Theoretically, it seems that a viable implementation of double conjugation is required for a successful formulation of a quantum theory of space-time. The 1st physical hint that this is true was initially but countered proposed by Albert Einstein, Boris Podolsky, and Nathan Rosen in 1935 using a unique gedanken experiment now known simply as the EPR experiment. This is an experiment that can exist in the depth of cognitive consciousness distinct from personal emotion and volition. It is not actually done in the laboratory but is deeply analyzed with much mental gymnastics. The one most famous of these thought experiments, was that of Schrödinger Cat which was also proposed in 1935 by Erwin Schrödinger to show the absurdity of the Copenhagen interpretation of quantum mechanics for the existence of limbo quantum states of wavefunction superpositions. In the 1980s, quantum cosmology asserts that it is physically impossible to perform any complete measurement on the whole universe but still there was no other options for replacing the Copenhagen interpretation. On the other hand, also in the 1980s, the EPR experiment was disproved by actual physical experiments performed by Alain Aspect and colleagues in Paris, France. The Aspect Experiment showed conclusively the existence of quantum entanglement that nonlocality is inherent in quantum mechanics. Moreover, the principle of nonlocality could not imply that information can be sent faster than lightspeed, suggesting it is also a relativistic invariance as well as directional invariance.

Together with the principle of nonlocality the implementation of double conjugation of quantum momentum field operators create the squares of energy, representing the quantum vacuum fluctuations of zero-point energies of space-time charges symbolized by symmetric singular Hadamard matrices of H-pluses and H-minuses. Its first appearance as positive square of total relativistic energy is given by +ℰ²=��²��²+��⁴��² and its appearance as negative square of energy is given by squaring the partial time derivative of the commutation relation: -ℰ²=4��²[∂/∂��(����-����)]². Therefore, 4��²[∂/∂��(����-����)]²+ ��²��²+��⁴��²=0 represents the continuous rationalized domain time dependent partial differential equation (whose concise integral notation is given by ∬∂ℋ=0) denoting the totality of both matter and antimatter as described by a quantum theory of space-time implementing double conjugation.