I think the questioner wants to know why time slows down.
Einstein discovered that no matter where you are and how fast you are moving any experiement you do will produce precisely the same results as anyone else...even if they are moving more slowly. This is important and has many implications.
For time slowing down understand that no matter who does the experiment, no matter their speed, they will measure the speed of light to be *exactly* the same as anyone else who measures it.
So you are in your spaceship moving along at 99.9% the speed of light and you do this experiment. You send a photon of light to your receiver at the other end of the spaceship. Thing is that receiver is moving away from the photon at 99.9% the speed of light. The photon has to catch up to the receiver which is moving away. If time did not adjust you would find it took a lot longer for your photon to arrive and hence you would measure a different speed of light than someone on earth would. But that is not the case. You measure the exact same speed as the guy on earth!
In order for the math to work out time needs to slow down (and distance contract) for the person moving at 99.9% the speed of light. Now it seems to move at the same speed as anyone else who does the measurement.
Note that as far as you are concerened everything seems normal. You will not notice the time dilation at all but the difference will become apparent when you return to earth where no one has been moving.
As other mentioned you cannot actually reach light speed. If you did your mass would become infinite (so would take infinite energy to move), the universe would contract to zero width and time would stop for you (so you'd never return to earth...the universe would end before you ever did another anything).
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