In 1905, Einstein established the equivalence of mass and energy: ��=����². However, 5 years earlier, in 1900, Planck established the equivalence of energy and temporal frequency: ��=ℎ��. However, however, 5 years earlier, in 1895, Boltzmann established the equivalence of average energy and absolute temperature: Ē=����. If this Boltzmann energy is now defined as the average energy of the quantum vacuum then Ē=0. The equivalence of these 3 formulations implies that the temporal frequency, the rest mass, and the absolute temperature are all equal zero. Although absolute zero makes sense for temperature and some elementary particles, it does not make any physical sense for frequency. Alternatively, Ē=0 can imply the change of energy Δ��=0, the same as saying that ��₂-��₁=0 → ��₁=��₂; ��₂-��₁=0 → ��₁=��₂; ₂-��₁=0 → ��₁=��₂; ��₂-��₁=0 →��₁=��₂. That is all the distinct fundamental quantities are equal to each other. Unfortunately, these linear functional equalities is not square-integrable belonging to Hilbert space. The 3rd alternative which is made more plausible by the inclusion of directional property implies that the numbers of +��² and -��² are equal such that their sum (+��²) + ��(-��²)=0 implies that ��=�� and |+��²|=|-��²|. This last alternative validates a physical equivalence of Newton’s 3rd law of motion that for every direction of square of energy there exists an opposite direction such that their vector sum is always zero.

The derivation of square of energy made the assumption of local infinitesimal motion mathematically expressed in the physics of angular motion denoted by an infinitesimal torque: ��=��´�� where �� is properly defined as the thermal force and �� is the radius of an infinitesimal circular motion. The scalar inner dot product of two infinitesimal torques is defined as the square of energy: ��²=��₁·��₂=(��₁´��₁)·(��₂´��₂). Expanded using Lagrange’s identity for vector product gives +��²=(��₁·��₂)(��₂·��₁)-(��₁·��₂)(��₁·��₂) and -��²=(��₁·��₂)(��₁·��₂)-(��₁·��₂)(��₂·��₁) where (��₁·��₂)(��₁·��₂)=0 implies the orthogonality of ��₁·��₂ or ��₁·��₂ or both in order to distinguish the quantum nature of +��² and -��² as space-time charges of H-pluses and H-minuses using singular symmetric Hadamard matrices.