This never made any sense to me whatsoever.
I’ve see all the physicists (Michio Kaku, Stephen Hawking, Neil DeGrasse Tyson, etc.) explain this principle but it doesn’t make sense. They say that if you were to go to the moon and back at a certain speed near the speed of light, you might return to Earth a thousand years into the future like what happened in Planet of the Apes. But if you were going at the speed of light, you would arrive at the time light takes to arrive there. Why the dip? What is being missed?
Small correction, but this bit isn’t quite correct:
During the time that you are just below light speed at a constant velocity, clocks that are “stationary” will appear to be moving slow to you. And clocks moving with you will appear to be running slow for a “stationary” observer. As I mentioned in a comment in another reply, the trip would feel short to you because the distance to your destination would contract to nearly zero. “Fast forwarding” (ie, having both you and a stationary observer agree that more time has passed on the stationary observer’s clock) would happen during the periods of acceleration/deceleration at the beginning and end of the trip.