Chapter 3: The axis of time

The moduli of Hubble’s distance and Compton’s length
The indirect proof for the hidden overall energy of the universe
The double rotation or the precession of the generalized Compton length
The g-spin and the precession of Compton’s length (NEW)
The infinity transformation of our reality to time and vice versa
The phase velocity of twice the speed of light and the 3 dimensions of the phase space of time

THE MODULI OF HUBBLE’S DISTANCE AND COMPTON’S LENGTH

In trying to understand the physics behind the final result of the scaling exercise, one is surprised and in great bewilderment. Because realize it well.

1. The square root rule is the summation of all individual mediating masses in the universe making up the overall modulus of Hubble’s distance. As well as the angular as the linear component of the neutral atom participate in this summation.

2. The atoms are randomly distributed. All with different directions of motion in a strict three dimensional world, that is in accelerated expansion. And on top of this all, the individual spins of the atoms in spatial orientation, are again randomly distributed, not giving any preferential rotation to empty space.

What is going on? Are we mad? Probably but, if one can overcome the summation of the composed vectors of particles in Hubble’s distance, one can also more or less accept that the components of the angular momentum are absolute in this summation. Of course, the other option is to reject this result and conclude the whole exercise was futile. However continuing is a challenge in trying to understand the underlying physics.

Suppose, both the results in the summation of the linear and the angular part are correct. The linear part is the pull against gravity as a reaction from anti-matter, because anti-matter is hardly present in our cosmos, but the twist or spin looks like a consequence of the force equilibrium per neutral atom (mediating mass). So if empty space rotates with a preferential direction then in the anti-universe space is preferential in the opposite way.

May be it is inconceivable, but one has not yet considered another imaginary direction, which could be a preferential overall direction for the whole universe. Meaning the whole of empty space has a preferential direction to time and naturally the anti- universe has a preferential direction for its own entire empty space, the anti-time. Anti-time is progressing in the opposite way, leaving the centre of mass of both universes at rest. Then one can conclude that gravity in each neutral atom generates a vector or component of a vector, the g-spin, to time. This is the first step into the transformation of our reality to the phase space of time or the barrier of nature.

In other words, nature has a little tiny Einstein devil, very clever indeed, who twist and pulls the space quanta and aligns these in the proper direction of time. The little man knows exactly how many atoms are assigned to him and he drives his sheep through some kind of barrier aligning them in one manner only.

Definition: The g-spin is the directional vector of gravity in the phase space of time. All atoms of one kind of matter have the g-spin progressing in one direction of time. The g-spin of an anti-matter atom propagates in the opposite direction of the one of normal matter.  Since the discovery of the hidden energy flux to time, it is most likely that the definition of the g-spin has a real meaning in physics. See The indirect proof for the hidden overall mass energy of the universe.

Note, the flatness of our expanding and rotating cosmos has been observed in the cosmic background radiation, which is supposed to be the remnant electromagnetic radiation a little while after the Big Bang. It seems that the back ground radiation, as observed, is polarised in one dominant manner, which can only point to the flatness of the material disk (the distribution of galaxies) of our cosmos. The absolute rotation as yet has not been discovered. Here it is predicted to be that way. 

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                                 Chapter 3: The axis of time

THE INDIRECT PROOF FOR THE HIDDEN OVERALL ENERGY OF THE UNIVERSE

RH is a vector summation.

The table represents the final results of the discussions in the previous chapter. It can be seen as a proof of the quantum cosmology of the force equilibrium between universes, because all parameters in the scaling exercise of this chapter were thoroughly scrutinized. The context in which this happened pointed to a non-relativistic model for accelerated quantum space (empty space) in three dimensions in which time is absolute. In fact all postulates of the three dimensional reality, as Newton’s principles as well as the quantum mechanic principles based upon Heisenberg’s uncertainty principle, are satisfied.

The illustrious equivalent mass for the accelerated empty space, mH, obeys the above mentioned postulates. The strange thing is that the extremely long wave length corresponds to Hubble’s distance of the relativity theory, but with a different meaning, for this distance represents accelerated quanta of empty space in linear and angular sense. Note that the zero energy of empty space means that the non-accelerated quanta cannot exit in this cosmology.
Like any particle in quantum mechanics mH has point like properties represented by a probability wavelength depending on its kinetic energy. Here this is always a momentary kinetic energy, except that the acceleration is constant. See note below.

Equally strange, but conform the laws of quantum mechanics is, that the overall mass of the universe obeys Newton’s law of gravity completely, for all mass is as thought contracted to a spatial point. But again the exchange of quanta of empty space every where explains why it should be like that. For rest mass is here a feature of empty space and not of the particle itself. So further analysis of mH could determine next to its mass, its spin properties. However this is not the topic of this section.

Having shown the identity between the cosmology based on GRT and the one discussed here, one is intrigued, why the overall mass in the model of the quantum equilibrium is half that of the critical mass for the model based on GRT (see table). This is exactly the case; if GRT embraces the four dimensional continuum of space and time, then the three dimensional equilibrium cosmology does not show all the energy, even or just because it is a non-relativistic cosmology. Still one can reason the ratio between angular and the linear mass energy is not derived properly, it does not hide the fact that the sum of both is half the spatial energy of the overall mass.

Since the equivalence between GRT and the equilibrium model is proven only one conclusion is valid. The conclusion that mass energy of ¼ Mtot c², disappears due to gravity to time as a flux of energy or time energy. This hidden energy, not unexpected considering our way of calculations, represents the labour of matter struggling against the attraction of an other congruent universe. So amazingly, due to the equivalence between both cosmologies, one can make this hidden energy flux calculable while the EPR-paradox is maintained and GRT is equally valid.
See, The analysis of Hubble’s distance and moduli of H-distance and Compton length.

Note, the reason why the factor fc = 4 has that value in the scaling exercise, is a consequence of the disappearance of energy to time.
Note, the definition of congruent means in overall energy and mass, but the equality in the distribution of galaxies between the universes has not been proven. Although the pairing of mediating masses in both universes must be an essential consequence to explain the preferential orientation of Compton’s length and Hubble’s distance.

Note: In i.e. a German book about quantum mechanics the different examples for the shape of the potential well in Schrödinger’s equation are given. (Rechenmethode der Quantumtheorie, by Flugge, Springerverlag, Heidelberg 1965) Here one finds a one dimensional solution of the S-equation, which can be applied to Newton’s graviton of mass mH. At the different levels of energy that exist in a linear increasing potential well due to acceleration of aH. Also an assessment of the total number of quantum states with Boson statistics can be made corresponding to
N = ?(mpl / mm) (power 6)

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                                 Chapter 3: The axis of time

THE DOUBLE ROTATION OR PRECESSION OF THE GENERALIZED COMPTON VECTOR. (dipole)

Let us perform another Newtonian exercise. What happens to a spinning toll (rotating), hanging freely in space, under influence of an external force? The answer is widely known. If the external force is attached in the right way and perpendicular to the vector of constant angular momentum, the axis of rotation of the spinning toll, then the force causes a precession with a right angle around the main axis of rotation. If no force is applied then no precession exists.

Transpose this concept to a mediating mass, as the representation of the ensemble of a neutral atom for empty space, contracted to the modulus of the generalized Compton length. The vector components of λ compose the external force (linear acceleration) and the vector of rotation of the spin of the ensemble. So one expects a precession of which the mass spin of the atom itself is the dominant part in the ensemble.

Let us make a distinction between a double rotation of a mass less point in two directions, not necessarily perpendicular and the above described precession. One axis is fixed in 3D-space the other rotates around it executing the spin of the mass less point. Then the precession and its spinning mass is equivalent to the double rotation. The only difference is the inertia and the presence of an external force. So the double rotation is the kinematical model for the dynamic process of precession.

In resumption, due to the external force one expects a precession of the spinning Compton vector or a full scale double rotation. In observations of our reality this kind of double rotation is obscured or is not present. The issue is that empty space is a representation of mostly nullified quantum waves. So due to interference between the mirror image of matter and empty space, the anti-universe, one part of the double rotation could be suppressed with respect to our reality. As a consequence, empty space, or the summation all its quantum processes could give an overall rotation.

The above sketched picture is speculative and needs further analysis. First question is; how is it possible for quantum waves, statistically, to interfere with one other? Only when these are aligned and are kept in a straight base line, which is the time axis. Secondly, gravity evoked as action in a pair of mediating masses, matter and anti-matter, causes a resultant effect in a single linear motion (actual accelerated motion), due to interference of both double rotations of the λ-vectors. This is the g-spin, of which the g-spin of anti-matter is opposite to the direction of the one of matter, the anti-time direction.

The whole mechanism of suppression of the precession and the main rotation is shown in the game of the double rotating vectors (dipoles) to be down loaded from this site. Firstly, the orbit of the point of the vector outside the origin, executing a double rotation on the surface of a sphere is shown and secondly, by proper choice the suppression of the double rotation into one straight direction can also be visualised by using a combination of an unique setting of the phases between the two super imposed double rotations.

The next step of the summation of all Compton vectors is more complicated to explain, but can be contracted into one idea, the infinity transformation, a procedure of transforming our reality with all its mediating masses into an other space, the reality of the time axis (later 3D-phase space of time). The time axis of the universe coincides with the one of a mediating mass. The gravity of our world is exactly equal to the gravity in the world of anti-matter, causing the two kinds of matter to crawl or progress in opposite direction of the time axis. So partly, the definition of the g-spin is explained.

Definition: The g-spin is the directional vector of gravity in the phase space of time. All atoms of one kind of matter propagate in the same direction of time. The g-spin of an anti-matter atom moves in the opposite direction of that of normal matter.  Since the discovery of the hidden energy flux to time, it is most likely that the definition of g-spin is a real meaning in physics.

Note, in the game of the double rotation the term dipole is used. Without any difficulty one can state that the composed Compton length, as is proven, has the properties of a vector. Or it means the idea of gravity as a neutral dipole to time has some equivalence. Also the g-spin is similar to the idea of a neutral dipole (energy tube of flux), but only in conjunction with quantum interference of its opposite partner. Then it represents in our reality the linear outgoing force and the absolute sense of rotation, of which the flux is passing through our space.    

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Chapter 3: The axis of time

THE G-SPIN AND THE PRECESSION OF COMPTON 'S LENGTH

How can it be that the two vector components of the generalized Compton wavelength scale linearly to Hubble’s distance? What has this result to do with a rotation of empty space?

The two vector components represent the rectilinear acceleration as ½λ and the angular momentum vector ½√3 λ. The composition of both gives the modulus and trajectory of λ, which is the direction for a photon, starting at the base of the both components.

With the supposition that the angular momentum is proportional to the precession of the spinning Compton length due to the acceleration, the constant angle between both components is explained.  For if aH is constant then the precession is constant. The precession is the effort needed to displace the spinning flux of λ with magnitude ½λ.

The g-spin to time or the disappearance of energy from the 3D-space reality is the reason for the formation of the spinning dipole (flux), which generates also the angular momentum or precession due to the external acceleration. But remember the spatial angular momentum is independent of the g-spin.

The explanation of the angle of 60 degrees between the two displacement quanta of empty space determines the g-spin. By following the excellent explanation of the definition of spin given by S.W. hawking in The brief history of time , 1st ed. 1989, one is able to derive that the g-spin has a spin of two and not that of a half.

Namely, with the supposition that the g-spin of the mediating mass regains its identity after 180 degrees instead of a full cycle of 360 degrees, one determines a ratio of three for the cycle frequencies; otherwise it was a ratio of six, corresponding to a spin of one. The factor of three is also the ratio of the frequencies between two double rotating vectors interfering to each other in the normal gravity mode, see the game of the double rotating dipoles. Was the spin a half spin particle then the ratio of the frequencies was 12.

It looks like the λ is the proper definition of the graviton of Hydrogen with spin equals two, but also the smallest rest mass of empty space has a spin of two. In conclusion, the mediating mass of an atom has a different spin than the electrons and protons, both Fermi particles of half spin, composing the mediating mass. This new discovered fact can only be explained if the graviton, mediating mass, belongs to empty space. A most astonishing result, which means it proves beyond doubt that the pyramid theory as a quantum theory of empty space is correct.   

Note: in the different sections of the chapters were the two vectors are mentioned, the above explanation was not understood completely. So here is the rectification, which even improved the overall analyses.

  Chapter 3: The axis of time

THE INFINITY TRANSFORMATION OF OUR REALITY TO TIME AND VICE VERSA.

The infinity transformation is the representation of the relation between absolute time, the accelerated expanding of and the preferential rotation of empty space. In part the infinity transformation is the proportional relation between Compton’s length as a vector and the Hubble’s distance as a vector. Then this denotes the validity of the term infinity. It is much more difficult to reason, but the energy flux of time of the entire universe runs from the radial infinity (Hubble’s distance) to all the mass points of matter, which is gravity.

See, The moduli of Compton and H-distance, and the analysis of the vector composition of H-distance.

The ratio of the moduli for H-distance and generalized C-length is the square root of the number of mediating masses, representing a neutral hydrogen atoms. This resumption almost defines the infinity transformation, which has only a meaning to time in the quantum interference mechanism of the double rotation. To state the resumption explicit, the gravity generation in the neutral ensemble of one atom translates directly in the overall generation of gravity for the whole universe. So if the Compton dipole executes some double rotation then the macroscopic dipole of Hubble’s distance does the same, which translates due to the presence of the interfering anti-universe a rotation of empty space with accompanying accelerated expansion (the anti-universe has opposing rotation).

The process of the infinity transformation and the interfering mechanism of double rotation of vectors into a linear accelerated motion is sufficient evidence to explain the definition of the g-spin at the time axis for matter and anti-matter. Except that the direction of the vector of the g-spin with respect to λ-vector (or RH) and both its components, has not been derived. The angular momentum of the λ-vector should be perpendicular to the plane of rotation in which the linear acceleration also resides. The g-spin is a disappearing vector not belonging to our reality and in opposition to the angular momentum vector rotating the quanta of empty space. With respect to the infinity transformation the angular momentum vector is the representation of our reality and the g-spin the one of the phase space of time.  Has the λ-vector the opposite rotation and accordingly the angular momentum point in the other direction, then the quantum of g-spin should have the opposite polarity to keep the direction of space rotation absolute in our reality and the propagation along the time axis is unchanged. The preliminary conclusion is that the half-spin properties of the Fermi particles are carried over to the phase space of time and expressed in the polarity of the g-spin. The preferential rotation of space is not a consequence of the special orientation of the angular momentum of the atom.

So what determines the absolute rotation? Obviously, it is the overall mass of the entire cosmos generating the gravity to keep it in balance with the anti-universe. For further explanation see; the characteristics of the pyramid model

The infinity transformation for the g-spin and the consequence of the absolute rotation of space has been explained sufficiently. What about a real proof? A fundamental theoretical derivation, or a summation based on quantum statistics for paired of atoms (anti-atom) is extremely complex and it is not yet performed in theoretical physics, even as all quantum mechanics is non-relativistic. The problem is left to those having an interest in this new theory. Note: Since the pairing of the λ-quanta to the anti-universe, the question is, if the polarity of the time quanta swaps synchronously or not? According to Denaerde, both the universes are congruent up to the level of the atoms, but from the point of view of the physics of quantum statistics and the macroscopic distribution of matter the last word has not been said and a proof will not be easy to resolve the question.

Another inverse infinity scaling is also possible. Equally one can divide the generalized Compton length through the square root of all the mediating masses. Then the resulting length is much smaller then Planck’s length and equally simply, one derives that this length corresponds to the imaginary radius of the event horizon of the mediating mass. By imagining that every tiny length represents a mediating mass any where in the universe, one has formatted the composed C-length of one mediating mass. So it is a similar summation procedure in absolutes as H-distance. All information of the universe is carried in a vector. The quantum information carried in Compton’s length is reflected equally in Hubble’s distance. If at a large scale all information is stored then at atomic level the same information is stored except for the time scale between both. The macroscopic vector (dipole) carries information of all individual neutral particles making up the evolution of stars and galaxies over an extreme long period. The microscopic vector carries per atom all information every where for an extreme short time interval, λ/c, but it is repeated perpetually and storing all information in the spin and precession of the neutral ensemble, while crawling along the time axis. A process which is adding each time quantum in succession next to the other. Then it is building the macroscopic quantum of RH, together with all the other atoms. One could even extrapolate that the loss of matter, may be one percent during the evolution of the universe, shortens the moduli. Based on common sense, one can state that matter converted into black holes cannot violate the conservation of matter.

Since the equivalence exist between GRT and the theory of the quantum gravity of equilibrium, only one absolute length has to be considered and the factor fc  = 2 can be put in the calculation below.

   N = Mtot / mm = ¼(mpl / mm ) power 4  ;  √N = mpl² / 2mm² = mm / mH . 

   λ = h / (mm c)  ;   λi = λ / √N = 2h mm / (mpl² c) = h mH / (mm² c) .

   λpl² = hG / c³  ;     mpl² = hc / G ;   λi²/ λpl² = 4mm² / mpl² 

   λi / λpl = 2mm / mpl   with   λi < λpl   With the definition of event horizon

    c² λi = 2G Mi   follows  Mi = mm  !    Also is:     RH λi = λ²   

To make a speculative jump for the purpose of λi in nature, because it is so much smaller than Compton’s length. It might make more sense if one relates λi to the quarks, the building blocks of the nucleons. Considering the phase velocity of 2c in the phase space of time, the quarks do not seem to carry only the information of our reality, but due to the structure of the phase space, the exchange of quanta in all the universes might be possible. Mainly, because the quarks cannot exist individually. So the quarks exchange momentary linkages to other time phases.

See, also early literature of the pyramid theory.

The conclusion in metaphysics for this section is that λ-quanta crawl along a straight line, forming a string of energy packets. This sequential behaviour is a direct measure for the causality of events to time. The storage of all information in our cosmos transferred to the phase space of time, acts as a huge immaterial memory bank for the evolving universe. The expanding space is a measure for the continuing addition of new information to the phase space of time.     

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 Chapter 3: the axis of time

THE PHASE VELOCITY OF TWICE THE SPEED OF LIGHT AND THE THREE DIMENSIONS OF THE PHASE SPACE OF TIME

The question of a phase velocity of twice the speed of light along the axis of time in the transposed world of our reality is of some essence.

In itself in a world of accelerated expansion of space all around, one could come to the observation of a velocity of c between material systems while the phase velocity, the speed of light, has a value of 2c. In this case one has an apparent phase velocity, because it seems that the velocity of light is always twice as far ahead for the same time interval, while the average speed is only half the light speed.

Similarly one can pose the question, what is the speed of the λ-quanta along the time axis? (These are summing in a straight line building the RH-quantum in time) In essence both quanta of the mediating masses in the universe and the anti-universe travel in the opposite direction from the centre of time (the origin of time). Without the understanding of the infinity transformation between the realities, the question is not easy to answer. The Compton length composed of a linear and an angular acceleration has not a constant speed. In the time interval of  λ/c, the end speed of c is reached, after which the cycle starts again going on perpetually. So does the λ-quantum crawl with an average speed of half the speed of light along the axis of time? That is correct. The average speed is ½c , but the phase velocity is 2c , because the end velocity of c is reached. It is essential for the exchange of probability waves, quantum waves, between the opposing λ-quanta. The average speed between both is c. An other way of saying is that the groups velocity is accelerated with an average speed of c and the phase velocity between both is 2c and constant.

Next one can try to analyse how the transposed space of both the universes, matter and anti-matter, relates to the 4 dimensional space time, the hyperspace, in GRT. After all both theories are equivalent. The phase space of time is a transformed space. In essence it is three dimensional, because the infinity transformation uses the interference of paired double rotating vectors. By guessing the physics, the Compton vector or the neutral dipole of either matter or anti-matter directs the quanta of space through some kind of membrane into a direction, not observable to us. May be one should say at the surface of the tiny membrane that the speed of light is reached and this is a cut off boundary for our reality.

Both our quantum 3D-realities of the universes are composed by non- relativistic quantum processes. In other words the light volume of a universe is expected to be twice Hubble’s distance in radius, but it is not due to the vector composition of the H-distance. Both universes belong from the point of view of GRT to one hyperspace with the c velocity as measure. This hyperspace has two event light cones stretching for 13.7 billion lyrs due to the onset of time and space. A trajectory of expanding empty space cannot coincides with straight path or zero geodesic of light. Both the 3D-volumes of 13.7 billion lyrs in radius have to be stored in a 4D-hyperspace of 13.7 billion radius, but 27.4 billion lyrs in diameter. Each universe with an average expansion speed of  ½c and bridging 13.7 billion lyrs of light volume in radius must exist together.

May be it is confusing, but the 4D-hyperspace is distinguished from the 3D-phase space of time, due to the existence of the phase velocity of 2c, but both cosmologies are equivalent. In an extension, the phase space of time has twelve event light cones in hyperspace, for a closed energy frame of the time flux is required. The energy flux of time can not disappear to infinity. The most simple poly face in three dimensions is an equilateral pyramid composed of four equilateral triangles, having six edges, the six time axes. Each axis serves two opposite propagating congruent universes, matter and anti-matter, all in complete symmetry.

Note: The relaxation of a 4D-hyperspace into 12 event light cones of congruent space filled with equal amounts of matter and anti-matter, just after the Big Bang, the Creation ex nihilio, may be far fetched, but the resonance properties of matter (anti-matter) in the phase space of time, is the reason why this is possible. Partly it explains it because GRT and the pyramid theory are equivalent. So this can only be a consequence of this kind of resonance representing the quantum mechanic properties of our reality. 

The last paragraph is an ad hoc supposition, but the essence of at least the three degrees of freedom of the phase space of time is fulfilled. Note; Denaerde when he launched the pyramid model in 1974 stated that the velocity in the phase space of time should be 2c. Only then it was not realized that the model stood for a quantum cosmology of accelerated and rotating empty space.

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