The proof for the equilibrium theory of quantum gravity is the leading article with proud title of THE PROOF THAT 22 % OF THE DARK MATTER ARE POLARIZED GRAVITONS IN EQUILBRIUM WITH 4 % BARONS AND THAT 78 %, ACTUALLY (74 + 4) %, ARE GRAVITONS FOR THE SPACE EXPANSION IN OUR COSMOS, THE DARK ENERGY.
Physics two is the precursor to this article and it shows the bumpy road, which is not easy to grasp even by an experienced reader in physics. Not because the new ideas are so unusual to grasp. After all, only Newton mechanics and some basic quantum mechanic principles are applied in physics two. No, the book reflects the struggle to come to terms with energy discrepancy between GRT and the new theory to be, which is finally resolved in the article of the proof. In the review of physics two it is tried to remedy these imperfections.
The follow up articles, not only the comments at the proof etc, etc … but the article of The interpretation of the energy identity is a more thorough explanation for the existence of the anti-universe, in fact more to the point than the leading article of The new discovery of the existence anti-universe, which was the result at the beginning when everything began.
By simple considerations it can be proven that Newton’s law of gravity has an accuracy of one in 10exp(+80). Under the condition of quantum equilibrium with three dimensional space, the weak gravity condition, the steady state of the Einstein gravitons of empty space, predicts this range of accuracy, determined by two characteristic dimensions: the inversely scaled dimension λi of our cosmos and the observable scaled size of our cosmos R (radius). Where:
λi = λ (1/√N) and R = λ √N while λi R = λ² with
λi / λpl (::) m / mpl
N is the total number of atoms in the universe and λ the generalized Compton length of the neutral atom or a mediating mass m. N is unique and cannot change in time as long as no atomic transmutations occur. The subscript pl, stands for the Planck length or its mass.
The quantum gravity theory of steady state for the three spatial dimensions is the hall mark for all modern theories in fundamental physics or theoretical astronomy. Only a theory which predicts the same or even better accuracy, under weak gravity conditions for Newton’s law of gravity, is most likely another candidate for the THEORY OF EVERY THING.
The first property of Einstein’s gravitons based on Einstein’s equivalence principle, is that a linear accelerated mass of empty space (quantum probability wave and under constant acceleration) at the onset, has always an opposite direction to the direction of gravity. In steady state all gravitons are a substitute for empty space, balanced to all the rest mass of matter in our cosmos. Consequently this cosmology is absolute in time but still has a time history due to fusion burning of matter, which is completely different from the observed evolution of the universe, often based and interpreted on the principles of the general relativity theory. Another property is that empty space in this cosmology is in continuous accelerated expansion and at first instance in contradiction with the principles of GRT, which naturally can be remedied. It is not further discussed in this summary.
By adding a second property to Einstein’s gravitons a precession due to acceleration, as a reaction to the spin in matter, not necessarily Fermi-spin, one can prove indirectly with respect to the Fermi spin that these gravitons are determined only by the species of matter, namely normal matter, anti-matter or conjugated matter. The last is reserved only to the theories adhering to the pyramid theory.
The consequence of the steady quantum state of empty space determines that the preferential direction with respect to precession can have only an overall macroscopic rotation, which is not identical to the spin of matter or the zero balance of overall macroscopic spin of the stars or the galaxies. Only a model of mixed gravitons, two preferential directions with respect to 3D-space, predicts the observed steady state of normal matter in present-day’s universe. The evolution in time as a runner up to the present-day universe in steady state might be a topic for the book, Physics 3.
An important consequence of the unique organisation per species, type of matter, is the prediction of the sun wheel drive for the stars. Even without an angular momentum of the star mass, the star starts to rotate due to fusion burning of the atoms. The conservation of angular momentum of the gravitons of empty space determines that the star mass begins spinning due to the change in the equilibrium radius for gravitons around the star.
The above remark is left as it is, but in Physics3, The precession shift of the polar axis of Earth, finally the outcome was that above was not true.
Note that the second property of Einstein’s gravitons for the precession is independent for the prediction of the accuracy of Newton’s law of gravity. So the added property of the precession polarizes the gravitons, which determines a distinction between the four species of matter as remarked above.
See for detailed explanations: The review of physics two: The steady state cosmology under accelerated expansion of quantized 3D-space.
THE PROOF THAT 22 % OF THE DARK MATTER ARE POLARIZED GRAVITONS IN EQUILBRIUM WITH 4 % BARONS AND THAT 78 %, ACTUALLY (74 + 4) %, ARE GRAVITONS FOR THE SPACE EXPANSION IN OUR COSMOS, THE DARK ENERGY.
The problem statement
Since the scientific publication of the observations in the back ground microwave radiation from the early universe at http://wmap.gsfc.nasa.gov/results , the distribution of the energy densities over the species of matter are well determined. These are 4% barons, 22% dark matter and 74% dark energy.
It will be derived that 22% of the dark matter are in fact gravitons in force equilibrium with the 4% barons. The difference in percentage is caused by the ratio rest mass of hydrogen, mat of 1837.153*me and that of the mediating mass, mm of the H-atom of 250.81* me , giving the ratio of 7.325.
Further is the percentage of 74% for the dark energy a consequence of the gravitons with an equivalent mass energy of mm , being accelerated up to 0.5225*c, where cos θg = √(2 / 7.325) = 0.5225 with θg = 58°.50 and
cos² θg = 0.273 . θg is the angle of precession of the graviton, polarized graviton, due to the vector summation of the components for the linear acceleration and that of the tangential velocity component of the precession. Together the graviton has an end velocity of c, the speed of light.
In the past, physics two; chpt 7 (now obsolete), an improper comparison was made between the estimates of the overall energy of the universe based on GRT, using the rest mass of the H-atom and that of the theory for the graviton equilibrium with gravity, using the mediating mass. Here with the following derivation it is tried to rectify this oversight. The achieved accuracy of the derivation in the energy balance is that hydrogen is the most common baron specie in our cosmos and any corrections with respect to the other atoms can be nearly neglected.
THE PROOF
The initial approximation
From previous considerations it is known there are a fixed number of gravitons per H-atom. Just take the kinetic energy mH of one graviton accelerated over Hubble’s distance with a constant acceleration aH , the constant of acceleration in vacuum for the H-atom, and divide by the total energy of the universe Mtot .The result, actually the reciprocal of it, is the total number of gravitons NH . mpl is the Planck mass.
NH = Mtot / mH = 1/ 8 (mpl / mm) (power 6). Similarly take the overall energy of the universe and divide by the mediating mass mm to find the number Nm of the barons. Nm = ¼ (mpl / mm)(power 4). The graviton mass mm is accelerated over the Compton length of the mediating mass with aH , extremely small because the end velocity over that distance is small. The ratio of NH / Nm = ½ mpl² / ( mm² ) , which is the number of gravitons per atom. The number of barons Nb = Mtot / mat is not the same.
See, book 2, chpt 6, Tying up loose ends.
It was also reasoned that the path of acceleration for the Einstein gravitons should not necessarily be up to the light velocity, because the acceleration is accompanied by a precession, which consumes the other part of the energy of the graviton. Secondly the graviton energy by the precession is proportional to the equilibrium radius of the system of the gravity mass embraced, the atom, planet, star or galaxy, by the outward going gravitons (accelerated quanta of empty space). It follows the proportionality of the precession up to the overall mass of the universe. Then it was concluded that Hubble’s radius for the graviton was composed as a vector of a linear accelerated and a tangential component for the precession, polarizing the Einstein gravitons. The suggested angle between the components in first approximation was 60°.
So the kinematical energy given by s * aH = ½ v² with v = ½ c, it makes the energy for the graviton wa = 1/8 mm c² ,while the energy due to the precession is wp = ½ (½√3)² mm c² = 3/8 mm c² , determining that 75% of all energy in empty space is stored in blind energy or precession energy of the polarized Einstein gravitons. Still the angle of 60° is not proven but an approximation by reasoning. See book 2, chpt 2, The grand correction: the idea of the vector composition of Hubble’s distance, and chpt3, The indirect proof for the hidden overall energy of the universe.
Now consider the force balance between the inertia of the H-atoms and the number of gravitons released in the time interval of a Compton length for the mediating mass. Take all atoms with inertia in the universe, subjected to the individual force balance, which is N1 ,while the number of gravitons per atoms in relation to the overall mass Mtot is N2 .Both energies from each side of the equilibrium balance should be equal, but realize that the balance is not an equality but an identity and explained further on..
½ N1 mat c² = 1/8 N2 mm c² (1)
giving N2/ N1 = 4 * mat / mm = 4* 7.325 = 29.3
The baron particle ratio is: N1 / (N1 + N2) = 1 / (1+29.3) = 0.033 .
The graviton ratio is: N2/ (N1 + N2) = 29.3 / (1+29.3) = 0.967.
Apparently, we have arrived at the right ball park, but still things are not correct, because the fraction of 0.25 graviton energy for the linear part is based on the end velocity of 0.5*c . On the other hand if the factor 7.325 can be related to a factor of 8, meaning mat / mm = 8 then N2/ N1 = 32 which brings the baron ratio to 0.0302.
The Corrections
The precise meaning of the energy balance becomes clearer. The pulling of the barons due to gravity generation internally must have a proper fraction attuned to the c-ratio for the linear acceleration. So attune the c-ratio to the inertia in the energy balance, but secondly, remember that the mediating mass consists of two particles, electron and proton, sharing by necessity the graviton energy equally, which involves two gravitons.
N1 mat = (2 / 7.325) * N2 mm with mat / mm = 7.325 (1a)
Giving N2/ N1 = 3.6625 * 7.325 = 26.83
The baron fraction is: 1/ (1+26.83) = 0.0359
The graviton fraction is: 1- 0.0359 = 0.9641
Cos θg = √(2 / 7.325) = 0.5225 and θg = 58°.50 and cos² θg = 0.273
Consequently one should try to find the weighted energy ratios, which are:
The barons, N1 mat / (N1 mat+ N2 mm) = 7.325 / (7.325 + 26.83) = 0.214
The gravitons, N2 mm / (N1 mat + N2 mm) = 26.83 / 7.325 + 26.83) = 0.786
The linear accelerated energy ratio is 0.273 and the part for the precession is 0.727. To check above energy balance independently, one multiplies the overall graviton ratio by 0.273 , which gives; 0.273 * 0.786 = 0.214 .
It shows why rel. (1a) is an identity and it is not an equality!
Make the connection to the observed ratios for the black matter of 0.22
and the dark energy of 0.74. The last should be 0.786 – 0.214 = 0.572 of the blind energy. However the ratio of 0.572 as the precession energy is wrongly interpreted, because the total energy ratio for the gravitons is 0.786, the summation of the linear- and the precession- energy together. Now the ratio of 0.786 does not confirm the fraction of 0.74 for the dark energy, but summing the baron fraction of 0.04 with the dark energy gives 0.04 + 0.74 = 0.78 , but is it allowed? The baron fraction of 0.0359 is not a part of the weighted ratios in the energy balance of 0.214 and 0.786 . The energy balance determined by standard science considers the fractions of barons, dark matter and dark energy independently from each other. In the calculation procedure here for equilibrium, 0.786 is the correct answer and therefore the baron ratio of 0.04 can be added to the ratio of 0.74. See: The physics behind the cosmic energy identity.
The proof of the graviton equilibrium theory is nearly finished except for the more exalted explanation in the following. If one takes in consideration the hyperbolic motion for the gravitons, for the gravitons are released at the atoms with nearly zero velocity and accelerated to 0.5525*c , then an additional correction for the energy is needed. See. Comments at the proof etc.etc.
The hyperbolic motion compared to the Newton path of acceleration gives a kinematical energy ratio of
Rhyp = shyp / snewt = 2 (cosh τ1 – 1) / β²
Where τ1 = (aH / c) τ is the normalized time interval of acceleration, but in fact the formula is independent of the constant of acceleration.
See, i.e. Special relativity, by W.Rindler; Oliver & Boyd 1960, or the Internet search-engines under ´hyperbolic motion´.
For β = 0.5225 then Rhyp = 1.266. The kinematical hyperbolic ratio brings the overall energy of the universe up to 0.786 * 1.266 = 0.995, which should give a real ratio of 1.00 at first impression. Here one meets the cosmic truncation error, which is an unexplained enigma, meaning it will take an in depth analysis of the principles in fundamental physics.
Elaborating on the cosmic truncation error for the steady state of our cosmos, one first should consider. What is the mean of inertia of all the atomic species at present ? Consequently link it to the β, corrected for the hyperbolic factor to make the overall ratio of the universe equal to one. The procedure can be refined in an algorithm , but with a desk calculator one finds the β = 0.5436 and the inertia ratio of mat / mm (the mean) = 6.768 instead of 7.325 , which is shown in the table at end of this paragraph. See also: book 3: The discussion on the cosmic truncation error.
First conclusion.
Obviously for the H-atoms, the linear acceleration up to β = 0.5225 means that 0.786 of the energy graviton ratio with an initial velocity of zero, reaches the overall energy in the universe composed in two parts, the linear and the precession, because the vector of the graviton reaches an end velocity of c. May be at first sight it seems unacceptable, but remember that one deals with an energy identity and not an equality. The left hand side of rel. (1) or (1a) corresponds to the baron energy stored in inertia, generating the equivalent gravity, while the right hand side belongs to the energy of the gravitons, the stress tensor of empty space, determining the possible 100% energy for the final velocity of c of the graviton.
β is the end velocity of the linear part of the graviton with respect to c.
The dark matter part (graviton equilibrium part) is 100% minus the free graviton energy or dark energy part.
The inertia ratio mat / mm = 2(1/ β²) with N2/ N1 = 2 (1 / β²)² .
mm is the mediating mass as mean belonging to average for all inertia of the atomic species. A more realistic mean of 6.768 of the inertia ratio lies at 100% overall. It appears that ratio of 7.325 is the only real one. The other inertia ratios are not completely understood. Multiply the hyperbolic factor with the percentage of the overall graviton energy (dark energy) to find the overall percentage.
Second conclusion
The kinematical correction of the hyperbolic motion of 1.266 compensates for the 0.214 fraction of the gravitons tight to the barons. It is the initial condition of the force balance. It shows that Einstein’s gravitons behave according to quantum mechanic principles, because all scaling is related to the Planck mass, and it behaves not according to purely Newtonian point like particles. See: The physics behind the cosmic energy identity.
General conclusion
Neither procedure of calculation is wrong. The estimates of the energy balance according to standard physics is correct and it should mention the three states of aggregation for matter or energy, of which two kinds are enigmatic and one kind is the normal state of matter for barons.
The equilibrium graviton theory in which Einstein’s gravitons of empty space are in force balance with the barons, is also correct. The estimates for the fraction of the graviton energy follow from the three dimensional quantum considerations involving the Planck mass. According to the energy identity, 4% of the barons is balanced against 100% energy of the polarized gravitons preventing the collapse of our cosmos and storing temporarily the gravitons over a finite time interval of 13.7 billion years.
See for the calculation of the age of the universe. book 2, chpt.2, The scaling laws of the equilibrium universe.
By rigorously denying the validity of the dark matter hypothesis, an entire new theory was born, of which the outcome in the end turned out to be equivalent to standard theories in physics. Although by introducing a constant of acceleration in vacuum, the nature of the dark matter and the dark energy in relation to barons was revealed. No other presence than baron matter is allowed in our cosmos.
COMMENTS AT THE PROOF THAT 22% etc. etc.
1. Any physicist in his right mind reading the proof, immediately tries to find out where the identity relation (1a) breaks down. This is not so difficult. Set up the energy balance for the neutron, which can only release one graviton group equivalent according to its mediating mass, equalling its rest mass, then the ratio of N2 / N1 = 4, giving a baron fraction of 0.20 and the graviton fraction is 0.80. It shows the upper limit for the stability of the identity with Rhyp = 1.238, suggesting that during acceleration of the graviton group the neutron decays. Similarly, take the Deuterium atom with its one electron, then the simple expression for the mediating mass used for the H-atom invalidates the energy balance by a factor of √2 * (1838.684 / 250.81) instead of 7.325. The square root of 2 comes from the neutron and proton in the Deuterium due to the calculation of its mediating mass and neglecting the binding energy between both. So the statement that the intertwining for the two graviton groups of electron and proton share the same energy, giving the factor 2 in the identity for Hydrogen, is specific for this atom. It shows, although the cosmic energy balance of the entire universe is correct for the H-atom, that the fabric of gravitons representing empty space, is clearly immensely more complicated than suggested by the for this unique identity. However it does not mean that for the other atomic species the identity by trial and error can not be restored. It is only not a very satisfying procedure without proper underlying quantitative theory.
2. Although it seems trivial, one should realize that the path of the photon in empty space follows the path of a single graviton having the velocity of light despite that this graviton is vector composed of two components. The group velocity of the gravitons near matter is much smaller than the light speed, but it is directed according to the vector composition of the two velocity components, especially outside the equilibrium radius of a gravity mass system.
3. The steady state of equilibrium of our cosmos is the present-day universe. It means that Hubble’s distance determined by the mean constant of acceleration for vacuum ( every atom generates another constant of acceleration) cannot correspond to Hubble’s distance due to the time dependence of Hubble’s constant, which is based on the assumption of the homogeneity for empty space in an evolving universe. So Hubble’s distance, half the horizon distance in observations, in the young evolving universe was always smaller than the one based on the mean vacuum constant of acceleration, which should be interpreted as a quantum parameter for empty space. Despite the constancy of the quantum probability wave length of Hubble’s distance, Hubble’s constant can be time dependent. I.e. the group velocity of all Einstein’s gravitons embracing all matter in the universe, just after the inflationary epoch, was less than the light speed.
4. The steady state for the present-day universe seems to suggest that it is independent of the presence of the super massive black holes in the galaxies. Although possibly the cosmic truncation error based on the H-atom, might determine other wise. See book 3: Discussions on the cosmic truncation error.
5. Obviously the gravitons are polarized due to the precession perpendicular to the direction of acceleration. Since it was surmised that the polarized gravitons are independent of the spin orientation for the Fermi-particles with respect to their propagation, it is clear there are two kinds of opposite propagating polarized gravitons in one three dimensional quantum space. The anti-gravitons, counter propagating, belong to anti-matter. A further elaboration follows in book 3, including the relation to conjugated matter and conjugated anti-matter. See also ´The physics behind the identity´.
6. The vacuum constant of acceleration is specific for each kind of atom. It has been more or less shown that this constant is invariant with respect to relativistic coordinate transformations. Note, as an example the kinematical hyperbolic ratio.
7. It appears that the weak angle of sin² θw = 0.23, which corresponds to an angle of θw = 28°.66 , where possibly the precession angle of θg = 90° - θw , but θg = 58°.50 . It is not too far fetched to regard the precession angle behaving as an complementary expression to the theory of the electro-magnetic weak interactions. In the weak theory the massive bosons W± and Zo are linked through the weak angle θw . However the decomposition of the bosons into polarized high energy gravitons is not unlikely. Taking this speculation a step further, even gluon showers released in very high energy collisions could be considered as high energy gravitons. Note: compare both relations to sin² 60° = 0.25, then sin² θw / 0.25 and cos² θg / 0.25 give 0.23 / 0.25 = 0.92 while 0.273 / 0.25 = 1.092. The product is 1.005. A possible check on this speculation, is a no Higgs-particles or other exotic debris, are observed in the new high energy collision experiments.
THE PHYSICS BEHIND THE COSMIC ENERGY IDENTITY
The physics behind the baron fraction of 4 %, which is in fact 22 % in terms of energy, is not easy to extract and certainly subtle.
Firstly, the gravity part of the energy of 22 % at the left hand side is the energy disappearing to time. Namely, internally in the capacity of gravity, while externally, 22 % of the overall 78 % at the right hand side represents the labour of the gravitons. The difference in energy of (78 – 22) = 56 % seems to be stored due to precession in empty space. Again note that the precession works cumulative by increasing the equilibrium radius of the mass involved up to the embracement of the entire energy in the universe. However the hyperbolic motion of the gravitons of 78 % dictates a continuous need to consume energy, which is again 22% in addition. So it is discovered that 22 % gravity energy to time is used to expand space in an accelerated manner. It points to a contradiction, not considering the complications due to the cosmic truncation error.
A way to restore the discrepancy is to introduce symmetry. Barons of anti-matter should generate gravitons moving in the opposite direction with respect to matter for the same 3D-quantum space. Namely time reversal as a symmetry could mean another quantum space, a time reversal operation on a vector which polarized Einstein gravitons are, is complicated. So these deductions need careful analysis which is left to book 3. In that respect the time flux of 22 % of normal matter could execute labour at the anti-gravitons of anti-matter and vice versa 22% of the time flux of anti-matter could drive 78 % of the gravitons in our 3D-space.
Taking the consequence of the above supposition, it means that the anti-gravitons interact with normal matter and vice versa. Then one has discovered the nature of the origin for the vacuum constant of acceleration.
The result of the symmetry considerations should be, showing the correctness of reasoning that gravity and the vacuum constant are equal respectively, without intervention of a polarity sign, for matter and anti-matter. What already is anticipated, for the anti-proton should fall in the Earth gravity identical to a proton and consequently the vacuum constant should act on anti-matter similarly, but possibly the precession is the opposite to that of matter.
However the flaw in the reasoning is that it should be reversed. The vacuum constant of acceleration can only act on barons or anti-barons and actually the barons are driving the expansion of the universe. The gravitons look like figments of thought or virtual quanta, quanta of empty space subjected to the vacuum constant. The vacuum constant is a reaction upon gravity in the capacity of anti-gravitons interacting to matter. The use of the equivalence principle applied to empty space as graviton quanta suggests empty space to be virtual matter. But it seems that the slow gravitons enacting dark matter under the attack of high energy particles (cosmic radiation) could produce gamma radiation. The enhanced radiation is observed, but the mechanism with respect to dark matter, or as slow gravitons, is under investigation. So in general the gravitons are less virtual than thought of at first. See, Gravitons as Wimps. (weak interacting massive particles)
It should be realized that by taking the anti-gravitons to normal matter and vice versa, that any graviton is connected to a baron of the opposite nature. All gravitons in one universe are somehow linked to the barons in the other universe. Further, never forget that 100 % energy of the gravitons comes from a vector composition, of which only 22 % appears accounted for directly (the linear accelerated part) and the other part is based on the property of polarisation of Einstein’s graviton.
The steady state cosmology under accelerated expansion of quantized 3D-space.
Introduction
Physics two consisting of 6 chapters is not easy to read. In fact it reflects the struggle of the author trying to grasp the topic he is researching. On the other hand, every bump or bend on the road to gain knowledge gives often a didactic highlight of how to understand nature. This is the main reason why physics two has not been rewritten. However most likely, the reader may be lost into details and loose the essence of overview. With this review it is tried to remedy this disadvantage.
To summarize physics two in short, it is a model in physics for the equilibrium of accelerated quanta of empty space in relation to gravity generated inside matter. Since in fact, the surrounding space is in steady state and it can not be relativistic, the model is purely spatial in three dimensions and it is considering mathematics, not complicated.
Since the proof of the equilibrium theory in the leading article, the understanding of the properties of the gravitons for the explanation of the expansion of empty 3D-quantum space is improved drastically. This review was written before the proof, so one may find some minor inconsistencies in text. For example, the term polarized graviton, or the one of the vacuum constant of acceleration are developed in the end or during understanding of the new theory and so there are more glitches.
A new constant in vacuum: A tiny outward directed constant of acceleration.
The discovery of the discrepancy during the 1950th between the rotation of the outer arms of stars in a galaxy, were the reason to introduce the dark matter hypothesis, which is not further explained in this review. However one can also replace this hypothesis by a tiny outward going force or a constant of acceleration, which pulls at the stars in outer region of the galaxy giving occurrence of the observed spiral arms. The idea was slightly more complicated and culminated in the MOND-hypothesis, but it is not accepted for reasons of fundamental physics. See; chptr.1, MOND-hypothesis versus dark matter.
A third solution for the above discrepancy is adding a new property to empty space. It is a tiny constant of acceleration every where, which is always directed outwardly from a centre of gravity, such as a star or a galaxy. The mechanics for the tiny constant of acceleration is the quantum mechanic force of reaction of empty space against the pull of gravity.
Having come so far, one should point out a crucial dilemma. In one way our cosmos is a steady state of equilibrium for a quantum force of empty space on the other hand the accelerated expansion of empty space violates the energy balance. Culminating in three dimensions there is a continuous drain of lossless energy to the 3D-infinity. Although the drain may be small, a lossless trickle of flux, beyond our window of observation, a spherical surface, it is not zero. Secondly due to the clustering of matter under the attraction of gravity, the recirculation or storage of energy quanta or gravitons in 3D-space happens, generating Newton’s law of gravity.
Almost per definition the flux for the drain of energy, disappearing through the orifice or the window of observation is the energy flux to time. Later on one learns to associate these orifices as a quantum resonance condition equivalent to the event horizons of black holes.
Note compared to the classic corpuscular cosmology based on Newton’s 19th century mechanics, the introduction of quantum properties for vacuum is different and leads to new exiting results at the end at this review: the sun-wheel drive of the stars burning fusion. The mathematics of this frame work for the 3D-quantum theory of gravity is simple compared to the general relativity theory (GRT). The advantage is that the model is independent of time and it fits flawlessly in the pyramid theory for the 3D-phase space of time. Namely, the flywheel in the pyramid is the analogue for the equilibrium of gravity under accelerated expansion of empty space.
Applying Einstein’s equivalent principle.
Take in a Newtonian world a mass less point and accelerate it under constant acceleration till it reaches the c-velocity, then there are two ultimate possibilities:
1.Make the constant of acceleration small enough, that travelled distance is equal to the longest radius in our cosmos, the observation of the universe. It is in the order of 14 billion light years. The order of magnitude of the constant of acceleration, aH = 10exp(-10) m/sec². This constant can be called Hubble’s constant of acceleration, as long as one realizes that as well Hubble’s radius RH as aH are dependent of the kind of atom. For any nucleus these parameters are different.
2.Similarly the constant of acceleration is high, if one applies it to the mass of an electron or atom. The scaling length is the generalized Compton length λ = h / mc. For a neutral atom the electromagnetic energy and the rest mass energy can be converted to the mediating mass of the H-atom. See, chptr.2, Derivation of the mediating mass.
This is the frame work for the definition of the Einstein gravitons. As soon as the scale length is fixed, the graviton has an acquired energy and the mass less point represents a probability wavelength in terms of quantum mechanics. The equivalence principle of Einstein for this definition of acceleration is, as at a local point that gravity equals the acceleration constant in opposite direction. So one is always considering an equilibrium of force at a point of local gravity. See, chptr.1, The relative acceleration constant.
Note: A model for gravitons as defined here could be expressed in quantum interference with photons in counter propagation (c-velocity of photons) formatting a group velocity for the relative slow accelerating gravitons. The mathematical formulation of this procedure is complicated and left to theoretical physicists.
However there is typical something strange going on. An accelerated point should in terms of quantum mechanics have a probability wavelength which varies over the distance of acceleration. Another point of consideration is that an accelerated energy parcel reaches its destination in half the time as a quant having a same constant velocity as the end-velocity for acceleration. In quantum mechanics this behaviour for the factor 2 can be of importance. Think of Bohr’s condition of ½λ for the electron staying in orbit around the proton.
Altogether the interaction of the quanta of empty space, Einstein’s gravitons, with matter determines a mechanism which is known as precession. Matter having intrinsic spin, not necessarily Fermi-spin, gives a precession of the rotation axis due to the execution of the angular momentum of acceleration. A quantum undergoes precession, a tangential velocity at right angle to the direction of acceleration and the momentary velocity. Stop the force and the precession of the axis ceases. Since all kinds of Einstein’s gravitons, generalized as of any magnitude, are accelerated quanta, they should all have a displacement due to precession.
The constant tangential velocity is a measure for the accelerated energy of the kinetic point. It is the reason for applying Bohr’s condition to the gravitons Einstein’s gravitons are accelerated till ½c-velocity. The angle between the components of the velocity is 60°. For example see, chptr.2, The grand correction the idea of the vector composition of Hubble’s distance.
It is clear from above definition that Einstein’s gravitons behave differently from the photon exchange between the Fermi-particles in quantum mechanics.
The quantum resonance condition for Newtonian black holes.
When it was discovered during the 19th century that light had a finite velocity, one was able to plug the speed of light in Newton’s mechanics in relation to gravity and find the radius for a gravity generating mass in which a falling mass point reached the speed of light. In that case the radius of a Newtonian black hole was the same as the radius of the event horizon for a real relativistic black hole complying to a 4D-geometry of Schwarzschild, given by the relation: λ c² = 2G M.
The scale for the radius λ, event horizon, can be a generalized Compton length of an atom or the radius of the universe given by Hubble’s distance.
See for the relation between Hubble’s radius and horizon distance or Hubble’s constant; chptr.6, Tying up loose ends.
From the quantum mechanic point of view for a Newtonian 3D-world a cut-off radius for the gravitons to a gravitational mass exists. This radius could be allowed as a quantum condition provided the graviton never reaches the c-velocity. (Mind the note about quantum groups velocity in the previous paragraph)
In a real quantum mechanic 3D-world at rest, time is absolute. Meaning that a mechanical event (change of momentum, etc.) is linked to the nearly infinitely far away space. A Cartesian coordinate system reflects this property. However this property of simultaneousness probes much deeper. For if all the atoms in a gravitational mass are at rest then the Newtonian condition for the black holes is valid as the analogue for the gravitons of empty space. So one has derived indeed a powerful tool for scaling of a 3D-world quantum mechanically at rest. See, chptr.6, Hindsight review.
This quantum condition, which is a condition of quantum resonance due to the property that all information any where is instantly available, validates the concept of event horizons of any size and it leads to the relation of the quantum mirror mass. 2M m = mpl²
Where M is the mass of a resonance black hole and m is an atomic mass or vice versa, m is the energy of an Einstein quantum with M the macroscopic mass of a star, galaxy or universe. M and m are the geometric mean for the square power of the Planck mass.
The mediating mass
See, chptr.2, The derivation of the mediating mass. The derivation uses the above mirror mass condition in relation to the linear accelerated quanta. The electron and the proton having opposite electrostatic charge must be neutral with respect to the representation of the quanta of empty space. The derivation is the only possible explicit mathematical expression. For all other neutral atoms the mediating mass can only be derived implicitly by for example an algorithm.
A nice feature in this derivation is that G, the universal constant of gravity, drops out of the expression showing that the electromagnetic properties of Fermi particles are dominant.
Another consideration for the mediating mass is that it is a contradiction, for as well the electron as the proton can behave individually, screened form each other, but still complying to Newton’s law of gravity. Still it is also valid that as well the electron, proton as the fictitious mediating mass drop equally fast in for example the Earth gravity, because their respective inertia does not appear in the equation for the accelerated fall.
However in a universe consisting of hydrogen, the mediating mass fits excellent with the theory of equilibrium of a quantum force. See the leading article, The proof of 22 % of dark matter….etc.
The free accelerated expanding space and the equilibrium condition for gravity.
See: chptr.1, The equilibrium hypothesis. Chptr.2The scaling laws of the equilibrium universe. Chptr.2, The equality of equilibrium radius and Hubble’s radius of acceleration. chptr. 2, The quantum equilibrium condition of the galaxies.
The scaling for an outward dynamic accelerated point, of which the constant of acceleration is equal to the local gravity at a certain radius of the gravitational mass, is very simple. It follows the discussion in the paragraph of Einstein’s equivalent principle.
If there is a constant of acceleration for vacuum then one can determine the equilibrium radius for the gravitational mass, in which gravity and the constant of acceleration in vacuum are equal. It is the equilibrium condition for any mass from atom, galaxy to the entire universe. Einstein’s gravitons within this radius return to this gravitational mass, making them imaginary, but beyond this radius the gravitons are accelerated and disappear to 3D-infinity. Beyond this radius the gravitons are subjected mainly to the vacuum constant of acceleration. The results of this exercise of scaling by applying the mirror mass condition, are finally fully appreciated in the leading article of The proof of the 22 % of dark matter,…, etc.
The important expressions are:
aH (::) mm³ c³/ (mpl² h) ; N (::) mpl (power 4) / mm³ ; RH (::) λm √N
mm, λm are the mediating mass and Compton’s length respectively. RH is Hubble’s radius and N is the total number of H-atoms in the 3D-universe in steady quantum state. Not only is RH the event horizon radius but it is also the radius beyond which the universe expands accelerated. Later it was realized that the number of quanta for the mediating mass, represent only 3.5 to 4% of the actual H-atoms. The rest is energy to keep the accelerated empty space in equilibrium. The conceptional error which is remedied by the proof of 22% etc. etc..
The last is a consequence of the mirror mass condition
The group velocity of a graviton at radius λm is: vm (::) c mm²/mpl² .
It is extremely small with respect to the c-velocity, but it is still a measure for the accelerated expansion of space around the atom.
See, chptr.2, The quantum drive for 3D-space with gravity as engine.
The accuracy of Newton’s law of gravity.
Applying the above criteria discussed in previous paragraphs, one finds the inversely scaled quantum length λi .
See: Chptr.3, The infinity transformation of our reality to time and vice versa; Chptr.6, Hindsight review. Chptr.6, The translation of Newton’s law of gravity in Einstein’s gravitons.
λi = λm (1/√N) and RH = λm √N while λi RH = λm²
The last expression is a measure for the accuracy of quantum space. λm is related to the mediating mass and N again to the total number of atoms. The importance of the inverse scaling is that one immediately understands why Newton’s law of gravity is extremely accurate. Again realize that Einstein’s gravitons relate to empty space giving those extremely small magnitudes of λi . λi / λpl (::) mm / mpl ; so λi is smaller than the Planck mass. The other property deduced from λi confirms the simultaneous condition for quantum exchange of empty space and matter. All information of the quantum world is instantly available between the two main characteristic dimensions λi and RH . The reciprocals multiplied by the c-velocity are an estimation of the time intervals.
Secondly, it is possible to understand why the vacuum constant of acceleration is always directed outward with respect to a mass point. The generalized Compton length, as a quantum field parameter is composed of all information coming from every direction in the 3D-world and from all other atoms in the universe.
The equivalence in energy of GRT and the model of graviton equilibrium.
Having found at the end of Physics 2 in chapter 7 the answers, it is much easier to understand the equivalence of energy between the graviton model and the estimates of the overall mass of our cosmos based on GRT. Straight away assume the equality of overall energy between the two theories and make sure one has the right expressions with respect to GRT. The last is the relation for the radius of the event horizon of black holes. Due to the model of quantum gravity for empty space, one can apply the condition of the event horizons for any radius of the 3D-world, again taking note that all gravitons are never relativistic and are only accelerated to half the speed of light. Moreover for GRT-cosmology all energy is concentrated in matter itself, neglecting e.m.-radiation, while in the model of graviton equilibrium all mass energy etc. is conserved in the empty space surrounding matter.
Under these constrains one can calculate the properties of Einstein’s gravitons and all other relevant constants for the hydrogen universe.
One condition is the acceleration of the graviton up to the Compton length of the mediating mass and the other condition is over a distance of the entire Hubble radius. Both appearances for the same graviton are accelerated by the vacuum constant of acceleration aH . The begin- and the end-condition of this graviton determine due to the energy balance of the two theories, the vector character and due to the precession with matter, the angle of 60 ° of the two components of the vector is determined. See, chptr. 2, The quantum drive for 3D-spacewith gravity as engine. The grand correction: the idea of a vector composition of Hubble’s radius. The analysis of the vector composition of Hubble’s distance.
The ratio between precession energy and linear acceleration of the gravitons is three, while in the end a quarter of all energy of the universe is pumped at the expansion of empty space. After eons of time, about 14 billion years, this energy disappears from observation. Reversely, one can reason that per atom cycle of the Compton’s length 25% of the energy disappears in linear energy and 75% is stored and conserved in rotation of empty space. The only conclusion can be that the energy re-circulates as energy disappearing to time. The orifices for the time flux are the windows of observation given by the radii of the surfaces for the event horizons for λi or RH.
Still astonishing is the square root rule of the atoms in Hubble’s radius and Compton’s length. But more overpowering is the proportionality for the precession, because with no force no precession, the graviton maintains during the eons of acceleration its continuous precession letting the
60°-angle be, for reasons that the equilibrium radius as a variable, embraces more and more mass. See also the paragraph of the macroscopic rotation.
Note that the g-spin to time is 25% of ½mm vm² . See, chptr.3, the g-spin of precession of Compton’s length.
The Fermi-spin and the precession of gravitons.
See, appendix , Scrutinizing the precession of the mediating mass
With the results of above discussion it is possible to look more closely into the precession initiated by the mediating mass. For the H-atom over a time interval determined by Compton’s length about 10exp(+20) gravitons make up the rest mass of the atom and these are accelerated away continuously (per each interval). The kinetic velocity of a graviton at the end at the interval is
vm (::) c mm²/ mpl² , which is a small fraction of the rest mass of the atom. Only at the end of the full trajectory of RH , these gravitons equal the rest mass of the H-atom.
It is important to realize because the spin of the atom ensemble is different from the ½-spin of the electron and proton representing the asymmetry in their respective rest masses. In other words one could either assume a coupling between gravitons and the Fermi-spin of the particles or no coupling at all. Another way of saying is that we do not know as yet, how the two components of the graviton interact with a photon, for this is the mechanism of exchange between the charged Fermi particles. However the scaling exercise so far, makes it crystal clear that the plane of precession for the graviton is through the axis of rotation and the direction of acceleration. It represents the overall spin of the ensemble making up the rest mass. So probably the gravitons are released in the plane of precession. Another consideration is that the released gravitons may change direction every λ-interval due to for example inelastic or elastic scattering or collisions between the H-atoms.
The idea of Einstein’s gravitons can only be applied after careful considerations. Therefore the analysis should be restricted to collision less, uniformly distributed matter under conditions of graviton equilibrium. Under these constrains one can reason that if there is a coupling of the Fermi-spin of a particle to the precession of the graviton for empty space then clockwise precession is caused by clockwise spin and vice versa..
The anti-commutation property for angular momentum relates to a 3D-spatial coordinate system. As a consequence the quanta of empty space are equally distributed and composed of clockwise and anti-clockwise gravitons. So empty space has always a zero- angular momentum and it can never carry macroscopic rotation.
However is there is no coupling between matter-spin and the precession of gravitons, or in such a way that the gravitons of spin 2 couple only in a specific way with the photons of the half spin particles, then the kind of matter determines the macroscopic precession of empty space uniquely.
In this way one has proved indirectly by means of the Fermi-spin that the gravitons of one species of matter, a neutral ensemble, could generate one kind of macroscopic rotation.
The macroscopic rotation of empty space
In the previous paragraph the two possible options between the Fermi-particles and the precession of the gravitons were discussed. One consideration was over looked. As long as one considers gravitons at atomic scales, Compton length etc., it is impossible to prove there is no coupling whatever between those two objects. This oversight is the result of equilibrium condition valid at two scales, namely Compton’s length and Hubble’s radius, both the vectors having an angle of 60° between their components. During the long travel of acceleration the gravitons start with low velocities as a consequence of their substitution mass, and reach ½ c- speed, but also the tangential component gains velocity proportionally; which is wrongly formulated. For the precession velocity is always constant, but the radii of equilibrium have to be integrated over all matter embraced, up to the final overall mass of the universe.
It means that the total mass in the universe, similarly as to Mach’s principle, determines the final state of the graviton at the end of the vector RH. Thus if the overall mass in the quantum condition for equilibrium is considered, then obviously the supposition about a coupling between precession and Fermi-particles is out or can not exist.
There are two boundary conditions for the equilibrium of the gravitons under accelerated expansion.
1.At atomic scale by mediating mass, the inversely scaled vector λi .
2.Macroscopically, the vector RH .
For these conditions empty space rotates macroscopically. At least, the model of uniformly and collision less distributed matter with random orientation for the Fermi-particles will have a preferential direction of rotation of it gravitons.
It is quite a challenge to prove that under the conditions of elastic scattering, atomic collisions, the gravitons do not change the orientation in polarity for the plane of precession. From above discussions and the conservation laws of matter for collision, one may surmise the existence of a coupling, but above analysis states the contrary. Again the conclusion is that the gravitons operate beyond the photon exchange between particles, Photons having c-velocity while gravitons are bound to group velocities.
Under the constrained that equilibrium or the steady state can only be maintained by a complementary universe, consisting of anti-matter and that both universes have separated 3D-quantum spaces, instantly created, the macroscopic preferential rotation of the gravitons is the only valid option. Naturally, the antimatter 3D-space has the opposite preferential precession for the gravitons, for the balance of angular momentum should be zero.
Note: one could subject Einstein’s gravitons to Liouville’s theorem valid in a multidimensional phase space of generalized coordinates and generalized momentum and try to find a condition for the Fermi-particles. However the initial condition of the universe coincides with the steady state of equilibrium of the gravitons. So it seems to be impossible to change the state of the macroscopic orientation for the rotation of empty space. In conclusion the gravitons making up empty space are bound to the kind of matter i.e. matter or anti-matter or conjugated matter (also in two kinds).
The condition for randomized 3D-empty space or the stochastic representation of Einstein’s gravitons.
Since it was discovered that 3D-space has a preferential orientation related to the kind of matter, it is important to find the number of degrees of freedom. If there are two degrees of freedom then one is reserved to the direction of acceleration and the other, the precession, can be reserved for a matter- and an anti-matter-universe, both in quantum equilibrium. It is most likely that both the 3D-quantum spaces cannot coexist, because the gravitons having also opposing polarity with respect to acceleration, generated by matter and the ones generated by anti-matter are in for destruction. This is just a working hypothesis which can be dropped later, but it confirms the hypothesis of existence of anti-time.
Using the last statement for the necessity of the existence of two separate empty spaces in three dimensions, maintained by gravitons, one can elaborate on the second degree of freedom. According to the properties of conjugated matter it seems that the conjugated matter can coexist in one space with normal matter and conjugated anti-matter coexists with anti-matter. See, chptr.4, Matter and conjugated matter. Chptr.4, The second degree of freedom.
Conjugated matter generates conjugated gravity then it is expected that conjugated matter has the opposite precession with respect to matter. So the 3D-space orientation for macroscopic rotation is the opposite with respect to the one of matter. Consequently it is most likely we found the means to unfreeze the macroscopic preferential direction of the gravitons. This extra degree of freedom for matter is the only explanation why the preferential macroscopic rotation is randomized. As was pointed out in the previous paragraphs the initial condition together with the equilibrium condition of 3D-space, prevents any chaotic representation for the precession of the gravitons, namely gravitons that are polarized into two preferential directions with respect to one 3D-space and then randomly mixed with respect to one kind of matter. This is impossible according to previous paragraphs.
In the present-day universe of steady state, matter is organized through the existence of black holes. It is surmised that quasars are early super massive black holes generating massive quantities of matter. (See, chptr.5, Quasars. Chptr.5, Super massive black holes: Black mirrors. Chptr.5, A scaling exercise for equilibrium black holes.)
The existence of these black holes, later in the theory black mirrors, suggests that per galaxy, the expansion of accelerated space is organized according to the preferential orientation for precession. Overall it makes the universe randomized macroscopically with respect to rotation.
See, chptr.5, The binary direction of the vectors of angular momentum for the galaxies.
The sun wheel drive for stars only. See, chptr. 6, The sun wheel drive of the stars.
The square root rule for the number of H-atoms in Hubble’s radius is valid for any mass system in which the pull of the expanding empty space is in equilibrium with the gravity generated by the mass system. Is the number of the galaxies Ng then the equilibrium radius is the square root of Ng times RH. See, Chptr.2, The quantum equilibrium of the galaxies.
Within this radius all stars mass is rotating making up the angular momentum of the system. If no atomic conversions or transmutations occur, nothing will change and everything is conserved. However as soon as fusion burning in the stars is included, inertia of mass is converted which should have an influence on the equilibrium radius and the angular momentum. Due to the change in equilibrium and the conservation of angular momentum of the galaxy, overall the system will be driven in increased rotation. For a single star the situation is slightly different.
See, chptr.5, A scaling exercise for the equilibrium black holes.
For a single star, burning hydrogen, the same reasoning along the lines of Newton’s theory is valid. According to the equilibrium condition, even if the star has no initial angular momentum or spin, the star will start to rotate. This situation is new and a consequence of the sense of rotation of empty space around the star, just beyond equilibrium radius. For only one type of Einstein’s gravitons is in equilibrium with matter. Because matter has no direct coupling at atomic scale to half-spin particles, a preferential orientation of the plane of precession exists. Secondly, always there is a preferential macroscopic direction with respect to the precession in relation to the empty space around the star, because all matter originated from the centre of the galaxy.
In addition there is the driving mechanism for rotation due to the super massive black hole at the centre of the galaxy, subjected only to the conservation of angular momentum of matter, generated from the black hole. It appears that atomic transmutation is a second source to drive the macroscopic rotation of matter in reaction to the precession of empty space and only fusion can change the equilibrium radius around the star itself. So consequently the angular momentum of empty space is conserved for the change in the radius of equilibrium.
Conservation of the angular momentum of our cosmos.
In the analysis around the steady state of the universe there were two situations applied to the entire universe.
One situation for the conservation of overall angular momentum is the determination of the number of black holes in the universe. See, chptr.5, Scaling exercise for the average number of black holes in the universe.
The second situation is; the total mass in the universe is compared by angular momentum two universes. See, chptr.6, Tying up loose ends.
Thirdly, if the conservation of angular momentum of the gravitons for the entire universe is applied, then according to the previous paragraph matter in our cosmos could start to rotate which is prevented in the real steady of our cosmos due to the appearance of conjugated matter sometime during the evolution, making the overall angular momentum probably zero.
The first analysis is not of interest, for in the steady state the black holes cannot exist together with normal matter. This is a consequence of the initial condition which requires the equilibrium of steady state is fulfilled instantaneously. The presence of real black holes contradicts this quantum state of the universe, separately, yes, but not together. A steady state of one kind of matter and black holes evolved from the same kind of matter is not likely. It is important to realize that the evolution of the universe in the sense of time requires a second degree of freedom, which of course is given by the prediction of the existence of conjugated matter in the pyramid theory, then again generating conjugated gravity. The time evolution to the real steady state, the galaxies driven by black mirrors, of our cosmos, is a topic for book 3.
However the time history for a one matter-universe in an equilibrium condition of quantum space, where matter is distributed uniformly, is probably as follows: Firstly, there was uniformly atomic matter, later there were uniformly distributed stars starting to have spin and not rotating around super massive black holes, then clusters or spherical or elliptic galaxies only slightly rotating, uniformly distributed and their borders expanding continuously up till the equilibrium radius is around hundred thousand light years, which is the present time. In case of a global uniform distribution of matter evolving in whatever, the competition between free increased accelerated expansion of space and the increase of the equilibrium radius goes hand in hand with the increase of the mass within the radii. In the end the restriction of uniform distribution can not be maintained due to the conversion of angular momentum of empty space into the macroscopic rotation of matter. Well, computer simulation could do this modelling perfectly for one type of matter.
Note, the property of the proportionality of the precession with matter embraced, is in general valid for all kinds of initial conditions, as long as the distribution of matter is uniform, uniformly spaced mass systems. Any dimension of the equilibrium radius as the onset for the steady state is allowed. For non-uniform distributed matter, the conditions are different for the precession and so far of little interest for the reconstruction of the present-day observed universe, a subject that belongs to book 3.