Analogous to population inversions of LASER systems, vacuum inversion is the amplification of certain directions of the quantum vacuum fluctuations of the squares of zero-point energies. Specifically, what is being inverted is the quantized direction of a spacetime charge. These vacuum inversions are made simpler simply by the fact that there exist only two distinct integral configurations of spacetime charges, the H-pluses and the H-minuses.

Odd numbers of vacuum inversion are grouped into matter configurations called fermions. Even numbers of vacuum inversions are grouped into the first power of energy configurations called bosons. The classifications of fermions are the quarks and leptons while the classifications of bosons give four distinct quantized interactions: electromagnetic, weak, strong, and gravitational interaction. The quanta of the first are the photons; of the second are the W’s and Z’s elementary particles plus the massless photon of electromagnetism. The quanta of the third are the gluons, which are the mediators of color forces that bind colored quarks into colorless protons, neutrons, and other hadrons. These elementary particles prefer to interact by the strong color forces. Theoretically, the quanta of the gravitational interaction are the hypothetical gravitons. However, a failure to detect them is a direct indication that an inherent inconsistency exists in the theories of all physical charges: electric, color, and hypercharges. This can be removed by a theory of spacetime charges through the realization of vacuum inversions of both odd and even configurations. Mathematically, these are embedded within an infinitely ordered matrix called a sieve of Diophantus, which hides all the multiples of two by two square matrices called Hadamard matrices as inverses of any arbitrarily, randomly selected two by two matrices plus a base matrix.