One interesting conclusion from the time slow-down is that, to light, no time passes at all. Since it's moving at the speed of light, it reaches its destination at the same moment (for it) that it left its starting point. Basically, light doesn't age!
Another interesting conclusion is that a particle with a very high decay rate that's created by energy hitting paticles in the Earth's upper atmosphere, under Newtonian physics, would never be able to reach the Earth's surface in time before it decays. However, since the particle is moving at speeds very close to c, it actually does reach the earth's surface in time to produce a blip on a radiation detector (and sometimes damage electronic devices!)
Lastly, one thing that's hard for people to grasp is that speed is all relative. If I'm moving away from earth at relativistic speeds, and I had a window, then people on Earth would look at my watch and see the seconds going by much slower than normal, and when I looked down at Earth, I'd see their watches moving really slowly. So, who's watch is "correct"? Well, both times are "correct." Since you're in different inertial frames, there is no time interaction between the two. Now, as soon as the ship slows down back to Earth's initial frame, that's when the time difference actually occurs and one watch ends up being the correct time (people on Earth, in this case), while the other one will have the incorrect time.
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