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.
Historically [
More than seventy years ago, Paul Dirac suggested that more than a coincidence was at work between the age of the universe in atomic time units and the ratio of the electric force between an electron and a proton to the gravitational force between the two [ k e 2 / ( G M p M e − ) = 10 40 ] [
Our reflections and insights on this issue have made us discover the theory of Relation (let us understand well: the word “relation” means connection, link, and it is not excluded that it means “unification”) whose mode of action decrypts the order of the cosmos. It proposes a model of quantum cosmology through an equation that builds a relationship between electromagnetism, Newtonian gravitation, special relativity, quantum physics and general relativity.
Let us compare the electrostatic and the gravitational forces between two protons in the same nucleus, with a distance of 0.2 nanometers [
Let us pursue Dirac’s suggestion on the time, and replace the ratio by a universal time factor with the constants G and c: F e / F g = t o c / G ; F e = F g t o c / G . And suppose we relativize the masses of the protons, in accordance with special relativity, as if they were moved with a speed of 200,000 km/s, we would obtain
k e 2 / [ R o ( 1 − v 2 / c 2 ) 1 2 ] 2 = G [ M o p / ( 1 − v 2 / c 2 ) 1 2 ] 2 / [ R o ( 1 − v 2 / c 2 ) 1 2 ] 2 [ t o c / G ] , (1)
thus we would have
k e 2 = M V P 2 t o c . (2)
[ M o p is rest-mass; M o p ( 1 / ( 1 − v 2 / c 2 ) 1 / 2 ) gives M v p , i.e., rest-mass + kinetic energy (T); v = 200 , 000 km / s = 2 / 3 c ].
Note that in this model, the speed of the relativized protons is identified with the estimated speed of the recession of galaxies and that it determines all other variables. We found reasonable to adopt the speed 2/3c. Since this is dependent on astronomical observations which are constantly evolving, the speed will be adjusted accordingly.
Particles come in pairs, each with a counterpart antiparticle
± k e 2 = ± [ M o p / ( 1 − v 2 / c 2 ) 1 / 2 ] 2 t o c (3)
2.3 × 10 − 28 kg ⋅ m 3 ⋅ s − 2 = [ ( 1.672 × 10 − 27 kg ) / ( 1 − 4 / 9 ) 1 2 ] 2 ( 1.528 × 10 17 s ) ( 3 × 10 8 )
2.3 × 10 − 28 kg ⋅ m 3 ⋅ s − 2 = ( 2.2439 × 10 − 27 kg ) 2 ( 1.528 × 10 17 s ) ( 3 × 10 8 ) .
We ascertain that the link between the charge squared and the relativized proton’s mass squared confers a universal time of 1.5283 × 10 17 s multiplied by c. That time gives 4.84 billion years [ ( 1.5283 × 10 17 ) / ( 365.24 × 24 × 60 × 60 ) ] .
This time for a speed of 200,000 km/s gives a time well below the 13 to 15 billion light-years expected. Relativized protons should be with a much lower rate to obtain these ages. Therefore, the radius t o c of about 15 billion light-years could be confused with both an electromagnetic wave and a gravitational wave. The two are transverse. However, since we assimilate the speed of the relativized protons to the velocity of recession of galaxies and that the latter is not evaluated less than 2/3c, we exclude this possibility.
The other alternative is to consider that the cosmological time of Equation (2) is a mathematical “linear time” that evolves as a “longitudinal” ray of light. A point particle on a cosmological space-time ray will go straight ahead, such as a Euclidean space-time line, from one point to another. It will cross the radial radius t o c (=A-Z), in 4.84 billion light-years. This radius can then become confused with a longitudinal gravitational wave or a longitudinal electromagnetic wave. Although we do not know these waves, they cannot be forbidden in theory. We believed for a long time that sound waves were exclusively longitudinal while they are also transverse.
Linear time, that is to say, the time required for a particle to travel a distance A-Z in a straight line as would make a longitudinal wave, matches with 15.21 billion years in circular time, or linear time multiplied by π. The circular time expresses the required time for a particle can travel the same length in rotating around the line, as would a transverse wave [
One can imagine that a wave rolled up around the radial line A-Z would travel it in the 5.21 billion years, which is linear time multiplied by π. It fits a transverse electromagnetic wave
k e 2 = M V P 2 ( π ) t o c . (4)
Of this expression, one must keep in mind that π is used for winding the particle spirally around the radial length t o c . It could be a transverse electromagnetic wave but it could also be a transverse gravitational wave. Mathematically, the equation should be
( π ) k e 2 = M V P 2 ( π ) t o c . (5)
From a physical point of view, we prefer however the Equation (4), because it allows highlighting, for the same distance, the transverse character (and thus electromagnetic) with respect to the linear character. It can be said that the second of the longitudinal wave is worth the second of the transverse wave divided by π. It means that a particle will browse transversely a distance A-Z while in the same time another particle will cover a radial distance A-Z × π. We estimate that it is adequate and corresponds roughly to the observations. The photon is the boson of the transverse electromagnetic wave of space-time.
It has been shown that space-time is electromagnetic (vacuum minimum energy, etc.). So, using the basic unit of time, the second, considered electromagnetic, the universe was estimated at about 15 billion light-years. Our equation, calculated for a relativistic velocity of 2/3c for the protons, gives 15 billion light-years using π. We estimate that it is adequate and consistent with the observations. The photon is the boson of the transverse electromagnetic wave of space-time.
If this transverse electromagnetic wave was unfolded into a longitudinal electromagnetic wave, the distance A-Z would be multiplied by π, what would give 47 billion longitudinal light-years. We would have, always at the speed of light, distances at least three times the length of the distances presently estimated. The seconds of this longitudinal electromagnetic wave would have a time three times shorter than the seconds of the transverse wave.
The particles that may be associated with longitudinal electromagnetic waves and longitudinal gravitational waves could be the neutrino and the graviton. The longitudinal electromagnetic wave already exists. The gravitational wave, which has always been considered to be transverse, would have been captured in 2015. This does not exclude the existence of a longitudinal gravitational wave [
We know that nucleons are forming 99.97% of the known matter. Neutron and proton are two states of the nucleon. Suppose that the protons of our equation are galaxies which move away at 2/3c, then we get a “cosmological equation” that determines the age and distance of the universe in relation to the speed of recession of galaxies. The more the speed of recession of distant galaxies decreases (velocity ~c2/c2 at the beginning toward lower speeds: v2/c2), the more they move away from the Earth and the more the age of the universe increases. Velocity, distance, and age are correlated for the first time in an equation. The flight of the galaxies at 2/3c corresponds to 15 billion years. Both numbers are roughly consistent with the real estimates of science.
The Equation (4), in the form
± ( π ) k e 2 = ± M V P 2 ( π ) t o c (6)
is the equation of the expansion. It establishes a clear mathematical link between electromagnetism and gravitation. The term “ ( π ) t o c ” corresponds to the radius of the universe. To the right-hand side, matter ( M V P 2 ), space and time ( t o c ) are mathematically related into one whole.
It can be seen in the Equation (1) that the expression G [ M o p / ( 1 − v 2 / c 2 ) 1 / 2 ] 2 / [ R o ( 1 − v 2 / c 2 ) 1 / 2 ] 2 links Newtonian gravitational force and relativity. We get a relativized Newtonian gravitation, which means, firstly, that gravity is a reality everywhere and, secondly, that special relativity is not only a mathematical utility, not just a Galilean reference frame without gravity. Both are linear theories applied to a tri dimensional Euclidean geometry with linear-plan space-time. These are applied to a linear two-dimensional Euclidean space-time with flat linear theories. In addition, electromagnetism is also a linear theory.
In Newton’s theory of gravitation, the force G M m / r 2 transmits instantaneously an energy or a signal. Newton was unhappy with the instantaneous or “action at a distance” phenomenon associated with gravity. Poincaré (1904), Minkowski (1908), and de Sitter (1911) agreed that gravity must propagate with the speed of light. For according to special relativity nothing moves faster than light, not even gravity. None of the several gravity theories—even from Einstein, that was consistent with special relativity in that the speed of the propagation of gravity was the speed of light—was satisfactory. In the proposed equation, the combination of the Lorentz transformation and toc ensures that the velocity of light or gravity does not go faster than the velocity of the universal constant c [
According to the theory of Relation, gravity is not a separate force, but an aspect of electromagnetism. Both forces are joined by the four-dimensional space-time. In fact, the gravity results from the dissolved energy of the expanding electromagnetism which does not stop creating the space-time. Deep down, electric and gravitational forces are part of a common superforce: electro-gravitation. Like magnetism and electricity are two sides of electromagnetism [
Here are other relativistic expressions that express the mass variation of a moving proton as a function of velocity and cosmological time. They do not take account here of π as if t o c was longitudinal and not transverse. The same applies to the rest of the paper.
( M o p is the rest mass; M o p ( 1 / ( 1 − v 2 / c 2 ) 1 / 2 ) , or Δ M p is the kinetic energy T; M v p is the relativized mass with kinetic energy; v = 2 / 3 c )
k e 2 = M o p + { M o p [ ( 1 / ( 1 − v 2 / c 2 ) 1 / 2 ) − 1 ] } 2 t o c (7)
2.3 × 10 − 28 = [ ( 1.6725 × 10 − 27 ) + ( 5.71 × 10 − 28 ) ] 2 ( 1.52 × 10 17 s ) ( 3 × 10 8 ) ,
or
k e 2 = ( M o p × Δ M p ) 2 t o c (8)
2.3069 × 10 − 28 = [ ( 1.6725 × 10 − 27 ) ( 1.3416 ) ] 2 ( 1.5283 × 10 17 s ) ( 3 × 10 8 ) .
Relativistic expression for kinetic energy of a moving proton (quantum mass)
T = M v p c 2 − M o p c 2 = M o p c 2 [ ( 1 / ( 1 − v 2 / c 2 ) 1 / 2 ) − 1 ] . (9)
Potential energy for the electrostatic field of point charges united to potential energy for the gravitational field
− k e 2 / [ R o ( 1 − v 2 / c 2 ) 1 / 2 ] 2 = − { G [ M o p / ( 1 − v 2 / c 2 ) 1 / 2 ] 2 t o c } / { [ R o ( 1 − v 2 / c 2 ) 1 / 2 ] G } . (10)
Formula of the total energy of the proton in function of e, c, and t o
k e 2 = M V P 2 t o c ; M v p = ( k e 2 / t o c ) 1 / 2 ; M o p = ( 1 − v 2 / c 2 ) 1 / 2 ( k e 2 / t o c ) 1 / 2
E = M o p c 2 + T = M v p c 2 = ( k e 2 c 3 / t o ) 1 / 2 (11)
E = M o p c 2 = [ ( 1 − v 2 / c 2 ) ( k e 2 / t o c ) c 4 ] 1 / 2 = ( 1 − v 2 / c 2 ) ( k e 2 c 3 / t o ) 1 / 2 . (12)
This is for the fermion. New formula of energy for the boson ( m o ) is
E = m o c 2 = M v p 2 h c / k e 2 (13)
k e 2 = M V P 2 t o c ; k e 2 = M V P 2 h / m o c ; k e 2 = M V P 2 h c / m o c 2 .
This means that electricity is a manifestation of energy like energy and matter are equivalent. Proton (and neutron) and electron are grains of electricity. The masses of proton and electron have EM origin: M v p = ( k e 2 / t o c ) 1 / 2 , and the matter is composed of grains of electricity. Matter atom is done of a multitude of elementary particles that are electricity, so properties of matter must be explained by properties of electricity.
On the basis of k e 2 = M V P 2 t o c = M V P 2 2 G M o / c 2 = M v p 2 2 G M o c 2 / c 4 , the new formula of the energy of the ordinary matter of the universe will be
E = M o c 2 = k e 2 c 4 / ( M V P 2 2 G ) . (14)
The Equation (2) [ k e 2 = M V P 2 t o c ] is written with a real and cosmological time (neither relative nor absolute) that governs the infinitely small and the infinitely large. It allows considering time as a real entity which contains in itself the difference between the past and the future. It can open a new chapter of the physics because so far, the more the physical theories have been developed, the more the notion of time has become evanescent. First with the introduction of relativity in 1905 which made it lose its absolute character; the notions of present or of duration turning dependent on the observer; an overt indifference where time becomes intimately linked to space for which this distinction has no meaning. Then with quantum mechanics, two decades later, who dived in the “fuzzy” the idea of time. The laws of microphysics show no preferred flow direction. At such an extent that for physicists if a broken glass is never spontaneously repaired, it is not because we cannot go back in time, but simply because the configuration “repaired” is less probable than “broken” [
Nevertheless, in the cosmological theories of Einstein, de Sitter and Lemaître, new ideas related to the character of universal space had been introduced, but no corresponding progress was achieved regarding the idea of time, except to the extent that the phenomenon of expansion tended to suggest a finite past, rather than an infinite past. Just as Einstein did make the progress that is known by analyzing concepts like that of simultaneity, similarly the next progress of physical theory will be obtained by taking again the analysis of time to the point where he left it.
The cosmological time found in the equation would be the age of the universe. The reference is the beginning of space-time from the Planck time. It would recover a character not absolute as before the relativistic revolution, but universal that would integrate the difference between the past and the future with the acquirements of this revolution that unites time and space. The energy associated with the immateriality and the mass associated with ordinary matter could be stored in two opposite and complementary structures. This “new” time and this new energy and mass ratio would redefine general relativity, making it global and compatible with the quantum rules [
If we admit that the universe is a kind of expanding super-atom that gives the age of the universe, then we have an arrow to the future which is the same of at least three arrows of time that distinguish the past from the future: thermodynamics (disorder increases) cosmological (universe expansion rather than contraction), psychological (we remember the past, not the future) [
In any event, the colossal amount of kinetic energy contained in the original proton varies with time. In fact, energy relieved by two energetic protons which move away from each other engenders the radius of the universe. The term “ t o c ” corresponds to the radius of the universe and represents the cosmological time linked to the universal thermodynamics. We say that this cosmo-thermodynamics time, that shapes the radius of the universe, stems from two charges in the form of relativized protons which run away from each other creating so the space-time of this universe. One could say that the pairs of protons go away simultaneously from the center in all directions and two opposite directions constitute geometrically the diameter. This simultaneity suggests another time behind the thermodynamic time that we could call “duration”. The velocity v of the Lorentz transformation indicates both the speed of the proton which decreases with expansion and its remaining mass (rest + kinetic energy). The released energy is propagated with velocity c, as an electromagnetic wave, which suggests that the frequency decreases with time [
Lancelot L. Whyte in a short essay, Archimedes or the Future of Physics (1927) [
Based upon the fundamental unit of time and on the fundamental physical constants, this cosmological time confirms the intuition of Paul Dirac, namely that the dimensionless number 1040 is not a constant but a variable of time in relation to the age of our universe. He thought that this number was determined by particle physics and also by the gravitational influence of the entire universe. In 1937 and in1938, he proposed that G varies like the inverse age of the universe, so as the universe expanded from the big bang, the gravitational constant, or force, became weaker and weaker as time passed until today when we experience the present very weak force of gravity. But he was unable to apply it to Einstein’s gravity theory [
For our part, we postulate that the gravitational mass of the universe varies proportionally to the age of the universe [
Ultimately, the theory of Relation considers that the mass of elementary particles changes with time (we do not speak here of the naked mass which remains invariant), that G is a fixed constant of the nature and that the space-time of the theory of Relation ( t o c ) is almost the same as that of special relativity (tc): a four-dimensional Euclidean space-time continuum [
According to the theory of Relation [
k e 2 = M V P 2 t o c = 2 G M o / c 2 , (15)
the kinetic energy of the squared mass of the relativized proton ( M v p 2 ) decreases in an inversely proportional way to the time and to the mass of the ordinary matter ( M o ). The time generated by the expansion is inversely proportional to the quantum mass which decreases and proportional to the ordinary mass which grows, while we keep G of general relativity as a fixed constant of nature. Although t o c looks like the Euclidian four-dimensional space-time continuum of special relativity [
If we write k e 2 = M V P 2 t o c = M V P 2 h / m o c , the cosmological time which extends from 10−43 s to 1017 s, associated with h and c, reveals the quantum structure of space-time itself, which means a limit to the divisibility of space and above all to the divisibility of time.
One can imagine big implications if we write
k e 2 = M V P 2 t o c = M V P 2 h / m o c = M V P 2 2 G M o / c 2 . (16)
In this proposed model of quantum cosmology, there are two associated structures (expansion and condensation) of the world and a time scale incorporated into two different theories, quantum mechanics and relativity, each of which is of fundamental importance. In
± k e 2 = ± [ M o p / ( 1 − v 2 / c 2 ) 1 / 2 ] 2 h / m o c = ± [ M o p / ( 1 − 2 2 / 3 2 ) 1 / 2 ] 2 h / m o c (17)
or
± k e 2 = ± M V P 2 h / p , (18)
we associate electromagnetism, Newtonian gravitation, special relativity and quantum physics. The formula t o c = h / m o c expresses the electro-gravitational field bound to M V P 2 .
Protons ( M V P 2 ) represent the stable particles of matter of the expanding universe. They move in every given direction at a speed less than c. So at any epoch posterior to the Planck era, the system fills the inside of a Euclidian sphere of radius t o c . The nearest particles from the center, which emerge from the Planckian era, seem to move away with a speed v very close to c. At the beginning, their rest mass is covered with a huge kinetic energy. The speed of the expansion decreases and the kinetic energy of protons are subject to a transformation into a sort of frozen energy, in bodies with mass. We suppose arbitrarily that the speed of the particles of the current universe is 2/3c [
By uniting E = m o c 2 of the relativity with E = h v of the quantum theory, we obtain t o c = h / m o c . This field produces energy packets which are bosons. The particle mediator represents as much the quanta-photon as the quanta-graviton. The latter (we are talking about the graviton from the big bang) carries the gravity and is similar to the photon of electromagnetism. Both are moving at the speed of the light, have energy but no rest mass. Their paths can be represented by straight lines in Euclidean space. If we talk of an electromagnetic field for the photon, we speak of an electro-gravitational field for the graviton. The electro-gravitational wave “ t o c ” could belong to the family of electromagnetic waves. A de Broglie wave is associated with their motion and is affiliated with the speed of the proton.
The term G M o / c 2 represents the structure of condensation, and general relativity in a more global than local aspect. Einstein saw a possibility to obtain a geometrical interpretation of gravitational forces analogous to centrifugal forces. Centrifugal forces and gravitational forces are proportional to the mass of the body which they are applied [
± k e 2 = ± [ M o p / ( 1 − v 2 / c 2 ) 1 / 2 ] 2 2 π G M o / c 2 (19)
± 2.3069 × 10 − 28 kg ⋅ m 3 ⋅ s − 2 = ± ( 2.2439 × 10 − 27 kg ) 2 2 π G M o / c 2 .
We then obtain M o = 9.82 × 10 51 kg . Because the mass is related to t o c and that t o is a “linear time”, the mass is 9.82 × 10 51 kg × π = 3.08 × 10 52 kg . This is approximately the estimated mass of the universe, which tends to confirm the version of Mach’s principle incorporated into Einstein’s theory [
According to this, the structure of space-time depends on the average distribution of all matter in the universe. And inertia of an object depends on the structure of space-time. Einstein’s equations produce the adequate Machian influences in a closed universe in which there is enough matter to gravitationally bend space on itself.
The expression 2 π G M o / c 2 means that the radius of the universe must be compressed so that the escape velocity is equal to the speed of light [
At Planck time ( ћ / c = 3.5177 × 10 − 43 s ), if we apply
± k e 2 = ± M V P 2 t o c = ± M V P 2 h / m o c = ± M V P 2 2 G M o / c 2 , (20)
the mass of the “baryon-proton” M v p will be 1.479 × 10 3 kg ( 2.3069 × 10 − 28 = M V P 2 3.51 × 10 − 43 c ).
The wavelength λ = t o c = R = h / 2 π = ћ = 1.05458 × 10 − 34 m . We use ћ with the Planck time and the Planck length: this is consistent with t o c , which is linear, not circular.
With the de Broglie wave that travels at the speed of light as that of the particle m o , the boson m o gives 2.09 × 10 − 8 kg ( k e 2 = M V P 2 h / m o c ). We employ h / m o c because quantum mechanics describes a particle, not a radius.
With k e 2 = M V P 2 2 π G M o / c 2 , general relativity determines the mass of the universe at Planck time, M o = 2.26 × 10 − 8 kg . We utilize 2 π G M o / c 2 (not G M o / c 2 ), considering that the term describes a mass with a circumference, not a radius.
Instead of having M Planck = ( h c / 2 π G ) 1 / 2 = 2.1768 × 10 − 8 kg , which seems to be one of two similar masses, we have M o m o = h c / 2 π G , which are two different masses: m o = 2.09 × 10 − 8 kg of quantum theory and M o = 2.26 × 10 − 8 kg of general relativity. The Planck mass 2.1768 × 10 − 8 kg is actually the average of these two distinct masses ( M o m o ) 1 / 2 . Their numerical value corresponds to Planck mass and that makes think of the famously hidden variables.
The new parameter M V P 2 , or [ M o p / ( 1 − v 2 / c 2 ) 1 / 2 ] 2 , is an essential element. Its value changes throughout the expansion. It can be suspected of being the non-zero mean value in the vacuum of the Higgs field. It would be the scalar field of the Higgs ocean at the origin of the inertia of matter which measures the force that must be applied to an object to provide it a given acceleration. One can also conjecture that it is a hidden variable in the sense that Einstein understood it: the mass of the particle associated with the wave that would commit a serious infringement of Heisenberg’s principle of uncertainty [
The Lorentz transformation of this variable [
The important point is that by virtue of the principle of Compensation of the theory, m o and M o are related. When m o decreases (as well as M V P 2 on whom
The cosmological time
One can find a mathematical relation binding the times that the quantum clock and the clock of general relativity assign respectively to a series of events. This relationship can be used to compare, or convert, the epochs in one scale in epochs in the other. Unlike those who think that these two clocks have no common point, that anyway we need “mass” to build a clock by pointing out that has no mass, we believe we can build a clock universal without necessarily needing a rest mass [
You can take the content of the energy of
These two clocks are interconnected due to the principle of Compensation. Thus, the particles which weigh 10−68 kg are the photon or the graviton of the empty space-time grafted to the mass of the current universe (~1052 kg). At the Planck epoch, the ordinary mass of relativity and the quantum mass of the photon (or graviton) had substantially the same value, about 10−8 kg.
In the theory of Relation, there are more than two interconnected clocks (4) that allow us to speak of the universe as a sort of universal metronome. Always by virtue of the principle of Compensation, there is a transformation of so-called “negative” energy into “positive” energy. The flat space-time ocean of special relativity merges here with Higgs ocean, also assimilated with Dirac ocean, themselves amalgamated with “ether” ocean (minimal energy of the vacuum). Even if each ocean retains its specficity, misunderstood, it is part of a vast ocean, the matrix of atom and vacuum. According to our equation, there would be a transformation of a space-time more and more flat into space-time more and more locally curved. (Einstein gave his power to the idea of local curvature of space by postulating that the geometry of the universe was curved by the masses it contained and that this geometry determined the movement of material objects within it).
It is presumed that at the beginning, as much matter as antimatter were created. Why has matter triumphed? Almost all of the specialists believe that a dissymmetry would have tipped in favor of matter. We do not believe that a surplus generated by the asymmetrical reaction of the particles, during a great annihilation, would have made a tiny difference favoring a bit of matter that would have structured itself to become our world [
But if it does not look that way and physicists seem to want to impose a violation of the CP symmetry which would leave an excess of matter, it is precisely because they have suppressed the negative energy.
We are thus at the heart of a problem which goes back to the conflict of ether in the nineteenth century. Einstein stopped this war in 1905, declaring that the “luminiferous aether,” the supposed carrier of light, to be unobserved, hence nonexistent. Around 1930, Dirac pointed out that the energy-momentum-mass relation
associated with special relativity, has two roots. It calls for both positive and negative energy:
He asked himself what to do with the negative energy solutions
Since all negative-energy states have lower energy than any positive-energy state, Dirac wondered why there were any filled positive states, since according to Hamilton’s law all entities tend to seek the lowest-energy state. He suggested that all of the negative energy states must be filled, like the filled electron shells in the Pauli exclusion scheme. Then, unless a “vacancy” occurred, positive energy particles would “float” on the surface of the negative-energy “sea” and stay positive.
Dirac’s “sea” of filled negative energy states, while it satisfied the equation, did not satisfy the physics community. Heisenberg, Pauli, Jordan and others excluded those solutions that have a negative E to get over the difficulty in the classical theory. They refused the requirement of a sea of negative-energy states, insisting that theory should be based on observables alone.
It has been decreed that only positive energy is real. This certainty has been mathematically padlocked with the positive energy theorem. Rules have been established not to violate the principles of Relativity (not to exceed the speed of light) as well as the principle of causality (not to allow travel in time that would authorize backward causation on a cause that has already produced its effects), and which are compatible with quantum theory (by adding “constraints” to its formalism which guarantee that the creation of a particle necessarily precedes its annihilation). Thus, causality is expressed by means of rules of commutativity of fields operators. We speak of particles and antiparticles which must have the same mass and opposite electric charges. A creation operator
We believe that this is how Physics has missed half of reality. Although it seems that we live in a universe of matter without constituted antimatter, there is no reason to eliminate solutions with negative energy in quantum mechanics [
We specify that the relation electrostatic charge-gravitational relativized mass, which is associated with a cosmological and thermodynamics time, has two roots
It calls for both positive and negative universe:
We are convinced that the recognition of the negative energy solution can find mathematical rules in the quantum theory of fields that allow the concept of antiparticle, and that of antimatter in general, to be compatible with relativity and causality [
The idea of negative mass must be taken seriously because of the desperate theoretical situation into which physics has been thrust by the anomalous behavior of discovered phenomena which cannot be explained by Newtonian gravitation and general relativity. The Allais eclipse effect is one of those. In the 1950s, Maurice Allais, interested in the influence of gravitational and magnetic fields on the movement of the paraconical pendulum, detected an exceptional deviation of the pendulum movement during the solar eclipses of 30 June 1954 and 2 October 1959. Allais, Saxl, and Jeverdan carefully observed the behavior of three types of pendulums during solar eclipses. The pendulums exhibited significant abnormal behavior at the beginning of the phenomenon, indicating that the Moon strongly interfered with the gravitational connection between Earth and Sun at that moment. This physical anomaly, dubbed Allais effect, linked to perturbations of motion of pendulums or instruments of gravitational measurement, was also observed with varying degrees of success by others during solar eclipses [
The pendulums detected disturbances that sometimes indicate a drop in gravity sometimes an increase. Either a kind of antigravity, as if the involved celestial bodies lost positive energy-mass (mass
During the eclipse, the Moon interferes strongly with the Earth-Sun gravitational connection. In an unstable equilibrium on the point of conjunction between the curvature of the Earth which makes it its satellite and the curvature of the Sun which would make it its satellite, the Moon would then act as a negative mass. It would repel the Earth and the Sun which attract it: an anti-gravity disturbance detected by the pendulum on Earth. This conclusion could be erected as a principle that we will call the “macroscopic exclusion conjecture”: The bodies which improvise themselves as a satellite around the central celestial body can only provoke repulsion, comparable to the principle of exclusion concerning the atom.
The equation
represents the super-hydrogen atom of the universe. The proton is contained in the nucleus, while the electron rotates around the nucleus at very high velocity in a circular orbit [
The gravitational force exerted by the proton on the electron of a hydrogen atom has the same magnitude as the electrostatic force of the super-hydrogen atom, in which the attraction between the positive charge of the proton and the negative charge of the electron keeps the electron in orbit around the nucleus at a distance of the order of the radius of the universe.
The two equations,
Classical gravitational charge is
Relativistic gravitational charge is
By substituting,
Here we have a new aspect of gravitation. In electro-gravitation, the gravitational mass is also called gravitational charge and proves to be the same thing as the inertial mass, within the principle of equivalence of general relativity [
If we replace in the macrocosm the proton by a star and the electron by a body which orbits in a circle around, we obtain the Newtonian formula of the universal gravitation in relation to electromagnetism. Theoretical heresy? Einstein tried in vain to unify gravitation and electromagnetism because the electromagnetic forces are proportional to the charge and not to the mass. By assuming that gravitation is a manifestation of electromagnetism, maybe it will be easier to bridge the gap with general relativity, which gives a geometrical interpretation of force mathematically consistent with gravitation.
The theory of Relation advocates the concept of a cyclic universe at variance with the “increase of entropy forever”, while it does not dispute that the present stars are melting away into radiation [
The ordinary mass of the universe increases with expansion.
With
At Planck’s time (
Let us stress that the mass of the proton (or electron) is a universal constant which remains invariant whatever the epoch. What changes with expansion is not the naked mass, it is the electromagnetic energy that forms a solid mantle; this mantle gets rid of his threads throughout the time to wrap and increase the gravitational mass. In Equations (7) and (8),
On a cosmological time scale from the beginning towards the current age, the masses of all the elementary particles would have decreased while the atomic dimensions would have enhanced. The mass of an atom decreases with time, but its electric charge remains the same. As a result, electrons should orbit farther and farther from the atomic nucleus. The electrons would reach lower energy levels, which would require a lower energy input to dislodge them; conversely, a smaller amount of energy would be released when an electron falls into an internal orbit. The radiation emitted by a current atom would be less energetic and would have a wavelength longer than that of an atom of the past.
A body traveling a spatial length in the empty space would undergo this effect coming from that electromagnetic space itself whose wavelength increases with distance. And paradoxically, according to the principle of Compensation of the theory of Relation, this same body would undergo the effect of the global increase of the universe. This is what would explain the Pioneer anomaly. The difference between the observed trajectory and the expected trajectory of a number of not piloted space probes traveling outside the solar system or on its margins, especially the Pioneer 10 and 11 probes, would be caused by the space-time which undergoes inertia (decrease of vacuum energy) for the benefit of an increase in classic gravitation. This has allowed measuring a tiny but constant deceleration of the order of
Within a great contraction, the galaxies approach each other by accelerating. Inside the galaxies takes place the phenomenon of the shrinkage of the atomic dimensions while the masses of the elementary particles increase. The electrons should orbit more and more near the atomic nucleus and attain higher energy levels, which would require a higher energy input to expel them. More energy would be released when an electron falls into an internal orbit; the radiation emitted by such an atom would be more energetic and would have a wavelength shorter than that of a current atom.
With the equation
we can have a mathematical look back into the cosmic past. If the universe was contracting, the velocities of the protons-galaxies (
This suggests that in distant galaxies, presumed old, the atoms that emitted light would have been smaller than the atoms of the present galaxies. The wavelength of this light would be shorter and this light would be less red than that produced by the same atoms in a terrestrial laboratory. The cosmological redshift could be explained in terms of shrinkage of atoms and of the ensuing weaker reddening of light [
In 1998, two independent teams of astrophysicists, relying on the observation of distant type 1a supernovae, announced that the expansion of the universe did not slow down as previously thought, but was accelerating. We have already expressed our disagreement with this interpretation [
In the equation
the arrow indicates the direction towards the future of the great cosmic expansion. The global mass
This relation between the standard model of cosmology (that of the big bang) and that of particle physics gives close exchanges between these two models, what establishes a maximum fundamental state of matter counterbalanced by a fundamental state of minimum energy for space-time. The boson
But this symmetry at the level of the equation can sometimes be broken at the level of the solutions. Under the effect of uncontrollable fluctuations (thermal, quantum, etc.), the dynamics of a system with some symmetry temporarily reaches a state that does not have this symmetry. One can invoke this spontaneous symmetry breaking mechanism as well at the microscopic level—such as the Higgs mechanism in electro-weak unification—than at the macroscopic level, like the Allais anomaly.
When the broken symmetry is a local symmetry, the arrows in the equation are momentarily inverted
which implies a drop in energy in the form of matter (gravitational) in favor of energy in the form of radiation. The particles of
A similar mechanism would apply to the Allais effect, discussed in section 6.4. The eclipse acts as an intermittent cosmological constraint that triggers a phase transition mechanism. The pendulum detects disturbances that sometimes indicate a drop in gravity sometimes a rise. Either a kind of antigravity, as if the marbles were hoisted at the top of the hat (mass
The cosmological time of this space-time is coming from the kinetic energy of protons. It is an indicator of the energy propagated at the speed of light. The element “
The equation theoretically binds energy to matter via the expansionist space-time at the speed of light. It transforms electromagnetic kinetic energy into gravitational mass, by considering the latter as a potential energy. Such a transformation, inconceivable in the modern physics, tidies up in two well-separated categories, the mass connected to the material world and the energy associated with the immateriality. According to the equation, the same quantity of energy which decreases since the era of Planck, on one side, and the same quantity of matter which increases by the other one. Such a dichotomy is made in the context of two structures: the structure of the expansion for the kinetic energy which decreases with cosmological time, and the structure of condensation which increases over the same cosmological time to become the present universe [
Thus in Equation (4)
The energy expanded creating space-time, and cooled. We can see this freezing in the formula in two ways because there are two speeds. First, the decrease of the speed of “
Our model is able to give regions of the observable universe the time to exchange heat since the big bang. Thermal equilibrium would have had time to settle and temperatures to become uniform. This allows us to refute the inflation phase at the beginning (with a factor of expansion and contraction of space of at least
According to the equation, the kinetic energy can be converted into time. Conversely, time can become kinetic energy. With relativity, mass and energy have been found to be interchangeable; now mass, energy and time can be considered as different manifestations of the same physical quantity. In this regard, time is a container of energy and has a mass. The electro-gravitational wave carries energy.
This radial movement is an electromagnetic wave. We can say that the radius of space-time belongs to the family of electromagnetic waves; the wavelength is the radius (~1026 m) of the universe and the period (~1017 s) is its age. Like in Maxwell’s electromagnetic theory of light, the wave of space-time is a wave of oscillating electric and magnetic fields propagating in space [
The idea embodied in the equation “
The first law of thermodynamics, the conservation of energy, is quantitative and considers the time as a simple “duration”, while the second principle is qualitative and involves the flow idea. The passage of time is irreversible as much as the expansion is irreversible and suggests a finished past [
The growth of entropy characterizes the degradation of energy. The processes transformers of one form of energy into another are also irreversible (we are always going from “hot” to “cold”). Entropy can be written in the thermodynamic form
We can make the equivalence with our equation:
The term
With time, the total entropy of the isolated system goes up moving toward a state of maximum probability. The variation of entropy is positive because the system receives heat. If we take the relation
However, the energy cannot come down indefinitely. It will reach the last level of the availability and will have no more transformation capacity [
The observation says that the expansion of the universe is almost offset by the gravity exerted by all matter. The universe dilates at a singular speed close to the critical line that separates the big freeze universe of the big crunch universe. We are very close to a point of balance between expansion and gravity. If all the energy released by the big bang was lower of a tiny fraction, the matter would return back and would collapse into a giant black hole. If it were slightly stronger, the matter would disperse so quickly that galaxies could not even form.
Although the world seems near its critical point, making it impossible to determine with certainty what will be its evolution, the provisional consensus is that the universe will end in big freeze, because it was found that the expansion was going by accelerating. It is postulated that there is some unknown energy that annoys gravity and causes the accelerated expansion of the universe. Einstein called the “cosmological constant” that element which could counteract the contraction caused by gravity. Rejected, then restored it is now called “dark energy”. One might think officially, since 1998, that dark energy exerts a negative pressure which has the effect of causing the acceleration of the universe. But it turns out that the interpretation as much as the facts are inconclusive.
We have questioned (section 8.4) the interpretation of observational data in mid-1990 of type 1a supernovae (SNe 1a). By measuring with unequalled precision the remains of fourteen supernovae at distances varying between 7 and 10 billion light-years, astronomers discovered that the light coming from them was 50% dimmer than it should have been according to the estimates of their distances. They interpreted the dimness as evidence that the supernovae were 10 to 15% farther away than they should have been if the expansion of the universe was slowing down. [
We believe that the basic rules of cosmology were truncated to the point of creating a cosmological anachronism. Previous to the estimation of recessions exceeding c, the radial flight of the galaxies was interpreted as a process translating a general expansion of space. It has often been proposed as an example of the expansion of the space that of a rubber balloon on the surface of which are stuck confetti which represent the galaxies.
If the balloon is inflated, its surface is stretched and the confetti is moving away from each other with an apparent speed which is increased in so far as the radius of the balloon is growing. In space-time, “length” may refer to temporal length as well as spatial length. So we can receive the radiations emitted in the distant past by a system that reached speeds close to c, to which the expansion of space-time gives an apparent flight velocity greater than c. This way of thinking seems long gone because it involves the center the universe [
In astronomy, telescopes are machines to go back in time. To see far into space, we must see far in time. Further we see, weaker we see. The more a galaxy is distant, the more it moves quickly toward the big bang, primordial explosion which gave rise to the expanding universe [
With this different astronomical vision, fundamentally spatial, whose velocity v starts from 0 to increase towards c, the flight of galaxies is today construed as a process of acceleration of isolated systems relative to other isolated systems. For theorists, it is as if, undeniably, the galaxies were moving away from each other with speeds which are all the greater in that the distance between them is itself larger. There are galaxies which recede from us at a speed close to ninety-five percent of that of light. Based on the Doppler effect of emission-line quasars, some redshifts are so important that in applying the Hubble formula, they display some radial velocities such as our galaxy and the quasars seem to be moving apart from each other at speeds exceeding the speed of light. No matter if, in the first place, a source of radiation that would exceed the speed of propagation of light, would necessarily be invisible since, in second place, the farce of the epicycles of inflation, that continues to accelerate the universe, will necessarily render it hyperbolic [
With relativity, the center is everywhere in the universe, which means that there is no real center. Strong with this a priori which excludes the irreversible time (and sometimes time itself), the reasoning of the modern astronomers led to this: the observer that I am and that I perceive as being at rest on Earth is part of a galaxy is, from that point of view, also in movement with a speed of expansion where there comes a time when it will be higher than the speed of light [
Since there is no center of the universe, one would think that the explanation according to which the radial escape of galaxies is the consequence of the initial explosion could not be retained. To explain the big bang, on the contrary, one will become Copernican again, and one will make general relativity to assert that space expands faster than light, because space represents neither matter nor energy. Which is senseless, because to explain the flatness of the present universe, Alan Guth suggested that the universe had ended up in a “false vacuum” at the time of the era of G.U.T. (10−35 s), and this excited state would look like an empty space, but filled with energy. In general relativity, the energy and pressure are sources of gravitation, and a negative pressure causes a gravitational repulsion. This repulsive effect would have provoked a period of exponentially accelerated expansion. The universe would have swollen to the size of the present universe. Around 10−32 s, the false vacuum would de-excite towards the true vacuum, the flatness, and all the energy of the false vacuum would have been released in the form of particles and heat. The universe would have restarted with a dark energy that would have made the flat space [
Apart depreciate relativity by making it appear that the false vacuum energy did not contain energy whereas the high expansion rate of the latter exceeded the speed of light, the theory of inflation brings an insoluble problem for the multiple theories of inflation: a dark energy that would contain the infinite kinetic energy, essential to the evolution of the hyperbolic universe, and that would have a density of 10122 times greater than that found in the empty space [
The experimental indications of a positive value for the cosmological constant also come from independent measurements of primordial density fluctuations observed in the Cosmic Microwave Background (CMB). The raw data from the experiences of scientific teams WMAP, COBE, Boomerang, and Maxima which have performed measurements on the fluctuations of CMB radiation favor the model of inflation. Inflation is a model produced from the high-energy physics, according to which the universe would have recorded, in the first fractions of a second of its evolution, a wildly high expansion rate, so that space would have become flat [
However, in the present situation, even though everyone seems to agree on the existence of a cosmological constant, its value deducted from astronomy is absolutely not compatible with that calculated by theoretical physicists. Several models are possible to calculate the value of λ within the framework of the theories of unification, but the predicted value in most cases is 10122 times superior to the limits prescribed by astronomical observation. Dark energy should be very dense, which is the opposite of the density of the vacuum.
The dominant cosmology, starting from the cosmic microwave background radiation, considers that the big bang occurred about 13.8 billion years ago. That is an obvious dilemma since astronomers observe stars older than the universe [
There is no question to minimize the importance of data collected by the experiments since never observational cosmology has reached such precision. But the bundle of more or less plausible assumptions to extract the cosmological parameters from observational data, error bars to calculate a range of angular spectra of CMB fluctuations which are then compared to the observed spectrum, the adjustment “at best” of various parameters that can be deduced, have left the door open to biased analyses and interpretations that should have been taken with much more caution.
For some silent scientist, the fine analysis of the angular fluctuation spectrum rather suggests that the maximum likelihood is 1.2 Ω. The experimental balance would tip in favor of a spherical space, finite volume, although in a large radius of curvature, and ever expanding thanks to the cosmological constant. However, the lobby of inflation, strengthened by the fact that
According to the theory of Relation [
Since galaxies are moving away at a constant speed estimated 200,000 km/s, the cosmological time is about 15 billion light-years and the relativized proton weighs
Certainly, a general dilation of the space-time would be unverifiable because we undergo it ourselves. Unless the solution is included in the cosmological constant (density measurement), the kinetic energy of the proton, which poured his energy into creating the space-time of our universe, is assimilated to a negative cosmological constant and a dark energy. It comes into play in larger scales and affects the expansion of the universe. It decreased by nearly 100%, from 10122 to around 100 at the present time. Because of the decreasing rate of speed, the universe expands more slowly. The kinetic energy acts as a positive pressure gas that binds the galaxies and slows the expansion. It exercises a tension which retains and brings things together, at the same time it spreads in the manner of a stretched elastic. It causes the deceleration of the universe [
Our equation is the first to include the irreversible time. During this time, energy constitutes a variable field, very high in the phases of the primordial universe, in agreement with the calculations of physicists, but which falls very low during cosmic evolution, in accordance with the value now measured by astronomers. Dark energy (or cosmological constant) would be a “tired” energy. Bear in mind to not confuse the tired dark light with the tired white light, which stipulates that the light could have been energetically degraded and thus redshifted, during his trip through space intergalactic. However, although the light undergoes the redshifts under the influence of the Doppler effect due to the recession velocity of distant galaxies, there is no evidence that today allows to permanently eliminate the theory of tired light [
We get a model of the universe that has the “temporal” behavior of closed models (in expansion-contraction), and which has the “spatial” behavior of spatially finite models. It can be likened to the oscillatory universe of Einstein-Tolman (1931), the Euclidean model of Einstein-de Sitter (1932), or the closed Friedmann-model (1922) [
The equation
We envisage cosmological history from the perspective of a cyclical universe. We saw in a previous article [
The formula introduces cosmological time into the heart of a physics that has never made the essential distinction between past and future. A cosmological, thermodynamic “space-time”, from the past to the future, joins electromagnetism, Newtonian gravitation, special relativity, general relativity and quantum physics. It is important to consider this space-time as precisely the dynamic variable that allows us to consider the entire universe as the physical system where quantum nonseparability can describe as being in union two (of) uncoupled objects that have already interacted with each other, gravitationally or by exchanging radiation. In this respect, the equation finally permits a quantum cosmology.
There is still much to be said about this equation, which distinguishes three types of mass: fermionic, bosonic and that of the ordinary matter of the universe. We can find the state of the fermions in relation to the exact changing mass of the bosons, for any state of the mass-energy in the “irreversible” time. The equation is therefore in line with Yukawa’s theory [
The author declares no conflicts of interest regarding the publication of this paper.
Bagdoo, R. (2019) The Equation of the Universe (According to the Theory of Relation). Journal of Modern Physics, 10, 310-343. https://doi.org/10.4236/jmp.2019.103022