Acordding to Einstein's Relativity, while Space-man lives for 1 day(just a number for example , not an exact number calculated from the corresponding relative speed), Earth-man can live for 1000 years (just an example number too). But from the view of Space-man, while Space-man lives for 1 day, Earth-man lives for 1 second. So while Space-man lives for 1 day, then how long does Earth-man live ? 1000 years or 1 second? Or 1000 years = 1 second actully ?！
Thank you in advance!!
If you consider this situation strictly in Special Relativity terms, i.e. as long as you stay in the classical SR situation and consider both reference frames inertial, there is no (falsifiable) answer to you question. Therefore, if there are no accelerations involved (and no acceleration appears in the Lorenz transform showing time dilatation), you can always claim that the other body is time dilated. Any proof showing otherwise should actually be interpreted as falsifying the very Special Relativity Theory as it currently stands.
This question makes my head spin for hours. And I think the point is the reference frame of Earth-man is not running in a high speed referring to a photon-reference-frame. So for a definite distance(let say, L) of a photon-clock, if the speed of a reference frame is bigger, the time takes less. So in the situation of Earth-man, the time takes more because the speed of his reference frame is smaller.
I don't think this is a paradox now too. It's a mistake make by the poor quality of the physics text book.