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ok let's restrict ourselves to frame S and don't jump to S' when we discuss.Let S(stationary) and S' (say velocity=0.8c) have identical light clocks and time between consecutive ticks is 1 second(meaning in any inertial frame, the frame ages by 1 second for each tick in a clock placed in that frame).Going by your equation Δt'=0.6 s meaning S' registers 1 second for every 0.6 s in S. Do you think that's correct?This equation says that the clock in S' should agemorethan the clock in S. Based on what we just established this is clearly wrong. The correct equation would be [itex]\Delta t' = \Delta t \sqrt{1-v^2/c^2}[/itex].