Firstly, at the infinitesimal level of physical reality, the quantum fields of the true vacuum can be described by the differential energy of the Lagrangian function of spacetime. This 4D function is constructed by taking the difference of the kinetic and potential energies. Secondly, this infinitesimal differential energy is equivalent to directed energy, a vector quantity with both magnitude and direction. Although Dirac theory of the electron is guided by the Hamiltonian energy function which is integral rather than differential, it did make the discovery of antiparticle called the positron simply by introducing the spin as described by a mathematical imaginary complex entity called the spinor. However, applied to symmetric particles such as bosons, Dirac equation failed. Theory of bosons is described by the Klein-Gordon equation. Although Klein-Gordon equation gives a relativistic wave equation, putting space and time on equal dimensional level using second time derivative; it gives negative probability density and negative energy states. Conversely, negative probability can be resolved by first derivative of space and time using the Dirac equation if and only if it describes spin half particles called fermions. The successful theories of both fermions and bosons together with QCD which predicted more spin half particles called quarks and spin-1 particles called gluons with the existence of color charges established the standard model of elementary particles.

Nonetheless, a return to the Klein-Gordon formalism of second derivative for both space and time seems necessary for the complete description of differential directed energy as a quantum theory of spacetime. The resolution is made by the simple assertion that differential directed energy is simply the square of energy. Furthermore, the spacetime variables are replaced by a pair of infinitesimal repulsive primary forces together with a pair of spacetime metric. From these, the square of infinitesimal energy of the vacuum is given by ��˛ = ��₁ ´ ��₁ ∙ ��₂ ´ ��₂ where �� is the primary force and �� is the metric and both are vector quantities. From vector analysis, expanded using Lagrange’s identity gives two distinct equivalent forms: ��˛ = (��₁ ∙ ��₂)( ��₂ ∙ ��₁) - (��₁ ∙ ��₂)( ��₂ ∙ ��₁) and ��˛ = (��₁ ∙ ��₂)( ��₂ ∙ ��₁) - (��₁ ∙ ��₂)( ��₂ ∙ ��₁). Since the absolute magnitudes of all primary forces are equal, the inner scalar dot product of a pair of primary forces in the same direction vanishes and is identically zero, giving two distinct topological structures of infinitesimal squares of energy: +��˛ = ((��₁ ∙ ��₂)( ��₂ ∙ ��₁) and - ��˛ = -(��₁ ∙ ��₂)( ��₂ ∙ ��₁)The first represents a single spacetime charge called H-plus. The second represents H-minus.