· 6.4. Electrons and positrons ..................................................... 47 6.5. The...
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PRIME THEORY
Transcript of · 6.4. Electrons and positrons ..................................................... 47 6.5. The...
PRIME THEORY
Laurențiu Mihăescu
Prime Theory
All of nature's forces in a single theory!
www.1theory.com
Bucharest, Romania, 2015
Third edition English translation: Laurențiu Mihăescu Revision: Doina Lereanu Cover design: Laurențiu Mihăescu
Copyright © 2015 by Laurențiu Mihăescu. All rights reserved.
No part of this publication may be reproduced, distributed, or transmitted in any form or by any means, including photocopying, recording, or other electronic or mechanical methods, without the prior written permission of the author, except in the case of brief quotations embodied in critical reviews and certain other noncommercial uses permitted by copyright law.
Premius Publishing House, 2015 Website: www.premius.ro E-mail: [email protected]
CIP Description of the National Library of Romania MIHĂESCU, LAURENŢIU Prime Theory / Laurenţiu Mihăescu. - Bucureşti : Premius, 2014 Includes bibliographical references ISBN 978-606-93843-1-2
530.145
To the memory of my father
Contents
1. INTRODUCTION .................................................................... 11
2. SPACE ................................................................................... 14
2.1. Initial hypothesis ................................................................ 14
2.2. Characteristics .................................................................... 14
3. GRANULARITY ...................................................................... 18
3.1. Granular postulates ........................................................... 18
3.2. The granular fluid ............................................................... 20
3.3. Granular equivalence ......................................................... 21
3.4. Granular collisions .............................................................. 23
4. FUNDAMENTAL LAWS OF THE UNIVERSE ............................. 26
4.1. First law .............................................................................. 26
4.2. Second law ......................................................................... 26
4.3. Third law............................................................................. 27
5. GRAVITY ............................................................................... 29
5.1. Preamble ............................................................................ 29
5.2. The gravitational field ........................................................ 31
5.3. Conclusions ........................................................................ 35
6. ELEMENTARY PARTICLES ...................................................... 37
6.1. Explanations ....................................................................... 37
6.2. Mass .................................................................................. 40
6.3. Charge ............................................................................... 44
6.4. Electrons and positrons ..................................................... 47
6.5. The electric field ................................................................ 51
6.6. Quarks and the strong interaction .................................... 54
7. PROTONS AND NEUTRONS ................................................... 59
7.1. Internal structure ............................................................... 59
7.2. The weak interaction ......................................................... 61
8. PHOTONS ............................................................................. 66
8.1. Internal structure ............................................................... 66
8.2. Creation ............................................................................. 69
8.3. Features ............................................................................ 76
8.4. Pair production .................................................................. 81
9. THE MAGNETIC FIELD ........................................................... 84
10. TIME................................................................................... 88
11. GALAXIES ........................................................................... 92
11.1. Formation ........................................................................ 92
11.2. Black holes ....................................................................... 94
11.3. Dark matter and dark energy .......................................... 96
12. THE UNIVERSE ................................................................... 100
12.1. Extinction ....................................................................... 100
12.2. Rebirth ........................................................................... 101
13. STABILITY OF ELEMENTARY PARTICLES .............................. 104
13.1. Introduction ................................................................... 104
13.2. Special granular collisions .............................................. 106
13.3. Internal granular kinematics .......................................... 109
13.4. Size of elementary particles ........................................... 114
13.5. Irregular granular fluxes ................................................. 118
13.5.1. Photonic fluxes ........................................................ 118
13.5.2. Gluonic fluxes .......................................................... 120
13.5.3. Annihilation of elementary particles ....................... 121
13.6. The granular pressure ................................................ 122
14. GRANULAR INFORMATION ............................................... 128
14.1. Information features ...................................................... 128
14.2. A definition of information ............................................ 134
14.3. Destroying the information ........................................... 136
14.4. Information and black holes .......................................... 139
15. EPILOGUE ......................................................................... 141
APPENDIX 1 ............................................................................ 143
APPENDIX 2 ............................................................................ 147
APPENDIX 3 ............................................................................ 149
APPENDIX 4 ............................................................................ 150
APPENDIX 5 ............................................................................ 152
APPENDIX 6 ............................................................................ 154
APPENDIX 7 ............................................................................ 157
REFERENCES ........................................................................... 163
Prime Theory
1. INTRODUCTION
Why this theory?
• Because at this very moment, in 2015, we still do not have a unified and complete theory of the Universe.
• Because it is not reasonable to believe that interactions simply propagate through space and exert effects at a distance, without any kind of intermediary.
• Because actual physics does not offer coherent explanations or theories of mass, gravity, electric charge, fields and elementary particles.
• Because the Theory of Relativity (Einstein) alone cannot create the whole foundation of the physics domain.
• Because the modern Standard Model of particle physics is incomplete, very abstract and it does not explain some basic concepts and principles.
In our time, with all the large particle accelerators and the unprecedented evolution of science in general, a complete model of the reality we are facing is still not available. Complex theories are describing the phenomena, the fields and the interactions. Vast quantities of experimental data and scientific observations accumulate, but they still do not reach the critical level needed to make qualitative improvements in explaining the elementary notions used by these theories. However, no philosophical, mathematical or any other form of barrier can stop us from discovering everything, because our thinking powers, our sense, logic and technology are continuously growing and developing.
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This means we are evolving every day and will eventually overcome all potential obstacles.
Any experimental limitations, any principles or theorems denying our possibility to fully understand a closed system such as the Universe may be surpassed by human creativity and intelligence. Therefore, I optimistically and full of hope propose this statement as a general postulate in the Prime Theory's introductive words.
It was my passion for electronics and physics, arising in early school years, which led me to eventually become an electronic engineer. The experience acquired until now in this field, at first mostly practical, was reinforced by a logical and mathematical exercise in the field of information technology, which helped me gain an interdisciplinary vision of the surrounding reality.
The decision to dedicate time to this theory came from noticing the lack of concrete accents in modern physics, mostly in quantum mechanics and astrophysics, which through an excessive number of abstract theoretical models moved away from the objective meaning of things, at the largest and the smallest scale. Equally important was the lack of unanimously accepted theories on fundamental physical quantities, concepts and phenomena, such as gravity, mass or electric charge. A descriptive approach, causal and logical, without complex mathematical equations that may easily hide the significance of real phenomena was likely to shed more light upon these matters.
Conceived such as to comprehend and to integrate as much as possible of nature's essence and principles, the Prime Theory is entirely based on classical and relativistic mechanics, with some new laws and postulates added as a personal contribution. To
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keep it simple, intuitive and very accessible, all the statements are followed by graphic representations and geometric drawings.
This theory will explain in detail the granularity of space, the interactions of the elementary units of matter, and the rules that now could be considered as the fundamental principles of quantum mechanics. The new perspective helps not only to build a solid basis of all modern physics, but, more important, it allows us to see the true nature of reality.
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2. SPACE
2.1. Initial hypothesis
Space is the unique and fundamental element the Universe is made of. Matter represents a special form of space, where its elementary components are in a structured state. Mass, energy and time are physical quantities derived from some special features of the space components.
This hypothesis changes the paradigm of whole physics: the genesis, evolution and dynamics of space are the base for the formation, shaping, moving and transformation of all things in the Universe. All the quantities and constants of physics are thus determined only by space, through its parameters at a given moment. The emergence of space means the emergence of the Universe. For a detailed analysis, we may consider as a starting point some current cosmological theories (temporarily taken for granted as ideas), such as the Big Bang and the Cosmic Inflation.
2.2. Characteristics
A precise definition is needed at first to clarify the meaning of the word space within this theory. In Newtonian mechanics, space is considered a three-dimensional empty framework, homogeneous and isotropic, with a linear metric, continuous, uniform and infinite, where matter can move and transform, waves can propagate and fields can exert their actions. Space has in some way an absolute nature, as does its measurement unit, presumed invariant in relation to other physical quantities also considered as constant in time. In this frame, time flows linearly, at a constant rate, and a body may move through it at any speed.
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Experiments have proven, however, that this simplified view is not accurate. There is a maximum value for speed in our Universe: the speed of light in vacuum, and in any frame of reference it has to be considered a universal physical constant, as postulated by the Theory of Relativity. This fact, in addition to the invariance of the laws of physics under a shift of inertial reference frames, fundamentally changes the way space, time, matter and energy are to be described. These physical quantities are no longer constant and uniform; they depend upon the relative speed at which a frame of reference moves towards an observer and upon the presence of gravitational fields. As there is no absolute frame of reference, relativity and its consequences are the mandatory concepts we have to operate with when designing any physical theory of our world.
However, by changing the optic, we realize that ourselves, who are looking for explanations, we are in fact located inside the Universe we wish to describe and understand. This is why we do not exactly "see" everything that is going on, especially if we assume that our Universe is closed and finite. Thus, we are not able to relate to anything outside this system, and all physical quantities should be defined in a relative and limited manner, with localized, temporary values that may be assumed constant.
Let us propose a mental exercise, positioning us as observers outside the Universe, at the time it was born and just after that. With a maximum probability, by collating and partially validating some current theories, we would notice at this zero moment the existence of an immovable "singularity": an enormous concentration of primal matter, located in a space region of infinitesimal size, which comes out of the stable state of high-density and high internal cohesion by a huge explosion.
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This matter is in fact the raw material that will later form the current matter; moreover, it will represent, in our theory, the single ingredient space is made of.
The Big Bang explosion created all the components of space, and that was the initial point of the space expansion process (as a three-dimensional framework). Now it would make sense to introduce new physical concepts - like motion, time and energy.
The Prime Theory considers that space has a dual nature, namely:
• It is a three-dimensional framework, finite, linear, uniform, empty, created in the primordial explosion, and which is ever expanding; very likely, it has an almost perfect ball-shaped form.
• It is a pseudo-fluid made up of an infinite number of identical spatial "granules" that are continuously moving in all directions within the three-dimensional frame mentioned above; this fluid specific properties will be discussed in Chapter 3.
The explosion of the singularity occurred in a fraction of a second, during which the highly concentrated "raw material" exponentially increased in volume and divided into an extremely large number of infinitesimal elements called "granules". All the primordial energy the singularity had at the zero moment was transferred this way to the granules in the form of kinetic energy.
Our scenario presumes that the granules, by their motion, generated the three-dimensional space and they are continuously expanding it. Spatial expansion does not require any energy consumption, because it represents only a geometric expansion
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performed by granules through their impact with a perfect elastic medium. Looking from the outer frame proposed above, we could see that, in an absolute way, the expansion of the newly born Universe goes on at a very high speed, probably over the light speed in vacuum c. However, it is reasonable to assume that the expansion speed has a lower value than C, the speed referred to in the Granular Postulate #1, Section 3.1.
The granules formed following the explosion normally move in radial directions from the center; but very shortly after the blast, the reflected granules on the space borders have appeared, and hence the first inter-granular collisions started to happen.
During this process, due to expected irregularities in the distribution of granular density, the first aggregations of granules started to form, leading to the creation of the first elementary particles; they soon began to aggregate into composite particles and simple atoms, and finally created the matter as we know it.
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3. GRANULARITY
3.1. Granular postulates
In regard to this process of genesis, the spatial granules can be considered not only the smallest division of matter, but also the smallest form of elementary, pure energy. They represent not only the primary element space is made of, and thus the Universe in general, but they are also the key element of this theory. The fundamental properties of these granules are as follows:
a) As primary constitutive elements of space, they have the smallest size possible in the Universe. We may assimilate them with spheroids of diameter d, a value very likely under the Planck's length [3] (other dimensions for comparison may be found in Appendix 6).
b) All the granules are the same size; moreover, they are identical and equivalent.
c) They are mobile, moving in an absolutely straight line, at a constant speed. Their speed is the maximum speed possible in the Universe, and this determines a speed limit for the movement of particles and the propagation of waves.
d) All the granular collisions are perfectly elastic. There is no other kind of interaction between granules, and their shape, integrity and stability are maintained for an infinite time.
e) Two laws of conservation govern the granular collisions, namely the energy and the total momentum are conserved simultaneously.
f) At this scale, we cannot talk about mass, neither in a quantum nor in a macroscopic way.
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Fundamental granular postulate #1
All space granules are moving at speed C (faster than light), which is the maximum possible speed in the Universe.
Note 1: As all the grains are identical, this postulate involves that all the grains have the same value of impulse (a vector quantity, a special kind of momentum), denoted with p, and the same amount of kinetic energy, denoted with e (a scalar quantity). In fact, p and e are the primary quanta of impulse and energy, i.e. the smallest existing amounts of these fundamental physical quantities.
Note 2: This superluminal speed is measured by an observer from outside our Universe, in any direction; the straight line of granular motion is observed the same way.
Note 3: This maximum speed C is a fundamental constant of our Universe, determined only by the primordial amount of energy stored in the singularity.
Fundamental granular postulate #2
The total number of granules in the Universe is constant; it will be denoted with N.
Note: With regard to the cosmological hypothesis described above, it is reasonable to assume the conservation in time of the initial quantity of raw material; if we add that interactions between granules are perfectly elastic collisions, which do not change their shape or their number, we may normally assume the conservation of the total number of granules.
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3.2. The granular fluid
The granular fluid is the material component of space and it virtually determines all its properties. As described above, the granules move in all possible directions at maximum speed. We may extrapolate from this fact a number of essential characteristics of this particular fluid:
• Any free region of space is occupied by the granular fluid, until it reaches the average local density; this happens with the maximum speed of the granular movement, C.
• Different values of the local density of this fluid lead to spatial anisotropy; this will determine the speed and direction of the propagation of waves through space.
• The mean distance between two granules is much larger than their diameter; given the average spatial density, this leads to a certain non-zero value of the collision probability between two granules and to a quasi-null value for the simultaneous collision of three or more granules.
• In this fluid, where chaotic collisions between granules happen continuously, we may identify groups of granules moving simultaneously on the same direction. They form directional granular fluxes, which existed ever since the first moments of the Universe. In a given space region, all the directional fluxes passing through at a certain moment compose the local flux, simply designated further as flux.
Why a fluid?
Because it has a number of properties and characteristics that are common to macroscopic scale fluids, for example to a chemical element or a compound found in gaseous state:
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• It is made of identical components which are elastically colliding;
• It is possible to assign it some specific fluid parameters, such as pressure, density, entropy;
• It allows the longitudinal waves to propagate.
3.3. Granular equivalence
Let be two granules, A and B, of light and respectively dark color, as shown in Figure 1. They move in the plane X0Y on directions having the angle α and β to the OX axis, at a constant speed C. You may observe their position at moment t1, the perfectly elastic collision at t2 and their position at moment t3.
Figure 1 - Granular equivalence
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By applying the conservation laws for this type of collisions, we may see that granule B virtually takes over the impulse of A and continues its trajectory, and vice versa. From the point of view of trajectories, the granules A and B are therefore equivalent, and we may even infer from this a fundamental principle of the granular fluid mechanics:
Directional granular fluxes maintain their absolute straight direction of propagation.
Moreover, we may calculate the average speed v� of directional granular fluxes. Figure 2 shows a granule A entering into a spatial region of cubical form with side length L, and the equivalent granule B exiting after several collisions occurred inside the cube.
Figure 2 - Granular speed
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This cube contains N3 granules, and P is the probability of collision on the traveling direction. We must also consider the non-zero duration t of the collision process.
After a simple calculation, the average speed of a granule is:
v� = C / (1 + C P N t / L)
We observe that the average speed is always lower than C and that it depends on the "linear density" of the granules, N / L; this allows us to infer another principle:
The speed of the directional fluxes depends only on the local average granular density.
3.4. Granular collisions
If we will analyze in detail the inter-granular collisions, considering the non-zero diameter of a granule, we will see a deviation in the equivalent granule's trajectory. This deviation has a zero minimum value and a maximum value equal to the diameter of a granule d, and it depends on the angle made by the trajectories of these two granules.
For a granule that passes through a region of space with equal directional fluxes, this average deviation becomes null. Figure 3 illustrates the collision of the granules A and B, moving in the same plane X0Y, on orthogonal directions.
The distance between the two horizontal lines Δy represents the trajectory deviation of the equivalent granule, in this case equal with the value d / √ 2 .
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Figure 3 - Granular collision
If we assume that there is a more intense directional flux Ф, vertically (upwards) oriented, constant over time, the equivalent granule resulting from A after several collisions will have a uniform motion downwards along the axis 0Y, which will be added to its initial movement. The velocity vector of the equivalent granule will therefore have an inclination toward the bigger flux, proportional to its intensity.
In other words, a granule is "attracted" to the source of the more intense directional flux, as shown in Figure 4. On exiting the area with increased flux, granules resume their movement in the initial direction.
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Figure 4 - Granular paths in areas with intense flux
Observation:
In areas with a bigger directional flux, a granule increases its speed only seemingly, because its movement is taken in a continuous manner by other, equivalent granules. Its "falling" speed is determined by the diameter of granules, by the intensity of the uniform flux and by the width of that area.
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4. FUNDAMENTAL LAWS OF THE UNIVERSE
All data described in the previous chapters lead us to a set of three fundamental laws governing our Universe, at any scale, i.e. from the granular level up to galactic proportions:
4.1. First law
Any distinct and quantifiable physical entity (waves, particles, fields, energy, and mass) is an organized structure of spatial granules.
Here it should be pointed out that these special structures are lying in the granular fluid of space; they keep their structural organization due to the special properties of this fluid (Chapter 3).
4.2. Second law
The total impulse vector of all granules in the Universe is quasi-null.
Mathematically, this law may be put into a formula:
∑ p�i = 0
which also means that in a closed universe, the total granular impulse is conserved in time.
Any irregularity in the shape of singularity or of the granular reflections during the expansion can change the total impulse value of zero, but we may assume that this bias is very limited. If all reflections at the edge of the Universe occur on a perfect sphere, any non-zero value will be preserved in time and will "dilute" in the increasing volume of the Universe. As the spatial granules transfer the impulses to each other during perfectly
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elastic collisions, their total impulse would remain unchanged in time. This phenomenon may be customized, theoretically, for any granular system located in determined regions of space, with a constant local flux. However, a precise localization at the granular scale is only virtually possible; here we are way beyond the quantum mechanics' uncertainty. As a matter of fact, we cannot think about any localization. At this level, the information itself is completely disseminated, thus it no longer makes any sense and even disappears as notion.
4.3. Third law
The total energy of the granules in the Universe is constant over time.
E = N e = constant
Any existing amount of energy or the exchanged amount between physical entities is a sum of elementary granular energies. The structuring that granules may have is in fact a grouping and a redirection of these minimal kinetic energies; a granular structure may have a temporary energy equal to the sum of these energy quanta, and may transfer it to other structures through the exchange of impulses between the colliding granules. This granular mechanics automatically determines the relative character of the kinetic energy a structure may have; the value of this type of energy will depend on the relative speed of the structure to an observer located in a reference frame.
Note 1: These laws of physics are valid ever since the zero moment of the Universe, just after the explosion. They have a postulate character because the orders of magnitude involved
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make practically impossible any scientific experiment designed to verify them.
Note 2: Due to their elementary and absolute character, the granular energy and impulse are special physical quantities, different from the macroscopic ones bearing the same names.
Note 3: These three laws do not apply to singularities, because their granules are in a different state, being in fact "glued" together.
Note 4: The last two laws are valid inside the Universe, but only if related to the external, fixed system of reference.
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5. GRAVITY
5.1. Preamble
If we are looking at the description of the granular fluid from the Chapter 3, we realize that space, at any scale, is crossed by directional fluxes of granules in a continuous manner. This phenomenon began at the zero moment of the Universe and it is an integral part of its structure. At global level and as a direct result of the Second law (Section 4.2), the Universe must have a symmetrical distribution of directional fluxes toward the center. Let be a section through the Universe - Figure 5 - where the visible area is drawn in light gray and S is a flat surface with two fluxes passing through it, perpendicular to its plane.
Figure 5 - Granular flux intensity
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There are figured both incident fluxes, φ1 heading to the right and φ2 to the left. The intensity of a directional flux is given by the number of granules that passes through a given area in the unit of time. From the total number of granules existing in the gray cylinder (obtained by projecting area S at the edges), a constant fraction composes each flux on its direction.
Flux φ1, for example, will be directly proportional to the average density of granules in the Universe and to the length (volume) of the cylindrical zone it is coming from:
φ1 = φ0 + k N L1 / V and φ2 = φ0 + k N L2 / V
V is the volume of Universe, φ0 the initial flux value, k a constant.
Figure 6 - Distribution of granular fluxes in the Universe
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By applying these formulas to a spherical body that is hypothetically placed in different regions of the Universe, we get a distribution of the intensity of incident fluxes as shown in Figure 6. It is to be noted that in the middle area, there is a balanced distribution of directional fluxes, but if the body is closer to the edges, the outward facing flux becomes dominant. The red vectors (the thicker arrows) show the direction of the resultant fluxes for each position.
A simple integral calculus shows that the resulting flux to a point situated at a distance r from the center has this formula:
φ = 2 r k N / V
Therefore, it is directly proportional to the distance r from the center and inversely proportional to the total volume V. Yet the real formula might differ from a linear variation because the diffraction on the Universe's edges was not considered here and the rate of space expansion is not exactly known.
5.2. The gravitational field
The ensemble of the directional fluxes incident on a body is called gravitational field.
The fluxes interact with a body through the collisions between the incident granules and the particles composing the body, especially the collisions with its atomic nuclei. There is a continuous transfer of impulse from the flux towards the body, which leads to the occurrence of a pressing force in the flux direction; this interaction will be detailed in the Elementary particles chapter. It should be noted that from the fluxes incident on a body, some go through it (depending on the density of the
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matter of which it is composed) and others are reflected in multiple directions (the reflected fluxes are diffuse).
The body is thus subjected to pressing forces exerted from all directions, whose direct effect is its compression until a state of equilibrium with the opposite internal forces is reached. However, if a single body would exist in the entire Universe, placed in an off-center position, the only force that would act on it, as a whole, would be the resultant of local fluxes. Thus, the body would be pushed toward the edges of the Universe by a force F (red arrows in Figure 6), that grows bigger near the edges (the formula from Section 5.1, due to the gradient of the resulting flux).
The most interesting case is that of two or more bodies placed in a "cosmic" neighborhood. They would be subject to the combined action of the force described above and of the gravitational "attraction" force described below. What this new force does is, in fact, to "push" a body towards the other one, due to the action of the omnidirectional fluxes. The incident fluxes are partially blocked by the presence of these two bodies (Figure 7, the light gray area). Presuming that the size of these bodies is generally small compared to the distance between them, it results that the solid angles that include the diminished fluxes will be small too.
Let us consider two cosmic bodies C1 and C 2, of diameters D1 and D2, with a distance L between them. The black arrows represent the local flows, whose resultant generates the forces of "attraction" F, which shall be exerted onto both bodies, along the axis connecting them. We will consider equal local fluxes in the region of the two bodies, of value φ, and equal opacity to the passage of fluxes through them.
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A simplified calculation, with the bodies considered discs and having D1 << L and D2 << L, leads to the formula (k a constant):
Figure 7 - The attraction between two bodies
F = k φ D12 D22 / L2
which, at this level, is in full accordance with the Law of universal gravitation (Newton).
Therefore, under the action of the two types of forces above (determined by the flow gradient and mutual shadowing), two cosmic bodies "attract" each other if they are close enough and they are "pushed away" if they are placed at long distances. If we analyze the size of the largest galaxies, we may estimate the
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threshold value where this force changes its direction, i.e. around 100,000 light-years.
Note 1. In this context, the inflation theory should be changed too; the space is continuously expanding, but not by a uniform increase in itself. Space, as a geometric frame, increases only by adding more volume to the edges of the Universe. The galaxies are receding from one another, and this is due to the flux gradient described above, and not to the space inflation. In the same way, the redshift of photons emanated by distant star clusters (billions year ago) is essentially due to these three causes:
• The Doppler effect, because the galaxies (most of them), and therefore the stars which emit photons, are moving away from us.
• The decrease of the average granular density of space with its expansion, which leads to a gradually increasing speed of photons in the intergalactic vacuum (their wavelength increases too).
• The gravitational effect, due to the variation in the intensity distribution of granular fluxes near massive bodies.
Note 2. The existence of the attraction and repulsion forces at cosmic level is consistent with astronomical observations carried out on galaxies, which found that galaxies are receding from Earth at a speed approximately proportional to their distance (Hubble law). During a very large time interval, after the first stars were grouped through the force of "attraction", the galaxies created this way begin to repel due to the force of "repulsion", which becomes dominant at long distances. Nevertheless, this phenomenon is more complex, and it cannot be described by a mere linear equation; it happens simultaneously with the expansion of the Universe (i.e. the space), which reduces the
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average granular density and therefore the intensity of the directional fluxes.
In a global manner, at this point in time all the galaxies are receding with non-zero accelerations, whose values increase with the distance from the virtual center of the Universe, but decrease over time.
5.3. Conclusions
The gravitational field, as described above, interacts with ordinary matter, i.e. the one made up of atoms and molecules. Granular fluxes collide with all the elementary particles (electrons, nucleons, etc.) to which they continuously transfer a directional impulse, and this phenomenon is equivalent to applying a force in the direction determined by the resultant local flux. The magnitude of this force is given by the intensity of the resulting flux and the area of the surface on which it is reflected. While predicting data about this phenomenon (that will be described in detail in the next chapter, Elementary particles), we need to mention that the area of particles is directly proportional to their inertial mass.
From this we may draw several important conclusions:
a) The inertial mass is identical with the so-called gravitational mass, both physically and numerically.
b) The gravitational force acts the same upon all the particles, and hence upon the atoms and the molecules they form. This force "pushes" evenly on the matter of a body (its magnitude is proportional to the body's density) until equilibrates the internal forces of electromagnetic nature.
c) At the atomic scale, the gravitational force has a value with
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many orders of magnitude below the intensity of other forces. If we lower the scale to the atomic nucleus and its components, this force significantly increases and even equals other resultant forces active at this level.
d) The mechanical work done by the gravitational force within an atom is zero, as well as the one produced in a system of atoms (for example, the movement of electrons in closed orbits in this constant field does not produce and consume energy). As a result, the presence of this constant force at the atomic scale cannot increase the temperature of matter, cannot disintegrate or transform it; the matter is only compressed until it reaches a steady state. In the case of big celestial bodies such as planets or moons, gravitation may indirectly cause heating due to the tidal forces. In the case of stars, which have a much higher mass, the internal pressure exerted by gravitational forces increases their density and raises the temperature until nuclear fusion reactions are ignited.
At the bigger scale of the Universe, the directional fluxes and those resulting in a certain point are distributed as shown in Figure 6. Their intensity, as well as the average granular density, is not constant over time; these values are continuously decreasing with the space expansion.
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6. ELEMENTARY PARTICLES
According to the fundamental First law (Section 4.1) stated above, an elementary particle is an organized, minimal structure of spatial granules that can freely move through the granular fluid of space. In the model we will use further, a particle has these defining characteristics:
a) An elementary particle has a determined three-dimensional geometrical shape that is stable over time.
b) The particle interacts with the surrounding granular fluid; however, this does not affect its geometrical shape.
c) A free particle remains at rest or it moves with a constant velocity (its value being under the speed of light c).
d) A particle has, during its whole life cycle, a constant granular density of the maximum possible value.
e) Any particle has a non-zero mass, which is defined as being a measure of its inertia.
6.1. Explanations
As postulated in Chapter 3, the grains are moving with the absolute, superluminal velocity C. Therefore, any granular structure, and hence the particles, must preserve this fundamental granular property; at the same time, the structure as a whole may have any subluminal velocity, in any direction. These two aspects may come together only in a construction like the one in Figure 8, which shows a section through an elementary particle with a hypothetical spherical shape, placed in a space region crossed by the uniform directional flux φ.
The granules inside the particle, regardless of their position, move with the maximum speed C on circular trajectories that
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form the alpha angle to the particle's movement direction (velocity vector v - the red arrow).
The particle always has a non-zero speed, therefore the α angle will also have a non-zero value. This difference between the angular velocity of a particle (seen as a solid object) and the direction of its movement will cause a permanent precession to all the particles. It may be also noted that not all the granules from inside of a particle have the same angular speed, because they are rotating at constant speed on circular trajectories of different radius values.
The granular layers of a particle are spinning at different angular speeds, therefore they rotate differentially. The trajectory of a free granule is perfectly straight, but we may take for granted that a granule from an internal layer of a particle, due to its collisions with the nearby granules, will actually have a curved path at all times. This thing must be corroborated with the continuous granular collisions between the external layer of a particle and the local fluxes, and thus it leads to the following explanations of the movement and of the structural stability that characterize any particle:
a) The stability and structural integrity of an elementary particle are provided and assured by the permanent impulse transfers that occur during collisions between the granules belonging to incident local fluxes and the granules from the outer layers of the particle. This external "pressure", which is continuously exerted, ensures the equilibrium and the internal cohesion of any particle; at the same time, it determines a maximum possible density for the internal granules, as they are all practically "glued" together.
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b) The incident fluxes on the particle's surface transfer impulses to the granules of the outer layer and then return, under normal conditions, with the same intensity. Due to its high internal density, a particle acts in fact as a "solid" body, which reflects the incident granules; this phenomenon will comply with the general laws of reflection. If the particle is moving at relativistic speed, these granules will have a relativistic reflection. In both cases, each granule of these fluxes transfers an equal, evenly distributed impulse, whose value does not depend on the particle's speed.
c) Therefore, any particle receives from the local fluxes a resulting null impulse; if these fluxes remain constant, the particle will keep moving at a constant speed v, on a straight trajectory, along with the precession motion described above. If the intensity of incident fluxes varies on a certain direction, the particle will be accelerated or decelerated. The effect produced on the particle's surface averages during larger time intervals, when the particle rotates several times and exposes all its sides on the different flux's direction; thus, its shape and its structural integrity are not affected.
d) From the laboratory frame of reference we may see that the granules located inside a particle are moving at speed C on a helical path, and the particle, seen as a whole, describes the same type of trajectory, having a pitch proportional with its linear speed v.
e) The change of the particle's uniform motion is due to the action of a directional flux, whose final effect is the increase or decrease of the particle's kinetic energy.
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Figure 8 - The internal granular impulses of a particle
6.2. Mass
Be a particle moving at constant speed v1 (Figure 9), observed from an inertial frame of reference. At the moment t1 an additional flux φ' starts to flow, constantly, in a certain direction and for a certain amount of time. Each collision between its grains and the particle's surface will transfer a new impulse to the particle. The sum of all these impulses constitutes a total impulse transferred to the particle, in that direction, and this is a phenomenon completely equivalent to the action of a force F "pushing" the particle during the same period of time. Naturally, at the other moment, t2, when the flux φ' stops, this particle will have a speed v2 higher than v1 (a bigger linear momentum). As the transferred impulse does not depend on the particle's speed,
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we can assume that as long as the additional flux exists, the particle has been accelerated by a force F having a constant value.
In nonrelativistic conditions, the particle will therefore have a uniformly accelerated motion, whose equation is given by the fundamental law of motion F = m a (Newton), where a is the acceleration and m is the mass. The particle's mass, as in the case of macroscopic bodies, shows the inertia (the amount of resistance) of the particle while changing its state of motion. Where does this inertia come from? If we take a look inside the particle at the moment t2, we may see that the plane in which the granules rotate makes a different angle with the particle's movement direction, α2. This is because granules keep moving with their absolute speed, but they adjust the orientation of their velocity (impulse) vector in order to compensate for the increased speed of the structure they belong. In other words, the global impulse transferred to the particle by the additional flux will change the direction of the impulse vector for all the constitutive granules. By analyzing these data, we may see that the inertia is directly proportional to the total number of granules a particle contains, which all changed their impulse direction when the particle changed its speed.
Mass is, in fact, a measure of the total impulse needed by a particle to adapt all its internal granular impulses to the global speed change.
As the particle has symmetrical shape, we may conclude that:
The absolute rest mass of a particle is a scalar physical quantity that only depends on the number of its constitutive granules.
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Figure 9 - Variation of the particle's granular impulses
The compaction of the particle's inner layers is the highest possible one. Therefore, its granular density (the number of grains per volume unit, ρ) will have a constant value; thus, its absolute rest mass will be directly proportional to its volume (k is a constant):
m00 = k N = k ρ V
In the closed system consisting of the new flux and a particle, seen from an inertial frame of reference, the total energy is conserved. The incident flux, through the impulse it transfers to the particle, generates the conservative force F, which performs a mechanical work on the distance between particle's positions at moment t1 and t2. This mechanical work shall be equal to the
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increment in the particle's kinetic energy; the speed increase is bigger if the particle's mass is smaller. We may infer from this statement that the minimum energy of a particle is reached when it stays at rest, and if using the mass–energy equivalence (Einstein) we get the formula:
E00 = m00 c2
and the energy of a particle moving with the absolute velocity v (relative to the fixed frame of reference) will be:
E = m00 c2 �1 / (1 - v2/c2)
In a relativistic case, the particle's mass increases with the velocity value, but its number of granules remains constant; this is happening because the amount of energy required to change the direction of impulses to all granules is now higher. Close to the speed limit c, the average angle between the impulse vectors and the direction of the particle movement gets a maximum value; although the speed of granules is C (C > c), this value cannot be reached by the particle as a whole due to the granular collisions described in Section 3.4. If we look at the dynamics of these things, we will see that the absolute rest mass is given by the number of granules a structure has, but the constant k is finally determined by the magnitude of the granular impulse quantum (the elementary and universal impulse value, the minimum amount of momentum that can be transferred through the inter-granular interactions).
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6.3. Charge
Considering the explanations given in Section 6.1, the proposed model of elementary particles uniquely connects the charge feature to their geometric shape. A free particle, with a non-zero charge, has a disc shape, with a diameter much larger than its thickness (estimated ratio of at least 100). This uniform disc shape, which is perfectly symmetric to the central plane, is among those special shapes allowing the particle's structural stability for a sufficiently long time. Figure 10 shows a generic elementary particle with a half-integer spin (the angular momentum) and the average angular speed ω, and the trajectory it follows moving in a horizontal direction at the constant speed v. We may also see the particle's real rotation, the precession and the global rectilinear movement it actually describes.
Figure 10 - The geometrical shape and the trajectory of a particle
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A closer look to this complex motion can be found in Appendix 1. In the middle of the disc, there is an empty space of cylindrical shape, with a very small diameter, which does not have a significant effect on the particle's dynamics and it will no longer be graphically displayed. In addition, the particle edges have in fact a round shape, thus all the sections through them are arcs of circles. The lateral surfaces of the disc are not plain, and this allows a definition for the charge:
The charge of an elementary disc-shaped particle is the measure of the concavity/convexity of its sides. Due to the symmetry of the shape, the amount and the type of charge are identical on both sides of the disc.
The charge is an additive quantity; therefore, the total charge of a particle is equal to twice the charge of a side. We establish as a convention that:
The positive charge will be the attribute of the convex discs, and the negative charge the attribute of the concave ones.
In the next graphical representations, all the particles with a negative charge will be drawn in blue color and the positive ones in red. The local fluxes, when reflecting on this type of surfaces, follow the rules described in Chapter 3; they will converge or diverge and will thus create a gradient of the resulting flux and a variation in the average granular density near the particle. Therefore, the charged particles will create "fields" in their vicinity, that will exert either attraction or repulsion forces between them.
The side surface of a charged particle has a round shape, which in geometry is called a spherical dome (cap). The
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magnitude of the charge, intuitively speaking, is the degree to which the incident fluxes are dispersed or concentrated, thus it will be directly proportional to the reflecting area of the particle and inversely proportional to the radius of the sphere that includes this area. Numerically, the charge Q of a particle side is:
Q = k A / R
where A is the area of the spherical cap and R the sphere radius, k a constant, as shown in Figure 11. By applying the formula of the cap area, it shows:
Q = 2 π k h
where h is the height of the spherical dome. We can see that the magnitude of the particle charge, which we will name electric charge, depends only on the height of the spherical dome. The volume V of the spherical cap is:
V = π h (3 r2 + h2) / 6
where r is the radius of the spherical dome.
Considering the value h (thickness) as being constant for different particles, and h << r, we notice that the volume of a charged particle is proportional to the square of its radius; therefore, the rest mass of a charged particle will have the same dependency. The volume of the circumscribed disc of the spherical dome, excluding the cap, is:
V = π h (3 r2 - h2) / 6
being approximately equal to the cap's volume for h << r.
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Figure 11 - The charge of the electron and of the positron
6.4. Electrons and positrons
The electron, which has a negative charge unit (-1) and its antiparticle - the positron, with a positive charge unit (+1), are the smallest charged particles; they both have the same mass and the same half-integer spin. The particles with the same sign repel each other, while particles with opposite signs attract one another. The mechanisms of these actions are shown in Figures 12, 13 and 14. As mentioned above, electrons are blue and positrons are red; for more clarity, they are figured with a stylized shape and a bigger thickness h. In addition, we will further assume that the distances between these particles are much bigger than their diameter.
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Figure 12 - The repulsive force between two electrons
All trajectories of the equivalent granules in local fluxes (represented in gray) are influenced by the charged particles, as described in Section 3.4. These paths are curved because the fluxes created by the particles are not constant; their intensity changes with distance (it will be shown in Section 6.5). The electrons will slightly "attract" the granules, while the positrons will "repel" them in the same measure.
The figures below show three granules coming from the top and right side of the frame, but those coming from below or from the left will have similar, symmetrical trajectories. Two electrons, represented in Figure 12, will repel each other due to the reflection and the concentration of local granular fluxes on the distance between them.
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Figure 13 - The repulsive force between two positrons
A similar mechanism works between two positrons, as in Figure 13, where the granular fluxes are reflected and thus they become more intense. In the case of not charged particles, or of those with no net electric charge, the granules are not significantly deflected or their deviations are compensated, therefore the local fluxes will exert a total null force on this type of particles. Figure 14 shows the mechanism by which the force of attraction appears between particles with opposite signs. Many equivalent granules, deflected by the positive particle, bounce back and then are trapped in the attraction of the negative particle, bumping it from behind. At the same time, they no longer contribute to equilibrate the fluxes around the positron, which is equivalent to a "push" toward the electron.
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Figure 14 - The attractive force between electrons and positrons
It should be noted that the granular deflection around the charged particles is not uniform, and this is due to the following simple reasons:
a) The particles, being in a free state, describe the circular motion shown in Figure 10.
b) Their shape determines a more intense phenomenon on axial directions.
c) The divergent or convergent fluxes decrease in intensity with distance.
d) Each particle moves with a certain global velocity.
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This way the forces acting between two particles with the same sign will create a torque, which perpendicularly aligns their angular momenta, as average direction. This leads to the important quantum mechanical principle of exclusion (Pauli exclusion principle), which states that two identical fermions cannot occupy the same quantum state simultaneously (considering the quantum state as the direction of the angular momentum). It explains at quantum level the inner structure of the atoms (electron shells), the volume they occupy, and their stability in time, as well as the wide variety of chemical elements and their combinations.
6.5. The electric field
The ensemble of converging or diverging granular fluxes, created by electrically charged particles in the surrounding space is called electric field.
The electric field is a vector field, with the direction given by the resulting flux's direction and the sign of the electric charge, and whose magnitude is given by the intensity of the flux passing through a surface perpendicular to its direction. The divergent or convergent fluxes, having conical shapes, increase or decrease their section area with the distance from the source.
It follows that the intensity of the divergent flux created by a charged particle, flowing through a constant section, will diminish with distance, and therefore the electric field will vary the same way with distance.
Figure 15 shows a section through a positively charged particle and the variation of the divergent flux reflected through a circular area, on the axial direction.
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Figure 15 - The electric field of positrons
As shown in Section 6.3, the charge Q is a measure of the divergence of the flux reflected by a particle; the intensity of this divergent flux, defined as the number of particles passing through a surface perpendicular to its direction in the unit of time, has a maximum value at the particle's edge. If we analyze only the horizontal fluxes, flowing perpendicularly to the particle's plane, we may see that only a part of the reflected fluxes gets through the observational section S - a part that gets smaller as the distance d to the particle gets bigger.
The radius R of a virtual surface located at the same distance, through which the entire reflected flux passes across, will be proportional to the distance d. Thus, we may write that flux E,
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which passes through the surface S, is only a fraction of the reflected flux, equal to the areas ratio:
E = k Q S / (π R2) = k2 Q r2 / R2 = k3 Q r2 / d2
where k, k2, k3 are constant values. This is a similar relation to the formula of the electric field derived from Coulomb's law. If we also take into account the continuous precession motion, we will have around a charged particle (considered as a point) a constant electric field, with an average value given by this relation, which leads to the validation of all known equations of the electric field (Maxwell). Figure 16 shows a particle with negative charge and the variation of the convergent flux it reflects through a circular area, on the axial direction.
Figure 16 - The electric field of electrons
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Area S is crossed, as in the case of the positive particle, by a concentrated flux that decreases in intensity with the distance d to the particle. In other words, the "focused" part of the total reflected flux decreases with distance because a fraction of the flux becomes divergent. The conclusion drawn for negative particles is the same: the concentrated flux, i.e. the electric field, decreases with distance following the same rule as the reflected fluxes of the positive particles.
6.6. Quarks and the strong interaction
Quarks are elementary particles similar to electrons and positrons, with the same half-integer spin, but with a higher mass (and therefore a higher volume). In this model, all the quarks will have the same unitary electric charge, i.e. they have the same thickness h as the electrons, as shown in Section 6.3.
They are stable particles that are only found in composite systems (hadrons), formed by two quarks (mesons) or three quarks (baryons). The Standard Model of particle physics describes six types (flavors) of quarks (and their antiquarks), but we will only analyze the UP and DOWN quarks, included in the composite particles of the atomic nuclei.
The quarks are confined into hadrons by a fundamental force called the strong interaction. Figure 17 shows the U and D quarks (and their antiquarks), along with an electron and a positron.
Quarks were created at the early stages of the Universe, when the granular density was very high. They have rapidly combined in nucleons (baryons) which formed the first atoms, and the strong interaction between them was not significantly dependent on the granular density of space.
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Figure 17 - The electron, quarks U, D and their antiparticles
The quark mass, larger than the one of the electrons, prevented the quark-antiquark pairs to accelerate enough before the creation of the field of strong interaction; therefore, they could not annihilate each other but remained bonded in steady structures. Figure 18 shows a generic meson Rho (a composite, unstable particle) and the connection formed between the two constitutive quarks.
Which exactly is the mechanism generating the strong interaction? In the first place, it should be mentioned that the scale at which this force operates is very small, i.e. the distance between the two quarks is approximately equal to their diameter, as shown in Figure 18.
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Figure 18 - The internal structure of a meson
Being so close, the particles are mutually blocking the granular fluxes coming on axial directions. This asymmetry of the local fluxes creates a force that "pushes" the particles toward each other. At the same time, external granular fluxes enter the space between particles and they are repeatedly reflected on the particle's inner surfaces. This creates a cylindrical region (the gray area) where the granular density is much greater than the average local one. The very intense fluxes in this region constitute the gluonic field; through their granular collisions on the surfaces of particles, they generate a "repelling" force, which is called the strong force. It equilibrates the pushing force above, and, as manifestation of the gluonic field, it provides an apparent stability to this composite system. The fluxes within the gluonic field are
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not uniformly distributed; the biggest density is in the axial area (dark gray), but there is also a convergence toward the negative particle. With its very high density, the granular structure called gluonic field adds a significant mass to the meson; in fact, almost the entire mass of the meson is given by this field.
Each quark composing a meson has the spin value 1/2; they both can have this vector (the angular moment) aligned, one parallel with the other, resulting a zero total moment for the entire meson, or misaligned, when the meson will rotate, and it will have the global spin of value 1.
Any asymmetrical force applied to only one quark, or a small perturbation of the gluonic field will lead to the loss of the composite structure's symmetry, so the meson will quickly become unstable and it will eventually disintegrate (decaying into a pair of pi mesons). The gluonic field generates, due to its gradient, an uneven distribution of forces on the quark surfaces; the negative quark is "pressed" harder to its center, and the positive one to its edges. This may result in an additional curvature of the quark discs, adding a color component to their electric charge.
The charge on the quark's external sides, even if it may have different colors (color and anti-color), remains unchanged, the total value being zero. The gluons, i.e. the bosons of the Standard Model of particle physics, which intermediate the strong interaction and carry the color, can be assimilated with compact, tubular-shaped granular structures of the gluonic field.
Globally, the force F12, which attracts the two quarks, is composed of the force determined by the pressure of the local fluxes and the force of the electric field. It equilibrates with F3,
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the force generated by the gluonic field. Appendix 2 describes the equations of these forces and how their resultant, force F, leads to a zone of stability for the distance between quarks, which eventually makes the whole ensemble to behave elastically.
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7. PROTONS AND NEUTRONS
7.1. Internal structure
The proton is composed of two up quarks and one down quark, placed as shown in Figure 19, and bound together by the strong interaction. This composite particle has the global charge +1, a half-integer spin and it is perfectly stable (either as a nucleon or as a free particle). Its charge can no longer be considered as a point; due to the presence in its structure of the different polarities and due to its global spin, we may assume that the geometrical distribution of the charge (a dipole in section) is balanced out in time to a uniform distribution, with an approximately spherical shape.
Figure 19 - The internal structure of a proton
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Figure 20 - The internal structure of a neutron
The aligned spins of the three quarks and the global mass distribution (with the greater density at the center) determines the stability of this composite particle. In the complex dynamics of the gluonic field, different color charges may be added to the quarks, but the global electric charge of the proton is conserved.
The neutron is composed of two down quarks and one up quark, placed as shown in Figure 20, and bound together by the strong interaction. This composite particle has a null global charge, a half-integer spin and it is stable as a nucleon and unstable as a free particle. Its charge, which should be equal to -1 (the sum of the charges on the external surfaces of the down quarks), is in fact zero due to the additional color charge produced by the strong interaction. The external surfaces of the
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two quarks will have both positive and negative charges, which will cancel each other; in Figure 20 the d quarks are represented having normal external surfaces.
The particle in free state is unstable as the two quarks with greater mass are placed on the outside, as well as the higher density regions of the gluonic field.
The strong interaction, through the forces described in Appendix 2, is also responsible for the atomic nucleus stability. Protons and neutrons (stable as nucleons) are held together in balance by this interaction, which acts on larger distances the same way as it does between the quarks of a nucleon.
7.2. The weak interaction
If higher energy is involved or if a perturbation exerts a force beyond a certain value, the quarks inside a nucleon may come very close to each other, concentrating the gluonic field on a small area and thus increasing its intensity. This region of high granular density, located for a short time in the inter-quark zone, and which can lead to quark transformation into other particles, generates the weak interaction.
In the Standard Model of particle physics, this force is carried out by the W+, W- and Z bosons. As shown above, the neutron is a composite particle, unstable when it is free; it decays, due to this type of interaction, into a proton, and emits an electron and a neutrino (an electron antineutrino in fact). One of the down quarks of the neutron interacts with the adjacent gluonic field and thus it generates an up quark and an electron, in a process that preserves the global charge.
n (ddu) -> p++ e- + ν�e
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Figures 21, 22 and 23 show two-dimensional geometric representations of the decaying process (beta decay), where neither particles nor the distances between them are drawn to scale. The very dense granular flux "presses" one of the down quarks and deforms it, so its peripheral zone will come off and the remaining part will self-adjust to the shape and mass of an electron. In this process, the ellipsoidal region with dense flux will be compressed, its density will increase and it will finally turn into an up quark. This quark will be repelled, but it will be shortly attracted by the other down quark (of the former neutron), and thus it will be included in the new proton structure.
Figure 21 - Initiation of the gluonic field concentration
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Figure 22 - Separation and creation of the new particles
The remaining part of the down quark on the left, meaning the peripheral zone, will shrink itself; it will become a neutrino particle with a toroidal form, electrically neutral, which has a very small mass. The null external charge of the left quark was conserved because the internal charge has been transferred to the electron and to the new up quark (-1 and +1).
During this interaction, the outer part of the gluonic field will generate another granular toroidal structure, similar to the one that remained from the down quark. This is congruent with the new theories of neutrino particles, which assume a non-zero mass and an oscillation between the three known types (flavors): electron, muon and tau.
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Figure 23 - Proton creation, electron and neutrino emission
These two structures composing a neutrino particle (Figure 24), each with half-integer spin, perform rotation and precession movements at different frequencies (dephased) due to the difference of their diameters and masses. These not synchronized internal motions of the neutrino particles could be a reasonable explanation for the experimental observations showing their type changes. In addition, the shape and mass of these two components could explain the helicity of the neutrino particle and of its antiparticle.
Thus, the fact that neutrino's spin is antiparallel to its velocity vector while the antineutrino's spin is parallel to its velocity may be linked to the masses of their toroidal components:
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• If the torus with a smaller diameter has a greater mass, it will rotate slower than the one with a larger diameter and the neutrino particle, as a whole, will have an antiparallel spin;
• If the torus with a smaller diameter has a smaller mass, it will rotate faster than the one with a larger diameter and the neutrino particle, as a whole, will have a parallel spin.
The neutrino particle is stable because its two components are very close, and there is a small force of gravity (due to the mutual shadowing of the local granular fluxes), greater when they are perfectly aligned. Very small mass, very small diameter and no electrical charge are the causes of a minimum interaction between neutrino and ordinary matter.
Figure 24 - A neutrino particle
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8. PHOTONS
8.1. Internal structure
The photon is a fixed structure of a granular directional flux, with a special distribution of the granular density in a certain space extent, which rectilinearly propagates on a certain direction at the constant speed of light c.
This important feature, namely its propagation on an absolute straight line, only occurs in the ideal conditions of a uniform spatial flux, as described in Section 3.2. If a photon enters a region of different density, a "refraction" process will occur, i.e. a change of direction, because the distribution of its component granules (considered rigid in section) determines different moments of time when the granules change their speed. If seen from its local frame of reference, the photon looks like a fixed spatial distribution of granules, in a region with an almost cylindrical shape, with a quasi-constant cross-section area. Analyzing a longitudinal section through that cylinder, we may observe that there is a modulation of the granular distribution, in both density and shape. From another frame of reference, a propagating photon may be seen as a "wave" consisting of two intensity oscillations of the directional granular flux.
To generate the granular structure of a photon, a certain amount of energy has to be used; more energy is required when the granular density variation occurs quicker and on a shorter distance. The energy stored this way in the granular structure propagates along with the photon and it may be integrally released when the photon is absorbed. If we accept two fixed limits, upper and lower, for the difference of density within the photon compared to the local average density (which seen in
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motion is the flux intensity), then the energy stored in a photon is inversely proportional to the length of its cylindrical zone (presumed of a constant diameter).
E = k / L
where k is a constant, L is the cylinder length and the wavelength of the two oscillations. The photon energy can be written:
E = k / λ = k ν / c = k2 ν
where ν is the wave frequency and k2 a constant. This is an identical formula with the photon energy expressed by the equation of quantum mechanics.
Figure 25 - The cross-section of photons
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Figure 25 shows a normal photon with a cylindrical shape, composed of two granular density oscillations, the regions A and B. In this longitudinal section, the region B, which has a higher density, is drawn in dark gray. The photon is symmetric to its longitudinal axis, thus this density distribution can be observed in any section. We may note four important aspects:
1) The photon moves at speed c in the red arrow direction, with the region of higher density at the front;
2) There is a small free space between the two regions A and B, with an almost null granular density;
3) The diameter of the photon's cylinder is slightly larger than the size of an electron or positron.
4) Both photon regions A and B are about the same size.
Figure 26 - The granular density of photons in the axial zone
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Figure 26 shows the graph of the granular density (y) on the length of a photon (x), in its axial zone. We may see the sinusoidal shape of the density oscillation toward the average value d�, and the space of very low density between the two regions A and B; the denser region is placed in front of the photon, on that direction it propagates.
8.2. Creation
We will consider two mechanisms that can produce photons: through the electron-positron collision and through the transition of an atomic electron to a lower orbit. In both cases, the mechanism by which the photons are generated is similar, namely by accelerating an electrically charged particle until it gets a very high speed, close to c, followed by a possible decelerating period. While the particle's speed increases, two processes will take place simultaneously:
1) As shown in Appendix 1, Figure A1.4, the spin of a high-speed particle stays oriented to its movement direction. If the speed increases, the average spin direction gets more and more close to the global velocity vector, and the particle's helical trajectory takes a higher pitch. Thus, the particle's surface becomes almost perpendicular to the global movement direction.
2) Section 3.4 described the granular trajectories near charged particles. If we ignore the deviation caused by the density variation, we may see that the granules of the local fluxes, moving at speed c, collide with the particle's surfaces and then bounce back through a simple process of reflection that complies with the well-known laws of this phenomenon. In case of relativistic particles, these granular reflections will become relativistic too. Thus, they will generate a new flux, collinear with the particle's
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global velocity. If we look from the particle's frame of reference, we may see that the granular reflections generating the collinear fluxes comply with the reflection law (Figure 27, right side and Appendix 3, relativistic angles), and thus the angles of incidence are equal to the reflection ones. From a fixed frame of reference (Figure 27, left side), we may note, however, that the direction of incident fluxes changes when the particle's velocity increases. Therefore, there are always incident fluxes that are reflected and combined to create a new, horizontal flux in front of the particle; the solid angle of those incident fluxes increases with the particle's speed. If the acceleration process continues and that particle reaches a relativistic speed, the horizontal flux it reflects to the right becomes more intense when its speed gets higher.
Figure 27 - Relativistic reflection
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This phenomenon is presented in detail (Figure 28) for an electron, but things are quite similar for a positron. At the same time, the horizontal flux reflected in the back of the particle, flowing in same direction, will decrease in intensity when the speed gets higher. The cylindrical space occupied by a particle executing its intrinsic rotation, not much larger in section than the particle's diameter, normally contains the horizontal fluxes of a presumed constant intensity.
But the perturbation produced by the accelerated motion of the charged particle in the uniform flux that surrounds it creates an imbalance between the total granular impulse it receives from the front and from the back, on its direction of movement.
Figure 28 - An electron at relativistic speed
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This flux variation is equivalent to the existence of a deceleration force, which increases as the resulting intensity of the front and rear fluxes, incident on the particle's surface, gets higher. The force increase between two moments of time is given by the difference in intensity of fluxes at those moments, i.e. by the difference between instantaneous velocities, which is equal to the particle's acceleration.
The intensity variation of that flux (the flux which is collinear with the particle's movement direction), localized in space and limited in time, creates a new granular structure, called photon, which moves at the speed c in the same direction as the emitting particle. The photon has a variable granular density, and thus it will be able to transfer a certain impulse when collides with a particle; therefore, we may assign non-zero values for its energy and impulse, which are corpuscular features.
The system particle - photon will conserve its global impulse and energy. Although the photon is composed of granules moving in the same direction, we cannot speak of a photon mass with the meaning described in Section 6.2, because it is not in fact a solid structure, with a maximum granular density. Considering the way a photon is generated, there may be two types of granular structures: one with a full density oscillation (as shown in Figure 25) and another with only a partial oscillation.
If the acceleration process of the charged particle is followed by a deceleration to almost its initial speed, the generated photon will be complete; if the particle disintegrates after the speeding up phase, the photon will be an incomplete one.
Figure 29 shows the stages of a complete photon creation, during the fall of the electron on a lower orbit.
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Figure 29 - Stages of the photon creation
It has to be noted that the cylindrical shape of the photon is not a perfect one; a photon may be emitted by particles that spin while accelerating, so its shape may have an additional curvature or it even can be helicoidal. A photon is composed of successive layers of granules with a circular section, arranged on a helical path; this path is similar to that followed by the particle that created it (Figure 30 depicts a very small region of the photon).
A complete photon, composed of two full oscillations of the granular density, will contain in the middle part a tiny zone of low granular density, caused by the thickness of the emitting particle. Between the time moments t1 and t3 the particle is accelerated, and between moments t3 (when it reaches the maximum speed) and t5 it is decelerated.
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Figure 30 - Longitudinal section of a photon - details
For each of these moments, a graph of the photon creation stages is drawn, having on the vertical axis the granular density and on the horizontal axis its length. If it had been the case of an electron-positron collision, where both particles accelerate and then annihilate each other, the resulting photons would have been incomplete and their density variation would look like the graph at moment t3.
Figure 31 schematically shows how the photons are generated by the two methods above, and the global conservation of the system momentum can be clearly observed. In the upper part of this figure we may see an electron in motion, with the velocity vector v, traveling toward a positron at relative rest.
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Figure 31 - Photon creation
While they come closer, both particles will tend to align their spin vectors on perpendicular directions, and the electric field variation will force them to move on circular trajectories. Next to the gray arrows, where the alignment process is completed, the force of attraction between particles becomes dominant and they will accelerate toward each other, until they will collide and annihilate (the annihilation process means that both particles will disintegrate, and their component granules will spread out into the spatial fluid).
During the accelerated movement, they both got relativistic speeds and thus each particle will emit a gamma photon on the pointed directions. The alpha angle of the emitted photons to the electron direction is calculated in Appendix 5, and it only depends on the electron's speed (and therefore on its momentum). As
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shown above, these two photons will be incomplete, as they only contain half of the granular density oscillations, from the mean value up to the extreme ones.
The lower part of Figure 31 shows the emission of a photon by an atomic electron, when it "jumps" to a lower orbit. This transition increases its kinetic energy and decreases the potential energy of the electron - nucleus system. The energy difference is emitted in the form of a complete photon, whose frequency can be determined as shown in Appendix 5.
8.3. Features
a) As showed at the beginning of Section 8.1, the photon energy is directly proportional to its frequency, and it is given by this quantum mechanics' formula:
E = h ν
where h is Planck's constant and ν is the photon frequency.
What does the photon frequency depend on?
Obviously, only on its wavelength, because its speed has a constant value (ν = c / λ). The wavelength is the length of a complete photon's cylinder, because this type of photon contains both granular oscillations. If we make a more qualitative analysis, and by assuming a constant density variation of any complete photon, it follows that the photon length depends only on the acceleration and deceleration intervals of the charged particle being in relativistic motion:
λ = (t1 + t2) c
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where t1 and t2 are the time intervals of the particle motion, with approximately equal values. We will therefore have:
λ = 2 τ c
where τ is the accelerating duration. The photon energy may be finally written:
E = h ν = h / 2 τ
and therefore we see that the photon energy is inversely proportional to the acceleration time interval of the particle.
The equation of particle motion is complex because the acceleration value is not constant in time (it depends on the Coulomb's force of attraction ~ 1 / r2, r being the distance, while the mass increases at relativistic speed) and the change rate of the decelerating force is not exactly known. Appendix 4 shows a simplified equation of the charged particle motion, from which we could deduce the time a particle takes to accelerate up to a speed close to c.
The photon momentum is simply obtained from the equation E2 = p2 c2 (considering the photon's rest mass as zero) and it has this formula:
p = h / λ
b) We have shown that its rest mass has to be considered zero, and obviously, the electric charge is zero too. Quantum mechanics considers that photons are bosons, and therefore they have an integer spin value. This spin parameter is somehow misused here, because photons are not solid structures that may be rotated (but an imaginary rotation of 360 degrees on any axis
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returns them in the same position). Photons have a fixed granular distribution, and they only exist in motion at the maximum speed c. If we take a look at their structure while they are in motion, we may see that photons also have wave properties, due to the sinusoidal form of their granular distribution. Moreover, we may assimilate their helical granular distribution (at a much smaller scale) with a rotation, giving this way a physical representation to the axial spin projection. This component will be called helicity, and it can have the values +/- 1 (+/- ћ as a matter of fact, because the global spin is √2 ћ). The helicity value +1 means, by convention, the rotation to the right (clockwise) from the photon's direction of movement.
c) In the common, classical understanding, this helicity is known as a circular polarization state. It would be generated by the "electrical" component of the wave, obtained by composing two vectors of the electric field intensity, rotated at a certain angle. But, as described above, the physical meaning of this rotational motion is given by the intrinsic movement of the particle generating the photon. Moreover, this angular moment has a fundamental role: to synchronize the spins in the mechanism of photon absorption by an orbital electron, or in explaining the Compton effect. Once again, my model gives a physical explanation to the abstract concepts of quantum mechanics and clearly establishes a connection between the corpuscular theory and the wave behavior of a photon.
d) The photon polarization has a wider meaning, due to their three-dimensional shape, not always a regular cylinder. As it has already been specified, their cylindrical shape may have a more or less circular (or even helical) deformation, depending on the trajectory of the accelerated particle and on the energy it has
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received. This curved shape is stable while photons propagate, but it will add a supplemental momentum to the photon; if seen in motion, as waves, photons may get a wider spectrum of polarization states, from the linear form with a certain angle to the elliptical ones.
e) The propagation speed of photons is c, the speed of light in vacuum. As established in Section 3.3, the photon, seen as a fixed structure of a granular flux, will travel at a speed that is given only by the average value of the local granular density.
f) The photon-particle interactions can be of several types:
• A photon may be entirely absorbed by an orbital electron; • A photon may inelastically collide with an electron, and thus a
lower energy photon is emitted (Compton effect); • A photon (with the energy above a certain threshold) may
collide with an atomic nucleus, transforming itself into an electron-positron pair.
The first two interactions occur similarly to the process of photon creation, but that process is inverted. The granular gradient along the photon, with the helical form described above, will determine the magnitude of the impulse transferred to a particle. Thus, the first part of the photon will accelerate the particle, due to the granular collisions of the intense flux, and then the second part of the photon will decelerate the particle with its weaker flux (the frontal flux becomes stronger). These interactions will have a different impact, which depends on the energy, their movement directions and the system this particle belongs. The creation of pairs is a completely different interaction, and it will be explained in the subsequent section.
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g) This model is also compatible with the "wave" feature of a photon. We may associate its granular density variation on the axial direction to the evolution of the "electric" field intensity, and its variation on the helical trajectory to the "magnetic" field intensity. Therefore, all the equations describing the electromagnetic wave propagation, deducted from Maxwell's ones, are perfectly valid.
h) The frequency of the photons emitted or absorbed in the orbital electron transitions is mostly in the visible light spectrum, and their internal structure was described above. If we take lower frequency photons, for example radio waves, will they have the same structure, but only with a greater length? To answer this, we have to check out how such waves are created. The oscillating electric circuits, including radio antennas, maintain a constant oscillation frequency, on a certain distance of a conductive material. The free electrons in this material, which oscillate in the electric field, are periodically accelerated and decelerated with exactly the same frequency. The amplitude and phase of their motion depend on the electric field intensity, but also on the electron position along the conductor. This way, each free electron will generate a different photon, which will be part of a larger, multi-photon structure, and this big structure may be associated to a complete electrical oscillation. The multi-photon structure will have a wavelength determined by the frequency of the electric oscillation, and its propagation speed will be equal to the speed of light. The spatial extent of this structure will thus be given by the oscillation frequency and by the interference of electrical waves inside the conductor, and its polarization must be associated to the direction of the electric field oscillation along the conductor.
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8.4. Pair production
A photon with the energy greater than 1.022 MeV may interact with a heavy nucleus and thus an electron-positron pair is produced (whose masses are 2 x 0.511 MeV). The remaining energy of the photon will be found in the kinetic energy of the new particles and in the change of the nucleus momentum. This pair creation mechanism is shown in Figure 32, and it is entirely based on the special field existing between a nucleon's quarks or between nucleus' particles. The resulting pair of particle and antiparticle can then be annihilated (the process described above), and two gamma photons will be finally emitted.
As shown in Section 3.3, the average speed of granules only depends on the granular density of the local fluid. In a region with high granular density, as the gluonic field, the speed of an incident flux becomes very low. We will now consider that the incoming flux belongs to a photon with the energy greater than 1.022 MeV. While passing through this region, this photon will suffer a "compression" process along its whole length, which will reduce its size in a proportion equal to the ratio between the speeds in the two mediums. This way the successive granular layers of the photon (Figures 25 and 30) will stick together; we may see, therefore, that a new high-density structure is being created, with a cylindrical shape, and a diameter equal to the photon's one. We have to add that the gluonic field has a higher granular density in the middle, and it will therefore curve the granules' trajectories toward the axis; thus, the new structure will be more compressed, in length and in diameter, until it will reach the maximum possible granular density. Furthermore, the helical arrangement of the photon's successive layers will generate an angular momentum for the new structure, which will start
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rotating, while it will continue its "slow" motion toward the exit from the gluonic field region.
If we analyze the granular density gradient within a virtually compressed photon, in an exercise of imagination, we will see that its first half has exactly the shape of a positron. The first structure created by a photon passing through a region of high granular density is therefore a positron; the same mechanism will generate an electron from the second half of the photon. The low-density gap between the photon halves will separate the two particles and it will create a short delay between their exiting moments. If the incident angle is not zero, the photon will also be "refracted" upon entering the gluonic field, and both newly created particles will keep this new direction. The photon is completely absorbed in this process, and its granular composition has been incorporated and distributed into the structures of the new particles.
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Figure 32 - Production of the electron-positron pair
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9. THE MAGNETIC FIELD
The variation of the divergent or convergent granular fluxes, created by an electrically charged particle in the space around it is called magnetic field.
This field is a vector field, which is oriented perpendicular to the direction of the flux, and its magnitude is given by the magnitude of the flux variation in time and space. The magnetic field is produced by the granular fluxes of the moving electric charges, and it shows the degree of their interaction with other electric charges in motion. The main quantity of this field is vector B, called magnetic induction; it is shown in Figure 33, where we may see that the field lines are of circular form. The direction of the induction vector is given by the right-hand rule: if the thumb points to the direction of the charged particle velocity, the curl of your fingers gives the direction of B.
After similar calculations as those for the electric field (Section 6.5), we notice that the magnetic induction is proportional to the electric charge q, to its speed, and inversely proportional to the square of the distance to particle, r. If the versor of the distance from a charge to the point where the induction is calculated is not perpendicular to the velocity vector, then the induction value will be given by the velocity component that is perpendicular to the versor. This fully complies with the Biot-Savart law for point charged particles, moving at a constant velocity v << c:
B� = μ0 q v� x r / 4 π r2
where μ0 is the magnetic permeability of the vacuum.
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Figure 33 - The magnetic field of a charged particle
The motion of another electric charged particle in vicinity is determined by the combined action of two forces, electric and magnetic (Lorentz force):
F� = q (E� + v� x B�)
Particles experiencing these forces will have a helicoidal trajectory, by adding a rotational motion to the linear one. A magnetic field, exerting a perpendicular force to the particle trajectory, will give it a circular motion.
A charged particle, which has an intrinsic motion of rotation and precession (as shown in Section 6.3 and in Appendix 1), features a continuous spatial and directional variation of the reflected fluxes. Such fluxes will accurately follow the evolution of
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the particle's spin vector, whether the particle is in motion or at relative rest. Therefore, regions with inhomogeneous rotational fluxes appear around the particle, which will produce different forces in different points, and thus mechanical momenta. These moments are called magnetic moments; as they are induced by the particle rotation, the quantum mechanics calls them spin magnetic moments. For example, a free electron will only have a spin magnetic moment (intrinsic), but an electron orbiting within an atom will have in addition an orbital magnetic moment. In other words, the interaction of rotational granular fluxes (produced by charged particles in their complex motion) is the base of the magnetic field's actions. The fluxes of each charged particle concur by superposition to the global magnetic field generated by an electric current or a magnetic material. The magnetic field will exert forces on the charged particles moving in conductive materials, and thus it can generate electrical currents or attracting and repelling forces.
We may see that these fields, the electric and the magnetic ones, can be converted one into the other and therefore they can be unified under a single name, the electromagnetic field. They have similar actions, determined only by the granular fluxes of the charged particles, through their intensity or their variation in time and space. We can easily observe now and draw the general conclusion that all known interactions (gravitational, electric, magnetic, strong, weak and photonic) are generated by the distribution, intensity, convergence, direction and variation of the granular fluxes.
The preceding chapters have shown that all particles are composed of spatial granules, and their stability, as well as the
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interactions between them, is determined by the particular dynamics of the granular fluxes.
The Prime Theory explains the genesis of all the particles and unifies all the fields into a single granular motion of mechanical nature, determined by the granular features of space and their evolution over time.
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10. TIME
This physical quantity is a derived one: it comes from the fact that space allows the granular movements and they are performed with a finite and constant speed. All the changes, transformations, movements and oscillations the spatial granules are going through, as fluxes or dense structures, happen at a certain rate, which may be measured by reference to another one, known and reproducible. However, movements through space have a relative character; a body in a frame of reference has a relative speed, and so does the flow of time in that system. The laws of physics take the same form in any inertial frame of reference, as they relate to the physical quantity local time, which does not have a constant rate in all systems. Let’s imagine we have a fixed clock, which ticks 60 times in a minute, and whose second duration is set by a constant oscillation of mechanical, electrical or optical nature; if this clock is accelerated up to a relativistic speed, which then remains constant, we will find out that it will show the same time rate to a local observer. But this time interval of one minute, as measured by the clock during its relativistic motion, is longer than the minute shown when the system is fixed, at rest. This has a simple explanation: all the physical phenomena (mechanical, electrical, etc.) are happening slower in a mobile system than they do in a fixed one, from the atomic scale up to the macroscopic level. The dynamics of physical phenomena changes with speed because nothing can happen instantaneously; we have shown that the space properties determine the existence of a maximum speed, which is the limit in this Universe. Any system that accelerates close to this speed limit slows down all its internal processes, because the
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component particles may not exceed that maximum speed, whatever direction they are moving on.
This theory unified all the possible interactions into a single one, of a mechanical kind, and thus it is obvious that any mechanical action of the granular fluxes exerted on particles will depend on their mass. In a mobile system, as masses increase with speed, all the phenomena will have smaller velocity and acceleration values. Thus, any mechanical or electrical oscillation (which can be used in the mobile system as a reference to calibrate a clock) will have a lower frequency, and therefore a longer period.
The same time dilation also happens to systems located in strong gravitational fields, i.e. in regions with more intense granular fluxes on a certain direction. The dominant flux will "increase" the mass of all the particles moving in its direction, and therefore all the interactions between them will happen at a slower rate. Similarly, any oscillating process would be used to calibrate a clock, its frequency will be lower than that of the same process running in a region with uniform granular fluxes.
Any material system is, at a moment, in a certain state, given by the states of its constitutive granules; all these granules, as shown in Section 3.1, are in continuous motion, colliding and exchanging impulses. The way they are moving leads to a resulting movement of the structure as a whole, which will also be in a state of relative and continuous motion. If we consider time as the resultant of the continuous motion of a structure in the three-dimensional space, on a certain trajectory, we may associate it with a direction, from the current state of movement to a future one. Thus time became as a vector quantity, whose "arrow" shows "the movement" from a state which has just
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passed to one that is to follow, and its magnitude is given by the ratio of the changing rate to another one, presumed constant, of a reference process. The meaning of changing rate - as transformation of a "past" state into a "future" one - shows that time is a special vector, whose direction may not be changed. The time difference between two systems moving at relativistic speeds, i.e. between the rates at which they are changing their states, corroborated with the intersection of their spatial trajectories, may lead (by mutual referencing) to an apparent "time travel", where two vectors meet: the past and the future. However, this is not a paradox; the processes within these two systems happened at different rates, and this can only be realized through direct comparison. For observers located in each system, the processes took place in exactly the same way, at the same speeds, with the same frequencies and on the same distances. Clearly, the current state of a system determines in a causal way its future state; this happens at any level, it is the "true nature" of things, which will always set up the direction of the arrow of time.
An observer, who cannot "look" beyond a minimum scale of things, could interpret what it finds at the granular level only as hazard, uncertainty and probability. If we add to this frame the huge numbers we can talk about at this level, we may conclude that, under a certain dimension of things, reality can only be described using a statistical approach, with temporal and spatial average values. Following this logic, the spatial graininess, which automatically implies a kind of temporal granularity, can be mathematically averaged, and the actual physical phenomena can be exactly modeled by continuous equations, at any spatial and temporal resolution we want, unless that critical level of dimension has not been reached.
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My current model presumed that space is continuous; thus, any object is moving through it, from granular structures to galactic formations, has a smooth, uniform motion, made by occupying all the intermediary positions along its path. Therefore, the time granularity remains only a virtual attribute; there is no need to quantify time at the granular scale since it cannot be measured at this level anyway.
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11. GALAXIES
11.1. Formation
As space expanded in all directions, its granular density has sufficiently dropped to enable the development of the first elementary particles. Quarks have quickly combined into protons, which attracted cold electrons and thus the first atoms of hydrogen were formed. The attractive forces between them, electromagnetism and gravitation, allowed accretion of these raw gaseous materials and thus they clumped together to form the first stars, mostly composed of hydrogen and helium. Usually much larger than our Sun, these stars of the early Universe were spinning very quickly; they also had a short life, a few tens of millions of years. Once ignited, their inner fusion processes created new elements, heavier than helium; when these reactions could not continue anymore due to the consumption of all fusionable materials (they generate energy when combining), the equilibrium of these stars could no longer be maintained and they exploded. A part of the stellar matter was spread around and it became the fuel source for future generations of stars, while the other part collapsed gravitationally into a very dense core, composed of heavier elements. The star genesis continued and it led to the emergence of various star systems, where the forces of gravity were balanced by the centrifugal ones. Large clusters of stars have been born this way, forming the first galaxies. We analyzed in Section 5.2 a few causes that determined the size of galaxies, but something should be added here. Some stars of very large masses turned after explosion into superdense cosmic bodies, of a very small size, for example neutron stars or black holes. The stars of this latter type, having an extreme gravitational pull, continue to absorb the interstellar matter or to
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incorporate other stars and even other black holes. This way they reached an enormous mass, of several million solar masses, and a huge density, which produced an even more powerful gravitational field. These stars further played a very important role, because they attracted groups of regular stars around them, leading to the formation of larger galaxies. Most of the galaxies were formed around a supermassive, central black hole, and this stabilized the movement of the component stars and determined their global dynamics. If we analyze more carefully the relation between the gravitational field and the supermassive black holes, we will be able to explain in a simple way the shape of many galaxies, the movement of their stars and even the "dark matter" they might contain.
Figure 34 - Section through a black hole
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11.2. Black holes
During the gravitational collapse of stars, the angular momentum is always conserved. Initially, a massive star spins with a peripheral speed of tens or hundreds of kilometers per second. After explosion, as it was shrunk and transformed into a black hole, its surface may reach a relativistic speed of several tens percent of c. Figure 34 shows a black hole in section, with a granular flux Ф reflecting off the surface and the trajectories of two γ photons passing nearby. For such a supermassive star, located in the center of a galaxy, we may state the followings:
a) Its shape is not a perfect spheroid; it is flattened due to the fast rotation around its own axis.
b) The incident fluxes do not pass through the star's body; they are relativistically reflected in all directions, forming a region of high granular density around it. The gravitational field of these stars has a maximum possible intensity, and this creates several layers in their internal structure. Thus, if the star's surface may still contain quarks confined by the strong interaction, as we go down toward the center, this interaction diminishes and quarks get closer to each other due to the higher pressure. At a certain depth, where the granular fluxes virtually disappear, the elementary particles can no longer hold their structures and they transform into a super concentrated granular mass. This is a new, inner star’s "horizon", beyond which only the granular fluid of maximum density may exist. We may even say that the interior of this kind of star is a new "elementary particle", with a huge size and mass.
c) The reflected fluxes have a rotational component, with the highest value in the central plane of the star, perpendicular to
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its rotation axis. Their gradient determines the "attraction" of the galactic stars to this plan and this explains the lenticular structure of most galaxies. The rotation direction of the reflected fluxes will determine the rotation direction of the stars in every galaxy. Furthermore, the presence of these fluxes makes the stars to spin quasi-synchronously on orbits, regardless of their distance to the center of the galaxy.
d) Photons are deflected into the star mainly due to the increasing gradient of the granular density around it, which reduces their traveling speed (Section 3.3). As a photon has a non-zero diameter, its component granules will successively and unevenly change their speed, so there will be a "refraction" phenomenon that will change the velocity's direction toward the higher-density region. At the same time, all the photon's granules will automatically "fall" into the star in the presence of a dominant flux (Section 3.4). As seen in Figure 34, there is a certain area (gray) around the black hole - the event horizon - from which photons cannot escape. The material bodies that reach this area, with any speed, are inexorably attracted to the star's surface, being "stretched" same time due to the gravitational field's gradient.
e) The stratification with depth and the relativistic rotation of the star's matter cause a part of the incident granular fluxes to be diffusely reflected by the surface and another part to be retained between the particles of the first layer. Therefore, the intensity of local fluxes will decrease proportionally to the depth and their remaining part will gradually be integrated in the granular fluid of the star's core. This phenomenon of granular absorption, combined with the accretion of the gaseous matter surrounding the star, leads to a continuous
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increase of the black hole's mass. Moreover, this granular accretion process should be added to the current genesis models and stability theories of the supermassive black holes.
f) The granular fluxes that cause gravity keep the shape and the internal structure of the black holes. Their intensity diminishes over time with the decrease of the average granular density of space, and this causes the decrease of the black hole's growing speed through absorption. Therefore, the actual quantum theories regarding the black holes evaporation through radiation and particle emission do not completely describe the phenomena occurring in the star's upper layers.
11.3. Dark matter and dark energy
The dark matter is a hypothetical form of matter composed of (unknown yet) mass particles, which could only interact gravitationally; it is presumed to represent about 27% of the total matter in the Universe. It has been introduced by astrophysicists mainly to justify the variation of the rotation speed of stars in a galaxy and the gravitational lensing effect of the visible light that passes through galactic regions. Obviously, these two phenomena may also be explained within this theory:
• The rotation speed of stars in a galaxy with supermassive black hole in its center has been explained in Section 11.2.C.
• The lensing effect can be explained by the reflection of the granular fluxes at galactic levels, on all the stars, gases and cosmic dust existing in the interstellar space. All these fluxes create a region of higher granular density around the galaxy, which will cause the deflection of photons in the same way it was described in Section 11.2.D. On the other hand, it is clear
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that the same spatial region also contains particle fluxes emitted by stars (composed of electrons, protons, photons and neutrinos), but they may not be held responsible neither for such a large mass as the dark matter is estimated to have, nor for the lensing effect being limited to the galactic region.
• As a part of the incoming fluxes does not return, the granular accretion of the black holes could also create a significant imbalance of the spatial density around galaxies.
The Dark energy is also a hypothetical form of energy (matter), representing approximately 68% of the total matter, and it has been introduced to explain the accelerated movement of the galaxies, away from each other. It is assumed that this form of energy would have a uniform distribution throughout the Universe, a constant density, and it would exert a repelling force at inter-galactic level that opposes gravity.
But the creation process and the accelerated movement of galaxies has been explained in Section 5.2., by the very essence of the gravitational effect. The granular fluxes’ gradient, at the universe scale, will always produce a force that pushes away the galaxies, and this happens simultaneously with space expansion. The magnitude of this resultant force is dependent on the average granular density of space and on the point's coordinates in the Universe; however, its accelerating effect will be perpetual.
In other words, using all the data contained in this theory, the dark matter and the dark energy cannot be evaluated as distinct physical entities; they both are aspects of the same thing: space. Seen as matter, through its component granules, space is responsible for all the existing mass and energy. Gravity, as an intrinsic phenomenon of space, is responsible for all the forces
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that exist at stellar and galactic level, setting their magnitude and their direction. Thus, the space characteristics may explain all the scientific observations that led to the introduction of these two mysterious dark "elements".
These interpretations highlighted two aspects of this theory that may be easily correlated with the General Theory of Relativity (Einstein): the variation of the average granular density of space is similar to the space "curvature" in the vicinity of big masses, and the rotational component of granular fluxes around cosmic bodies is the gravitational effect of frame-dragging.
One more thing, very interesting, should be added here: if space, seen as three-dimensional framework this time, will continue to expand, then its granular density will decrease at the same rate, as well as the intensity of gravitational fluxes. Besides observing the galaxies’ recession, could we measure this space expansion? Could we analyze this phenomenon by laboratory experiences? It is reasonable to think that space has a profoundly relative character, and thus we are not able to measure its dilation through other means. We have seen that the granular fluxes interact with matter and generate forces at any scale, from the surface of elementary particles up to stars and galaxies. The intensity of these fluxes keeps the shape and proportion of elementary particles, determines the dynamic equilibrium with the other forces existing at their scale, and all these things are directly reflected at macroscopic level in the objects’ dimensions, interactions and movements.
If we take a calibrated bar of 1 meter, which would absolutely expand by one percent of its length for example, we would not be able to realize this, nor to measure the length difference if all the other things around us would expand by exactly the same
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percentage. All the velocities would change, and therefore the waves of constant frequencies would change their wavelength by the same percentage. One mention here: the dilation would be infinitely small at quantum scale, and it would be caused by the decreasing of the elementary particles' mass with the reduction of their number of component granules (presuming that the size of the granules and their properties do not change over time).
In conclusion, the phenomenon of space dilation (when space is seen as three-dimensional framework), in conjunction with the simultaneous decrease in intensity of the gravitational fluxes, gives space a relative character and does not modify the functionality of its material component. The granular structures, from particles up to cosmic bodies, and their interaction laws are not affected by this phenomenon. This fact naturally extends the relativity of space as fundamental and general principle, because it now may exhaustively describe our Universe. Theoretically, a new physical quantity might be introduced, invariant over time, whose formula would contain the volume of space multiplied by the intensity of gravitational fluxes.
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12. THE UNIVERSE
12.1. Extinction
Since its birth, the Universe is space, space is matter, and matter is energy. It all began with a singularity, whose entire energy was concentrated in a single "point"; it suddenly exploded and turned into a vast, continuously expanding three-dimensional space, containing the same amount of energy, but distributed in a virtually infinite number of granular quanta. The granules obeyed a few simple laws of kinematics; over an extended period of time, these laws determined the organization of granules into elementary particles, and the complex interactions between them at a small, quantum scale. These particles will later allowed the emergence of the atomic matter and its concentration process.
We have shown that the gravitational fluxes determined the star formation process, the evolution of the first galaxies and their movement throughout the Universe. They all continued to move and transform according to the laws of physics active since the zero moment of the Big Bang. All means grains, particles, atoms, planets, stars, galaxies; matter, in any form and at any scale, mechanically interacts, transfers impulses and conserves the global energy. As a result of gravity, we may notice at cosmic level that larger quantities of colder matter are concentrated into smaller volumes, i.e. into black holes. It does not necessarily mean that the Universe is going to end this way, called "heat death". This theory has introduced an average granular density of space, which decreases with the space expansion. In this context, another scenario would also be possible, that could happen even before the heat death. The average density might reach an extremely low value, when the structural integrity of elementary
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particles could no longer be held. At that time, all the matter would decompose into granules, which would dissipate in the global granular fluid of a very low density. Anyway, gravity will set the ultimate fate of our Universe, over a limited duration of time.
12.2. Rebirth
If we are to corroborate the possible extinction variant described in Section 12.1 with the granular absorption process that black holes go through, described in Section 11.2.e, we could simply figure out a logical explanation for the existence of the primordial singularity and for the explosion that generated our Universe. But to this end, some new hypotheses should be added:
1) This is not the only Universe that ever existed; tens or hundreds of billions years ago, another similar Universe existed, which we will simply call U1. No one can state with certainty that it was the first one, nor that it was unique, or that there is cyclicality in the birth and extinction of the universes.
2) U1 has had exactly the same granular composition, with the same characteristics, and its physical laws were identical. The constants of physics, however, compared to those in our Universe at the same age, were different; U1 had a much greater mass, and therefore its granular density, that determines these constants, was higher.
3) Space, seen as a three-dimensional framework, already existed or it was created through the expansion of U1; it was not generated at the birth of our Universe, and this does not change my version of the inflation theory. On the contrary, we may now very easily explain the granular reflections on the edge of the Universe, by collisions with the first universe's granules. Basically, the explosion of that singularity and the inflation that followed
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happened in a space region of U1 where the granular density was extremely small.
4) U1 had a similar evolution to that of our Universe; first, the elementary particles were created, which were gravitationally attracted to each other, then stars formed and exploded, and all the galaxies were formed later around the supermassive black holes. During all this time, U1 continuously expanded, its matter cooled down and the granular fluxes increased the masses of the black holes.
After tens of billions of years, U1 got into extinction phase, pursuing a scenario similar to the one we described in Section 12.1. Now it only contains a few supermassive black holes, placed at enormous distances from each other, in an empty space of very small granular density (that continues to decrease). These black holes absorbed so much matter, that the internal pressure of their central regions transformed the superdense granular "fluid" into a superdense solid. The granules of this solid core are fused together and thus they occupy an extremely small volume (the Granular Postulate #2 is no longer valid here, nor the fundamental laws). The incident gravitational fluxes determine the existence of a pressure gradient, which is still able to maintain the balance between all internal layers of the black hole. With the decrease of the average granular density of space, some of the smaller black holes simply dissolved into the spatial fluid. When a certain threshold of the granular density is reached, the incident fluxes can no longer maintain the integrity of supermassive black holes with solidified cores. Their outer layers dissolve, and their solid core, whose stability was ensured by the external layers' pressure, now explodes. This is a simplified model of creation and explosion of the primordial singularity from which our Universe was probably created.
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It is likely that other singularities of U1 might explode and create other universes, which might simultaneously exist with ours; but they would be located at such big distances that their observation would be impossible. Thus, we find that U1, at the end of its existence, will be "reborn" by creating a new Universe (or several universes, a Multiverse); the mass of these "child" universes would be smaller, as would be the mass of the singularities they could eventually produce, and therefore the cyclic extinction-rebirth phenomenon could be discontinued.
This simple model should be improved in order to answer some other fundamental questions, such as: how did the primordial universe come into existence, and what its substance was made of? Following the trend showed by the modern science, that offers answers like "from nothing", I have conceived my own hypothesis, widely described in Appendix 7.
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13. STABILITY OF ELEMENTARY PARTICLES
13.1. Introduction
To begin this analysis, we shall consider a free electron, which is represented in a cross-section in Figure 35, with a granular structure and a form described by the granular postulates (Chapters 3 and 6). The granular fluid that surrounds the electron on all directions will exercise a continuous and constant pressure on it (force F), which results from the impulse transfer between the spatial granules and those of the particle. We will further demonstrate how this action of the granular fluid ensures the shape and stability of electrons (this explanation may be extended and easily applied to any elementary particle).
It should be recalled here that all the granules that form the electron (whose internal structure is assumed to have the maximum possible density and where granules are bonded to each other) are constantly moving, rectilinearly, at the absolute speed C. In fact, they are rotating on quasi-circular trajectories, due to the internal granular collisions or those with the spatial granules. The average tangential speed of this rotational movement have a constant value, lower than C (due to collisions), and the angular velocities are different on trajectories of different radii. It may be estimated that inside the electron there is a quasi-constant number of granules, theoretically within two limits:
• Above a lower limit, in order to allow the existence of the electron's distinct shape: a very thin and curved disk;
• Below an upper limit, in order to allow the electron's shape stability during the intrinsic movement or during an externally induced one.
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Figure 35 - An electron at granular scale
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Considering their proximity and their traveling direction, these constitutive granules may create inside the particle three types of granular aggregation areas:
A. Compact zones (we would call them "clusters"), in which the granules are bonded to each other and, for a short time, they have the same direction of movement (their speed is postulated as constant);
B. Free zones, in which the granules are at a distance from each other, separated, and where they collide according to the known rules.
C. Filamentary zones, in which the granules are arranged linearly or irregularly on compact, one-dimensional rows.
These three types of zones have a short, limited lifespan, during which their shape and size randomly vary; all their component granules continuously move from one zone to another or they are exchanged with the external ones.
13.2. Special granular collisions
We must describe now two special cases of perfectly elastic collisions that occur between the granules from the compact zones or between the granules of the compact zones and those of the free zones. Based on their direction of travel, they may be collinear collisions and orthogonal collisions. Both cases shall be subject to the momentum conservation law, in the closed system consisting of all the granules that collide.
The first case assumes that a granule collides with a compact, linear group moving in the opposite direction, as shown in
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Figure 36. We may see how the solitary granule continues to move on its path, as an equivalent granule; the group of granules also keep moving on its way, holding the same initial structure. The impulse of a single granule is p, and the impulse of a group is n p, where n is the number of the component granules. In conclusion, this simple type of collision does not affect the global granular motion; it only causes a very small delay whose value is proportional to the number of granules in that group.
The second case involves the collision between a granule and a compact, linear group, going on a perpendicular direction, as shown in Figure 37. We may see how, after collision, the solitary granule is "reflected" in the opposite direction, under a certain angle that gets wider as the number of granules increases.
Figure 36 - Collinear collisions
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Figure 37 - Collisions on orthogonal directions
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There are three situations to analyze, namely the groups of 1, 2, and 4 granules; the total impulses of their groups are respectively q, r and s. By applying the impulse conservation law, we may see that after collision the impulses of the group and of the granule are reversed in regard to the system impulse vector (the angles α and β are reversed). The angle α that the group will move by after collision may be easily calculated from the rectangular triangle formed by the impulse vectors:
tan (α) = p / n p = 1 / n
The final direction of the group forms twice the angle, 2 α, with its initial direction (vertical); the same angle is formed between the reflected granule and the horizontal direction. Here we may easily notice that, in the case of a very large number n, the group would suffer a very small deviation of trajectory, and the solitary granule would almost go back on its initial direction (practically obeying the laws of reflection).
The mechanics of collisions between large groups of granules is actually more complex. Equations describing this type of collisions might be exactly determined only if all the granular parameters are known, such as the diameter d, the speed C and the elasticity constant.
13.3. Internal granular kinematics
Regardless of the distribution of the aggregation zones, we may assume that the internal granular kinematics of a particle consists in a global rotation motion, in such a way that each granule will move on a quasi-circular trajectory of a constant radius, whose center is placed exactly in the geometric center of
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the particle. This assumption is based on the description of the special granular collisions from Section 13.2, in conjunction with two other statements:
A. The granular fluid's density around the particle is higher than the local average value, and it increases closer to its edge. In other words, the spatial outline of a particle is fuzzy, not very well defined, but the boundaries may be dynamically established as the geometrical limit of particle's larger parts, the granular compact zones.
B. Any description of the internal granular kinematics within a circular section through the particle may be generalized for its entire structure, which is in fact a collection of overlapping, circular-shaped layers of different radii values.
The variable density described above, bigger near the particle's edges, may be justified only by the presence of the granular compact groups. Thus, any incident granule coming toward the particle's "surface" may behave in two different ways (or in any combination of them):
- If only free zones are present on its path, it would cross the particle as an equivalent granule, with an additional delay due to the very high value of internal density.
- If a compact zone is present on its path, the granule will be reflected back and thus the granular density around the particle will increase. A very important effect in this case is the small deflection of the compact zone's trajectory, which will be oriented after collision towards the interior of the particle.
Essentially, the "pressure" exerted by the granular fluid on a rotational granular structure is manifested by the continuous "bending" of the trajectory of its compact zones, keeping their
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global rotational motion. Thus, the external granules either will pass through the particle, having no effect on it, or will act toward maintaining the rotation of its internal zones, in which case the final effect is the stability of its shape and initial dimensions.
Figure 38 (the upper part) shows a circular section through an electron that is composed only from fixed, linear filamentary groups; all those one granule-wide rows will hold their structure unchanged on very small distances. To keep the analysis simple, we will assume that the particle is only formed of this type of groups, tied to each other, and these hypothetical granular "filaments" contain a very small number of constitutive granules (tens). The horizontal group of four granules, which moves in the vertical direction, is bumped at a given time by an external granule. As mentioned in Section 13.2, the group will change its trajectory with the angle 2 α. It will go farther on this new direction, covering the distance s, when another external granule will bump into it, and this phenomenon will be repeated in a similar way, over and over again. In the rectangular triangle formed by the small segment s and the radius r (of a circle circumscribed to all the triangles) we may write:
sin (2 α) = s / 2 r
However, r = n d, where d is the diameter of the granules, and therefore we will have the equality:
n d = s / 2 sin (2 α)
But we already know that tan (α) = 1 / n, and by applying the tangent half-angle formula we will get:
4 d = s (1 + 1/n2)
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Figure 38 - Circular sections through an electron
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This equality may be approximated, in the case of a large n, by:
s ≈ 4 d
This final formula says that, for a rotating structure composed of filamentary areas, the closed circular trajectories of these areas may be maintained for an indefinite time only if the compact areas receive continuously an external impulse, at a constant time interval. This period has an approximate value equal to the time required for a granule to get through the space s, which is four times the diameter:
Δt = 4 d / C
The granular fluid around the particle may simply allow this because its density increases closer to the particle's "surface" and because the direction of the global impulse vector is always perpendicular to the areas where momentum is transferred.
The general conclusion is this: once a rotational granular structure (a discoid) is formed, symmetrical with respect to a central axis and having the size within certain limits, the granular fluid that surrounds it can ensure the stability of its shape and size for an indefinite time period.
In Figure 38 (the lower part), you may see how, between two quite different moments of time t1 and t2, a linear filament "dissolves" itself (as the component granules rotate at different angular velocities, on pseudo-circular trajectories of different radii). However, these areas are permanently rebuilt by the addition of new granules, detached from other compact areas. All this granular dynamics, apparently of a chaotic nature, helps in fact to keep the integrity, the shape and the initial size of the
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elementary particles. The rotation of the internal layers at different angular velocities generates, on the average, a global angular momentum for the particle as a whole, which is immediately reflected in the existence of its intrinsic precession motion (spin). It has to be mentioned that all velocities and impulses above have been related to the particle's rest frame.
13.4. Size of elementary particles
We have taken into account for the following estimations only discoidal shaped particles, the electrons in fact. It is clear that the electrons have almost constant dimensions, and their physical form does not change during the global rotation movement and intrinsic precession. Nevertheless, are we able to determine exactly their radius or their thickness in absolute values? Could we calculate them at least as multiples of granular diameters?
Intuitively, an elementary particle cannot have however small dimensions, let's say the width of ten granular diameters for example. Its thickness, which is by far the particle's smallest dimension, may not have this particular value; a particle should not be affected by the granular collisions that could move the compact groups by one granular diameter to any direction. These groups, which in fact give "hardness" to particles (even if they continuously change their shape and size), are present in the entire volume of the disc, at any distance from its geometric center. They are so numerous that if some would dissolve or disappear, the structure as a whole will not be affected.
How could we find at least the upper size limit, i.e. the maximum radius a particle can have? First, this secret might be hidden in the size of compact groups. At a relatively large distance from the center, the rotation velocities (on the trajectories
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considered as circular) of the granules from adjacent layers vary much less than those of the granules closer to the center. As consequence, we may infer and state that the average size of the compact groups is bigger if they are located at a greater distance from the particle's center (and here we consider all dimensions of a compact group, i.e. length, width and height, relative to the centerline of the particle). We may logically assume that they also have a longer lifespan as the distances on which they move rectilinearly are greater.
Let us imagine such a compact group in a position of extreme eccentricity, where it interacts directly with the granular fluid around the particle. For the sake of simplification, we will suppose that it has the shape of a rectangular parallelepiped, and one of its sides is the interface with the outside, as shown in Figure 39. The average impulse transferred through this side, within a certain period of time, is directly proportional to the area of this surface. As we have seen above, this impulse will curve the group's trajectory with an angle inversely proportional to the number of component granules, i.e. with its volume. But this volume is the number resulting from the multiplication of the exposed area by the height h of the group. The temporary direction taken by the compact group has an angle of inclination given by this relation:
tan (α) = 1 / h (h is expressed in number of granules)
In order to ensure the stability of the entire granular structure of an electron, we have shown above that a certain proportionality must exist between this number h and the radius r of the orbit the compact group is rotating on. Intuitively, however, we may infer that the height of a group increases if all
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the angular velocities of the component layers have closer values. The angular velocities of two successive granular layers are:
ω1 = C / r and ω2 = C / (r + d)
where d is the diameter of a granule. Their difference is:
Δω = C (1 / r - 1 / (r + d)) = C d / r (r + d)
As d is assumed much smaller than r, we may write:
Δω = C d / r2 i.e.
h 1 / Δω r2 / C d
Figure 39 - Compact granular groups
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This alleged proportionality of h with r2 instead of r (as for the filamentary groups of small radii) implies that, at big radii, the average impulse transferred by the granular fluid is no longer strong enough to deflect the trajectories of those groups forming in the peripheral areas of the particle. It is possible to establish this way an upper limit for the diameter of elementary particles, which will finally depend only on the size of the granules and of their compact groups, as well on the density of the granular fluid surrounding the particle.
Another important feature of the disc is its thickness. The lowest value of the thickness was analyzed above. Assuming a maximum granular compaction in the axial direction of the particles, this thickness may be also expressed as a multiple of the diameter value d, as it is virtually equal to the number of circular overlapping layers that form the disc. As showed in Chapter 6, all particles have a continuous motion of precession on a helical trajectory due to their internal granular rotation. The rotation of a particle (considered to be a solid body) on this path makes that its inner layers (also considered solids, of circular shapes) to synchronically rotate on orbits with radii of slightly different values. This tends to displace the layers relative to one another, more as their rotation radii are more different. The effects of such different angular moments are compensated by the pressure of the granular fluid and by the rotation of the compact groups, crossed on the axial direction by many granular filaments. These filaments also contribute, by their continuous oscillation, to the global dimensional stability. In other words, the thickness of a particle shall be established as a result of this dynamic balance, the major role being played also by the local granular density.
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The compact groups, of different sizes and shapes, may thus form solid and stable discoidal structures, whose radius and thickness stay within fixed limits. These stable structures (we have seen that they can also take toroidal shapes) are the elementary particles that make up ordinary matter. They might also be viewed as special vortexes that can freely exist for indefinite time periods in the spatial fluid, keeping their rotational motion by the simple action of the granular mechanics.
Note: check http://www.1theory.com for more info and for our software models of the elementary particles.
13.5. Irregular granular fluxes
Everything in the sections above was based on the assumption that the elementary particles lie in a uniform granular fluid, and that the intensity of the granular fluxes is constant on any direction. Let's now consider two special cases, where some other directional fluxes also act on a particle, seeing if they can modify its internal structure.
13.5.1. Photonic fluxes
This is the case of a photon of any frequency in a head-on collision with an electron. Figure 40 shows three successive layers of that photon, whose granules constitute a supplemental flux, incident on the left side of the electron.
The resulting action of this supplemental flux, considered as uniform only for a short time, is the transmission of an additional impulse to the electron's compact groups, which will eventually incline their trajectories more to the right.
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Figure 40 - Photon-electron collision
As this action is presumed uniform and evenly distributed in the entire granular structure, all the electron's internal granular impulses will be reoriented on a different angle and thus the particle's speed will increase a little. The effect shall accumulate for each layer of the photon colliding with the electron (c > v), thereby causing a uniformly accelerated motion to the particle. When this phenomenon ceases, the electron will continue to travel at the maximum speed it has gained in the process. In the same way, the layers having a lower density than the local average one will produce a similar effect on the electron, but the particle slows down (got negative acceleration). As these uniform photonic fluxes are wider than the electron diameter, the elementary particle's shape and size are not affected at all.
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Anyway, the real photonic fluxes will act alternatively on both sides of the particle during their larger collision intervals.
13.5.2. Gluonic fluxes
This is the case of a concentrated granular flux, formed inside a composite particle; for example, check the gluonic field existing between the quarks of a neutron (Figure 41). As it has been shown, the flux of the gluonic field is not uniform, having a higher density in the axial zone of these two particles. The d quark is in a state of relative equilibrium, i.e. the total average flux received from the left is equal to the one received from the right. But the flux from the right is not uniform; thus, the compact groups formed in the quark's central region receive a more intense impulse and they will shift along the OX axis, to the left.
Figure 41 - The gluonic flux
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This thing is balanced out, within certain limits, by the internal granular dynamics of the quark, but it produces a deformation of the particle's geometry (see the color component) and hence its electric charge changes. If these limits are exceeded, the quark d may divide, and its central part turns into an electron.
13.5.3. Annihilation of elementary particles
An electron and its antiparticle, the positron, may annihilate each other if they got close enough. Their electrical field can accelerate them up to relativistic speed, and each one of them will emit a gamma photon during this process. At the end, these two particles will collide, disintegrating themselves; in the closed system they formed, the total energy and the total momentum are conserved quantities.
If we assume that both particles were initially at relative rest, using the mass-energy equivalence, this may be written:
m0 c2 = h ν
where m0 is the rest mass of the electron (or of the positron) and ν is the frequency of the incomplete gamma photon. We have shown in Section 6.2 that this mass is in fact a relativistic one, (because all particles are in a permanent state of movement) and it is proportional to the absolute rest mass m00, whose value is given only by the number of electron's component granules. With regard to the origin of mass, which is based on the modification of the granular impulses, we may take the following conclusions:
- The mass of a particle, originating from its own movement and from the number of granules, is not directly converted into the photon's energy. During its accelerated motion, the charged particle has created all the granular layers of the photon, and only
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at the collision moment it loses by disintegration the internal structure that generated its rest mass. Put it simply, the electron’s granules are not the ones forming the emitted photon. There are in fact two separated processes: the re-orientation (concentration) of the spatial granules into a new flux that will constitute the photon, followed (after annihilation) by the spreading of all the particle's granular groups throughout the surrounding granular fluid.
- The mechanical collision between these particles is a "plastic" one, and they will temporarily create a new body containing both their structures joined together. The new structure is unstable and it will immediately dissolve into space, its component granules being thrown on random directions. The energy initially consumed to concentrate a number of granules and thus to create the structures of these two particles (and therefore their mass) is entirely lost in the annihilation process. This is not about the basic energy of granules, which remain unchanged (postulated in [1]) whether they belong to a structure or not; this is about energy seen as flux, as granular concentration. The annihilating process is practically yet another confirmation of the mass-energy equivalence (Einstein), because both these physical quantities represent the same thing, which is a structured, directional grouping of the elementary, granular energies into fluxes or into particles.
13.6. The granular pressure
It has been shown in Section 13.4 that the elementary particle dimensions are finally determined by the properties of their component granules (diameter, impulse, perfect elasticity) and by the local granular density. This density, which is a characteristic of the spatial fluid, is the parameter that can vary greatly from the
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average value of the Universe. And the simplest example is the inside of a superdense star, i.e. of a black hole. As estimated in Chapter 12, this type of star, due to the pressure gradient with depth, can "dissolve" the elementary particles (quarks) in their component granules, thus forming a solid core. We also know that these stars are spinning very quickly, with relativistic peripheral velocities.
The high density of the granular fluid in the deeper layers of the star shrink in size the composite particles (but their mass will increase); the electric field tries to compensate this, but all quarks will eventually collapse and merge into the amorphous granular matter. Being similar with the structure of a particle, this first level of the core is composed of compact granular groups, much bigger this time, rotating at the speed C around the stellar center.
You may see in Figure 42 (a section through the star center) how the gravitational force (F) exerted on the outer layer creates a certain pressure on the surface S1. As a result of the geometric concentration and of the granular impulse propagation into the star depths, the equivalent pressure on the surface S2 is much higher, while on the surface S3, at nucleus level, it becomes extremely large, reaching a value that allows the solidification of the granular fluid in Z1 zone. In other words, this region is perfectly similar to the internal structure of an elementary particle, in which the granules are practically glued together into compact groups; also, these layers and the granular groups may rotate at different angular velocities.
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Figure 42 - Section through a black hole
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We have shown that the gravitational fluxes cannot pass through this type of star; they either reflect on its surface or remain captive inside it, contributing to its continuous mass growth. This mass supplement causes an increase of the internal granular pressure and thus the outer zone of the solid nucleus, Z1, will exert a higher additional pressure on the central region Z0. This central zone of the nucleus is the place where pressure reaches a maximum possible value. We estimate that in the case of supermassive black holes (having masses of billions of solar masses), the pressure within the region Z0 exceeded a critical value, and even the granular solid changes in there, entering a high compressed state. What are the special features this compressed granular solid might have?
1. Compact groups joined each other, forming in region Z0 a completely solidified spheroid, where the internal granular layers have the same rotation speed (lower than C), regardless of the radius of the trajectory they are moving on. Here is the place where the granular postulates are no longer applicable, as well as some laws of physics. The granules of this zone have a different dynamics, and by their huge number, they virtually transform zone Z0 into an accumulator of kinetic energy.
2. The granules were described in Chapter 3 as some discrete, minimal, identical, ball-shaped elements of space with a perfectly elastic behavior in the collision processes. This behavior suggests the elastic nature of the primary "material" these granules are made of. Therefore, it is possible (at least theoretically) that a sufficiently high pressure might shrink, distort and finally turn them all into a special, compressed state. In other words, zone Z0 may also be considered a high-capacity accumulator of elastic potential energy.
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3. Regardless of their rotation velocity (even relativistic), the outer layers of the black hole (those formed by quarks) are continuously experiencing a state of dynamic equilibrium, determined by the equalization of the centrifugal forces with the gravitational ones exerted on them.
Let's now consider this phenomenon along with the perpetual mass accretion (from granular fluxes, interstellar gases and dust, from incident photons and particles, or even through the assimilation of other stars) and with the decrease of the average granular density all over the Universe (considering that the star evaporation is negligible). We must also emphasize the fact that the outer layers of the star, composed of elementary particles (quarks), have a mass value that relativistically increases with the peripheral velocity. Could the stability of this supermassive star change over time? When its mass reaches a certain value, could the star undergo a gravitational collapse due to the compression of zone Z0? Could this collapse immediately determine the star explosion?
We would answer "yes" to all these questions, and this may logically be argued. In the granular model of this supermassive star, the necessary conditions for explosion might be fulfilled in a very distant future, over tens of billions of years, when:
• The average granular density of space will drop below a critical threshold, as well as the intensity of the gravitational fluxes that maintain the stellar structure. As a result, the star's diameter will increase a little.
• The star's mass will exceed a critical value, and therefore the solid region Z0 will fail to the immense pressure and it will abruptly compress, reaching the minimum possible size, of infinitesimal value.
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This scenario is well known in fact, being similar to the explosion of a supernova. The other regions of the star collapse too, while the angular moment is conserved. As a result, the peripheral speed of star's outer layers increases, and thus the centrifugal force may become greater than the gravitational one. The moment these outer layers are expelled into space is the moment when the star's explosion is triggered. The internal layers also quit the state of dynamic balance, allowing the enormous energy stored inside the stellar core to be dispersed throughout the space. This event of truly cosmic magnitude has all the characteristics of a Big Bang, and it might validate the hypothesis of primordial explosion through which our Universe was formed, described in Appendix 7. The region Z0, consisting of compressed granules, which reached minimum dimensions during the collapse, would correspond to the singularity introduced by the current cosmogonical theories. More, the normal stellar matter (the already existing quarks) will almost evenly spread through space, being supplementary accelerated by the granular fluxes generated by the explosion.
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14. GRANULAR INFORMATION
14.1. Information features
First of all, what is the concept of information, generally speaking? From a technical and scientific point of view, information means a representation, a reflection of reality, which by using of a set of symbols accessible to humans may quantify a group of parameters of a material or virtual object. If some specific characteristics of the object are encoded using those symbols, the resulting information gets a deeply abstract character, but it will allow in this form concrete processes of analysis, comparison, compression, storage or transmission at a distance. The information associated to a generic object may thus describe to a certain degree one or more of its properties.
Informational postulate #1
A certain finite amount of information may be associated to a hypothetical physical object, which may describe it exhaustively.
Meaning, if we had this amount of information, we could create an identical copy of the object, which would not be different from the original. This idea leads us toward other important features of information:
A. The information has a universal character, and it exists within any physical entity, as an intrinsic quantity of the material objects.
B. As an object has a certain shape, or a certain mass value, it also contains a finite amount of information. Therefore, as direct consequence of this first postulate, only a finite amount of information may be added to a physical object (due to the discrete nature of its matter).
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C. The other form of energy, i.e. photons, may also contain information; thus, it is possible to transmit any information at a distance by such means.
D. As the information contained by any material object has a finite value, we may introduce a new physical quantity, namely the information density.
In this context, we have at least two new questions:
Q1- Can we retrieve all the information a material object holds?
Q2- What is the maximum value of the information density?
To answer these questions, first we have to establish the basic unit of information and its representation. And if this unit of information may be read, written, duplicated or transmitted at any scale of matter. It can easily be inferred from above that information is automatically associated with energy, no matter its form. As there is a minimum energy amount, we may intuitively assume that it could be associated to a minimal information value. A complete definition of information in the Prime Theory's perspective may be given if we analyze it from all points of view.
First, it is easy to identify a measurement unit for information at macroscopic level. Here, all things are very clear as they are dominated by certainty, and it comes natural to establish a binary association (a minimal system) as basis of this measure. Two complementary attributes of a simple object may constitute a minimal characterization system, such as: up-down, black-white, yes-no, open-closed, present-absent, fixed-mobile, positive-negative, even-odd. These attributes can provide an absolute, precise, general and univocal representation, a minimal encoding method of the basic macroscopic information.
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As postulated above, any object may contain a finite amount of information as it consists of a finite number of atoms (molecules), in a finite number of quantum states, with a finite number of atomic bonds. Regardless of dimension, position, energy or time uncertainties that are present at quantum scale, the macroscopic information contained within an object can be complete and certain. This simply results from the finite energy (mass) value of the object and from our capacity to determine all its macroscopic parameters (the measuring devices do not affect them significantly). There is one more explanation, coming from the information "reduction" close to the atomic scale, which directly results from the properties of matter.
How could we find out the minimum amount of pure and uncorrelated information contained by a particle, a photon or a system of particles? And how could we measure it?
• The isotropy of the three-dimensional space automatically implies certain symmetry of the information carried by an object; therefore, this information is redundant and it may be further reduced. More, the global movement directions are no longer representing primary information in the object description, and neither its relative position in space.
• Near the atomic level, we are getting closer to a physical limit of information, as atoms are the "bricks" of any material object. This is in fact another level of information (it will be described below), which also includes a certain redundancy and a specific correlation. We further assume that all elementary particles forming the atoms are identical throughout the universe, having the same fundamental parameters. The only specific features they may have are the state and energy in those systems where they belong.
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• The temperature of an object, as reflection of its particles' kinetic energy, also adds a certain degree of informational entropy, which should be eliminated from this analysis of the "pure" information.
Upon its creation, an object stores intrinsic information that may change in time if its state changes; it may even disappear, totally or partially, when the object disappears. In conclusion, we may identify three layers of information within physical objects:
1. The macroscopic information, which is averaged in general, describes a global characteristic of an object, such as its size, shape, speed or color. The minimum amount of information at the macroscopic scale is one bit, which can have two basic states in binary representations like open-closed, yes-no, high-low, zero-one, plus-minus, etc.
2. The quantum information, which is dominated by uncertainty and probability, describes for example the atom's state, the spin of an electron or the polarization state of photons. At this level, the primary information can be measured using a special bit, the qubit, given by the superposition of two quantum states, 0 and 1:
|ψ⟩ = α |0⟩ + β |1⟩
where α and β are the probabilities of the two states and
α2 + β2 = 1
This type of information is directly linked to the number of distinct states particles and photons may have, namely of their degrees of freedom.
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3. The granular information, which is stored at the level of the building blocks of elementary particles and photons. An elementary particle, created by granular fluxes, may have a set of special, implicit features such as mass, charge or intrinsic spin. All the same, a photon may have some proper features: it may be complete or not, it may have a certain frequency or shape. But all these data are directly associated to that particular structure, and they should no longer be described. At the granular level of space, the primary information is exactly the existence of a granular flux, rotational or directional, at specific space-time coordinate of a reference frame.
This structuring process of the granular fluid becomes relevant this way, and therefore we suggest that the granular information might be given by the probability of existence of an elementary particle or photon, which is equivalent to the presence or the absence of a specific structure of the granular energy quanta. The granular bit could be given, in the relativized context of a presumed closed space, only by the overall probability of existence of a certain granular structure inside a system, at a given time, but not related to any spatial parameters.
In the case of the largest known system - our Universe, these bits would globally reflect the granular energy concentration, a sort of granular entropy; thus, the value of 0 would mean that the system is completely amorphous (maximum entropy), and 1 would mean that all of its granules would be constituted in structures. The granular bit would actually show the distribution of granular energy in that system, its capacity to be the primary medium of information, and therefore, the possibility to be used as base for the next informational level, i.e. the quantum information.
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Numerically, this bit would be given by the number of structured granules reported to the total number of granules. However, it cannot be used to work with information, because it only provides the necessary support for the two higher levels of information. There is no other information below the granular one, only free, equivalent granules that form the uniform spatial fluid. More, this homogenous granular medium (any density would it have) "dissolves" any kind of information, because the information is in fact, as well as the energy, only a temporary granular concentration. For the sake of simplification, the granular bit might be graphically represented as a sphere circumscribed to particles or to photons (Figure 43), which is moving along with them, setting this way the boundaries of the closed regions of space that may contain or carry information.
Figure 43 - Granular information
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These bits correspond to zones A and B, where the granular density varies from the average value d�. Their minimal spheres will only give a binary information, namely if that zone is an informational medium or not. The higher levels of information may be spatially marked as larger, shape-shifting regions, which may include one or more minimal spheres.
14.2. A definition of information
Regardless of its type (macroscopic, quantum or granular), information is a description of the granular fluxes' concentration at different dimensional scales, and therefore of the elementary energy concentration. It has a static, intrinsic aspect, representing the granular structure's proper energy, but also a dynamic aspect, as measure of the state of structures, of their organization and of their energy transfers, in the complex systems they may belong.
In other words, information is a "pattern" of energy, the form in which the granular energy is aggregated, and it describes its structuring degree relative to its uniform distribution in the spatial granular fluid. Information does not exist without the base of a granular flux, i.e. of a concentration of energy, and it disappears once the flux "dissolves" into space. Considered at granular level, its existence is based on the spatial regions with higher or variable granular density, like particles and photons. When some energy is transferred to other structures, the associated information may be transferred at the same time, partially or completely. Those three informational levels, L0...L2, i.e. granular, quantum and macroscopic ones are all represented in Figure 44, the upper part. At the bottom, we may see an example of informational "fields"; due to their dynamic shapes, they may overlap the space regions where the ordinary matter and energy are located.
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Figure 44 - Levels and fields of information
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These three-dimensional fields are the only regions of space that may contain information.
And the answer to Q1 is that we cannot find all the information contained by an object, because at least its quantum part has some inaccessible components, while the others ones may only be read through destructive interactions.
We may effectively work with information up to the quantum level, the lowest possible one, which sets up in fact the upper limit of the information density (Q2).
How can we work with information? Creating and storing information means to build or modify a structure, and this implies the use of a certain amount of energy. In order to read the information we need to interact with that structure, and this should produce a measurable response; the interaction also requires a transfer of energy. At macroscopic level, this interaction is minimal and it does not change the object being studied. On the other hand, the quantum information may be only recovered through fundamental interactions, which will change the states of particles or of their composed systems.
14.3. Destroying the information
Once created, the information may be copied, modified, or transmitted at a distance. The granular information stored in granular structures is lost the moment they are destroyed; as it is the basis for the other two information levels, all the information will automatically be lost. Thus, upon the annihilation of an elementary particle or the absorption of a photon, their component granules will spread throughout the surrounding granular fluid of space. In these processes of destructuring the concentrations of energy, the associated information is also lost,
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but a more appropriate and precise term to use is dissolution. As the granular energy is conserved, the granular information will be also preserved. However, due to the specific characteristics of granules, the dissolution process transforms and geometrically distributes the structured information support on the surface of some virtual spheres, centered on the source of information, and whose radius increases at the speed of light, c. This projection of the granular information on a sphere is an ideal process, which can only happen in the empty space. If the ordinary matter is present, the informational "shadow" projected on the sphere will spread out randomly due to the multiple granular reflections on the particles of matter. In both cases, the information will not be lost, it will just be impossible to recover from its diluted form, which will continuously expand in the spatial fluid. The semantics of the term "lost" is thus different when it refers to information, the true meaning being now "unable to be retrieved" instead of "disappeared".
Informational postulate #2
In the closed granular space of our Universe, all the information is conserved over time.
Explanation: the granular postulates ensure the linear propagation of all granular fluxes, however small they would be. Therefore, even the fluxes consisting of a single granule will have a linear trajectory if no reflections on material structures occur. Thus, the informational shadow can continuously extend through the spatial fluid, maintaining all fragments of the original information, until it reaches an almost zero density, equal to that of the empty space. The informational postulate #2, applied to the information level L0, is a direct consequence of another
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postulate saying that the total number of granules in our Universe is conserved over time (Granular postulate #2).
We may put this in a different way: the Universe contains all the existing information at granular level, whose average density has in consequence extremely low values. At a certain moment, a concentration of granular energy occurs somewhere (for example, an elementary particle is created); same time appears a concentration of granular information, as shown above. This information, extracted from the spatial "ocean" of information, has a maximum density and the same localization as the particle, going along with it during its lifetime. When that particle is annihilated, the information it contains, as well as the energy, splits into pieces, dissipates and goes back to the spatial fluid.
The example above could be generalized to include composed systems of any complexity, and therefore this postulate may apply to all the informational levels.
Informational postulate #3
The maximum propagation speed of any kind of information is equal to the speed of light in vacuum, c.
This is an automatic consequence of the granular kinematics postulates, corroborated with the fact that the informational support, i.e. the granular structures, has an upper limit of the traveling speed.
This postulate also assigns a relativistic character to the transport of any kind information, which will depend on the reference frames as well.
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Informational postulate #4 Within the closed space of our Universe, having the current value of granular density, the probability that the granular information will spontaneously appear is quasi-null.
The granular information, as well as the concentration of energy into structures that might generate it, cannot appear spontaneously anymore; the value of the granular density, much lower now than in the early ages of the Universe, drastically reduced the odds of a granular structure to emerge by chance. On the other hand, the current value of this density is high enough to ensure that all existing structures (or the ones that will form in the future) cannot spontaneously disintegrate.
14.4. Information and black holes
If we consider a macroscopic object that falls into a supermassive black hole, passing beyond the event horizon, we may notice how it loses all the information, on every level. The first one to disappear is the macroscopic information, once the object is torn apart and transformed into elementary particles (they are assimilated into the top layer of the star). The quantum level information will be immediately lost too, because the bonds between particles are destroyed when they got into the deeper layers of the star (formed only by very close quarks). In time, the granular information will also be lost as the object's quarks will soon pass through the granular horizon and the solid core of the star will assimilate them. Globally, the energy of the object will be stored in different layers of the star, and it all could eventually accumulate right into the stellar solid core. However, all three types of information this object contained, meaning the particular way its internal energy was structured, will be completely and
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irreversibly lost at the moment of granular disintegration. This is similar to the loss (dissolution) of information into the spatial fluid, as the empty space and the stellar core are both amorphous regions of quasi-uniform granular distribution, from which the information cannot be retrieved any more. The only difference may be the speed of the process; in case of the star, it could happen quasi-instantly at the core level.
Practically, a black hole absorbs all surrounding information and then dissolves it into its body. But there is structured matter between the two horizons, the event horizon (outside) and the granular horizon (inside), which could constitute an informational support. However, any information would be added to this region will be immediately lost into the very dense matter of the star, which does not actually allow any kind of complex structural organization.
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15. EPILOGUE
We analyzed the history of our Universe from the initial moment up to the present time, we launched a hypothesis on its birth and we described a possible scenario for its extinction. In my opinion, all above explanations for the emergence of matter, for its transformations and interactions are rational, coherent, and based on laws and principles of physics that are valid at any moment, in any place. The entire process of creation and evolution has been completely natural, and thus it may be easily explained and understood in every detail. Chance and randomness, which must be considered in regard to such a big space, such a long time and such a large number of extremely small particles, have played a special role during this process; however, they should not be confused with some divine intervention, not even at the very moment when the first alive cell emerged in this Universe.
Even if it would have not been formed in the First Bang (the model described in Appendix 7), but in a later Big Bang, our Universe is not a virtual one; it does exist, it evolves, it is as real as possible. If we admit that it is a closed Universe, as considered by the present theory, we will have to fight with a gnoseological limitation that stops us from acquiring a complete knowledge upon it. However, it is our duty to explore and expand our scientific understanding until we reach that limit.
We have shown that the three-dimensional Universe is bordered by the two-dimensional surface of the primordial "bubble", which encloses it completely inside a dimensionless "nothing". Seen as such, from the outside, the Universe does not exist; even if it is continuously growing in volume, this apparent
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"infinite" increase can only be perceived from the inside, where space does exist. This is the only thing that brings a touch of virtuality to the nature of our Universe, which may be more emphasized by its ephemerality.
Space, as described within this theory, keeps its duality during the expansion, even if one of its components "dilutes" in this process. Both components of space remain separated, and they will not be able to merge again into the nothingness they presumably came from. As any reason for the expansion to stop was not found yet, we will consider that the spatial expansion is perpetual; all the granular structures, from particles to galaxies, created in billions of years, will therefore cease to exist at a future moment, when a major cosmic cycle will come to an end.
***
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APPENDIX 1
The trajectory of the rotational spin vector of a free particle with half-integer spin, in an absolute rest state, is displayed in Figure A1.1 (the graphic representation [4]) and it should be seen in a three-dimensional perspective; thus, the black arrows are more distant than the gray ones. As we have already shown, this intrinsic precession motion of the particle is due to the rotation of all granules from its internal structure. But the precession is constrained by another condition: the instantaneous velocity vector can be neither collinear with the global velocity vector v�, nor perpendicular to it. The particle will therefore have a global rotating movement; it will return to the same point, with the same spin direction, after two complete revolutions.
Figure A1.1 - Trajectory of a free particle at rest
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However, if the particle moves along the horizontal axis at speed v > 0, it will describe a trajectory as shown in Figure A1.2. The frequency of this precession is constant and it depends on the particle's shape (its moment of inertia in relation to the axis of rotation) and on its granular angular speed; but the wavelength has a variable value, because it also depends on the speed v of the global rectilinear movement. As it is a free particle, the axis oscillation (wobbling) will not be added to the precession motion.
Figure A1.2 - Trajectory of a low-speed particle
Figure A1.3 shows the trajectory described by a particle moving at very high, relativistic speed. In this case, the possible directions of the instantaneous velocity vector (as well as the spin directions) are confined to the space between the two cones, oriented in the direction of the velocity vector, as in Figure A1.4.
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Figure A1.3 - Trajectory of a high-speed particle
All parameters of the rotation and precession movements have been estimated [1] in the relativistic speed zone, leading to the following results:
• The circular movement has a speed approximately equal to 95% c.
• The diameter of the circle is equal to 105% of the Compton wavelength (h / m0 c).
• The rest mass is in fact a relativistic one, and its value for a "fixed" particle would be 30.6% of m0.
These data, in conjunction with those of Section 6.2 and the Granular Postulate #1, give a more clear meaning and a concrete value to the absolute rest mass of an elementary particle - m00,
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which we have seen that only depends on the total number of the component granules.
Figure A1.4 - Spatial distribution of the instantaneous velocity
Now we may also calculate the upper limit of the granular speed, by the simple composition of those two perpendicular vectors, tangential and the longitudinal velocities:
C ≤ √2 c
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APPENDIX 2
Force F12 has a spatial component, F1, and an electric one, F2. The formula of the first force is therefore analogous to the gravitational pull equation (because they have the same origin, the local fluxes), where x is the distance:
F1 = k / (x + x0)2, x ≥ 0
The electric force increases linearly on short distances and decreases quadratically on long distances:
F2 = k2 x / (x3 + k3), x ≥ 0
The force generated by the gluonic field is similar to the pressure exerted by an ideal gas (equation of state p V = constant) on a surface of constant area:
F3 = k4 / (x + k5), x ≥ 0
The stable balance will be reached when:
F1 + F2 = F12 = F3
Figure A2 shows the attraction force F12 (in blue), the repelling force F3 (in red) and their resultant force F = F12 - F3 (in green), following the distance x [5]. Point A is one of stable equilibrium; if the distance increases, F12 will increase too, and on short distances F3 will also increase. The entire gray area, up to the point B, is therefore a zone of relative stability, in which the ensemble of the two quarks will act "elastically". Beyond the point B, the attraction force will no longer be dominant and the system will lose its balance.
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The energy required to get the particle out of its stable state is equal to the mechanical work of the force between points A and B (the hatched area):
E = ∫ �F1 + F2 - F3� dxBA
Figure A2 - The inter-quark forces
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APPENDIX 3
We will consider a mobile frame of reference that moves at speed v along the OX axis. A beam of light γ is emitted in this frame under angle φ to the same axis, in the direction opposite to its velocity. From the fixed laboratory frame, that beam will be seen moving at the angle α, which can be simply calculated with this formula (obtained by projecting the velocity vectors onto axes and their relativistic transformation):
tg α = sin φ / γ (cos φ - v / c) = sin φ �1 - β2 / (cos φ - β)
where β = v / c. For φ = 45˚ and β = 0.5 we get α = 69˚, i.e. the real angle significantly increases with the speed value.
Figure A3 - The change of angles with speed
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APPENDIX 4
The one-dimensional model of the accelerated relativistic motion of a charged particle has a simple equation, which may be expressed by the equalization of the Coulomb force with the accelerating force plus the one required to change the photon's granular flux (we only presume its proportionality with acceleration), where mass will have a relativistic value. Let x be the spatial coordinate of the particle, r the distance to the source of the electric field (considered as fixed).
Fe= e2/ 4 π ε0 r2 = e02 / r2
is the electric force, where r = x0 – x.
Fa = a m0 /�1 - v2/c2
is the accelerating force, a being the acceleration and v the speed of the particle.
Fg = (1 - k) a m0 /�1 - v2/c2
is the decelerating force, with k < 1 as a constant. By equaling these forces, we get:
Fe= Fa − Fg
e02 / r2= k a m0 /�1 - v2/c2
where a = x = - r and v = x = - r, and therefore we have
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e02 / r2= - k r /�1 - r2/c2
We may find out from this equation the exact evolution of the distance r in time, as well as the instantaneous speed and the time elapsed until the particle reaches a certain speed.
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APPENDIX 5
The alpha angle calculation:
It can be simply done by applying the conservation of the momentum and of the energy in that system, considering speed v as relativistic:
m c2 + m0 c2 = 2 h ν energy conservation and
m v = 2 h ν cos α momentum conservation
By replacing β = v / c and m = m0 /�1 - β2 we will get
cos α = β / (1 +�1 - β2 )
which shows that at v = 0 photons are emitted in opposite directions, while at v ≈ c those photons are collinear.
The energy of photons emitted by orbital electrons:
In the particular case of a simple atom, classically treated, after the quantization of the electron's orbital angular momentum, the speed and the orbital radius will depend on the quantum number n:
v = 2 π e02 / n h and r = n2 h2 / 4 π2 m0 e0
2
and the total amount of electron's kinetic and potential energy may be written:
E = Ec + Ep = - 2 π2 m0 e04 / h2 (1 / n2)
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The energy difference between two orbitals with the quantum numbers n and m will give the energy, and therefore the frequency of the emitted photon:
ν = π2 m0 e04 / h3 � 1
n2 - 1m2�
where m0 is the rest mass of the electron, e02 = e2/ 4 π ε0 and e
is the electron charge.
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APPENDIX 6
The spectrum of dimensions
Objects (distances) Usual units Meters [SI]
Observable universe 46 billion light-years 4.4 × 1026
Virgo cluster 54 million light-years 5.1 × 1023
Andromeda galaxy 2.5 million light-years 2.4 × 1022
Milky Way galaxy 120 thousand light-years 1.1 × 1021
Proxima Centauri 4.2 light-years 3.9 × 1016
Earth - Sun 8.3 light-minutes 1.5 × 1011
Earth - Moon 1.3 light-seconds 3.8 × 108
Earth 12.7 thousand kilometers 1.3 × 107
Eiffel tower 324 meters 3.2 × 102
Adult male 1.75 meters 1.8 × 100
Coffee beans 0.5 centimeters 5.4 × 10-3 Paper width 0.2 millimeters 2.0 × 10-4 Red light 700 nanometers 7.0 × 10-7 Hydrogen atom (Bohr) 52.9 picometers 5.3 × 10-11 Gamma rays 5 picometers 5.0 × 10-12 Proton 1.7 femtometers 1.7 × 10-15 Planck length 1.6 × 10-35 Space granularity [3] ~10-48
This table offers a perspective on the size of some important structures in our Universe and on the distance to them. We may
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notice that all starts from the quantum estimation of the space
granularity - of a value about 10-35m, while the structured matter covers a very wide dimensional spectrum within an observable universe of about 1026 m.
Note: Regardless of modifications caused by the space granularity [3] to the photon's features during propagation, the effects are uniformly averaged on long distances and thus such a small value may be justified. Anyway, this value is not exactly the granular size taken into consideration by the Prime Theory.
Figure A6 - Structures in our Universe
We may notice here (Figure A6) the elegance of the Universe: a quasi-infinite number of tiny granules has been built and shaped over time, only by the action of gravity, increasingly larger and
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more complex structures, such as the elementary particles, the atoms, the stars and the galaxies. In fact, all the fundamental forces described by this theory concurred in creating these material structures. They all have in common the same granular mechanics, but each force had a specific contribution, depending on its intensity or range.
Thus, the strong and the weak interactions act at the smallest scale, in the femtometer range. They ensure the inter-quark bonds and keep the internal cohesion of the atomic nuclei.
The electromagnetic interaction allows the formation of atoms, keeps them stable and allows their chemical bonds; its value becomes significant at picometer distances.
The photonic interaction was treated separately because of its special nature, being described in Chapter 8. Photons propagate through space and thus they can transport energy at any distance; this energy may be transferred afterwards to another structure or it may be converted into electron-positron pairs.
The gravitational interaction is the primary force that shapes things at any scale, on any distance. It lies at the base of all the other forces, by providing the granular fluxes they use to exert their actions, and thus it is solely responsible for the configuration, the movement, the stability and the evolution of any material structure in our Universe.
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APPENDIX 7
We found out how a universe in the extinction phase may give rise to a new one, which also explains the way our universe appeared. But how did the primary universe came out, and from what exactly? In line with the current hypotheses that include the formula "from nothing" (having some logical reasoning), a mechanistic model will be presented below, which could explain the genesis of both space and matter. In fact, according to the presumptions made in this theory, it will be about the three-dimensional space and about its component granules. If their appearance could be explained, this theory would become truly complete, as the evolution will simply continue in a predictable way, following the already known laws of physics.
To begin, let us assume the existence of a primal "nothing" that cannot be defined accurately due to the lack of any perceptible properties (stage 0 in Figure A7). Anyway, it has no spatial dimensions, and therefore no shape and no precise location. The normal time does not yet exist, since it can only be associated with material systems moving at a certain speed through space. All the same, the energy does not yet exist, in any form; as it will appear at a later moment, we will assign it the value zero at this stage.
At a given moment, which could be considered the absolute origin of time, this undefined "nothing" turns into two components, perfectly alike and complementary, which we will designate further as space and anti-space (stage 1).
These components have three spatial dimensions, a well-defined shape (which may vary in time), and they can move relative to each other. We could imagine them as two separate
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entities of approximately half-spherical form, being close to one another inside a primordial three-dimensional "bubble" that floats within the presumed non-dimensional "nothingness".
Figure A7 - Stages of the primary universe generation
We may assign to each component some special characteristics, similar to those of the matter, such as density and energy. Therefore, if one of them will have a parameter of a certain value, the other will have that parameter of the same value, but negative. As these two components are mobile, the energy they possess is of mechanical nature. The amount of their initial energy will be denoted with +E and respectively -E. Any movement performed by one of these components will be perfectly "reflected" into the other, which will move exactly the reverse way. The energy will not be transferred from one to the
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other, only its distribution will change over time. However, regardless of the internal movement, the total energy of this system will be conserved in time, as well as the energy of each component (stage 2).
The next significant step in the evolution of space and anti-space is the moment when, due to the internal (presumed random) motion, one of the components fully incorporates the other one, geometrically speaking (stage 3). Both entities remain distinct, but one of them, supposedly the space, surrounds the other on all the three spatial dimensions. For the plasticity of this description, we could add two new attributes: one of the components becomes "full", while the other becomes "empty".
At a later moment, the "empty" component, which we assume is located on the inside, will divide in two parts, also empty, having the same total amount of energy, E. These parts will continue to move within the "full" component, and sometimes will collide to each other elastically or will bump against the edges of the primordial "bubble". With each collision, the splitting process will repeat with increasing speed and the size of the resulting "empty" parts will decrease continuously (stages 4 and 5). Each elastic collision of the empty parts against walls will extend the bubble's outer surface, and thus it will increase in volume. This phenomenon happened very quickly and finally produced the following results:
1. The normal, three-dimensional space appeared in its current form: a geometrical framework undergoing a continuous expansion; it emerged from the "full" component described above, initially called space;
2. The spatial granules appeared, but they emerged from the component called anti-space, the "empty" one. The
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phenomenon of division continued up to a certain limit, when all the "empty" granules got to the smallest possible size; at the same time they reached the highest possible speed, while their total energy is conserved. It should be noted that the movement of granules through space happens without any loss of energy, at a constant speed; the inter-granular collisions are perfectly elastic, and thus they do not change the value of granular energy quanta.
3. The process by which a fluctuation of "nothingness" produces those two spatial components, followed by the division of one of them, constitutes a global phenomenon, which happens simultaneously within a large three-dimensional volume (and as it represents the absolute beginning, we might simply call it the "First Bang"). This makes it fundamentally distinct from the explosion of a singularity (the "Big Bang"), because the singularity is a massive concentration of already existing granules. On the other hand, if we accept the hypothesis of the "First Bang", the geometrical expansion of space will only occur in this case, and at a lower speed. A singularity, which may form in a long time, will thus explode within an already existing space; its granules will no longer bump into the edges of a primordial bubble: they will just collide with other granules already distributed throughout the space. In this case, the spreading speed becomes virtually equal to the maximum granular speed (Chapter 3). Several singularities might form this way several universes inside that primordial "bubble" and their granular density will have a slightly different evolution over time, decreasing at a lower rate.
This hypothesis on the birth of the primary universe naturally raises a few questions:
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A. What has determined the division limit of the "empty" space? B. Why do all the granules have the same size? C. In addition, is their size variable over time?
In order to answer questions A and B, we must first take into consideration the perfect elasticity of the "raw material" those components of space are made of. By similarity with the macroscopic effect of surface tension and of the internal pressure of fluids, we may infer that all granules have a perfect spheroidal shape (that shape of minimal area), and their minimum size is established by the special "fluidity" of those two spatial components. For the same reason, the "pressure" exerted by the "full" component has eventually forced all the granules to have the same dimension.
The answer to question C is affirmative. As it was already shown, the "full" component of space is continuously expanding; it increases in volume, and thus its "density" is getting lower. This may decrease the "pressure" exerted on granules, which may increase in diameter evenly. However, this fact is impossible to prove, it cannot be confirmed by any physical experiment. We are at the dimensional scale of matter constituents, and there are no measurements to perform. On the other hand, whatever hypothetical measurement we would do, it will be relative to other presumed constant quantities of the universe, which in fact would also have variable values.
If things are seen in the new perspective of space granularity, the natural length measurement unit should be exactly one granular diameter, and thus all spatial dimensions would get an absolute character. This measurement unit is practically impossible to use; but its possible invariance is further induced to the level of granular structures, to elementary particles. These
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particles, being granular collections of constant shapes, could be used as absolute dimensional references. Unfortunately, here we also have a variable parameter, namely the granular density of space, which finally determines the number of component granules in any particle. This dimensional variation would be further transferred to any macroscopic structure.
All these aspects lead to the idea (already stated in Section 11.3) that all fundamental physical quantities associated to a granular type universe have a deeply relative, uncertain and unquantifiable nature. Therefore, inside this kind of universe we may work with a minimal set of basic physical quantities, which are only presumed to be constant over time.
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REFERENCES
[1] Gallon, Ian L. October 2005. An Investigation into the Motion of a Classical Charged Particle. Physics Note 15.
http://www.ece.unm.edu/summa/notes/Physics.html
[2] K.A. Olive et al. (Particle Data Group), Chin. Phys. C, 38, 090001 (2014). The Review of Particle Physics
http://pdg.lbl.gov/
[3] P. Laurent, D. Götz, P. Binétruy, S. Covino, and A. Fernandez-Soto. Phys. Rev. D 83, 121301(R) - June 28, 2011. Constraints on Lorentz Invariance Violation using integral/IBIS observations of GRB041219A
http://sci.esa.int/integral/48879-integral-challenges-physics-beyond-einstein/
[4] Microsys Com ltd., 2014, WinDraw software utility
http://www.microsys.ro/windraw.htm
[5] Prime Theory's main website, 2015, formulas, models and related software
http://www.1theory.com
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Notes
General assumptions in this theory:
• The term relativistic speed means at least a few percent of the speed of light (c);
• The term waves propagating through space means photons, if it is not specified otherwise.
• The term absolute, used to describe the speed, mass, trajectory or the kinetic energy, means that the physical quantities are measured (or things are observed) from a special frame of reference, considered fixed in relation to our Universe.
• The words between quotation marks have a figurative sense.
New term proposal:
For granules, as minimal elements of space, whose dimension and kinematics were described within this theory, we propose a new, special English term:
granulon (-pl. granuli)
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