Computational Emergence: New Paradigm

Computation has turned the philosophical idea of emergence into a virtual laboratory for exploration of large scale complex structures developing in systems formed by small scale simple components. The laboratory is realised in efficient form by the Finite Element Method FEM covering all areas of continuum physics including fluids, solids and electro-magnetics modeled by the classical partial differential equations of Euler, Navier and Maxwell.

Computation thus brings new life into the classical models of continuum mechanics describing small scale simple local physics in terms of differential equations, by exhibiting the large scale global result as emergence by solving the equations typically by time stepping. In particular, the turbulent flow of a fluid with small viscosity like air and water can be simulated by computational solution of the Euler equations (expressing Newton's 2nd law and incompressibility in local form).

In general, emergence can be explored if solutions can be computed. With increasing computational power more of continuum physics can be explored as emergence in a FEM laboratory. 

Quantum Mechanics QM as the physics of atoms and molecules appears to fall outside this paradigm, because the basic mathematical model in the form of  Schrödinger's equation is uncomputable by involving $3N$ spatial dimensions for a system with $N$ electrons bringing in exponential computational complexity. Exploration of emergence in systems of atoms and molecules is thus not possible by computation because of exponential complexity, which can only be a big disappointment for a physicist seeking to understand emergence in atomic systems. 

There is however a version of QM named RealQM which is a computable because it has the form of classical continuum physics in 3 space dimensions. RealQM opens the possibility of exploration of emergence in systems of atoms as forms of chemistry and protein folding. 

Emergence emerges as a central concept of physics, open to  exploration by computation. Effective large scale models may be formed once emergence is uncovered.