as ticking at a slower rate than their own local clock, due to them both perceiving the other to be the one that's in motion relative to their own stationary frame of reference.

Common sense would dictate that, if the passage of time has slowed for a moving object, said object would observe the external world's time to be correspondingly sped up.

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.

Special relativity indicates that, for an observer in an inertial frame of reference, a clock that is moving relative to him will be measured to tick slower than a clock that is at rest in his frame of reference.

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Conversely, also proper time ef of B is shorter with respect to time if in S′, because event e was measured in S′ already at time i due to relativity of simultaneity, long before C started to tick.

The reciprocity of the phenomenon also leads to the so-called twins paradox, where one person staying on Earth and one embarking on space travel should apparently expect each other to age the same amount of time since they both see the other as moving at equal speeds from their own frame of reference.

The dilemma posed by the paradox, however, can be explained by the acceleration changes inherent to the traveling person's trip, which not constituting an inertial frame of reference, is not covered by special relativity.

The proper time between two events is indicated by a clock present at both events.

It is invariant, i.e., in all inertial frames it is agreed that this time is indicated by that clock.




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