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Observer A is swings on the springs, while the observer B is stationary nearby. (See diagram: http://www.frozman.si/slike/Vzmet.jpg )

According to the theory of relativity to observer A the time flows slower due to its speed (as in the paradox of twins), as the time flows to observer B. But this is just a half of the story.

At each oscillation, the observers touch. When they touched, by the theory of relativity t is time of one observer, and at the other one is t'.

Two different times in the theory of relativity can be described by two events, but they can be also only one event, depending on the circumstances of the observation. When observers observe the same event of their touch at the point of contact, two different times mean two touches, according to the theory of relativity.

Only one touch on one period (as it really depends), in this case in accordance with the theory of relativity, occurs only if t = t '. This means that times are running synchronous.

In the theory of relativity we can prove both: that the times of the observers runs differently and also that times are running the same speed.

FR