The Third Transition in Science: Beyond Newton and Quantum Mechanics -A Statistical Mechanics of Emergence
Since Newton all of classical and quantum physics depends upon the "Newtonian Paradigm". Here the relevant variables of the system are identified. For example, we identify the position and momentum of classical particles. Laws of motion in differential form connecting the variables are formulated. An example is Newton's three Laws of Motion and Law of Gravitation. The boundary conditions creating the phase space of all possible values of the variables is defined. Then, given any initial condition, the differential equations of motion are integrated to yield an entailed trajectory in the pre-stated phase space.All of this fails for the diachronic evolution of our or any biosphere. Evolving biospheres are entirely outside the Newtonian Paradigm. Perhaps astonishingly, we can use no mathematics based on Set Theory. A consequence is that for any universe such as ours with one or more evolving biospheres, there can be no final theory.The implications are large. We face a third major transition in science beyond the Pythagorean dream that "All is Number". In face of this, we must give up deducing the diachronic evolution of the biosphere. All of physics, classical and quantum, however, apply to the analysis of existing life, a synchronic analysis.But there is much more. We are on the edge of inventing a physics-like new statistical mechanics of emergence.