A new equation is found in which the concept of matter-space-time is mathematically connected; gravitation and electromagnetism are also bound by space-time. A mechanism is described showing how velocity, time, distance, matter, and energy are correlated. We are led to ascertain that gravity and electricity are two distinct manifestations of a single underlying process: electro-gravitation. The force of gravitation arises of electromagnetism—inherently much stronger—divided by the cosmological space-time. The radius of space-time belongs to the family of electromagnetic waves: the wavelength is the radius (10
26 m) of the universe and the period (10
17 s) is its cosmological age. For the first time, the cosmological time, considered as a real physical object, is integrated into a “cosmological equation” which makes coherent what we know regarding the time (its origin, its flow …), the matter, and space. It sets up a mathematical model allowing us to interpret dark energy (or cosmological constant) as being both “negative” and “tired” energy. After an introduction with a brief history of unifications and the presentation of two roughly equal ratios arising out from Dirac’s large-number hypotheses which relate to the ratio of electric force to gravitational force and the ratio of the age of the universe to the atomic time unit associated with atomic processes, we present in §2 this new equation of quantum cosmology which operates the reconciliation between the macrocosm and the microcosm. In §3 and §4, we discuss the irreversible cosmological time resulting from the equation, as well as the role of the mass (heavy) relative to the gravitational constant G. In §5 we discuss the links that the equation establishes between gravitation (structure of condensation) and electromagnetism (structure of expansion), between relativity and quantum theory. We apply the formula to Planck’s time. We speak of the new essential variable
, and briefly of a new principle, the principle of compensation. In §6 we discuss the negative energy solutions banned by physics, and we deplore that half of the universe escapes us. We present the electro-gravitation in §7, from the equation which represents a super hydrogen atom. In § 8 we show that the global mass (gravitational) is variable: it increases during the expansion while the mass of the elementary particles decreases. In §9 we approach the spontaneous symmetry breaking; when it occurs, the arrows of the equation are momentarily reversed: such a mechanism would apply to the Allais effect, also mentioned in §6.4. §10 and §11 deal with the energy linked by the equation to matter through expansive space-time. The equation transforms electromagnetic kinetic energy into a gravitational mass, considered as a potential energy. Entropy increases according to the arrow of time towards the future. In §12 we discuss of the prevailing theory of inflation. We note the similarity between the proclaimed acceleration of current expansion and inflation. Physicists have interpreted the positive cosmological constant in terms of vacuum energy which would be 10120 times higher than the dark energy density deduced from the astronomical measurements. However, the high theoretical value of the vacuum energy (and the cosmological constant) has no observable pending in the cosmos. In §13 we suggest that these several orders of magnitude difference problem are solved by the theory of relation, which indicates a deceleration of the expansion. Finally, in § 14, we close by speaking of a model of cyclic universe and about the object of this paper, a dynamic equation that allows to build a quantum cosmology.