Chapter 1: Introduction

Introduction to the Reader
MOND- hypothesis versus dark matter
The EPR paradox & Bell’s Theorem
The equilibrium hypothesis
The constant of relative acceleration

 

 

NOTE OF WARNING BY THE TRANSLATOR

The whole concept of the existence of a three dimensional phase space of time to maintain our reality is not of this world as Denaerde first introduced the pyramid model (1974) and brought it to the attention of some people.

After a considerable time (2005) a way was found to translate the model in terms of well known fundamental concepts and ideas in the science of physics. Mainly as a point of reference they were the principles of quantum mechanics and general relativity theory. The translation itself was using the Newtonian principles and Heisenberg's uncertainty relation. The mathematics stayed simple but more difficult to grasp is the underlying understanding of the physics, the working of quantum mechanics in the phase of time and the relation to matter and gravity. This all because of new perspectives of our reality were introduced.

Since the theory is heavily related to Denaerde's religious philosophy (revelations), e.a. the existence of eternal life is carried due to the existence of immaterial conjugated gravity field or the phase space of time is the absolute memory bank of all events of the evolution of our cosmos can be associated with the existence of God, one should be careful with copying the new ideas to other areas of science without mentioning the original source of reference. Although according to Denaerde his revelations were for the good of all mankind and not for a particular religious faction, the influence of the religious concept of personal guilt due to copying without consent can not be ignored, or the normal courtesy of giving the source of reference will suffice. In the opinion of the translator a reference to the pyramid model or theory (or Denaerde) seems to be adequate.

 

 

                     INTRODUCTION TO THE READER

Since the appearance of the article about the MOND-hypothesis in the Scientific American of 2002, the pyramid theory made a jump in the right direction. You will find all of this discussed below including the explanation of the MOND-hypothesis. As such the hypothesis was not in agreement to fit the pyramid theory, but the idea behind it boosted our physics model considerably.

To explain it in some more detail, the MOND-hypothesis is based on a careful construction not to violate the principle of physics dictated by the general relativity theory (GRT). In our ignorance, in the beginning, we did the opposite. The supposition was made that a constant acceleration, extremely small outward pulling, of which its influence could only be seen at large scales as those of the galaxies, acted on matter every where in the universe. As will be explained, such a force, for acceleration times mass equals force, existing at infinity, goes against all common sense in physics. From this error came the idea of the equilibrium of matter systems (galaxies) all over our cosmos. The idea of an equilibrium of forces opposing gravity, while vacuum or empty space was still expanding around the galaxy, is the base for the equilibrium hypothesis, replacing the MOND-hypothesis. Integration of this idea with the concept of the three dimensional phase space of time was not too difficult, because the earlier work acted like a preprint. To be fair, in our discussions over a period of 30 years, Denaerde hinted to the existence of an equilibrium of forces between the matter and the anti-matter universe, but it was not taken up until now.

However the rigorous application of the equilibrium hypothesis did not work out entirely. The concept of a force of equilibrium for the entire universe is still valid, but one cannot hide the acceleration of the galaxies with respect from each other. The break down came when it was realized that the derived quantum acceleration from the scaling exercise was not absolute but relative. Meaning the centres of mass of the galaxies would experience less acceleration if its velocity increases. See the constant of relative acceleration. Because one is dealing with force based on a quantum mechanism, the acceleration does not obey the laws dictated by GRT. The set up of the discussion is as follows:

The first chapter is for preparation of the grounds and for the explanation of some problems in today’s astronomy. The second chapter treats the scaling exercise and proves the results in relative simple calculations. The results are almost unbelievable. The cosmology based on the general relativity theory is equivalent to the quantum cosmology of accelerated empty space. As a consequence the existence of a universe consisting of anti-matter for reasons of symmetry seems to be a fact.

The third chapter tries to integrate the results of the previous chapter in transforming the quanta of empty space to propagate along a straight line, the direction of time, due to the behaviour of gravity as vector. The fourth chapter explains the pyramid model with respect to the three dimensional phase space of time. May be a conjecture, but certainly not fantasy either. But the fifth chapter gives some unexpected results about the scaling and the number of black holes in the universe. All within the constrains of the new discovered quantum properties of empty space.

The whole derivation of chapter 2 to 5 is not very easy to understand, mostly for the reason that the author did not know where it all was leading to, and sometimes the wrong assumption was made. So if one looses the overview in the purpose of the chapters, it is advised to read chapter 6 first. Chapter 7 is the discussion and the proof for the self-consistency of the new 3D-quantum theory, while in the appendix certain difficult topics are reviewed.

What is most astonishing to realize is that Newton could have reached the same results three centuries ago, had he known solely the principles of both the antagonistic theories of the 20th century (GRT and non relativistic quantum mechanics). For it is not even necessary to know these theories in detail, but only the principles of physics they stand for, had to be understood. However having found the quantum mechanic equivalent of GRT (the new properties of empty space under external force of another universe), one actually is completely at a loss, was it not that this strange new theory for gravity was available, the pyramid theory, providing the other necessary answers.

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MOND HYPOTHESIS VERSUS DARK MATTER

From 1950 onwards the observations within the galaxies, as clusters of stars like our Milky Way, as the motions of stars emitting light, were refined enough to conclude that the velocities in the outer rims of the galaxy did not correspond to the gravity calculations based on the density distribution of matter in these galaxies. In fact by introducing non radiating matter the density distributions could be corrected, explaining the higher rotation velocities in the outer parts.

In the mean time computer models based on the dark matter hypothesis, are refined enough to explain partly the rotational behaviour for a large class of galaxies. In the following, the dark matter hypothesis is not valid.

See the Scientific American, June 2002. Galaxy evolution; by G.Kauffmann and F. van den Bosch.

However being stubborn, some astronomers thought about another explanation for the behaviour of the stars in outer rims, without having to add invisible halos of dark matter. The idea is not too bad, for careful analyses of the rotations required only small outward going correction forces to get these higher speeds correct. This is the MOND-hypothesis, standing for modified Newton dynamics. To Newton’s 2nd law, force equals mass times acceleration, a higher order term proportional to the square power of the acceleration is added. The higher order term only becomes significant if the forces are extremely small. Just these small forces for the acceleration have the tendency to accelerate the stars outwardly, explaining the rotational behaviour splendidly.

See, The Scientific American, Aug 2002. The Mond-Hypothesis;
M. Milgrom; and commentary: Not a bad idea; by A. Aquirre.

In the pyramid theory the MOND-hypothesis is replaced by the bold assumption that a constant acceleration is acting on matter everywhere in the universe. This assumption violates theoretical principles in physics, ea. the question of how such a small constant acceleration is generated in the infinitely faraway space; or how matter subjected to an outward directed acceleration will empty the universe from within, but also in the end all matter has infinite mass, because it reaches the speed of light. In short, violation of Einstein’s general relativity theory. (GRT), and it was for these reasons that the MOND-hypothesis was chosen.

 The reason to stick with our assumption here, making it implicitly adaptable to the pyramid theory, is that one can overcome these objections by thinking of a universe of equilibrium of forces. The calculated Hubble’s constant of acceleration of about 1.6*10exp (-10) m/sec² compares to the constant used in the MOND-hypothesis of 1.0*10exp (-10) m/sec² and based on observations of the galaxies only.       

 

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THE EINSTEIN-PODOLSKY-ROSEN PARADOX & BELL’S THEOREM

Nowadays, this well known paradox stands for the impossibility of the unification of the general relativity theory and the theory of quantum mechanics based on Heisenberg’s uncertainty principle.  In layman terms it means that information of an event cannot be known beyond the distance in space travelled by the speed of light. For more than half a century the observations in quantum mechanics contradicted the light to distance interpretation. Bell’s theorem is the mathematic formulation of the paradox in favour to quantum mechanics. For literature of subtle experiments testing bell’s theorem, one can find: Nature, sept 2003, letter to nature; violation of Bell’s like inequality in single neutron interferometry, by Y. Hasegawa, ea...

The pyramid model incorporates Bell’s theorem as the steady state of the resonances of particles in the phase space of three dimensional time. In this way all information of a particle is known everywhere in our three dimensional reality. In addition gravity could be explained similarly by this theory.

The discrepancy in understanding of the EPR-paradox may be caused by the use of two kinds of extremes in both theories. In GRT and the special relativity theory Lorentz-transformations using the four dimensions of time and space with the speed of light as absolute reference, are the basic frame work for these theories, Cartesian coordinate transformations have supported most of the quantum mechanic experiments of low energy. Lorentz transformations describe the behaviour of mass systems relative at rest, but mostly closely to the speed of light. They are without doubt absolutely valuable in the physics for high energy collisions, but why particles maintain perpetually their rest masses is not explained.

 The more than centuries old Cartesian coordinates transformations are only spatial and independent of time meaning time is absolute and the same every where. In terms of quantum mechanics absolute time could mean, the information of events is more or less instantaneous available everywhere. The world of matter and space is strictly three dimensional. So it seems reasonable that the theories based on Cartesian coordinates include the information for the resonance conditions of atoms and could explain the rest masses. Besides, all Newtonian laws are well known and the formalism is readily available.  This consideration lands us in the mathematic frame work based on the Schrodinger equation, valid for electrical charged particles under conditions of quantum mechanics. However, there is also a not explored method, which may give us the information about gravity and rest masses. 

Consider Newton’s kinematical relation or energy relation for a mass under constant acceleration a ,or called the rectilinear acceleration.

                                                       a 2s = c²

Where s is the covered distance to reach the light speed c. The mass m appears not in the expression, because it drops out of the energy expression. The initial velocity before acceleration is of no consequence, everything is in absolute rest, not moving. Normally, the probability wave length of a particle for its energy is;

                                                        λ = h / mc    

Where m*c is the momentum of the overall energy of the particle, here the rest mass. Apply this uncertainty principle in the reversed way at above relation.

                                                       s or 2s = h / ms c

Where ms c is the equivalent momentum due to the distance between events in quantum exchange. The acceleration or equivalent quantum force is:

                                                        a = ms c³ / h 

 Briefly, it seems one has a tool to execute scaling exercises for rest masses in relation to Newton’s law of gravity, which is also valid per unit mass. If a is nearly infinitely high, s is very short and approaches the Planck length, vice versa if s is extremely large bridging the Hubble’s distance for the universe, a is very small. The advantage of this type of transformation should be clear. As soon as a and s are combined to their product, the uncertainty condition disappears.

 However, this type of quantum transformation is unexplored and has ambiguities. The tool is not unique. One has to define it. What shall s be? s or 2s?

 By applying the definition;

            a = ms c³ / 2h    or      a = ms c³ / fc h

 By introducing a dimensionless factor fc , one can assess if the used definitions in the scaling exercises are correct or not.

Secondly, why not use the relation;    a 2s = v² ?  This is explained in the section; the constant of relative acceleration.

 

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                                       THE EQUILIBRIUM HYPOTHESIS

 

In first instance the equilibrium hypothesis replaces the MOND-hypothesis by making the bold assumption that there is outward going constant acceleration acting on matter everywhere in the universe. It is directed always opposite the direction to of gravity, but it is constant and not changing in value. The consequence of this bold assumption is that one finds out where it goes wrong and tries to find the means to correct and if impossible to drop the hypothesis.

It seems, due to the direction of this constant acceleration that it is a reaction force to counteract the generation of gravity. This force should be somewhere in equilibrium. The rigorous consequence of equilibrium is that the system is at rest, may be moving but not accelerated.

As well known, Newton’s law of gravity applies to the universe at rest and is absolute in three dimensions. Or in terms of quantum mechanics, all information about gravity contained in 3D-empty space is instantly available everywhere. Taking the consequences, one should apply this law to all matter in the universe. One should surrounds it with a big sphere with a radius that as light travels since the beginning of the universe, the Hubble distance, and make the supposition that the universe is in equilibrium with the anti-universe with the same mass and overall size. Apply Newton’s 2nd law. The force is equal inertia times the acceleration and the result are:

                 Mtot aH = G Mtot² / RH²      or    

                  aH RH² = G Mtot    

aH is Hubble’s acceleration and extremely small. RH is Hubble’s distance (radius) and G is the universal constant of gravity. aH  does not seem a reaction force to gravity, but it is also a force to keep the universe in equilibrium.

There is only one radius in general where there is equilibrium of forces. For radii smaller or larger, one should correct it into a resulting net force. Then the net force could be attractive within the equilibrium radius or an outward going force for radii greater than the equilibrium radius.

For galaxies having billions of stars, there should be a radius of equilibrium. Beyond this radius the stars are pulled away and internally the stars are contained by the net gravity and their rotation around the centre of the galaxy.  The point seems that the galaxy centre representing centre of mass of the overall mass of the galaxy, is subjected to the acceleration aH. Because aH is constant, one can calculate the time interval RH = ½ aH t² to reach the edge of the universe for non-relativistic conditions. However, at RH the galaxy reaches the light velocity and the galaxy inertia mass goes to infinity, simultaneously with all mass in the universe, because its time interval is the same. This contradicts with Einstein’s GRT.

After having discovered a contradiction, one should try to rectify it and restore the equilibrium condition. The only way it seems, is by making the following suggestions.

1.       Every galaxy has one or more super massive black holes.

2.       Every super massive black hole is in equilibrium of forces nullifying the out ward going force acting on the stars surrounding the black hole.

It means that gravity generated by the black hole is compensated by a rectilinear acceleration directed outwards (opposing gravity). In fact, whatever the reality of the spin- or event horizon of the black hole the force should be reduced by zero. See the section about super massive black holes etc. and the scaling of the equilibrium black holes.  So one should apply the equilibrium hypothesis for the spin horizon.

                  Mg ab  Rb² = G Mg Mb             or

                  ab Rb² = G Mb

 Mg is the galaxy mass, Rb is the spin or event horizon and Mb is the mass of the irreducible mass of the black hole.

However how clever the idea of the equilibrium hypothesis may be, as an intermediate step to our understanding, it was useful. Especially the question could be analysed, if the quantum acts on the centre of mass of a inertia system (galaxies, stars) or not, since it turned out that every atom in our cosmos has a equilibrium of forces between its own generated gravity and the momentary outward directed quantum acceleration.

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THE CONSTANT OF RELATIVE ACCELERATION

 

The constant of relative acceleration is a consequence of two principal considerations. By rigours application of the equilibrium hypothesis based on the consideration that the gravity spin in every neutral atom is in equilibrium with its reaction quantum force, the mass centre of a galaxy does not seem to be subjected to this force and consequently leaves the galaxy at rest. Then basically, violating Hubble’s law to scale the distance in our cosmos. The other consideration is that a constant of acceleration according to GRT, makes the galaxies having infinite mass at reaching the speed of light.

The point is that one forgot to consider the influence of the quantum mechanism accompanying the constant acceleration, for by supposition and so by definition aH is a quantum force. The behaviour in nature of bodies, microscopically, is a consequence of interference of quantum mechanic waves (probability waves) determining the groups velocity of the body, while the static waves propagate with phase velocities of the order of the light speed or higher.

So it may be possible that the quantum force of acceleration depends on the real velocity of the body subjected to this acceleration. Realizing this, it was luckily very easy to rectify our definition for the constant of quantum acceleration.

Using  s as the path for the group waves of quanta, one can write the formula slightly different. See Einstein-Podolsky-Rosen paradox

  

                    a1 2s = c²              a2 2s = v²

       (a1 – a2) 2s = c² - v²            arel 2s =  c²(1 - v² / c²)

Using:   s = h / (ms c)         arel = (ms c³ (1 - v²/c²)) / 2h

Replace the factor 2 by fc for the explained reasons.

Immediately one sees that arel goes to zero if v approaches the speed of light c. Secondly, any real mass subjected to continuous relative acceleration leaves its rest mass unaffected.

Force = m arel = m0 / (1 - v² / c²) * (ms c³ (1 - v²/c²)) / (fc h)  = constant

Or:   force = m0 * ms c³ / (fc h)  ;  force =  m0 * as .    With as the absolute acceleration and m0 the rest mass of the body.

Still GRT is violated, because one cannot explain the expression of the relative acceleration according to the principles upon which the general relativity theory is based. But it seems that according to the EPR-paradox one is in agreement with Heisenberg’s uncertainty principle.

Note: The force on a body subjected to relative quantum acceleration is always constant, even when it is moving with a speed c. So all relative mechanical systems experience this force as absolute in relation to their rest mass. It confirms why the scaling in the next section actually works, because the whole exercise began with the absolute quantum mechanical definition of the acceleration. More over in that exercise it is proven that rest mass is a feature of the mass of the vacuum quanta and Planck’s mass. See, The scaling laws of the equilibrium universe. 

In the early work of the pyramid model, the string resonance theory described the phenomena of the rest mass being a property of nullified energy of vacuum or empty space. The link from the phase space of time to our reality could never been made explicit, up till now.

  

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