It has been said by the late mathematical physicist Heinz R. Pagels that one criterion for a theory of the universe is that it must not leave open unanswered questions about a “preorigin.” Otherwise it is not a true theory. For example the universe began as something called a primordial seed. This would then leave behind with the open question where did this seed come from? The alternative idea is that the universe began as a creation ex nihilo, created out of “nothing.” This satisfies the criterion that it leave no unanswered question about a preexistence state. But what is “nothing?”

The answer that some physicists would give is that “nothing” signifies the lowest energy state of the quantum vacuum of squares of zero-point energies, which is composed of both positive and negative aspects. Since there are equal numbers of positive (+��²) and negative (-��²) squares of zero-point energies their one global sum is identically zero, while their many local sums are not. The positiveness and negativeness is a consequence of the underlying topology, since their absolute values |+��²| and |-��²| can neither be called positive or negative and |+��²| = |-��²|. On the other hand, the dynamics of the underlying topology implies a working principle of directional invariance. This principle asserts the physical existence of space-time charges as H-pluses and H-minuses where and when H-plus represents +��² and H-minus represents -��². Since these are second order singular symmetric Hadamard matrices their matrix sum is always identically zero. Consequently, the principle of directional invariance suggests the existence of directional non-orientable equilibrium if one square of energy is defined as the inner scalar dot product of two infinitesimal torques, while each torque is the local outer vector cross product of a local infinitesimal thermal force and its shortest space-time metric between two temperature gradients and whose local infinitesimal motions create local gauge invariance and whose local sums and local products respectively create electric charges and masses for both ordinary matter and energy.