I've read that as we go faster time dilates and so time slows down. So my question is that If suppose a person in a spacecraft accelerates to the speed of light. After sometime (in his prospective) he decides to decelerate finally to much much lower than the speed of light. Then during all of this how much time will have passed for everything outside? Will he be able to decelerate at all? I mean for an outside observer, who by some means, is able to see everything that is happening in the spaceship, will the person be frozen (in time) and therefore not able to push the button that decelerates the ship and ultimately travel infinitely in time and space? (again another assumption that the fuel does not run out). And (in the prospective of the space traveler) after pushing the button where will he be in time with respect to the observer? I hope I am able to convey my problem. Thanks in advance.

A good question. The nub of the matter is this: if something is moving literally at light speed, then the amount of time between two points along its trajectory, measured in its frame, is 0. So your hunch is right in one way: at light speed (along the edge of a light cone), time doesn't pass.

However, if we try to accelerate a massive body (for example, a spaceship) to light speed, we'll fail. Close enough for present purposes, the reason is that as the body accelerates, it takes on mass, and that mass approaches infinity as the speed approaches c. So your space traveler will never arrive at "frozen" time.

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