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As objects move faster, their time slows down. I understand this, but what I'm having trouble with is intuitively grasping the concept of "time slowing down". A book I'm reading gave the following scenario:

Assume Person A is floating in space, while Person B flies past at a very high speed. If they were to communicate via radio (with electromagnetic waves moving at light-speed), Person A would hear Person B slurring their words.

Why does this happen? Is it because Person B's time runs slower, and so from the reference frame of Person A, he talks slower? I'm sort of able to wrap my head around this, but I'm having a hard time doing it.

What would happen if Person A and Person B somehow had a conversation, while Person B was at their high speed and Person A was stationary (just as a thought experiment). When Person A spoke, would Person B take a long time to react (relative to Person A)? On the other hand, when Person B spoke, would it seem like Person A was speaking really fast (from B's perspective)?

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Here is another scenario. A person moving on the train moving at relativistic speeds shines a light on a mirror in front. He sees it (almost) immediately. On the other hand, a man on the stationary platform will see the light shine, and move diagonally towards the mirror. Since the train is moving at relativistic speeds, the light would be seen to be moving more to reach the mirror. This then results in time dilation due to more time required.

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