Chapter 9: Fundamental Physics

Section 16: Quantum Phenomena

Reproducing quantum phenomena

Given molecular dynamics it is much easier to see how to reproduce fluid mechanics than rigid-body mechanics—since to get rigid bodies with only a few degrees of freedom requires taking all sorts of limits of correlations between underlying molecules. And I strongly suspect that given a discrete underlying model of the type I discuss here it will similarly be much easier to reproduce quantum field theory than ordinary quantum mechanics. And indeed even with traditional formalism, it is usually difficult to see how quantum mechanics can be obtained as a limit of quantum field theory. (Classical limits are slightly easier: they tend to be associated with stationary features or caustics that occur at large quantum numbers—or coherent states that represent eigenstates of raising or particle creation operators. Note that the exclusion principle makes classical limits for fermions difficult—but crucial for the stability of bulk matter.)

From Stephen Wolfram: A New Kind of Science [citation]