There are two rival theories of time: static and dynamic. The Special Theory of Relativity is one of the strongest arguments for static time. However, the defenders of dynamic time claim that their approach is also possible in a relativistic setting. This debate supported the third theory: the hybrid theory of time. The aim of this paper, however, is to argue that the hybrid theory (combining both static and dynamic elements) is against the nature of the Special Theory of Relativity. The argument is motivated by H. Stein’s attempt to separate definite past from indefinite future by timelike and lightlike relations in and on the past pointing light cone. The paper shows that this approach leads to restricted and extremely unintuitive notion of co-presence. This is considered as a serious objection against the animation of static time in a relativistic setting.