does time control any physical dynamic ? from the atomic clock , to biology or is time more of a abstract mathematical measurement of movement ?
As in control, do you mean describe? I would say no, not fundamentally anyway. In fact, time isn't even an observable. We just keep assuring ourselves that perhaps time should be physical because it is part of the vacuum but essentially we can't observe time. All we can do, as sentient observers, is sense a time pass. It is a completely abstractual creation. A marker if you wish that humans have invented and no more.
I'll add to this, that things like past and future don't even exist in relativity. Wordlines are static and in GR a global time completely vanishes. Time isn't even fundamental - it cannot be applied for instance to a big bang scenario because there is no geometry at the big bang and obviously, time is a geometrical factor of geometry in relativity. Time is local, but not physical or observable.
Yup. In fact, the renowned Julian Barbour is doing just this: omitting time from equations and describing dynamical properties of matter using observable quantities in physics. He argues this is how physics should work. His idea is noval and a real approach to the time problem. We can in other words, describe as much physics as we like in principle without resorting to time.
