In fact, phase “time slows” is incorrect. If you were sitting in a space rocket, moving at high speed, all processes would be the same, and time, for you, would “go” at the same “rate”.
The reason why it’s called time slowing is because when you traveled some distance with high speed and then compare the testimony of your clock and the Earth one, then clock on the Earth will be rushing.
This all phenomena happens just because one fact: speed of light is constant and maximum possible.
So, aging processes does NOT slow down, and time does NOT go more slowly, it just occurs that for you it was needed less time to travel, than for Earth observer to “wait” for you.
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