Does clock really run slow inside a high velocity rocket ship?

Question

In time dilation, does clock really run slow when it’s in high speed? Is that means the mechanical parts of the clock run slow? Or , It’s just the other inertial observer who thinks that the other one’s clock is running slow.(because the successive light signal is taking more time to reach the destination)

And, If the biological/atomic process is not running slow for the traveling twin in twin paradox, isn’t it impossible that he will be younger when they meet?

Answer 1

At high speeds, time really does slow down as you get close to the speed of light. All processes (not just mechanical clocks) slow down, including things like radioactive decay as well as everything biological going on inside your body. This means you yourself do not notice your clocks running slow inside the spaceship.

The twin paradox is a more complicated thing to wrap your head around and I recommend reading the reference provided by John Rennie.