Any theory attempting to describe space-time quantization cannot simply bypass the emergence of the science of quantum chaos. Partial, incomplete, and superficial understanding of quantum chaos could have been responsible for the rise of, firstly, quantum field theories with their infinite degrees of freedom for equipartitions of infinitesimal zero-point energies of quantum vacuum fluctuations of virtual particles and secondly superstring theories of double, triple, and quadruple increase in dimensionality of space-time energy configurations. Unfortunately, both of these major divisions still cannot provide conclusive plausible explanations for the existence or nonexistence of the scalar spin zero Higgs boson, the magnetic monopole, or the massless spin 2 graviton. Moreover, there is no resolution for the chirality or handedness preference of natural selection. That is the fact there are more left-handed particles than right-handed ones and matter versus antimatter continuous broken spontaneous symmetry.

Although two major attempts toward complete descriptions of dissipative nonlinear dynamics were developed in the early years of the 20th century, namely Einstein’s 16 nonlinear field equations of general relativity and Dirac nonlinear spinor equation for the spin-½ electrons of which the former belatedly postdicted the nonlinear (accelerated) expansion of the universe and the latter properly predicted the existence of antimatter, they remain theoretically disjointed. Fortunately, a subtle connection does exist. This is the square of energy. Dirac insisted on the plus or minus square root of energy solutions which beg the question for negative energy while Einstein relied on the positive spherical-elliptic curvature of the momentum-energy tensor (pE) which needed the lightspeed factor to reach the absolute quantum state of double hyperbolic geometries of square of energy since cp=E and cpE=E, where cE=S represents the space-time continuum and E=H represents space-time quantization defining a new p=H/S equivalent to old p=E/c of photons. Both are subsumed in the total relativistic energy formulation given by E=cp+mc. Consequently quantum chaos arises logically from the two dimensionality of square of energy.