Beyond the Newtonian Paradigm: A Statistical Mechanics of Emergence

Since Newton, all 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 are defined. Then, given any initial condition, the differential equations of motion are integrated to yield an entailed trajectory in the prestated and fixed phase space. It is fundamental to the Newtonian paradigm that the set of possibilities that constitute the phase space is always definable and fixed ahead of time. All of this fails for the diachronic evolution of ever-new adaptations in our--or any--biosphere. The central reason is that living cells achieve constraint closure and construct themselves. With this, living cells, evolving via heritable variation and natural selection, adaptively construct new-in-the-universe possibilities. The new possibilities are opportunities for new adaptations thereafter seized by heritable variation and natural selection. Surprisingly, we can neither define nor deduce the evolving phase spaces ahead of time. The reason we cannot deduce the ever-evolving phase spaces of life is that we can use no mathematics based on set theory to do so. We can neither write nor solve differential equations for the diachronic evolution of ever-new adaptations in a biosphere. These ever-new adaptations with ever-new relevant variables constitute the ever-changing phase space of evolving biospheres. Because of this, evolving biospheres are entirely outside the Newtonian paradigm. One consequence is that for any universe such as ours with one or more evolving biospheres, there can be no final theory that entails all that comes to exist. The implications are large. We face a third major transition in science beyond the Pythagorean dream that “all is number,” a view echoed by Newtonian physics. In the face of this, we must give up deducing the diachronic evolution of the biosphere. However, all of physics, classical and quantum, applies to the analysis of existing life, a synchronic analysis. But there is much more. We begin to better understand the emergent creativity of an evolving biosphere. Thus, we are on the edge of inventing a new physics-like statistical mechanics of emergence.