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WHY our time would run slow if we move with the speed close or equal to the speed of light, and is that time dilation restricted to only just '' time' ' or it affects our biological time also (does it stops or slows down our ageing process) ??

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Time dilation is a consequence of the observation that the speed of light (in a vacuum) is a constant.

Insofar as the human ageing process is a kind of clock it is also affected by this effect. Identical twins who meet after one of them has accellerated to an appreciable fraction of the speed of light will have eged by different amounts when they meet.

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