Beyond the Newtonian Paradigm: A Statistical Mechanics of Emergence

Abstract: Since Newton, all classical and quantum physics depends upon the "Newtonian Paradigm". Here the relevant variables of the system are identified. 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 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 any biosphere. The central reason is that living cells achieve Constraint Closure and construct themselves. 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. We can use no mathematics based on Set Theory to do so. 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 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". 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. We begin to better understand the emergent creativity of an evolving biosphere. Thus, we are on the edge of inventing a physics-like new statistical mechanics of emergence.