Planckons and elsymons

Part 1. Bereshit... (In the beginning...)

Bereshit – in Hebrew the first word of the Bible

     At the outset it should be noted that this article, just as the preceding one* (and those that follow) presents reasoning, not "new truths." It poses questions, including those which are not ask at present; contains explorations, hypotheses and their verifications. As a result, we get a quite surprising picture, though rather consistent logically, something that may even turn out to express the real nature. What if it doesn’t? That's fine, too. Creative wandering supports the objective truth or confirms the validity of the current assumptions. Let’s see...

     Although this article is not written in the convention of scientific reports, rather in the manner of popular science, the main addressees are the readers having had some preparation. The thing is that the material has not been scientifically verified and includes altogether new concepts that may be hard to recommend to young readers (and yet, let them use their unblemished criticism). It is also difficult here to refer to any sources, and there is no question of quoting or citing opinions of people involved in research in this field – which is a pity. This in fact applies to all the articles of this collection, which I hope will not discourage scientists (and others) from reading this document and the other ones included in this extensive work.

Contents

Introduction

1. Maximons - Planckons

2. System of two planckons (and a lot of reflection). The idea of bosons transferring forces under a big question mark (gravitons???)

3. Mass defect of a system of two planckons

4. Resultant mass of a system of two planckons

5. Elsymon – particle

6. Field saturation and energy contained in a gravitational field or the memories of the old times

Associations, reflections and thoughts  

Introduction

Phenomenology fails where there is no possibility of direct empirical observation of the investigated systems. This is obvious, if only due to the semantic meaning of the term phenomenology. This applies in the same measure to quantum mechanics and the general theory of relativity. So probably these theories, or rather their research procedures cannot be used as a criterion of correctness in relation to scales beyond empirical insight. Each theory has a limited range of appropriateness, and therefore applicability. My attempt to explore this undersize reality is, evidently, very arrogant. But hey, the dice is cast.

So how to check the validity of considerations, in particular the validity of the conclusions to which they lead? It's easy. The conclusions of the deliberations lead to certain expectations, anticipations of the observational and experimental effects. Compliance with predictions make presuppositions notable. So in that case are such considerations (without direct empirical basis) less scientific? They are perfectly scientific, provided that they are based on universal fundamental laws, deduced earlier, and confirmed without exception in all phenomena and dimensional scales. They would be scientific even if the empirical data did not corroborate the conclusions and hypotheses emerging in the course of investigations. But, as it will turn out, the conclusions of the reflections contained in this work do not contradict the results of research conducted in the scales enabling empirical exploration, even though they are not based on generally accepted procedures.

One can search hard for errors in the assumptions (particularly in the preceding article) and immediately give up reading, even if no errors were found. So this article would be beyond any attention, it wouldn’t exist for a careful critic (let alone the next ones...). But one can also make an effort to check the reasoning, to confront predictions against empiricism. I would consider this approach to be more scientific. Patience, openness, good will... well, we are entering the field of psychology. And what about curiosity and resulting from curiosity selflessness?...

1.    Maximons - Planckons

     Using universal constants G, c, h (G - the gravitational constant, c - the speed of light, h - Planck's constant), there can be derived (constant) formulas, expressed in units of length and mass. Here they are:

One can also create the value expressed in units of time. Suffice to divide  

 

by c: 

This value I consider as less important, less essential as a tool for exploration of nature. It is simply a secondary value and there won’t be much need for using it. Besides, you cannot treat time at the same level as the values which constitute the parameters of material beings.

     These values were introduced as "natural units" by Max Planck already in 1899. There are quite a lot of these natural units, yes, as there are many various physical values. We will focus basically on two most fundamental, outlined above. There is no need to examine other in relation to the specific content of this work. Markov (1966) called them maximons. Nowadays these values are called, respectively, the Planck length, Planck mass, Planck time and so on. The term maximon I will use later to describe something else.

   The rationale for this name lies in the numerical values of these new constants determining, perhaps, the limits of applicability of present-day physics, since modern physics is not able to describe the reality in the scales below the limits set by the magnitudes of these values. 

    The above described “maximons” are named quantum maximons because the formulas defining them contain Planck constant (that’s why index q). Here are their numerical values:

   Value ,  that is the Planck length, according to the current interpretation, is the limit value. Smaller distances are beyond the capacity of modern physics. These distances cannot be linked to any physical entity. Such a length (distance) can be found in superstring theory. Planck mass is also puzzling. It is huge even in comparison with the masses of the most massive particles (instead of being, as one could expect, much smaller). Planck mass is not therefore the limit value, but as we will see, this does not diminish its importance. In view of Planck mass, the Planck density, as it will be shown in a moment, is huge. We get it, of course, by dividing Planck mass by volume... Volume of what? A cube? Or maybe a sphere? Let us assume that it would be more appropriate to rely on symmetry, possibly the most perfect, spherical symmetry, so that there wouldn’t be some special directions and the distance be clearly defined. After all, we quietly assume that space is isotropic. Let us suppose, then, that Planck length is the diameter of the sphere, the volume of which will help us to determine density. Therefore we receive:

     You can also create the "classic" limit values. They are the ones that are called here maximons. Expressions that define them do not contain Planck constant, and instead there is the elementary charge. Here they are:

 As one can see in these formulas we express the elementary charge in CGSES units (Electrostatic CGS system (centimetre, gram, second)), where k = 1, and:

Thanks to that the defining equations are very simple. Here are the numerical values of these constants: 

Since I consider the electromagnetic field as secondary in relation to the gravitational field, I will not dwell upon (classic) maximons. However their existence, in particular their parameters, maybe a little disquieting in view of the findings to which I will arrive based exclusively on quantum limits. It’s about physical meaning. Let's initially look at this thing. So let us transform the formula into the formula for maximon's mass (5):

Let’s have both sides squared, and then multiplied by G and divided by the square of the distance. We will obtain:

 The left side of this equation is the Newtonian gravitational force, and the right side - the Coulomb force. So we come to the physical sense of mass . It turns out that it is equal to the mass of a material point which with an identical point interacts gravitationally with the force equal to the Coulomb force of mutual interaction of particles with elementary charges, placed at the same distance from each other. Maybe it's a clue towards the unification of electromagnetism and gravity? I think it’s far too early to resolve this matter at this stage. For now, I think, we can stop here. So let's return to quanta.

  Does the physical meaning of Planckon sizes concern only specific (limit) numerical values? If there were specific physical objects endowed with the features defined by these values, they would be very interesting creations: incredibly small and extremely dense. To such a hypothetical entity we will give the name Planckon. Quantum gravity??? I leave this question unanswered. For the time being we have no base for an answer.

Or maybe Universe at the birth of expansion was a planckon? Probably not, since its parameters are clearly defined, and Universe is changing. Besides, if planckon exists, what would force it to undergo sudden change? But let it be. How to reconcile these changes with the basic features of nature, which are expressed by the basic principles of physics, for example, laws of conservation. Not just that. If planckon was once everything, then what is it now? Universe? A being so complex, containing each one of us, creatures endowed with their whole worlds inside them...? It would be, of course, in flagrant contradiction with the essence of elementary being. Therefore, that’s not the way. Let us look at it differently. Planckon has a certain mass. As we know mass is an intrinsic parameter of each body, every particle and every physical system. So maybe planckon is a kind of particle? If so, would it be an absolutely elementary particle, or an absolutely elementary being that I mentioned in the previous article*? So could it be that planckons, a huge number of them, are the primary matter, and matter known to us, in all its forms, is built of them? I wonder where it will lead us, this (precursory) assumption that planckon is a particle.

In previous work, in an article devoted to the gravitational pull of material points I drew attention to the possibility, and in fact imperative, of the existence of an absolutely elementary being. This was dictated by philosophical considerations (and the logic of the narrative). Planckon would be just such an entity. Today it is an idea. Two hundred years ago (1808) John Dalton introduced to chemistry the concept of an atom** as an indivisible being, the smallest indivisible part of a chemical element. He concluded that the possibility of infinite continuous quantitative division of matter is not consistent with the existence of permanent weight (mass) ratios of the elements forming chemical compounds. However, in his day atom was more of a philosophical idea than realization of the existence of a concrete physical being with specific characteristics. At that time nobody even thought of experimental detection of such a thing (as something totally unrealistic).

One hundred years ago atom was already a concrete being subjected to empirical research. In 1911, Ernest Rutherford discovered the atomic nucleus. Today, the atomic structure is (already) known to each (self-respecting) high school student. There are many (quite a lot) subatomic particles, and the standard theory systematised them in an elegant manner. Perhaps now it is time to get to know the structure of the particles. The structures of all the particles, not only hadrons. This is indicated by the fact that despite the diversity of their "private" features, they have something in common. The standard theory has them systematised. This was possible under the condition of the "genetic" affinity, under the condition of unity of the whole matter. So there should be an element common to them all, a repeatable being, which is a structural unit of all matter. Certainly deeper (even much deeper) than the scale at which quarks "operate". It is another thing that so far this hasn’t been yet considered. Is that the reason to give up? Planckons? Yes, but let’s not get ahead of ourselves. I just don’t want to be baseless.¹¹

2. System of two planckons (and a lot of reflection).

    Plankton has certain mass, so it is the source of gravitational field. Due to the fact that this mass is extremely high in relation to its size, we can ask: "What is the Schwarzschild radius of an object with planckon mass?" To calculate this in a general way, we will use the formulas (1), (2), and the formula for gravitational radius:

Here is the calculation:

 We get the same relationship with respect to maximons. We see that Schwarzschild radius is equal to twice the planckon’s diameter. It follows that planckon is invisible, in any case to an observer who uses photons as a way of acquiring information. Are photons of any use here? Is it a virtual particle? If so, then it is completely different from those known to us. The fact that it can be called a black hole is, in the context of further deliberations, an insignificant detail. First and foremost we will focus on what takes place inside, below the horizon (of events?). This line of research is actually suggested by the result of the last calculation. 

   However, before we get inside, and to have a pretext for entering, we have to start with a system of planckons. In view of their negligible size, smaller than the gravitational (Schwarzschild) radius, it is natural to examine the mass defect of such a system. We confine ourselves to a system of two planckons. Let us treat them as thoroughly elementary particles. Planckons’ parameters (as limit parameters) give rise to a claim that in fact planckon is this absolutely elementary being, which I mentioned in the preceding article (*) while promising to characterize it, which I am just doing (starting to do). Even if de facto it is exclusively a philosophical idea (just as it was with the atom two hundred years ago). 

   So that we don’t run out of links in our investigations let us start with something that we already discussed in the previous work, that is with mass defect in nuclear systems (*). It is known that the total mass of the nucleons forming the nucleus is smaller than their summary mass when they are not connected to each other by strong forces. The mass defect is the difference between these masses. In the "classroom" explanation of the mass defect it is pointed out that pulling apart particles which attract each other requires external supply of energy (to do the work against the forces of attraction). And what happens when an external nucleon reaches the nucleus and is bound by it? Without going into the details and possible variations, it can be stated that if it is absorbed by the nucleus, the excess mass is equal to the energy of the emitted photon, generally gamma photon.¹² The point is that the total mass of the system is now smaller than it was including the mass of the neutron before its bounding.

     Therefore, (...) when a nucleon from outside reaches the nucleus (...) if it is absorbed by the nucleus, the excess mass (...) is emitted in the form of energy of the emitted photon. In the case of gravity, however, the situation becomes awkward. There is of course no problem to describe the free movement of body, from the point of view of energy relations in the system such as Earth. It is not a problem even for a high school student. Problematic, however, are the elementary systems. In their case we cannot talk of dissipation of energy in the thermodynamic sense. Temperature as a measure of the average kinetic energy of molecules loses here its raison d'être, it is not relevant. Also temperature as a value characterizing radiation is not relevant here because there is no heat radiation in such limited systems. And it is difficult to think of the emission of a photon which energy would be equal to the mass defect, because: At what point of mutual approaching this would happen, if it was to happen at all, given the fact that gravity is not electromagnetism? By quantization? Emissions of "gravitons", although they are only hypothetical constructs, and the chance of detecting them is simply zero? And even if gravitons, then how often? By the way: What would gravitons be, if planckon is the absolutely elementary creation?

   And if the photons ... Then one photon, or many? How many? How often, (and again) each one? What kind of photons?*** After all, gravity is continuous (regardless of the hypothetical gravitons, which existence raises my serious and well-founded doubt). In addition, gravity, in comparison with the electromagnetic interactions, is extremely week.¹³ But maybe in spite of all, gravity is also quantized****, though it is not about gravitons. In this setting the idea of force transferring bosons is under a big question mark.

     Any possible quantization of gravity immediately brings to mind the characteristics of planetary systems. The movement of planets is a bit like the orbital motion of electrons in an atom. Obviously, it is not the same. But it is an example of cyclic movement (see the content of the link with three stars), where the planets move along the stationary orbits. Do these orbits meet some quantization condition? They do take their assigned places? Classical, Newtonian description does not provide for this. But we have a Titius-Bode***** rule. Case open. Maybe dual gravity will be of some help. And what about elementary systems?

     Let’s move back to particles. In the case of cyclic movement the subject is closed - the system does not radiate. Suppose that it is a non-cyclic movement. In this instance, with the mutual approach of particles, does radiation occur? Rather no, when it comes only to gravity.

     Let's go back to electrically charged particles. We should note that smaller mutual distance corresponds to the smaller gravitational mass of the system. Is therefore emitted photon whose energy equals the difference of mass defects? Probably not, because this is the gravitational interaction. Gravitational mass of the system is smaller while the binding energy increases. And even if, the binding energy with respect to atoms and their systems, is minimal and absolutely unmeasurable. This can be calculated (see the previous article). Is the answer really no? Surely, during nuclear transformations photon is emitted, the photon with particular energy equal to mass defect. It is emitted, because the final state (and the one at the start), is unequivocally defined. We not expect emission when the final state is not defined. In addition, we are dealing here with particles interacting electromagnetically, individual particles. The situation is (phenomenologically) different when we are dealing with a stream of charged particles. Their accelerated movement, for example, somewhere in the accretion disk of a neutron star or closer, in the accelerator, makes them a source of radiation. It would be interesting to consider the matter from the structural point of view (structure of particle, interactions of particles forming the stream). 

As you can see, we touch here the problem of unification of both nuclear and electromagnetic interactions with gravitational interactions. So let the young take care of it. I think they will first try to prove that it is all nonsense - negative motivation is generally stronger. It's part of the fun. However, if they have already spent some money to buy this book, they should try a little harder. Maybe it’s worth it.  

     Let's go back to planckons. We have already accepted that they are the absolutely elementary being (even if it's just a working hypothesis). But returning to the interactions... If planckons are the real, absolutely elementary particles, then in their interactions they cannot exchange photons and other bosons, such as gravitons ("force transmitters"), which necessarily, as not being planckons, would have to be more complex creations. Moreover, photons (or other bosons) are to be built from planckons, through their interactions. So we have a kind of contradiction. It is therefore difficult - at this basic level of material being – to accept a model of interaction based on "force transmitting bosons." Not only that. The interaction between planckons should be rather of a gravitational character. Gravitons? In the light of what has been already said, their application for this position has to be rejected. In other words... Interaction between two absolutely elementary particles, consisting (according to today's paradigm) of the exchange of complex particles (bosons), is something unreal, simply absurd, even if the mass of a single planckon is much larger than the mass of the boson-go-between. After all, boson itself should be made of planckons, as a result of their interaction. Or the interactions by means of said bosons...?

     And when it comes to a body, that is a system (even of only of two material points), what would be the source of gravitons (or other bosons), thanks to which we feel that this system attracts us? Would it be the centre of the mass of the system (Nature is fair)? A place where there is nothing? A unique place in space? Let’s not multiply beings beyond need. It is not about some gravitons. They are simply misbegotten children of mental inertia, children of paradigms that have created quantum mechanics, which actually operates with great success, but in a completely different area (at a different scale), and in addition without gravity. Hence the conclusion, even general, that gravity does not need any intermediaries. This is another argument for the fact that it is the primary interaction. So perhaps here we have a starting point for attempts at deterministic interpretation of quantum entanglement?

     This quite automatically begs the question: Is the gravitational interaction immediate (not at the speed of light)? This would the heresy beyond heresy. Oh, the pile is piling up. After all, the range of gravity is infinite, and its existence in time is unlimited. In addition, new sources of gravitational field do not come into being. One can just about propose the law of preservation of elementary sources of gravitational field, because planckons are indestructible and new ones are not created. So you do not have to wait for the execution of order. You do not even need to order anything. Well, all this merits some consideration. The cosmological principle alone leads to the conclusion that Universe is a self-agreed over-object, and the pace of its development determines global time. Development of Universe in its every element, even at the smallest scale, takes place in the same way. There will be a lot about this in the following articles.

   As you can see, the die was already cast. This obliges us to take another path with respect to gravity, as well as in relation to the paradigm concerning "the transfer of forces". Is there such a way? I think so, and I think that it would also lead to the unification of all forces of interaction (including gravity); unification that (certainly) does not takes place at the scale of our physical sensations, and not even at the atomic scale. Somewhere much deeper at a correspondingly high concentration of matter. It can be assumed that we are dealing here with the matter of neutron stars and matter of galactic nuclei. Matter of great concentration existed also in the beginning of the Big Bang. Well, here everyone agrees... Creators of superstring theory moved in that direction, but became confuzzled by unconquerable mathematical infinities. No wonder. Applying to the same being the theories of which one does not feel gravity, and the second uses gravity to drag everything towards the point of singularity, is something truly excessive...  

3. Mass defect of a system of two planckons.

    Here we return to the issues that we already deliberated on in previous work, which dealt with gravity of a system of material points. For the record, the numerical value of mass defect of a system should equal the difference between the value of the potential energy at infinity (zero, there the mass defect is also equal to zero), and the value of the potential energy corresponding to the actual mutual distance of these bodies (as we known it would be negative). The conclusion: the mass defect is numerically equal to the potential energy of the system in a given position, with the proviso that it is a positive number.

     In a symbolic notation: 

Let such a system be made of two planckons. Next we will

 calculate the potential energy of this system. When planckons touch each other (figure A above), the 

distance between their centres is of course: . When calculating the potential energy we will rely on the Newton’s law of gravity. However, the formula: 

cannot be used directly, because it does not take account of the mass defect. Here's how this mass defect can be defined:

 This equation is essentially identical to the formula (4) of the previous work. Here, however, the masses are equal. 

     That’s because mass defect it is the difference between the total mass corresponding to a very large distance (in case of planckons we are talking about their doubled mass), and the mass of the system in a given setting when the distance is small enough so that the mass defect should be taken into account. This can be written as follows:

Is the formula (8) correct? We will examine it later when better outfitted in essential resources. If it is correct, then the results of calculations based on it should be consistent with each other, and they should also meet certain expectations. In the case of material points, we have received a satisfactory result.

   First we will calculate the mass defect of two planckons touching each other (see Figure A above). In this case r = L, mass defect is equal to M, and the mass of the system is equal as much. Indeed. To ensure oneself it’s enough to refer to the following equality: 

 We will use it several times. To demonstrate its correctness it suffice to rely on the equations defining Planck values appearing in this formula - good exercise for high school students.

   So the Planck length  can be defined as such the distance between two planckons that from outside the system "is viewed" as one planckon. Encouraging result. In addition, it reminds us of the result of a similar calculation made in previous work, and concerning two material points, as well as fairly similar, new definition of the gravitational radius, that makes it a general case. This would indicate that in our current study we are pursuing the right path.

   And what is the distance, if the resultant mass is equal to zero, that is when the mass defect of the system is equal to double the planckon mass? Is that at all possible? Good question, because to satisfy this condition, planckons would have to penetrate each other. This is depicted in Figure B. So let us make another step forward. Let’s note 

that there is no reason for our planckons to be covered with crust resisting attempts to get inside them. The existence of such a shell would mean the existence of additional repulsion, but let’s remember that by assumption planckons constitute absolutely elementary being. Repulsion (the resistance of the crust) would indicate the existence of some additional, unaccounted for, interaction, and it would also testify to the structural complexity of this absolutely elementary being, that is to the existence of some (dual) interactions at an even smaller scale, which would in turn contradict the fundamental assumption, namely that they are absolutely elementary beings. Anyway, this potential interaction, this outright new world would be literally indescribable. Planckon can be described only because Planck parameters are based on observables. Add to this that the existence of such a shell would not be probably consistent with the properties of matter as we know it. But to come to this conclusion, we should get to know better the world of planckons and their systems, and also be able to connect it with the world of our perception. That is the purpose of our research. Apart of it, the Occam's razor warns us against the hasty introduction of the new beings.     

   Finally we realize that looking at planckons penetrating each other, we simply state that it is about interaction of two gravitational ("source") fields. Thus such creations (planckons) would be the elementary sources of gravitational fields, and with it, the building blocks of all matter (including radiation). The condition for this would be the existence of gravitational repulsion (as it was with the system of material points). It’s worth noticing here that the gravitational field, in general, is conservative: centrally and potentially. So in a natural way we expect that the planckon’s field (the field of an absolutely elementary being) is just like that, which means that is not a vortex field (field of non-zero rotation). Anyway, features of planckon’s field – as of the absolutely elementary being - should affect the characteristics of gravitational fields (and other force fields) at any scale levels.

Damn ambitious plan to push through..., or just unruly thoughts. 

   So let us draw our planckons even closer to each other and let’s ask: "What should be the distance between their centres, where the mass defect is equal to their total mass, that is: 

Using equation (10), we get:

 As you can see, in this case the system is "invisible" (also for sensors detecting gravitational field), because its gravitational mass is equal to zero. What does this remind you of? Of course photons. And if we bring them even closer to each other? Then we have gravitational repulsion. Are there any repulsive particles? Neutrinos? Oh, those unruly thoughts... ²¹

4. Resultant mass of a system of two planckons.

From the calculations above it transpires that the mass defect of a system of two planckons equals to the mass of one of them when the distance between their centres equals Planck length. The mass of the system comes to zero when they are separated by half that distance. So we see the absolute convergence of these conclusions with the results of calculations carried out in the preceding article, dealing with the system of two material points (for the record, Planck length is equal to half the radius of gravity). It turns out that the results of our research are most general and independent of the size scale. This of course encourages further investigations. Let us determine the gravitational mass of two planckons, taking of course into account the gravitational mass defect. As we already known, it is defined as follows:

where:  m* is the sought mass of the system. Using the formula for the mass defect, we get:                

         

 because, as we know:              

 Formula (*) can be easily tested. We will do this only for the two cases for which we know what to expect. When: r = L (planckons touch each other).

as expected.

When: r = 0,5L we have:

as expected.

Of course, let us immediately note that in case of a still smaller distance the mass becomes negative. Judging by the formula (*) we find, too, that when r tends to zero, the negative mass tends to infinity. We are dealing here, of course, with the negative gravitational mass of the system, which therefore repels every object with a positive mass. However, already in the first article of this series, devoted to material points, I drew attention to the fact that the elements of such a system also mutually repel each other with a force rapidly increasing as the distance between them decreases. [The thing is that the mass of each separate point is positive. However, they are in a field, which intensity is directed outwards of the system. The closer they are to each other the greater the intensity. Therefore these points are under a force facing outwards, which is manifested "phenomenologically" as mutual repulsion. That’s how the matter can be interpreted.] Actually, this leads to a stop, regardless of the initial speed with which they were approaching each other. We'll ascertain it already at the end of this article.     

     This fact enables the concentration of matter in a single point. By concurrence with quantum statistics this could mean that planckon is a fermion. After all, is it not a foregone conclusion that at this scale range they lose their meaning? They can be an expression of the most general characteristics, the source of which may be actually the planckon range. Of course, it also associates with Pauli’s exclusion principle. And if we go further, we can even come to conclusion that the existence of the Pauli’s exclusion is the proof of the existence of dual gravity. The possibility of planckon being a fermion can be indicated by the result of (quantitative) consideration which I have already presented in my book published in 2010. They show that plankton’s angular momentum is equal to 1/2ħ. One of the articles of part three is dedicated to this question. Therefore, singularity appears only on paper. My dream is that even paper rebuffs it.  

May it be that by principle any single body, any particle can have a negative mass? Let’s note that negative mass is the gravitational mass, which means that it applies only to a system. But each body, each particle makes a system. Only a single planckon cannot have the negative mass, because it’s not a system. But then it’s hard to consider its mass to be positive. Neither positive nor negative, nor zero. That’s its political wisdom - you might say. [Is political correctness equivalent to wisdom? I think it's a rhetorical question.] It is known "they are either with us or against us" - no minuses or pluses. Bowing down to paralytic Europe. This is however difficult to write down. Well, it’s good that the mass of a planckon has a special designation. You can try a different way. Positivity is the norm, general standard, while negativity is something special, conditioned by gravity. Something unique as antimatter versus matter... In this context we should note that an electric charge, called negative or positive, is actually a convention, the physical quality in both cases gravitationally positive. And what about neutrino? We’ll come to it. Everything in due time. We still have a lot in front of us.

5. Elsymon – particle

   Above I drew attention to the possibility of repulsion between planckons. If so, then there is an energy niche - in the middle between attraction and repulsion (depending on the mutual distance of planckons). It simply automatically conditions the possibility of vibrations. This also provides for the possibility of planckons connecting each other, of creation of stable systems. Thus a number of planckons can be joined together, any number (though up to a certain limit). For an outside observer the mass of the system (say averaged mass) can be equal to zero. At this point it does not matter what shape, what geometric form it takes, what is its topology. Zero mass suggests that it might be a photon. Various photons.

   Of course, mass can also have a non-zero value - positive or even negative. So we come to the preliminary qualitative model of the structure of the so called elementary particles. Their mass depends on the number of planckons, and on how deeply they are interconnected. It may be very small compared with the mass of a single planckon: for example it may be the mass of an electron. "If so, then why the masses of all particles are relatively close to each other (by maximum factor of 10^3)?" Perfectly legitimate question. The preliminary model answering this question is presented in the next (sixth) chapter. But let’s not jump ahead of ourselves. For simplicity sake the system of interconnected planckons we will call Elsymon (elementary system of matter)******. Is elsymon really a particle? Maybe only a virtual creature. There is a benefit, however, not only in the fact of writing down these fantasies. After all, thanks to them we see more sharply, first of all that the thought does not have to be subordinate to "official" beliefs. Returning to elsymon, let’s ask: "Can every elsymon be a permanent creation? Or maybe there are some selection rules by which only certain elsymons deserve to be detectable particles?" One can expect that the (more or less) permanency is a matter of symmetry, or specific structural asymmetry, according to which a particle is built (at planckon scale). It is a matter for further research, although some suggestions will appear already in the next chapter of this work.

At the beginning of our discussion, we calculated the gravitational radius of a single planckon. In this context, we noticed that in the case of a system of planckons, due to its maybe even considerable mass defect, the radius of gravity is smaller and tends to zero as the mass of the system tends to zero. We have already noted, moreover, that in the more general case an elsymon, even if very complex, can show a small mass because a substantial part of its mass is closed (high mass defect). Such a composite elsymon may, however, have a relatively large volume. It follows that: a) the mass of a particle (elsymon), while relatively small, can correspond to the masses of elementary particles; b) due to relatively small mass, the gravitational radius of such a system (and not a single planckon) is very small in relation to the elsymon’s volume. Such a particle is therefore "visible" (its detection is possible), although c) is not possible to experimentally and unambiguously determine its dimensions and spatial characteristics. It is possible that the particle itself is a complex system of planckon vibrations. Thus its status quo at a given moment cannot be specified (uncertainty principle). So our particle is a variable creation due to the dynamics of the vibration that certainly occurs in it; it doesn’t have to be spherically symmetrical. Besides, to examine the system one needs to intervene in it making the result the matter of statistics and probability, which of course brings to mind quantum mechanics. This motif can constitute an interpretational completion of this branch of physics.

6. Field saturation and energy contained in a gravitational field or the memories of the old times

    For a very long time I have been intrigued by the problem of saturation. This phenomenon manifests itself, for example, in the existence of chemical compounds. A molecule of a durable chemical compound does not tend to bind any additional atoms. I omit here the possibility of bonds in the crystal lattice, and skip the fact that particles at very close range interact as dipoles, quadrupoles or multipoles. That’s not the point. It’s about the existence of saturation, like in the case of a molecule of methane, the simplest example of a saturated hydrocarbon. The field around the carbon atom enables binding of only four hydrogen atoms. Much time has gone since I started to be puzzled by the problem of saturation, particularly in gravitational interaction. Is the presence of other bodies around the source of the field having an effect on their total field, and, of course, on the field around the source? Is there a possibility of its saturation, kind of liquidation of the field due to participation in the interaction of a sufficient number of bodies, elements of the system? Intuition told me yes, there is. Lack of saturation would render the field’s energy infinite, which in fact would contradict the principle of its preservation. I didn’t come across anything like this in the research literature. Is the saturation simply irrelevant because the science of gravity went in the direction that is not consistent with the quantum vision? Perhaps. Could it be thought that there is no limit, that there may be an infinite number of sources, that it is enough to have the principle of superposition? Could it be thought that it is a trifle, triviality? That there is no problem at all? Or maybe it just got swept under the carpet?

   I imagined (in those old days), maybe a little childishly, atom, as well as the source of the gravitational field, as a ball with a limited (however) number of hands. "After all, the energy contained in the gravitational field around a body cannot be infinitely great. Can’t be infinite, and therefore limited because around the less massive bodies field is weaker. Not infinite, even when it comes only to energy density." [I considered this matter in the Appendix to the previous article. There I noticed that the total energy of a field around the source point is equal to half of the invariant mass of the source (with a minus sign).] The existence of diversity of fields, depending on mass of source-bodies was a sufficient clue and motivation for reflections and thoughts. The body of greater mass would have more of these "hands" than a less massive body. The summary energy contained in a field around it would be greater. This would even suggest some form of quantization - including gravity. The same of course applies to all bodies. Bodies join hands. The closer they are the more hands are joined, the more these bodies are bound to each other. So it is conceivable that all hands are occupied. No spare ones left. Then such a system is simply gravitationally saturated. There is no gravitational field around it, which also means zero mass. What does this remind you of? Are these only some naive speculations?

   But I have a little problem here. Everything fine, provided that the masses of bodies are equal (the same number of "hands"). However, this is a (very) particular case. And if the masses are not equal (which is generally the case)? Then zero is not achievable, is it? Yet from (general) considerations concerning material points it transpires that gravitational mass of the system can also come to zero when the masses are varied. So is the model with "hands" a dud? It is too simple? It seems to me that, apparently (no reason to immediately give up), this model could hold only for the most basic systems. In a moment we'll see what justifies this hope.  

   This brings to mind the lines-of-force model. It’s a pity that the thought of saturation, once it occurred, was not continued, was not developed. Would the content of the preceding paragraph justify it? It is rather about something else. Well, the concept of saturation is not consistent with the paradigm that is currently absolutely binding, namely that gravity means only attraction. When I was young dreams were like reality. And today? Reality is almost not a dream. Although as for now, it is rather only my personal reality.   

   And planckon? Probably it has a limited "single digit" number of hands, for example four (why more? Nature is modest). Three of them join hand-with-hand with three other planckons forming tetrahedron²², an elementary cell (three-dimensional space?), which has also four free hands. Such identical cells can thus join each other (as single planckons) into more complex systems, which are also sources of the gravitational field. They can also create closed forms of various sizes. Photons? ... This model probably explains why the masses of the particles we know are of comparable magnitudes (see previous section).

   There is also another possibility, no less interesting. Planckons, still having four "hands", can create a dodecahedron in which each of the walls is a regular pentagon.²³ Here it is worth noting that the regular pentagon is associated with the golden ratio of line segments, which in turn is related to the Fibonacci sequence. Golden ratio manifests itself in nature in countless forms, both in animate and inanimate nature. As we can see the number of planckons connectivity options is, however, not infinite (due to the assumed in this work existence of saturation of the gravitational field - no matter how appears its mathematical model. This is for the workshop). That suggests the possibility of some selection rules while modeling (on paper) the structures of elementary particles. Is it only fantasy? Maybe, though probably not baseless, in any case at least at this stage of analysis. But the die was cast a long time ago.

   The description of interaction of material points, and in this article – interaction of planckons, brought back to life my thoughts from the seventies and earlier years of the last century. It looks like saturation really exists. The field of the system is weaker (in terms of energy content) than the total field of separated components. The weaker field means smaller mass. With the right number of them and their appropriate concentration the field may even disappear. If there are a lot of them the field may disappear even when the concentration of matter is not all that great. The most obvious example of such a saturated system is... Universe. The cosmological principle, which constitutes the base of my thoughts, actually the only a priori condition for modelling Universe, simply demands that the intensity of the gravitational (cosmological) field should everywhere equal to zero. And other universes? They do not see ours (Just as we do not see them, despite the widespread acceptance of various interesting visions of such prominent popularisers like Michio Kaku). If they exist, each of them is an autonomous, closed space. Nothingness? And what the Bible says about the beginning of the Big Bang? In the beginning was “emptiness and chaos” – not at the same time. Chaos was somewhat later (the conjunction "and" may indicates succession in the course of events). At first URELA (Ultra-relativistic Acceleration – there will be more about it in the following articles), and then the phase change (chaos, fraktalization, temperature).

    In my youth I was asking myself another question: What is the total energy contained in the gravitational field around a specific source? For example, the calculation of energy contained in an electrostatic field between the capacitor plates is not a problem even for a high school student (provided he/she is not too modern, that is knows nothing, because the mind is in the tips of the fingers running over the tablet screen). Nobody, however, pondered on gravitation. „If gravity is the curvature of space then the question above does not correspond to reality”. Is therefore gravity devoid of materiality? And yet its magnitude is conditioned by the mass testifying to the presence of matter. Here it is worth to look into the previous article, and more specifically to the Appendix at its end. There, I come to the conclusion-hypothesis that the energy contained in the gravitational field around a (spherical) point source, is equal to:

 This is, of course, hypothesis. I wonder where it can lead to. For example, in relation to a single planckon. I will give the answer elsewhere. Here I will just blurt out that it leads to the calculation of planckon’s spin angular momentum: 1/2ħ, or to unveiling it as Fermion.

  

Associations, reflections and thoughts

  ¹¹) In this context, there may be a justification for associating planckons with Higgs particles, and the field produced by a multitude of planckons with "an ocean, or the Higgs field." It would be, according to current opinions, filling the space continuum. All of the particles interact with it (via a boson of the same name), though unevenly. [And why unevenly?] For this reason masses of particles differ from each other. The introduction of something like this to the theory was an urgent need. Without this the standard model would be incomplete, since it would not have been able to show the cause of the diversity of particles’ masses. [And what is the cause of this cause? It's probably a matter of the structure.] Higgs boson gained great fame; it was even called "the divine particle". Apparently it was finally discovered in the LHC. This Great Discovery requires, however, confirmation.

The concept of Higgs bosons is based on the procedures of quantum mechanics, quantum field theory which does not consider gravity. At the same time the inherent equality of gravitational and inertial mass is taken as something well established. The existence of the Higgs field apparently allows for the differentiation of masses of inertial particles. What about gravity? I think it's a kind of inconsistency. And if consistency, then wanting.

Let's say that the Higgs theory, and in fact the theory of the whole group of six physicists  (Robert Brout, Francois Englert, Gerald Guralnik, Carl Hagen, Peter Higgs and Tom Kibble) somehow deals with the questions: "Why the mass of a defined particle is such, and not another? Why the mass of particles differ from each other in that particular way? Why they actually vary?" After all, this theory does not interconnect (because it cannot) the known characteristics of particles with the way they are structured. It simply does not touch the structure of particles (and its conditions), particles which remain, in particular leptons, rather point objects. Is it actually possible to understand the diversity of particle masses in the absence of links between their properties and their internal structures? Judging by our conclusions, we can infer that the mass of a particle is primarily determined by its structure and by how densely its elements are packed together. I presume that this approach – based on the postulated duality of gravity and resulting from it planckon model - may advance our understanding of the question of differentiation of particles. We will soon find out that the structure of particles is determined by gravitational interactions, which is a foreign concept to quantum theories. It is worth noting that the planckon model responds easily to the questions posed a little earlier (those with which the standard model doesn’t seem to be managing too well), and as we shall see, also answers questions which leave the standard model (along with the Higgs field and bosons) helpless, and will even tackle the questions which the standard model is not even capable of asking.

     And what is the physical meaning of the vacuum energy? – Well, just another question.

      Considering planckons or actually the environment which they create, we will come to conclusions which make even an alternative to the Higgs’ concept. My approach to the problem is indeed different, and apart, the questions which have been already asked (the ones above) and many others can be also answered on the basis of the planckon model, and moreover it leads to, as I mentioned above, to unveiling the structure of particles, and even the principles underlying their construction. Of course, my role is just to present an idea. If it is correct ... Let’s hope. There will be a lot of material for PhD theses. I think that at the end of this digression it is worth noting that Higgs particles are bosons. And what about planckons (if indeed they are not just scientific aid)? But let’s not get ahead of ourselves (although I already blurted out something).

     Incidentally it is worth noting that Planck mass is not the mass of the Higgs boson. It is much greater. The ratio of their masses amounts to 10^17. In addition, our boson decays (average lifespan is 1.6 · 10^-22 sec.). And, anyway, what is the physical cause of the disintegration of the H boson (and, of course, of other particles)? ... Wait, if it decays, in addition so quickly, how does he know that it is a proton, not electron (for example)? And what causes its decay? Self-made? Then why the disintegration time is average? This would mean that the decay is caused some external factor. Let’s remember that particles of the same kind are indistinguishable. Maybe the guilty ones are background neutrinos of diverse energy (it is only a working hypothesis). Why neutrinos? About this some other time. Can our boson, before it falls apart, have the time to determine the mass of the particle which causes its decay (say neutrinos)? I agree, it is a naive, boyish question.

     So I renew my question: Can we also qualify planckons as bosons? It will turn out that no, that they are fermions with spin 1/2. This would be consistent with our assumption of dual gravity. As you can see, it's not the same zip code.

   We shall see that the "vacuum energy" fits very well with planckon model. It is possible that the ocean of planckons creates material background for observable entities (not the Higgs Ocean). Maybe it also has something to do with the Big Bang and with the process lasting very briefly at its very beginning, of an accelerated exponential expansion (though not inflation but URELI – we’ll get to it in the subsequent articles). There is still a lot ahead of us.

   ¹²) As an aside, let’s note that mass defect of nuclear systems, although it is associated with strong forces, means also that the total gravity of two nucleons (it doesn’t matter that it is immeasurably weak), is smaller when they are together in the nucleus, in comparison with their summary gravity when they are separated. That’s because the gravitational field depends on the mass of its source. This problem might have baffled already a long time ago, and skipping it only because of the relative weakness and immeasurability of the gravitational field of such small systems, I think to be wrong, because it makes the picture of the reality incomplete. Our capabilities in the field of measurements should not constitute here (and not only here) the criterion of existence. Another cause of this omission, perhaps no less important is that the general theory of relativity (the theory of gravity) does not consider mass defect because it doesn’t enter into the reasoning behind its structure. I already wrote about this in the previous article.

   The above remarks require some further thought. For if we express the mass defect as the difference in energy of strong interaction in two states, we get a very high energy, gamma photon energy, emitted as a result of specific nuclear transition. This energy appears to be inadequate in view of infinitesimal, completely negligible difference in the intensity of the gravitational field. "It's just resulting from Einstein's equation equivalence of mass and energy, having nothing to do with gravity." You can say so, however mass is a "building block" of (space curving according to GTR) gravitational field. And the gravitational field itself... after all, it has infinite range, so it is scattered in terms of energy in an unlimited expanse, far beyond the nucleus. That’s also worth considering.

   Let some "nuclear charge" keep getting smaller (as in a different situation, electric charge, somewhat like mass defect). We would then have to do with the "nuclear mass" defect or (in other circumstances) loss "of electrical mass, that is charge". But there is no such thing. For example, the mutual approach of electron and proton does not cause continuous (!) change (decrease) of their charges. Charges are simply invariant. And yet mass decreases, and it happens regardless of the fact that potential electrical energy of mutual interaction of these particles also decreases (naturally, equivalent to a certain mass)***.

   In any case, there is mass defect... gravitational mass defect (or what comes to the same thing, inertial mass defect) of the system. The total energy equivalent to it may therefore be quite large, so that in the case of nuclear transformations (e.g., neutron capture) causes emission of gamma radiation. Let’s not forget that mass defect is expressed in units of energy. As it can be seen everything, kinds of, comes down to gravity. We can already venture to say that gravity constitutes the base for other interactions. Further considerations will confirm this observation.

   On this occasion let’s note something seemingly insignificant, that immeasurably small mass defect is equivalent to a relatively large, by all means measurable energy. Contrary to popular opinion, this could mean that gravity is very important, if not the dominant element of reality also in the scales, in which is ignored. Apparently the nucleons in the nucleus are so squeezed that considerable (gravitational) mass defect of their system does not allow their further mutual penetration. [Would the statement - "No wonder, after all nucleons are fermions and so the Pauli exclusion principle applies." – closes the matter? Let’s not wind up the problem with a little rule because it is not an explanation. And where does this prohibition come from? Most likely, from dual gravity ...] Do we by any chance come near to unification of gravity with strong interaction? Electromagnetic? After all gamma photons are emitted. Even if we only get the feel of it, it is worth considering, and not discarding the matter just because the theory (one or another) does not consider this issue, for example due to the weakness of gravity in atomic systems. Soon we will actually come to conclusion that despite all, gravity is not so weak..., and judging by the huge planckon’s mass, we can already put forward a thesis that gravity is the primary interaction, and even the building material for the other ones. There is rather no question of randomness in this regard.

¹³) Let’s note that the energy of electromagnetic field is quantized. One can assume that this is related to the fact that the elementary charge is indivisible (there aren’t any small parts of it). By the way, this fact actually is the cause of the whole "mess" of quantum mechanics, even though today a key theme of reflections within it is the wave-particle duality and the uncertainty principle including probability concerning measurable quantities (in the context of the doctrine of observability) and identified as a solution to wave equation for given conditions. This does not apply, however, to mass, which changes continuously due to the continuous changes of systems’ gravitational potential energy. So it is difficult to immediately (for instance on the basis of the remark in the underlined sentence just above) talk about quantization of energy of gravitational field (although nowadays this is talked about - such physicists’ dream based on the currently "natural" premises)****. It is difficult, without the imposition of specific conditions, and without the adoption of some other premises (see reference***), to expected quantization of energy changes in a gravitational system. It is hard to expect the emission (or absorption) of specified particles as a result of changes in its condition.

     It is difficult, so it can be done... As it turns out (see the same reference), it is possible, moreover with the participation of photons despite the fact that getting closer (or further apart) does not take place in sudden jumps but continuously. Yes, with photons... but under the condition that the target state is determined unequivocally, as, for example, in the case of neutron absorption by atomic nucleus. This solution would be consistent with the often mentioned fact of a link between nucleus mass defect and emission of gamma photon of equal energy. Of course, this does not solve all the problems. Rather indicates a promising lead.

     And what if the target state is not specified and, for example, the elements of the system approach each other? Then we cannot expect radiation of energy equivalent to system’s (progressive, continuous) loss of mass. In this situation, the only solution is to come to terms with this, that is to accept as possible that the gravitational mass of the system decreases (gradually, as its components approach each other). It is formally equivalent (as the distance between elements diminishes) to gradual increase of the negative mass, compensating the positive mass of the system. That’s how it can be modeled for a quantitative description. Incidentally, we have here one more argument confirming the idea that gravity is the basic, primary interaction.

It would seem that an alternative solution is a gravitational wave taking excess energy. Yes, but what would be the length of this wave? Variable in time? Variable on a continuous basis? This is certainly not satisfactory.  

   It is not, however, about the "substantial" mass of particles. Matter does not diminish just as no new particles come from nothingness when the elements of a system move away from each other (mass increase). This should be emphasized. It's just about the decrease of potential energy of mutual interaction. It’s about the resultant energy. In this situation the potential energy of interaction would be the algebraic sum of negative energy (of attraction) and positive energy (of repulsion). When one decreases, the other increases by the same amount (principle of conservation). Of course, this transformation in pure form can be separated only in extra-micro-scale, below the threshold of quantum interactions (electro-weak and strong), which dominate above. One can also presume that the forces occurring there are quite large. Gravitational forces. Let’s note that we can also have a situation in which both forms of potential energy are numerically equal. At that moment the system is set to zero. It disappears as a gravitational existence. It can be assumed that at this point its electro-weak and strong interactions also disappear. In this state all interactions will unify with gravity, which becomes further, deeper, the only agent of change. And with elements getting still closer to each other... gravity starts to repulse. Is it a too far-fetched fantasy? Not anymore, because we have behind us the previous article (*).

     And what about specific bodies? Each body is a system of certain gravitational mass (which was discussed in the said article). If it is compressed, for example as a result of gravitational collapse, its mass decreases. How long (along with thickening of matter) the mass can decrease? First of all, it could mean that the measured mass of each body is greater than the mass of the substance therein. By how much? By the amount of energy of its gravitational field. What is that "substance"? It is a subject for further research. By the way, "it would mean the possibility of the borderline of compression, corresponding to the substantial mass." And what is it that has that substantial mass? Wait, wait. At the deeper level there is also repulsion, and thus the field again. So is it that the system has solely substantial mass only in case when it is devoid of the characteristics of attraction and repulsion (has zero mass)? I think so, because then it does not produce field (which also has mass)... So it would mean that the substantial mass does not exist, would it? So field is everything, is it? And what about planckons? Still a lot more thinking in front of us. What kind of matter is this about? Probably not the one we know from autopsy. So is it only a fantasy?

   And how it in case of planckons appropriately close to each other? (after all, they are forming our bodies)? What does mean "appropriately"? Touching each other? And what is this point of contact, when talking about the field? Display stage for force transmitting bosons? What bosons? All of them are made of planckons... Is it at all possible to unambiguously determine the "substantial" mass? Besides, just a moment ago we lost faith in it. But the "material matter" (not field) probably exists. We’ll think about it further on. So here you go, questions live their own lives and they are very impatient...

   As we know, mass defect has an impact on other interactions. It is particularly noticeable in relation to the atomic nuclei (which is commonly known, and even exploited, not necessarily for the sake of peace). Yet mass is the source of gravitational interactions (not of those strong ones). What kind of conclusions can we draw out of this? You can venture to say that this issue concerns only gravitational interaction, although at a higher level of the organization of being, which means in our experience, it appears as an effect associated (for example) with strong forces. Therefrom one could draw the conclusion that gravity is the fundamental, basic interaction. Other ones result from it! The primary character of gravity is attested by continuous (not step) changes in energy. This continuity would be the indication of its primary character. Is it right? From a philosophical point of view "it is acceptable." Quantization, in any case its probabilistic aspect, is thus the secondary effect of complexity which is however "controlled", but by the indivisibility of elementary charge. And gravity? Its continuity has also a limit, at a much deeper level. It is determined by the absolutely elementary being, which we have already started to identify with planckons. Is that heresy? Well, that’s the outcome (heresy, or rather the outcome?)

   ²¹) Let's return to our two planckons and to our result. "It's not that unequivocal" –some readers may object - "it depends from which side we look at it." The system shown on the figure is not symmetrical (like a sphere), although it has highlighted axes of symmetry. "So gravity does not disappear for an observer located at close range and outside the centre of the straight line segment between the centres of planckons." Let us remember, however, that our figure is only an approximate illustration of the case. It does not cover (as yet not explored) planckon’s special topological characteristics. After all, this system can be seen as a kind of dipole with the field that disappears very quickly with distance. So interaction can occur between (zeroed) systems located very close to each other. The range of this field is, of course, the shorter the greater number of planckons are contained within it. Doesn’t it bring to mind the nuclear interactions? You can also approach this issue differently. Planckon’s specific topology makes the system gravitationally invisible (despite the lack of full symmetry), and its dipolar character does not play a role here (What is this specific topology?). Is it convincing?        

     You can also tackle it from a different angle. The system on the above figure is static. It’s a fair assumption as a matter of fact, but we have to deal with vibrations with the specific internal dynamics of the system. The possibility of repulsion fits into this picture. This may have an impact on how we "see" the system (for example, as something absolutely symmetrical), as well as on its behaviour in an external field, which may induce (an extra) asymmetry. The system, however, becomes then the field source (it is not anymore gravitationally zeroed). This is reminiscent of diamagnetism, and it also associates with photons - which do not have the inert mass, yet they are responsive to the external to them gravitational, and not some other, field (in this context, not as the result of physical curvature of space). Interesting here is the fact that photons do not respond to electromagnetic field. This is quite meaningful. Don’t they react, because they transmit themselves? This fact could have drawn attention already a long time ago. Now, however, there's a very appropriate opportunity. Which of the concept presented here is correct? It is a matter for further research, although we have an interesting foothold - vibrations of planckons forming a system. And how to put it mathematically? This should be tried even by those who utterly reject the whole concept. We will come back to these issues, but for now let’s note that the latter option reminds of classic quantum approach. On this occasion it is worth adding that, since we already mentioned vibration, very promising are resonance situations. This may help finding stability conditions of planckon systems, help creating (on paper) specific selection rules. In addition, it somehow reminds us of the concept of strings (especially these vibrations). Actually one can see here the bridge between deterministic gravity and indeterministic quantum mechanics. Have I overstretched...? We'll see further.

²²) In reflection ²¹) I drew attention to, among other things, the possibility of existence of planckonic vibrations forming elsymon. What kind of vibrations can occur in a single tetrahedral cell? Symmetry requirements demand that vibrations take place in pairs with a phase displacement of 180 degrees. And in a system of such tetrahedra? The system may be stable under a condition of proper adjustment, which means that there may exist only such systems which are internally resonant, adjusted and stable. In such a system, all the vibrations that occur simultaneously should belong to the same Fourier family.  It is also worth noting that the external to the system (gravity) field can disrupt the system vibrations, its harmony, and cause, for example, its decomposition. As we can see, not all planckon systems can be particles (elsymons). The set of possible options is limited. Of course, we know that from empirical research. I invite younger readers to conduct more detailed investigations. I think that based on my fantasies it will not be an impossibility to find a (theoretically) appropriate selection rules. As a result, I am confident, they will get something similar to the standard model, but this time based entirely on gravity. This is the novelty. In addition, this time, the young and curious will have to attack the problem "from below". We have here a great mass of research topics.

²³) For Sumerians number 12 had special significance. Was it because of this dodecahedron? Did they know something? Or maybe it was known to someone who conveyed to them this knowledge (as "divine message" only to the initiated priests,). This number was a sacred number. They knew (believed) that the solar system contains 12 heavenly bodies (including the moon and the planet Nibiru as well as Pluto). How could they know it? But that’s not what I am here about. From them came 12 zodiac signs - still in force. Clock face is divided into 12 segments. The Bible refers to 12 tribes of Israel. The product of the numbers 12 and 5 (the number of fingers, pentagon, regular dodecahedron), gives the number 60, which forms the basis of the Sumerian counting system. There are a lot of other examples. Also in the Torah you can find a lot of Sumerians’ legacy. Who knows, maybe Moses on Mount Sinai received the same message, which was bestowed upon Sumerians two thousand years earlier? The mysterious, encrypted, message designed for those who would be able to decipher it? The message intended for all and not just for the chosen few Sumerian priests. The message encrypted by letters of the alphabet. Moses, as the first in history, introduced alphabet (no longer hieroglyphs), the still used Hebrew alphabet. On the basis of Hebrew letters the Phoenician alphabet was created, and later Greek and Latin. Hebrew alphabet has 22 letters, and each letter has its numeric equivalent. Why 22? Just "accidentally" human being has 22 pairs of chromosomes (not counting the sex chromosomes XY and XX). In total, each cell of the body has 46 chromosomes.  

   In the Torah, that's right, right there, you can find a lot of encrypted information. Today, ciphers breaking is done by scientists, cryptographers using computers with high computing power. Commonly (already) known is the so-called Bible Code. Also, centuries ago, the sages of the Torah come to interesting conclusions. They didn’t involve themselves with intrusive (and devious) proving of the existence of God (Something the Catholic dignitaries excel at). If someone wants to prove the existence of the divine, it means that his faith is only a facade, facade behind which various (generally not very glorious) things were happening (and happen).

   In this regard Nehunya ben Hakanah, who lived between the first and second centuries, deserves particular attention. Based on the Torah, he calculated the age of Universe: 15.3 billion years. Another sage Ramban (Rabbi Moshe Ben Nachman), who lived in the thirteenth century, presented a model of Universe at its very beginning, consistent with models under consideration today, even concurrent with the one evolving in my work. These two examples should suffice.

   Going back to the number 12, that’s the number of years to complete the (basically compulsory) education. Is it just a coincidence? Modern European culture is largely based on the ancient heritage, among which greatly exposed Greeks constitute only very modest link. It is a pity that some barbarians burned the library of Alexandria. Also in our time burning of books is not just a prank of some paranoid criminal.

   Perhaps regular dodecahedron made of planckons fulfills a unique role as an important structural element. Did they know about it? They knew the sacred number 12.

Let’s come back to Earth. After all, all these perpetrations of mine are only phantasy.

Some interesting data I scooped from the books: Zecharia Sitchin - "The Cosmic Code (The Earth Chronicles, Book VI); Jeffrey Satinover - "Cracking the Bible Code".

*) „The dual character of gravity”

**) This year was published his textbook, in which he explained the introduction of the concept of atom in chemistry. The idea came about already in 1803.

***) From classical electrodynamics it is known that the accelerated movement of charged particles is accompanied by the emission of electromagnetic radiation. This is true provided that it is not cyclical movement. Non-cyclic accelerated movement of a particle, say charged one, means, firstly, its participation in a specific interaction, and, secondly, an irreversible change in potential energy shown in the change in kinetic energy. "Irreversible", for only then it will make sense to talk about radiation. If it is reversible (cyclic movement), the emission of radiation is not possible because it would mean a lasting change in system’s energy, and thus the annihilation of cyclicity. And yet the cyclic phenomena exist. (The total) energy of a cyclic system is constant. Such a cyclic system is energetically invariant, of course, only when it is left to itself. In particular, this applies to elementary systems, such as atom (constant electron orbits). Therefore, no wonder that atom does not emit radiation despite the fact that electrons circling around the nucleus accelerate all the time. This brings to mind one of Bohr’s postulates. After a hundred years, it is no longer a postulate. Although gravitational mass during this movement may vary (ellipse) and speed (as a vector quantity) is changing, the system is stable. However, if, for example, as a result of a collision with a particle electron loses part of its kinetic energy, then, of course, it falls to a lower level. After emission of a photon of a specific energy, which is conditioned by electromagnetic interaction (e.g., visible light), atom is set in a new (stationary) state.

       During the non-cyclic accelerated motion of an electrically charged particle we have emission of radiation. At what moment? Consideration of this issue is beyond the scope of the topic under our consideration. So that’s how it is when it comes to charged particles. The situation is different in the case of gravitational interaction. In the case of closed orbit all is clear. But does emission of some radiation occur during the non-cyclic motion? When it comes only to gravitation, it’s rather unlikely.

****) In another work, an essay dedicated to black holes, I drew attention to the possibility of quantization of gravitational energy, but in a very specific system, in the nucleus of the galaxy enclosed within by gravitational horizon. "Physicists’ dreams", even the most daring, do not go into black hole, as if it was forbidden fruit. We are dealing here with the conditions of extremely strong gravity. Apart from that, already in this work I have actually suggested (in the form of a question) that the (possible) very existence of planckons seals up the existence of the quantization of gravity. Quantization, as we know, means the possibility of portioning. Treating gravity as "element" of a continuous nature and limitlessness depth, simply excludes even the possibility of renormalization used in quantum field theory – and for (formally) this reason that theory does not consider gravity; and the more so the possibility of its quantization. Something else, when gravity has its specific source - is atomistic. In this case, the quantization does not preclude continuous field changes. Atomism of gravitational being. I am convinced that this may enable renormalization to include gravity. Certainly, however, the matter does not end here.

*****) Already in the eighteenth century Titius discovered an interesting regularity concerning orbits of the planets of the solar system. Bode popularized it, apparently attributing the discovery to himself. For some time the rule was even called the Bode’s rule. Today we speak mostly about the Titius-Bode law (T-B).

     The idea is that planets orbiting the Sun do not occupy random positions. Now, the average distance of each planet from the Sun can be summed up in a simple mathematical dependence. If we take as a unit the average Earth-Sun distance, we have: 

                                                                    a = 0,4 + 0,3n

where n equals zero, and consecutive powers of number 2: 1, 2, 4, 8, 16, 32, 64, 128. The number 0 corresponds to the planet Mercury. Here is a table that compares values for individual planets with their actual distance from the Sun.

Planet	n	T-B	Actual distance
Mercury	0	0,4	0,39
Venus	1	0,7	0,72
Earth	2	1,0	1,0
Mars	4	1,6	1,52
-	8	2,8	-
Jupiter	16	5,2	5,2
Saturn	32	10,0	9,54
Uranium	64	19,6	19,2
Neptune	-	-	30,1
Pluto*	128	38,8	39,5

*) Pluto was recently removed when it was decided that it is a dwarf planet, like many other bodies found in the Kuiper belt. As you can see, we have a surprisingly good compliance and it is hard to dismiss it as a coincidence. Oddly no planet corresponds to number 8. Even more puzzling is the fact that located there planetoids (asteroids) were discovered (the largest of them) thanks to the T-B rule. Odkryto je na samym początku XIX wieku (Ceres: a = 2,8; Pallas: a = 2,8; Juno: a = 2,7 and Vesta: a = 2,4). Also puzzling is the "absence" of Neptune. But this does not have to testify against the T-B rule. This may be an indication that after the formation of the solar system, there happened an event (collision) which distorted full compliance. Perhaps between Mars and Jupiter circled a planet which broke down and dispersed, perhaps Neptune, the twin planet (as it now turns out) to Uranus, for the same reason suffered a gravitational push. I will not concoct stories inconsistent with today's knowledge. I think the best answer to the question: "Why?" we will get by studying the writings of the Sumerians (and not today's astronomers). To make it easier I encourage you to read a book by Zecharia Sitchin entitled The 12th Planet.

   Nowadays this rule is not treated too seriously because it is not know where this regularity comes from, what makes it physically justified. There is no foothold. So as not to foster joyful works of amateurs, it is simply ignored, or at most it is seen as "mysterious accident." But maybe there is quantization of orbits, also in relation to the planets of the solar system (and generally in relation to all the planetary systems)?

******) Elsymon. A lot of time after the introduction of the name, while re-reading the manuscript of the book, on the basis of which I wrote this article ("Let’s fantasize about the Universe II. Into the depths of matter: gravity in sub-dimensions"), just before its release, I felt a bit strange. Some shivers run down my spine. After all, El comes from the Hebrew Elohim (like in EL-AL Int-EL, etc.), And the word "siman" in Hebrew means sign. Sign of God… It’s worth reading the first sentences of the Torah (Genesis) and associate them with the context of this work. Probably a long time ago somebody knew a lot…

May 2013

The next article in this series: "The potential energy of the planckon system. Suggestions concerning the construction of particles. What is the dark matter?"

Content: Derivation of the formula for the potential energy of two planckons. The physical meaning of the results. Specific suggestions relating to the construction of particles, based on the planckon model and dual gravity.

The Universe from the very beginning: panelsymon, accelerated expansion - Urela [Ultra-relativistic acceleration] (not inflation) ending in the phase change. The essence of dark matter based on the planckon model and urelian expansion.