A much quoted scientific musing of the late John Archibald Wheeler (1911-2008 ) regarding the theory of gravity is that it is not a force acting at a distance; it is mass gripping spacetime, telling it how to curve, and spacetime gripping mass, telling it how to move. This semblance of scientific tautology has been around since Wheeler started his research on the theory of gravity, which remains unresolved to this day. However, from the perspective of a quantum theory of gravity, it can be agreed that gravity is not a force but neither is it the exchange of quanta of gravitons as many physicists of the quantum field theory of gravity suggested. A simpler but more intuitive explanation is that it is the collective actions of infinitely countable numbers of mass directors called space-time charges. They are the quanta of vacuum fluctuations equivalent to the squares of zero-point energies.

Mathematically, a mass director is defined as an axial vector of infinitesimal length approaching a null vector analogous to the imaginary-complex spinors. It always has a pointer as its quantized direction. If the absolute magnitude of this pointer is defined as square of energy using symmetric singular Hadamard matrices then two distinct space-time charges (for mass or energy directors) can be defined: the H-plus and the H-minus. Independently of any coordinate system but dependently of Hopf-Möbius topology, an H-plus always points the opposite direction of an H-minus. A system of 1 H-plus and 1 H-minus is a system of zero mass and zero charge. A system of 2 H-pluses and 1 H-minus gives a physical director along the direction of the unpaired H-plus. These H-pluses and H-minuses can interact by matrix addition and multiplication satisfying both the associative and the commutative properties. However, they cannot interact by the undefined operation of matrix division or the defined matrix subtraction, although their counting magnitudes can be operated by basic arithmetic. Hence, mathematical directors as idealized physical directors like mass and energy directors form sets of abstract algebraic structures called rings.