Angular (rotational) motion is an observed property of most of the structures in the visible universe, from planets to stars and to galaxies. In the scale of human anatomy, the circulatory system is divided into 2 distinct topologically equivalent directional flows, through the veins and through the arteries. The first is directionally inward back to the human heart. The second is directionally outward, away from the human heart. In the scale of molecules, the atoms composing each molecule can and do rotate about each other at speed comparable to the varying speeds of sound directly proportional to the ambient temperature. In the scale of subatomic structures, the electrons rotating the nucleus of each atom vary in speeds between 1% to 10% lightspeed. The slower electrons are found closer to the nucleus and occupy lower energy levels. In the scale of subnucleon structures, although the rotational motion of the quarks cannot be observed, it can be assumed to vary in speed much closer to lightspeed. In the scale of Planck length of the quantum vacuum, it is physically logical that the maximum rotational speeds of the space-time charges is exactly lightspeed, which established their zero rest mass equivalent to theoretical rest masses of the gravitons, gluons, and photons.

Since the linear momentum of a photon is defined as its energy divided by its speed (��=��/��), a physical contradiction arise that slower photons of the same internal energies have greater momenta. On the other hand, if the square of photon’s energy is defined equal to the product of square of lightspeed and the square of its momentum (��²=��²��²) then the decrease in speed of the photon is compensated by the increase in its rest mass such that the square of total relativistic energy is conserved: ��²=��²��²+��²��⁴. The square root of ��² is ±��, which allowed Dirac to postulate the existence of antimatter if and only if its directional properties are described by the imaginary entities of Cartan’s spinors. Cartan is the founder of Lie algebra, whose restricted formulation is equivalent to the algebra of Hadamard matrices for describing the speed of spinning square energy.