Let there be two bodies a and b. Let a be on Earth and b in space with velocity $(√3/2)c$. Then let the time interval which has passed (on the earth) be twice that of the time interval of which passed in space for b, (i.e. the time for b is dilated for body a).
Does b also feel that the time interval which it passed with a spaceship in space is twice that of the time interval of a which passed on the earth? I ask this because for b relative to it, a is also moving with velocity $(√3/2)c$.
Special relativity predicts that either clock runs more slowly than the other, as judged from the other clock's system:
http://www.people.fas.harvard.edu/~djmorin/chap11.pdf David Morin, Introduction to Classical Mechanics With Problems and Solutions, Chapter 11, p. 14: "Twin A stays on the earth, while twin B flies quickly to a distant star and back. [...] For the entire outward and return parts of the trip, B does observe A's clock running slow, but enough strangeness occurs during the turning-around period to make A end up older."
Special relativity's prediction that either clock runs more slowly than the other (as judged from the other clock's system) leads to absurdity unless "enough strangeness occurs during the turning-around period to make A end up older". However, during the turning-around period, the traveling twin is very far away from his stationary brother so the "enough strangeness" idea (Einstein devised it in 1918) is simply idiotic.
