Physical (Chronological) time
Physicists claim that time is reversible and physical laws operate in both time direction. Yet some feel somewhat uneasy about time reversibility. Entropy obviously cannot be reversed. It is equipped with a time which points only forward. Now watch your aging neighbor, does his appearance change as result of entropy accumulation? Obviously not, since even an old timer gets rid of some of his entropy. Schroedinger believed that he does not feed on energy but on negentropy.
In the CA universe time is irreversible Take our CA#2058, which is destined to evolve from larva to adult and cannot retrace its history backward. Each of its states "knows" who was its predecessor and what will be the structure of its follower. Its current structure, depends on all of its past states. They all are responsible for it and if one is missing or defective the present CA will be different. In biology this property is called differentiation, which cannot be reversed. Once fertilized, a zygote continually differentiates and its properties emerge. In biology you cannot reverse the flow of phenomena, which is impossible even in the CA. The concept of reversibility is simply meaningless!
The physicist will respond in irony:"Give me any CA state and I shall run it in both directions". This is an illusion, since the time which the physicist manipulates is the time of the observer. Yet each state of the CA has its internal time which it carries and updates from state to state. It is independent form the observer's time. It may dilate and shorten without any relationship with the outside world. It is even more relative than Einstein's time, and is called here biological time. From now on the arrow will stand for directed change, or differentiation.The third history depicts CA#2058 in biological time, which will be explained in the next chapter.
Consider now our expanding universe. Does it really follow the relativity model?. Perhaps the Big Bang was a seed of a CA which expands in the same manner as CA#2058 does. A universe which differentiates, and we differentiate in it.