Emergence of Time and Observable Physics

A new idea, which is deeply rooted in noncommutative geometry, is proposed in this paper to connect general relativity, quantum theory thermodynamics, cosmology and the foundation of quantum mechanics. The emergence of time and the arrow of time become natural in the new scheme. 1. the issue of time An important question is asked explicitly in some literatures such as [2], which concerns with the relation of time, gravity, thermodynamics and quantum theory towards a mathematically consistent theory. The issue of time has been an elusive question in physics since the beginning of this discipline. In generally covariant theories such as general relativity, string theory and etc, time is incorporated to spacetime and no preferred time can be distinguished from spacetime in the context general relativity. In GR, given two points in spacetime, the only thing we can say is that the two point are spacelike, time like or in light cone. However, the concept of the arrow of time is deeply rooted to our everyday’s life. For instance, between today and tomorrow, according to our experience,there should be an arrow. However in GR, today and tomorrow are merely timelike.(Assume we are in the same space). The second law of thermodynamics so far is the only physical law that shows the arrow of time: the entropy of a system S is always increasing with respect to the arrow of time. In statistical mechanics, when we consider a gas system, we find