It is brought forward that viable theories of the physical world that have no variable at all that can play the role of time, do not exist; some notion of time is one of the very first ingredients a candidate theory should possess. Almost by definition,time has an arrow. In contrast, time reversibility, or even the possibility to run the equations of motion backwards in time, is not at all a primary requirement. This means that the direction of the arrow of time may well be uniquely defined in the theory, even locally. We explain these statements in terms of the author's favoured deterministic cellular automaton interpretation of quantum mechanics, also to be referred to as `vector space analysis', and expand on these ideas.