They may not come from events that still have to be specified, because in that case conflicts may arise: if event A affects the features of event B then event B should not react back to modify event A, otherwise the rules cease to be unique they will literally be circular, making them either self-contradictory or ambiguous, and for that reason they would not be suitable to explain observed phenomena. The data that we have to enter into the program may come from events calculated earlier. Regard the laws of physics as a computer program to calculate the next sequence of events. Whenever we build a model of our universe, one that is controlled by вЂњlaws of physics,вЂќ it should come with a completely unambiguous prescription of the order in which the laws of Nature should be imposed on all events that take place. Our universe is known to carry a memory of things that happened in the past. This in fact will bring us to provide a definition of time that is more primary, more basic than all other ingredients of our model, including the notion of space. It is difficult, probably impossible, to devise a model of our universe, if no ordering is defined for the model to describe the events. Whenever we build models that explain the existence and nature of the events, it is of extreme importance to have such an ordering of events it allows us to explain them sequentially: one event can be the cause of a subsequent event if its time variable is lower, or it could be the consequence of an event if its time coordinate is higher. It allows us to define an ordering (or at least a partial ordering) of all events. This ordering defines an orientation, called the arrow of time.

It is the only coordinate in which it is meaningful to define an ordering in the values given, the order of time. The coordinate that indicates time, is a very special one. The number of coordinates needed, usually real numbers, is called the dimension of space-time. The events are characterized first of all by their locations in space, and moments in time, all together indicated in terms of coordinates. The universe as we know it is characterized by a framework called space-time, in which events take place. What distinguishes quantum systems from classical ones is our fundamental inability to control the microscopic details of the initial state when phenomena are studied in the light of some theoretical model. It is also summarized how our more rigorous causality condition affects Bell's theorems. We explain these statements in terms of the author's favored deterministic cellular automaton interpretation of quantum mechanics, also to be referred to as вЂњvector space analysis,вЂќ and expand on these ideas. The only viable causality condition is one that is symmetric under time reversal. It is explained that a rigorous definition of time, as well as a formulation of the causality and locality concepts, can only be given when one has a model for the physical phenomena described. This means that the direction of the arrow of time may well be uniquely defined in the theory, even locally. In contrast, time reversibility, or even the possibility to run the equations of motion backwards in time, is not at all a primary requirement. 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. Institute for Theoretical Physics, Utrecht University, Utrecht, Netherlands.

Quantum causality