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Suppose you have two observers, A and B, in space, and that these are moving relative to one another. Due to time dilation, their clocks will tick at different rates. But how do you know whose clock ticks faster?

In other words, if a spaceship travels at a speed near c away from the earth, why do the astronauts age less than someone who stays at the earth and not vice versa? Couldn't you instead say that the earth travels away from the spaceship?