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       figtitolo.gif (4762 byte)           THE QUANTUM SPACE  

Aldo Piana           

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PART II : Contents








PART III : Contents








PART IV : Contents



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Aldo PIANA   -   Corso Monte Grappa n. 13   -    10146  TORINO  (Italy)


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Until a few years ago, the idea of space, a fundamental product of our imagination to integrate the formation processes of figurative thinking, has always been that of an abstract empty volume, all through the history of human knowledge.

This idea is so deeply rooted in our minds that it is hard for us to perceive the consistence of physical space as concrete, or at least as different from absolute vacuum.

The undulatory theories, origin of modern physics, showed that the idea of space as an empty volume did not provide any comprehensible explanation of its phenomena. The ether theory was proposed as a solution to these new problems, but it soon had to be abandoned since the experiments of Michelson and Morley did not confirm its validity in any way. The ether theory, which postulated an empty space filled with a sort of fluid, did not alter the old concept, with which it could easily be integrated.

The theory of relativity changes space radically. The concepts of space and space-time curvature grants space a more active role in the formation of the universe. In other words, space is no longer simply an empty inert container, but becomes an integrating part of the universe, together with matter and energy.

The change is only apparent, however, since Einsteinian space is still considered rigorously empty.

In reality, the curvature of space is determined by the fields present in space and not by space itself, just like time distortions solely depend on the velocity of moving objects with respect to luminal speed, which is finite, invariable and unexceedable. Moreover, no hypothesis accounts for mechanisms allowing the interaction between fields and space or between time and space.

I find that the inappropriate relativistic involvement of empty space has represented a big obstacle to the spreading of relativity, opposing it to our conceptual abilities.

The more recent quantum theories all postulate, one way or another with diverse approaches, that space is not totally empty: from the spacial configuration derived from Heisenberg's principle of uncertainty to Dirac's ideas, which hypothize a space filled with a "sea" where pairs of virtual particles can form very short-lived electrons and positrons; to the space configuration of Higss' hypothesis, up to the extremely recent proposal of a team led by Abai Ashtekar of a space structured in rings thought to describe gravitation as a quantum phenomenon.

All these quantum theories seem to agree at least that the content of space must be much greater than previously thought. We also have to bear in mind that, as revealed by gravitational effects, space is also filled with an amount of dark matter, matter of unknown nature, ten times or more greater than the drectly observable one.

Cosmological problems moreover tend to spur the formulation of increasingly exotic hypotheses to account for matter-energy interactions during the first few instants of the universe's life, to explain the formation of matter instead of antimatter, which is present in much lower quantity, and the origin of matter concentrations from which stars and galaxies form, starting with an isotropic universe.

This gives rise to a plethora of often aesthetically fascinating hypotheses of fluctuations mutuated by excited states and phase reversals, of strings of extremely high densities capable of managing the expansion starting from the Big Bang, of multidimensional or parallel universes.

In any case, all kinds of advanced research is related to space; although the abstract concept of empty space still hasn't been totally overcome and separated from that of a real physical "space" which could occupy it utterly, and no scenery that contemplates all mechanisms of observed phenomena has yet been developped.

For these reasons we keep facing the embarrassing problem to reconcile our experience with an interlocutor whose influence is clearly detectable but whose nature remains completely unknown.

The physical space, though its nature seems to be studied without much enthusiasm, is actually the only possible connection among all observed or predicted phenomena, being the constituent of the environment. In the absence of a physical space to include them, classical physics, relativity, quantum mechanics and cosmology are still too often conflicting with one another, in spite of their individual achievements.

The attempt to make space the common ground for all scientific disciplines therefore deserves our commitment; especially because this could help us both find an answer to unsolved mysteries 1) (To Footnotes) and to questions still to arise, and overcome the acrobatic stunts that our intellect has to make in order to understand the more advanced concepts.

In order to find a connection between the various physical theories and their adaptation to our logic, I have tried to draw up a series of hypotheses which would allow us to make current ideas suitable to a model of the universe that can integrate them, starting from a basic concept on the nature of physical space.

The outcome of my work might lead to quite promising developments and exhibit an unprecedented global descriptive ability. Moreover it can best fit the mechanisms (or, in other words, the operating systems) of our intellect.

Furthermore, the connection between the various theories all related to the proposed model allows us to figure out the cause of many conflicts seen up to now and to seek a possible solution.

The basic hypothesis on the nature of space has originated from the consideration that all we observe, matter or energy, is made up of discrete elements, the quanta. In this scenery, the only really continuous element - which might even sound like a paradox - is physical space. 2)  (To Footnotes)

If we try interpreting our observations the other way around and hypothize that physical space itself is made up of quanta, i.e. discrete particles, instead of being a continuum, it seems to acquire a structure more consistent with our experience.

But a few problems will have to be solved in order to accept such a configuration.

If the space of our memory - that empty volume where particles, atoms and stars should move freely - is completely occupied by quantum space, then a possible collocation must be found for the objects of our experience and mechanisms must be hypothized which allow the dynamic they exhibit.

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(See fig. 1A 1B 1C which suggest a plausible structure of quantum space. Figures 1D and 1E instead report the images of surface density waves detected by the tunnel effect scanning electron microscope, which seem to confirm a planar hexagon arrangement which well fits the hypothized distribution of space quanta)

It must be pointed out however that quantum space must not be perceived as a new maybe revised and improved edition of the "fluid" predicted by the ether theory. This was just a hypothetical passive and inert medium, in which energy and matter were immerged and moved causing events in accordance with our observations.

Quantum space instead claims to be the protagonist of our universe, with energy and matter as counterparts, but only as "guest stars" 3), (To Footnotes) the concepts of which will need to be partly revised, as we will see.

In such a quantum space, however, space quanta and material quanta should coexist in the same volume, and the motion of the latter in a non-empty medium could be seriously impaired, if not impossible.

In order to reconcile the coexistence of material and space quanta in the same volume, we could extend our hypothesis and consider them as different aspects of a single entity.

We then must figure out what distinguishes pace quanta from material particles, how the transition between the two states.

The assumption that space quanta and material particles are different aspects of a single entity, however, suggests the hypothesis that space quanta change state to become material particles, or parts of them, when they become the site of a discrete amount of energy.

The motion of material particles and of quanta which mediate the energy transfer, and their very existance, then turn out to be totally apparent. It is energy which, by moving between space quanta, makes them detectable to our senses and our sophisticated instruments. It's almost as if it "lit them up", or, in more appropriate terms, it "materialized them" along the way.

From now on however, I will deal with objects or particles in motion using the potential of a tested conventional language.

This conventional language will however need some adjusting, to point out that in quantum space motion itself is quantized, since motion as we always knew it - the actual shift in position of an object, with its temporary presence in any of the intermediate positions - cannot occur.

Quantum motion consists in the transfer of energy along space quanta, believed to be static at least temporarily: the particle, or the particles which make up the object, disappear from their initial observed position and reappear in a first intermediate position at a finite distance, and so on until the final position is reached. In the gaps between intermediate positions, the object, or the particle, is not observed as such, and can only be detected in the form of waves. The wave-particle duality confirms this behavior of matter. Later on we will deal with complex systems and object, and we will see what they are actually made of and which constituent remains unchanged during motion even in the intervals during which particles can only be seen in the form of waves.

Hypotheses of this kind, however, would only be weird and useless science fiction concepts, if they were not in accordance with theories already confirmed empirically.

Let's see how we can study the history of physics and cosmology to spot the evidence that can prove their validity. But before looking for possible detailed correlations there is still a couple of general questions to answer:

The quantum space here hypothized exhibits enormous inconsistency with both classical and modern theories, and what about our observations?

If matter is the interaction between space quanta and energy, could it cause distortions detectable by our instruments? Could it affect our calculations? Or would it force us to revise our ideas?

The answer to these question is an absolute NO.

The nature of matter has no effect whatsoever on our detections, simply because they are obtained with material instruments, along with our senses, which are therefore under the same conditions as the observed objects 4). (To Footnotes)   Our calculations cannot be influenced in any way either, as they apply to analogous parameters and to objects of which they analyze the different values without considering their real nature 5). (To Footnotes)

It follows that quantum space does not modify in any way the physical laws we experience in the classical physical space (meaning a multiform entity with blurred boundaries). On the contrary: the acquired scientific knowledge can profit from a common ground and can make a big leap of conceptual quality.

The final section of this article will deal with the promising prospects of our knowledge's future, favored by the development of these ideas, provided they are confirmed, of course, by basic experiments about which I will provide some suggestions.

Now it's time to take into account the various indications which make the hypothized quantum nature of space plausible.

To detect such indications, a comprehensive review of our scientific knowledge is required. This review would imply very hard work; however we can proceed analyzing samples of more evident and more easily verifiable elements.

So let's begin to study the possible collocations of subatomic particles in quantum space.

We currently know a myriad of particles and antiparticles, all of them but two are characterized by a great transforming ability. The only stable particles are the electron, which apparently lacks any internal structure with an estimated infinite average life, and the proton, whose internal structure is constituted by quarks, with a supposed life of at least 1040, years or more, according to the latest estimates. Up to now however no decay has been observed which could be reliably attributed to the proton.

Starting with the neutron - which is stable inside the atomic nucleus, with an average life similar to the proton's, but only lasts about ten minutes when free - all particles have very short average lives and quickly decay in ways which are often predictable only statistically.

The free neutron, which is made up of three quarks, decays into an electron, a proton and an antineutrino. The three constituent quarks play an active role in the neutron decay, in that they transfer their energy onto five particles, the three quarks of the proton, the electron and the antineutrino. Particles that appear and disappear, leaving the total amount of energy of the changing systems unaltered: what scenery could be more appropriate than quantum space?

Quantum space is not only consistent with the population of known particles - which is likely to be extended with the increase of the energy used in modern accelerators - but it even seems to be its only rational explanation.

In quantum space, the particle could be considered as the result of energy interaction with one or more space quanta 6). (To Footnotes) Only one space quantum might be involved in the case of particles without an internal structure, such as leptons, quarks and intermediate bosons, whereas for particles with an internal structure, like baryons and mesons, more space quanta, not necessarily adjacent and distributed in a determined volume, might be imvolved in the transformation produced by the action of energy.

The characteristics of the particle this interaction creates depend on the kind and the features of the discrete amount of energy occupying the region where the particle appears.

Could we formulate an even more tantalizing hypothesis.

Even particles which apparently lack an internal structure, thus even quarks and perhaps also electrons, would not be constituted by just one space quantum, but rather by a group of close or adjacent quanta. This hypothesis seems to have already been partially confirmed by recent experiments carried out at the Fermilab where, using the highest possible energies, the preons seem to emerge as constituents of the quark.

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Preons might exhibit a tetrahedral arrangement (the simplest three-dimensional array for space quanta, see fig. 2) and the particle's characteristics might be exclusively determined by the combination of mutual motions. The apparent absence of an internal structure seen in impacts between particles and energy levels lower than or equal to those used at the Fermilab can be explained with an insufficient penetration into geometrically distorted space around the particle which, as figure 3 shows, exhibits a perfectly spherical configuration even in the proximity of the space quanta of the tetrahedral arrangement.

These hypotheses are clearly quite daring, but still deserve to be carefully considered because they might very much simplify the unification of forces.

Along with space quanta - directly involved in the interaction with energy or charge, thus becoming observable particles - also the surrounding space undergoes a deep change.

In the case of leptons, quarks and intermediate bosons, i.e. particles made up of only one space quantum (or of a group of preons), space quanta outside the particle change their state and become carriers of the fields over boundless distances, whereas the near ones acquire characteristics which configure and determine the particle's mass. The number of imvolved quanta, or mass quanta, is proportional to the energy amount acquired by the particle (see fig. 4). The relativistic correlation between mass and energy, the behavior of particles during processes of decay and in matter-energy transformations not only represent no obstacle to this hypothesis, but they even suit it perfectly.

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The hypothized nature of mass implies two important consequences: first, the mass of a particle must always be a multiple of the unit a single space quantum can acquire (or can increase following a quantum proportion). Secondly, no observable particle, including the photon, should turn out to be absolutely massless. We must use the conditional here, since we still have to define the mechanisms behind energy-filled space transformations. So far, moreover, the hypothesis doesn't even allow us to determine whether the quantum directly occupied by a charge (or by a discrete amount of energy) also takes part in mass formation together with surrounding quanta, which seems likely, or wether it only represents its origin without playing an active role.

It is interesting to see how relativistic effects on masses can be reconciled with hypotheses on the origin and configuration of mass in quantum space. This subject will be dealt in the later chapter which analyzes such considerations formulating hypotheses which must be taken cautiously for now, though very tantalizing and well integrated in the proposed theories.

The thorough analysis of the relation between the particle and its mass in quantum space, which is correlated with the interaction between energy and space quanta, might radically change our view of physical phenomena with surprising consequences, perhaps allowing us to better suit them to our logic.

For particles with an internal structure, like baryons and mesons, the transformation of space caused by the energy that occupies it is much more complex. The resulting particle turns out to be composed of a series of space quanta, each occupied by a fraction of the particle's total energy. Such space quanta are not adjacent, and they are distributed in a determined volume within which the space geometry is further deformed, in a manner different from the deformation on space outside this volume, where the behavior is similar to that of structureless particles.

This configuration type perfectly fits the characteristics of particles and their behavior; it enables us to understand their internal structure, the quarks' fractional charges and their indivisibility, along with the nature and function of gluons. It can account for nuclear forces restrictions and for the particle's internal dynamic, as well as for kinds of behavior observed in processes of decay. It is not certain however that the fractioning of the particle's total energy, observable on its constituent quarks, corresponds to the hypothized value; it might just constitute a statistic element, useful for the mathematical interpretation. Rather than stable particles, quarks may be seen as transitional aspects of the continual exchange of charge fractions between the space quanta which make up the nuclear particle inside the space within it. The individual space quanta gradually acquire all quark, antiquark and gluon configurations which compose the particle itself, but they cannot let their characteristic energy escape out of the volume it comprises, being obstacled by the spacial configuration.

The space quantum's ability to acquire a charge, or better to allow its passage, is however influenced by a "predisposition" according to environmental conditions determined by the vicinity of constituent charges of material particles.

This concept needs to be explained further.

The energy temporarily stored on a space quantum in its orbital path changes the space quantum into a detectable material particle and surrounds itself with a multiform field which modifies the ability of surrounding quarks to accept charges or to allow their passage.

Such a modification results in the change of space geometry around the charged quantum, so to affect the motion of all nearby charges, by selecting more convenient paths.

The idea of proximity is obviously only relative, as it merely refers to the degree in which charged particles influence surrounding moving charges. Such influence has no space boundaries (as we will see in detail speaking of RELATION) but it decays rapidly as it is proportional to the inverse of their square.

The geometrical deformation a particle produces on its surrounding space affects the trajectories of nearby moving particles but is in turn affected by the geometrical deformation such particles induce, by their charge, by the mutual velocities.

The global change of quantum space geometry therefore turns out to be extremely complex but also absolutely consistent with relativity's concept of space curvature, defining it as a macroscopic effect of the combination of geometrical deformations in every point in space.

The change in state of an individual space quantum due to the proximity of charged particles can exhibit any value and we can conventionally define its status as "STATE LEVEL OF SPACE QUANTUM". (Figures 4C - 4D - 4E - and 4F show the trend of state values measured on planes at various distances from a mass or charge array, arranged as in figure 4B, and highlight the volume trend of the induced space deformation).

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The STATE LEVEL therefore characterizes the degree of the space quantum's energy transfer capacity, and is simultaneously the origin and the outcome of the fields, accounting for their nature, origin and laws.

We are now able to comprehend the formation and space distribution of fields: energy on one or more quanta modifies the state level of the surrounding quanta. The state level of individual quanta is inversely proportional to the spherical surface with the charge at its center.

The STATE LEVEL represents a composite value, resulting from the sum of all fields, of every kind, which provide for a complex status of the space quantum which will select the orbital path of energy shifts according to the charge's type and intensity that originates it, and to the type and density of the charges which can be relevant during transfers.

The absolute value of an individual quantum's STATE LEVEL is not relevant in itself, however. What matters in the definition of energy shift paths is the space distribution of state levels and the relative differences among the involved quanta along the orbital path. In other words, the geometry configuration of space is determined by the degree of the difference between state levels of adjacent quanta, no matter what their absolute value may be.

The space quantum's STATE LEVEL is a concept that gives rise to a series of considerations related to our observations; among them, here are some of the most relevant:

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We could go on listing further indications in favor of the quantum space hypothesis and of the many combinations that make it so plausible and also quite aesthetically fascinating. However, this article aims to propose a comprehensive model for the universe, and thus it will be necessary to consider its structure and organization as well.

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Our Universe is structured following a series of complex systems, arranged in hierarchical scales of increasing orders, both parallel and inserted one into the other like a kind of increasingly large and complex Chinese boxes.

This structure, already described in detail, is fairly clear both at a microscopic and a macroscopic level. However we find it hard to comprehend its working mechanisms and its organization, and to perceive its unimaginable vastness 8). (To Footnotes)

We won't go too far into its complexity, but dealing with the quantum space hypothesis we will need to realize how such system hierarchies can fit in, and analyze the interactions which link first the systems' components, then sets of systems, and finally systems and sets of systems to quantum space. This will be important in order to determine how such interactions can act selectively without destroying their internal structure.

To be precise, a complex system is a dynamic, organized and articulated system, made up of a large, usually a huge number of elements, all directly related to the others 9) (To Footnotes):  the originating set behaves like a unitary element with respect to the outer environment, almost as if it lacked an internal structure.

In order to fully understand the interactions between the complex system and the environment - being the environment outside the system structured according to the various arrangement levels of the systems - we will need to consider their relations taking into account particle motion behavior in quantum space.

As we have previously seen, particle motion should be only apparent and merely produced by the movement among space quanta of discrete amounts of energy or charges.

The system then is not constituted by the elements we commonly know, but rather by a set of charges or energy "globules" distributed in space, which identify those constituent elements we observe. Charges and "globules" move along preferential composite orbits determined by mutual field interactions.

In principle, the elements' motion within the system, even if the whole system is itself moving, is not altered by the external environment, as internal preferential orbits cannot be modified by external fields: the inner layout formed by dynamic structure of the state levels of space quanta, which represents the ORGANIZATION OF THE SYSTEM, moves integrally along the orbit of the system.

In other words, the heart of the system is represented by the complex geometry of inner space, drawn by the interaction between spherical surfaces at a scalar state level, radiated by the fields. Such a geometry defines energy's orbital paths, that is the layout, which combine with space quanta to form the system's constituent elements.10) (To Footnotes) Inner space geometry is also that component of a system which remains unchanged even in the intervals when material particles are in the form of waves.

The orbital geometry changes constantly because of the mutual motion of internal components along a low or very low-frequency cyclic path. The cycle is determined by the finite - though huge - number of possible combinations or permitted positions which can be occupied in inner space.

A system acts like a central unitary element with respect to the system of the next upper order which contains it, whose field structure at first glance doesn't seem to influence its evolution.

There is an upper limit for the number of elements in a complex system, which depends on the type and intensity of their bond, along with general geometry deformation conditions of the space surrounding the system. The stronger the bond, the smaller this upper limit is, since the strength of the bond also restricts the constituent elements' freedom and the degree of their possible interactions, thus preventing the development towards a higher complexity. Later on we will instead see the effects produced by the conditions of the system's external environment.

It is interesting to study the behavior of the forces which bind the systems' constituents.

The nuclear force and weak interaction are only effective at very short distances at a nuclear level, and regard the distribution of "condensed" energy in observable particles. In quantum space, nuclear forces are actually very likely to be only apparent: let us see why, using the example of the nuclear force.

The concept of nuclear force originates from the classical view of particles: spheres with precise identity and exhibiting a typical behavior according to _their charge, along with other characteristics which we can neglect here. They will attract particles of the opposite charge and repell those of equal charge, with a force proportional to the inverse distance squared.

Within the nucleus, more particles of the same charge are packed at very short distances, or they even touch one another, so their mutual repulsion is extremely strong and a counterbalancing at least equal force is required in order to allow the nucleus' stability.

Atomic nuclei stability is then possible only thanks to the strong force, but no hint suggests how and from which it is generated.

Quantum space instead calls for a revision of the particle and atomic nucleus concepts: as noted above, particles originate from the interaction of a discrete amount of energy 11) (To Footnotes) with one or more space quanta distributed over a determined volume. The nucleus therefore is not made up of a set of particles, but is constituted by the sum of their energy over a determined volume of space. The particles which have built the nucleus have lost their identity, spreading their energy all over the volume of _space where the nucleus appears.

There's no limit to the amount of energy a space quantum can acquire. Such amount is however determined by the quantum's state level and by the distribution of levels around it. Therefore, the total amount of energy contributed by single particles in the nucleus is not concentrated on just one quantum, and is not uniformly distributed over internal space quanta which undergo a constant oscillation of state levels, which causes and justifies exchanges. The fraction each of them can acquire keeps shifting from one to the other. However, the fluctuation of internal state levels almost always lies over the minimum level required to prevent energy from escaping - we have to say almost, because under particular conditions of decay the so-called weak interaction becomes effective.

How can this configuration be in accordance with the experimental results which show an internal nuclear structure causing inelastic collisions and emitting its building particles during decay or crushing?

As for inelastic collisions, the answer lies in the dynamic structure of the nucleus which projects it's internal geometry's high irregularities to the outside (see above fig. 6A - 6B - 6C - 6D - 6E, which show level differences measured on external spheres placed at various distances from a set of hypothetical masses or charges arranged as in figures 6F and 6G). During decay, instead, particles form again, since this is the only form in which the energy that escapes the nucleus can recombine with quantum space, at least in detectable form.

The effects observed from outside the nucleus exactly correspond to those which would be caused by the presence of a strong and a weak force. The apparent origin, nature and range of these forces however can only be explained by quantum space.

When we are finally able to find a solution to the complex internal geometry and dynamic of nuclei, that will allow us to go beyond the apparent paradox which restricts the strongest forces of the universe to a very tiny space, whereas the weakest, gravity, has no range limit.

Outside the nucleus, the electromagnetic force is effective at atomic and molecular levels, managing both the organization and energy exchanges among the systems' components and among systems, up to the highest possible hierarchical level where a significative distinction between positive and negative charges can be made 12) .(To Footnotes)

The electric bond (also known as chemical bond) allows to achieve the highest degree of complexity with the highest degree of interactions among the system's constituent elements. Its amazing versatility occurs because electric fields of opposite charges can compensate each other at a local level by acting selectively at various levels.

When the effect of the electromagnetic force is neutralized the gravitational force comes into play, regulating motions, organization and exchanges among the systems of higher order.

This task distribution among the various forces justifies their hypothesized unification at big energy concentrations, more precisely at high state level values, because each of then requires a specific volume of space and a determined systematic structure (or geometrical "range") to become effective. In a scenery with very high energy concentrations, in which the structure of space geometry tends to become a single spherical system at an extremely high state level, the gravitational force annuls and absorbs any other force.

As the system's complexity and size increase, or as superior hierarchies are reached, binding forces decrease because of the larger distance, or because they are partly neutralized. The resulting gradualness of the forces' action substantially reduces the order of possible interferences between systems and their subsystems. For a system, its subsystems are like monolithic elements, because their binding forces prevail.

But there are limits to the resistance opposed by a system against the influence of the environment or of its superior system.

Even if external influences turn out to be much lower, the system's internal motions are not totally unaffected by the change that the dynamic evolution of external levels can cause to internal cycle evolution. Even a very small variation induced on a point of the geometric layout of the system can lead to changes in the cycle, which can accumulate in successive cycles, transforming them until they are destroyed.

When a system tends to a higher complexity than that obtainable with the highest number of elements allowed by the bond type and intensity and by local state levels, determined by the external environment, we'll have a system of a superior order, where the constituent elements are lower-order systems, not necessarily of the same order.

As an example of system hierarchies, we can take the proton constituted by quarks as a first-order complex system (for now we'll ignore preons). The second-order system will be the neutron, the third will be the atomic nucleus, the fourth is the atom, the fifth the molecule (obviously with the various suborders of all particles with an internal structure, of the various nuclei and atoms of the elements with relative isotopes, of the countless molecular combinations), and so on up to planetary systems, galaxy clusters and superclusters, or in another context to biological system.

Each of the complex systems we mentioned clearly exhibits the correlation between the maximum number of constituent elements, the nature and action of the bond, and the complexity of possible interections within the system.

The functioning of the universe can only be understood if we take into account its structure which is based on a hierarchy of complex systems, since it determines the modulation of state levels, charge transfers and the space-energy interaction which allow its existance. It will also be important to interpret the functions which the system's internal structure carries out on the increasingly large structures that include them, although this is more difficult to do.

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The theory of Relation, chronologically the first among those proposed by this model of the Universe, arises from the consideration that every physical phenomenon originates from an energy exchange among the involved objects, and between these and the external environment. It is then not so absurd to hypothesize that the event might only take place if the involved object and the environment can supply the necessary amount of energy at the same time absorbing the produced amount.

It is easy to realize that an object involved in an exothermic phenomenon, for instance, must be in some way predisposed in order to produce the energy necessary for the phenomenon. But it’s not so easy to infer that a similar predisposition could be required to allow the energy absorption of the environment. Reversing the energy exchange direction, the same is true for endothermic phenomena.

Relation then hypothized that a relation had to exist between objects involved in a phenomenon and the external environment capable of tuning their actions.

In other words, Relation can be understood as the extension and applicative mechanism of the principle of Mack.

In the physics of classical space Relation might have been seen as an interesting hypothesis from a conceptual viewpoint, but in any case it would have been impossible to verify its effects. In this regard recall the unsuccessful attempts to reconcile the principle of Mack with laws of physics and current theories.

In quantum space, instead, the theory of Relation can account for the interaction necessary for events to occur, because here both the objects’ movements and energy exchanges among different systems or between systems and the environment are represented by changes in the trajectories of moving charges or discrete energy quantities. This can be comprehended more easily if we analyze the influences exerted on the objects’ movement.

Let us see such influences in detail.

At a local level, any moving object or particle – which we can identify as <a>   - exhibits a conic, easy identifiable and perfectly describable trajectory. At least, this was true in classical physics; in quantum mechanics the trajectory is no longer perfectly describable, and becomes a probabilistic track.

In quantum space, a probabilistic track may be interpreted as the consequence of the articulated space arrangement of state levels and of complex space geometry.

In this example we will overlook the probabilistic hypothesis for simplicity’s sake, but this is just a terminological simplification which does not affect the meaning.

Object <a>, like any object, is however part of a complex system that includes it - which in this example we hypothize to be of first-order - and follows its movement. Its trajectory, as seen from outside the first-order complex system, is no longer a conic; it turns out to be, in the simplest case, a cycloid.

The first-order complex system is in turn part of a second-order complex system, which is part of a third-order system up to a hypothetical nth-order system, each exhibiting a mutual motion on conical orbits with respect to the systems to which they are directly connected, whether of the same or of a different order.

If we now consider the motion of object <a> with respect to any reference axes system, whether inside or outside the nth-order complex system, it will at first glance appear to be absolutely chaotic.

We will see that the motion with respect to the axes follows a cycloidal track of a minimum order of n-1 (conical orbits which lie on conical tracks evolving on path conics, in multiple series, whose minimum level is equal to the number of connected systems minus one).

In order to follow such a track, object <a> must constantly modify its direction and speed with respect to the reference axes, to keep track of the motions of every system that includes it.

In classical physics, object <a>’s change in direction and speed with respect to the reference axes would be only apparent, since the axes are imaginary and therefore lack any kind of relationship with the object in question.

In quantum space, the reference axes instead materialize in the layout represented by space quanta; object <a>’s change in direction and speed then becomes real with respect to physical space.

But particle motion, as previously noted, is only apparent, caused by the energy movement along space quanta. Such movement follows preferential paths (or composite orbits) determined by the interaction between the type, degree and transfering speed of moving energy with the differences among state levels encountered along the path. In other words, it is determined by structured environmental conditions.

In quantum space, therefore, the energy identifying the constituent particles of object <a> must move along highly complex orbits, determined by space quanta’s constant state level variations induced by the mutual motions of all components of the complex systems’ hierarchy to which the object belongs.

Here is when the theory of Relation comes into play, to explain the mechanisms allowing object <a> to constantly modify its movement path, to follow those of the systems to which it is related 13) (To Footnotes).

In quantum space, RELATION is the theory which hypothizes the relation that modulates each space quantum’s state level according to every space quantum’s level and its distribution.

The consequent rule states that any material particle or space quantum which interacts with energy transmits its own state level to all space quanta, with spherical diffusion at constant total surface intensity at all distances, thus modifying the state level of every single space quantum in inverse proportion to the square of the distance.

The quantum state level, the sum of all fields of any kind which involve a determined quantum, draws up the general geometrical space configuration through continuous fluctuation.

But only the gravitational field acts universally. All other fields, which are generated in both opposite charges, locally neutralize each other. Their constant effect however is not limited to the formation and structuring of complex systems’ hierarchies. In fact it appears again through these systems at the gravitational level.

The state level of each space quantum acquires the connotation of building block of the universe’s organization. With respect to levels of surrounding quanta, all oscillating synchronously but with different widths according to their position, it creates the dynamic layout which determines the transfer of "charges" or discrete energy amounts, the constituents of the world we can observe.

At this point the probabilistic hypothesis reappears with force, the only plausible hypothesis in a stunningly complex scenery where it can nevertheless go hand in hand with the deterministic hypothesis.

Relation implies some important consequences which represent a fundamental conceptual step forward in the comprehension of phenomena, which doesn’t even force us to revise the physical laws known up to now.

First of all it must be pointed out that in the context of RELATION, i.e. of the connections among space quanta, time doesn’t exist, and quantum space is rigorously three-dimensional (its mathematical description however requires the addition of a fourth geometrical dimension, as we will see below). If time could exert any kind of influence at this level, this would deform energy transfer trajectories in such a way to cause the rapid disruption of the complex systems, and consequently of the universe these systems constitute.

Time arises when energy starts moving among space quanta with transitions in wave form. The upper limit of such displacements’ speed is the speed of light. For this reason the succession of the space quanta involved in energy displacements represents the delay line from which time originates.

State level variations induced by charge displacement instead do not undergo any delay, as they don’t imply any energy transfer.

The gravitational effects of Relation, therefore, express themselves in two different ways and with different characteristics.

On the one hand, the gravitational state level of space quanta oscillates synchronously with the masses involved in phenomena originating field perturbations, without any time influence On the other hand the motions of the masses originating gravitational perturbations are represented by the displacement of energy or of charges strictly related to time.

For these reasons Relation can coexist and integrate with Relativity, as it does not contraddict the space-time concept; on the contrary, it even suggests its connection mechanisms.

Moreover, Relation can explain the inconsistency between Newton’s Gravitation and general Relativity, which seems to be caused by an inappropriate overlap. In fact, the former deals with the distribution modalities of fields with the absence of any time influence, whereas the latter takes into account phenomena mediated by energy or charge exchanges and displacements which generate time along their path and then are influenced by it, playing a role in the origin of fields and of induced space geometry deformations.

It must be pointed out, however, that an incomplete consideration of all the parameters that contribute to configure space geometry will lead to approximations which do not allow the total unification of Newtonian and Einsteinian thoughts.

Relation implies that field variations of any kind, including gravitational waves, cannot propagate at luminal speed, but they must follow the synchronous patterns indicated above.

Relation also produces even more amazing correlated effects: the CONTINUOUS MODELLING of every point in SPACE, the NONDIMENSIONAL EQUIVALENCE, the SCALE INVARIANCE.

The CONTINUOUS MODELING of every point in space, or every space quantum, originates from the state level variation which all quanta must undergo because of the movements of energy, masses or charges in the entire universe. Each quantum exhibits a different state level variation, according to its position, which determines a constantly changing configuration of space geometry, from the smallest detail to a global level.

A relevant consequence of continuous geometry modeling is represented by system evolution: two perfectly identical objects or systems cannot exhibit an identical evolution, because they occupy two different volumes of space, and will therefore be subjected to a different influence on the distribution both of internal and external adjacent state levels, and their orbital layout will consequently evolve differently; a different evolution cycle. Of course, the difference in the evolution of two equal systems due to a different development of the orbital layout are usually so small that they can’t be detected by our measuring instruments 14) (To Footnotes) .

The NONDIMENSIONAL EQUIVALENCE, another peculiar effect of Relation, depends on its intrinsic nature or in other words on the nature of its generating fields. As we have seen the condition of a space quantum interacting with energy is transmitted at any distance to all space quanta, with spherical diffusion at constant total surface intensity.

The nondimensional equivalence is a direct consequence of Newton’s third law, which, if rewritten so to fit in Relation, can extend its range of influence and explain its mechanisms.

From nondimensional equivalence follows that two systems conected in a system of a higher order exchange a communication of the same total value, they mutually influence the distribution of their internal state values with equal global intensity, no matter what their dimensional ratio is. (see the chapter and figures 7A and 7B concerning nondimensional equivalence).

The nondimensional equivalence has many noteworthy implications. First of all, it allows us to understand why and how every action causes an equal and opposite reaction; but the most surprising consequence is that two or more systems dynamically connected to each other (and no object or system in the universe can escape this condition) find themselves in absolutely equal conditions, no matter what their dimensional ratio is. The relation between them is totally unrelated to their dimensions. To put it in a human context it’s not possible to determine which of them leads the game, managing the superior system they belong to.

SCALE INVARIANCE. Fig. 6A through 6E report examples for geometry deformation produced on a reference sphere by a mass or charge array placed inside it. Again, it should be pointed out that geometry deformation reveals itself by influencing the state value of space quanta placed on the reference sphere. The greater the distance to the center of the mass or charge array, the smaller the geometry deformation becomes, decreasing proportionally to the square of the reference sphere’s radius. Thus, when this radius is only 3 or 4 times the array’s average radius the reference sphere is apparently not deformed (see fig. 6A).

But if we carefully examine the differences between state values in radially correspondent points on spheres with different radii, it will become evident that as the radius increases, level differences tend to maintain a similar surface configuration at all distances, though their values do decrease. The surface trend, therefore, is towards invariance with respect to the ratio between the square of the reference sphere’s radius and the square of the average radius of the mass or charge array inside it. The graph in fig. 8 outlines the comparison between relative state values measured on points A, B, C, D, E, which are radially corresponding and placed on reference spheres with growing radii R. It highlights the tendency to maintain the geometrical deformation shape, no matter what the distance to the energy concentrations which generated it.

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In quantum space, gravitational mass is hypothesized to be a kind of halo surrounding the particle, which – as we said above – is made up of one or more space quanta interacting with energy. The halo of mass directly originates from the action of the particle’s energy on surrounding space quanta, which thus share this energy and are no longer "free" quanta.

This isn’t just a change in the state values, but it’s also a transpass of the particle’s energy on the nearest space quanta. The energy of the particle can modify the condition of halo quanta in two different ways:

In the former case, space quanta should be able to "contain" a fixed amount of mass, whereas in the latter the quanta would only have to respect a minimum limit in order to become a mass carrier at the same time providing clear-cut boundaries to the halo.

For now we are not able to determine which of the two hypotheses is more likely: both can account for mass-induced effects, of which we’ll speak later on, without exhibiting clear inconsistencies.

The presence of a mass halo, moreover, exerts geometrical deformation on quantum space, by acting on the state value of quanta following the laws of Relation. The combination of all deformations caused by the masses placed in a determined volume will reveal itself, at a macroscopic scale, in the form of space curvature.

But classical physics considers two different types of mass: gravitational mass and inertial mass, which differ from each other for the effects they produce.

The gravitational mass of an object exerts attraction on other bodies, expressed in a force which communicates acceleration to the two bodies aimed at their center of mass. Inertial mass instead represents the resistance a body opposes to acceleration.

Relativity has a different interpretation for gravitational mass (the force derives from the curvature of space), but for now we can consider the effects to be the same.

Nothing suggests that the two masses are the same thing, and therefore have equal values. But measurements carried out so far have yielded the same value for both, within the instrumental limit of one part to 1012, and this leads to the unexpressed tendency to consider them equal.

Even though gravitational and inertial masses both originate in quantum space from the same mass halo, identical for both, the effects produced in phenomena that involve mass are very different and their value cannot coincide either, in spite of the similarities yielded by measurements carried out so far. Relativistic effects moreover highlight value and behavior differences to the extreme.

Let’s begin by considering how and why the two mass types differ, and why no difference between their values has yet been found.

The graph of fig. 15 plots the two masses as forces acting on two bodies whose dimensions – absolute or mutual – are not relevant. From this graph we can immediately infer that the apparent forces exerted by gravitational masses act exclusively towards their center of gravity, whereas those exerted by inertial masses can have any direction, as a reaction to the external force which tends to accelerate one of the bodies.

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The effects produced by the two mass types also exhibit other important differences which will be highlighted later; for now let’s examine the relation between their values.


Mg = gravitational mass of the specimen object in kg. ;   Mi = Inertial Mass ;

g = gravitational acceleration ; a = acceleration of specimen objetc ;

Ms =  total mass of the reference inertial system, always in kg. ;


1)      image556.gif (1496 byte)


and on the Eart, where g  and Ms   are : g = 9,81 ; Ms = 5,98 . 1024

Mi  will be :

2)      image558.gif (1664 byte) 

The difference between inertial and gravitational mass is then far too small to be detected by current instruments, the sharpness of which, like we said, does not exceed 1 to 1012.

We can see that both the difference between inertial and gravitational mass and the sensitivity of the instruments required to measure it depend on the ratio between the product of the acceleration exerted on the specimen body times its mass and the product of the gravitational acceleration times the mass of the reference inertial system where the comparison is made.

Once we have determined the quantitative differences between the two masses in a given inertial system, we should ask ourselves what they actually represent in quantum space. We have already seen that gravitational

mass reveals itself by producing a geometrical space alteration determined by the variation of its constituent state quanta’s value. The geometrical deformation redefines the orbital paths of objects moving around the mass that generates it, and it determines preferential paths, exactly emulating the effects produced by a force.

In the graph of fig. 15 the mass m1 acts on the paths of the body with mass m2 with combined actions which emulate the effects of a force g1 aimed at the center of mass O, while the mass m2 generates the force g2 which acts on m1.

In order to fully understand the operating mechanisms, it is important to consider the gravitational mass as a consequence of the interaction between two or more volumes of space which are being deformed by an energy concentration. These volumes are represented by an array of several smaller volumes (systems of various complexities), which are in turn made up of concentrations of even smaller volumes, up to those representing atoms and particles.

The laws of the nondimensional equivalence regulate the ratio between the volumes, or bodies, mentioned above, but this ratio results to be direct and with constant unidirectional acceleration.

The inertial mass instead does not derive from a constant ratio between two bodies. It originates from the relation between the bodies and an extraneous force which tends to apply an acceleration in addition to the gravitational acceleration, with any value and direction. The nondimensional equivalence here does not allow to accelerate an individual object and requires for bodies to be accelerated or moved in pairs, in opposite directions.

This way the whole balance is maintained. The center of mass of the two bodies is not displaced with respect to the systems of higher orders to which they belong, and the effects on Relation are restricted by the state level alteration being basically limited to the moving masses’ surroundings.

The nondimensional equivalence therefore requires that any accelerated body is associated with a mass, which we can call mass of support, whose opposite motion prevents the center of mass from shifting. Thus the force accelerating the body acts both on the body and on the mass of support with an action inversely proportional to the masses.

Let’s examine specific consequences and effects.

If the mass of the body to be accelerated is equal to the mass of support, the two bodies will move away from the center of mass at equal speed; the maximum speed the two bodies will be able to achieve with respect to quantum space can’t exceed the half of the speed of light c, since the body cannot move away from the mass of support faster than c.

This behavior, which we may define as a kind of gravitational red-shift applied to masses, occurs because an accelerated body moving away from the mass of support has to go through a region where the state values piled up around the mass of support are dragged in the opposite direction because of recoil. The absolute velocity of each of the two moving bodies is proportional to the state value increase generated by the other, and thus inversely proportional to the masses.

It follows that a body can be accelerated to speeds which near that of light c only if the mass of support’s value is so high that its recoil velocity becomes close to zero.

The rule that prevents objects moving away from their masses of support from exceeding c has absolute validity. However, only in the hypothetical case where two masses have no gravitational relation whatsoever with the surrounding environment will we be able to identify with certainty the mass of support in one of them.

In real space, where all systems are gravitationally linked to a system of a higher order, when an object is acted upon with a force strong enough to move it away from the mass to which it is directly related, at a speed higher than c, the system of higher order could become the mass of support.

The consequent effect should also cause us to observe objects moving faster than c with respect to the apparent mass of support. This is confirmed by astronomical observations of atypical objects characterized by extremely violent explosions. It must be pointed out, however, that this is due to two different reasons which can affect our observations both separately and combined. One reason may simply be the wrong identification of the mass of support we mentioned earlier; the other, as we will see below, may be that we are observing objects already in motion with reference to quantum space at velocities which come close enough to the speed of light.

The differences between gravitational and inertial masses are irrelevant in normal conditions but become astonishing at relativistic speeds.

First let’s consider the gravitational mass of an elementary particle. This mass does not undergo any change caused by accelerations to relativistic speeds, at least until the difference between the speed of light c and the particle’s speed is higher than the value of the mass halo’s diameter.

If the gravitational mass underwent the increase predicted by the Lorentz transformations for inertial mass that would produce a cosmological consequence which would be hard to reconcile with current theories: the huge mass increase of the material expelled by the Big Bang moving at speeds equal or very near c would have stopped or drastically reduced its expansion. The galactic systems we observe on the edge of the universe known so far which seem to move at speeds close to c wouldn’t be able to survive the collapse caused by their components’ huge mass increase.

So let us examine the variations of gravitational mass produced by a relativistic effect. The mass halo is constantly recreated by the moving energy constituting the particle, until the particle starts moving through space at a speed which allows it to cover the shifting distance plus the radius of the mass halo within the limit of c.

Once this ratio between luminal speed and particle speed is exceeded, the gravitational mass gradually decreases, up to a limit value below which the particle’s mass disappears and is turned into pure energy.

The formula used to calculate the gravitational mass is therefore, where:

c = the speed of light

Mg = gravitational mass

V = particle’s velocity;

m0 = rest mass at ;

r = diameter of mass halo

f = diameter of the particle without its mass halo (expressed as a fraction of r).

The limits within which the gravitational mass shifts from a normal value to the lowest possible value will be:

3)      image559.gif (1044 byte)   ;       image560.gif (1064 byte)

Within such limits, the gravitational mass becomes:

4)      image561.gif (1023 byte)image562.gif (988 byte) 

In order to calculate gravitational mass variations at relativistic speeds, I have expressly referred to the mass halo of an elementary particle, since for an object made up of a myriad of particles and subsystems all in mutual motion, velocity V, as used in the formula, should also integrate the velocities of all moving internal components, as related to space. That would make calculations virtually impossible, both because of the many parameters involved, and, if that’s not enough, because the slowing down of internal motions caused by the body’s acceleration must also be considered (time stretching).

The inertial mass exhibits a completely different behavior at relativistic speeds. Its value increases even much faster than predicted by the Lorentz transformations.

We have seen that the nondimensional equivalence calls for a precise ratio between the limit velocity of an accelerated body and its mass, with the recoil speed and the mass of the body considered as mass of support; this ratio is expressed through the inverse proportionality between speed and mass, where the sum of the velocities of the two orbits can’t exceed c.

Therefore, if:

Mir = the accelerated object’s relativistic inertial mass;

Mi = inertial mass calculated as in 1);

V = velocity of the accelerated object with mass Mir


5)       image563.gif (1560 byte)

and extending 1):

6)        image564.gif (1616 byte)

The inertial mass’s value as derived from formulae 5) and 6) however can only be applied when the system of accelerated mass and mass of support is not itself moving with respect to quantum space at relativistic speed.

If the system is itself moving at a significant speed V2, the value for inertial mass derived as shown above, will need to be corrected to take this aspect into account.

In figures 16 A and 16 B two cases are portrayed:

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In figure 16 A) the system moves through space at speed V2 ; its direction is consistent but tilted by an angle q (less than or equal to p /2) with respect to the direction in which body P is moving at speed V, with reference to its mass of support. Body P’s actual displacement will follow the resultant at speed (V + Vm) relatively to space – this speed cannot exceed c.

Vm represents V2’s contribution to object P’s motion; P’s inertial mass will therefore be:

7)        image565.gif (1543 byte)

Solving for V + Vm = Vr, with respect to the angle:

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8)          image567.gif (1340 byte)

In Figure 16 B) the system’s displacement direction is not consistent with that of P, as they are tilted by an angle q whose value ranges between p /2 and p .

The actual displacement of P will occur along the resultant at a speed not higher than c with reference to space. But P’s displacement velocity V with respect to the mass of support M2 could turn out to be higher than c, with a upper limit of 2c. Formulae 6), 7) and 8) remain valid, but the mass of support Mg contemplated in 6) will be that of the gravitational system of the higher order. The formula used to calculate V is therefore:

9)         image568.gif (1363 byte) 


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Fig. 17 shows the accretion curvature of the inertial mass at relativistic speeds, as predicted by the Lorentz transformation, whereas fig. 18 shows the accretion curvature in quantum space, derived applying the concepts expressed above.

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In figure 7 A two objects are portrayed, which are supposed to be connected to each other in a system. The smaller is made up of only one conventional particle, whereas the larger is made up of more particles. The overall value of the influence these objects exert on each other, which determines both internal and external state values, is absolutely identical, as each particle exerts its action with a constant value on all other particles which find themselves at the same distance, regardless of their number.

In the equation below the equivalence between the sum of the influences exerted by particle p on particle p(1 n) and the sum of the influences these exert on particle p is highlighted.

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The following equation, which follows from the one just mentioned instead represents the effect which has been called the "remote spectral Action", as a tribute to Einstein’s definition. This effect is a consequence of Relation, (see fig. 7 B) and concerns the correlated behavior of particles among which no communication at luminal speed is possible, which however exhibit a form of connection capable of tuning their action no matter what the distance between them is. Such correlated particles, originated as systems, remain part of it, regardless of the sizes it acquires. The "ghostly" object which represents a support for both particles could even be the entire Universe.

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Another consequence of Relation is the invariance of scale of space geometry which is determined, as we have seen, by the volume distribution of state levels.

In the chapter on Relation we have already mentioned that the shape induced by the presence of mass, charge or particle concentrations tends to be conserved, at any distance. Figure 8 shows this tendency at growing distances.

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But the most peculiar aspect of the invariance of scale is that any space volume, no matter its size, will exhibit a geometrical distribution which exactly reflects the "massive" distribution of the whole universe as seen from its center.

Let us examine this tendency in detail.

Let us consider a determined volume of space of any size, assuming it is spherical for our convenience, and let us suppose we can measure the state level of its constituent quanta. Clearly, the measurement of the state level is at present completely out of reach for us (we can calculate it if it is referred to separated masses, charges or fields, but we still have no idea of the unit of measure that must be adopted in order to take into account all the influences which determine the state level). However this could be considered possible in a conceptual experiment.

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The state levels Vs1 and Vs2 determined by a mass, measured in points P1 and P2 (see fig. 7 C) where a diameter intersects the surface of the sphere, allow us to compute the distance d and the mass M (or charge) of the body placed on the extension of the diameter which determines them, this if the radius of the sphere is known.

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Now let’s suppose to make the spherical volume in question larger or smaller, up to a radius Rb (obviously with the same center). The calculation derived from the state levels Vs1b and Vs2b, measured in points P1b and P2b, where the diameter intersects the surface of the new sphere, will yield the same values for d and M at any scale ratio.

The proposed calculation only aims at highlighting the characteristic of the invariance of scale and the way it operates; in practice, the distribution of state levels within any volume turns out to be so complex and articulated that any attempt to extrapolate the information it contains is at present totally unthinkable. For now we must be satisfied with the awareness that such information exists and hope that it can be at least partly deciphered in the not too distant future.


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As I have formulated my ideas I have pointed out that they do not replace current theories, nor do they call for variations of the originating physical laws: it is then natural to wonder how they can be useful.

My initial objective for this work was to coordinate physical theories and laws, adapting their concepts using an abstract model allowing our interpretation mechanisms to be more consistent with the operating methods of our intellect.

Even if my ideas were merely a device to translate into more comprehensible terms difficult concepts and laws sharply contrasting with our logic, that initial objective would have been achieved.

However, every single examined indication is consistent with the proposed model and with the consequent reinterpretation of physical laws, and no phenomenon we have observed, or simply hypothesized following current knowledge results to be incompatible with the originating theories. For these reasons, such theories are very likely to be not only an interpretative device, but also the description of the reality that surrounds us.

The model then is no longer abstract, and becomes real and concrete.

Moreover, as these theories represent a cross-disciplinary link, they can be temporarily accepted, until they are verified, as a structural global model for our universe, in the absence of a similar comprehensive model. Those who refuse to accept them, if only provisionally, might have to tackle the embarrassing problem to propose an equally functional alternative model.

Theories of this sort however bring with them many particular implications which will require a deep cultural review not only in a merely scientific sense. For this reason a long time might have to go by before they are completely accepted, with consequent delay of their application and development.

My ideas do not modify current physics, which maintains its validity, but the same is not true for future research, which could profit from them in terms of new highly interesting methods, orientations and prospects, enabling us to define our goals with greater approximation.

The development of such theories, the determination of parameters which describe their functions, their mathematical treatment, the necessary experimentation, all represent a very challenging task, which will require massive human resources, excellent organization ability and high technological standards, with consequent high costs.

Let’s examine a possible method to test and develop these ideas, also considering the difficulties to be overcome.

The experimental tests I have mentioned - such as the transitional modes of field variations, the search for gravitational waves and the attempt to define the laws that regulate their diffusion by means of laboratory experiments, the experiments with large particle accelerators studying collisions occurring with increased state levels – are difficult to put into practice, but they are nevertheless within the reach of our technology, and they might provide the first indications supporting quantum space theories.

Other important experiments concern:

Still at the experimental level, classical experiments might be repeated in a way that would allow us to observe the influences that might be induced by specific space conditions. This would not only provide more accurate statistical data, but it could also be helpful in determining which directions the investigation should take.

But the key to these theories’ development and application will be the mathematical treatment of space geometry determined by the interactions with energy.

In this respect it is disarming to realize that we currently do not possess either the mathematical methods, nor the adequate computing instruments necessary for this objective and a huge amount of work will be needed in order to acquire such means.

What are the reasons for my pessimism? Quantum space is, as we have seen, rigorously three-dimensional, but the treatment of its geometry requires the introduction of a fourth space dimension, in addition to the three Cartesian dimensions (length, width, height): depth.

In fact, the "objects" that quantum space geometry must describe are not homogeneous surfaces or volumes, but rather inhomogeneous volumes, and therefore we need to know and represent

the condition of each point, or quantum, inside it. Moreover, quantum space geometry is dynamic, it changes constantly according to the mutual position of the discrete energy amounts (particles) moving inside it. If this were not enough, we have to keep in mind that any three-dimensional object has two types of external surfaces: a "visible" physical dimension, determined by the distribution of its constituent atoms, and a surface determined by the point of equilibrium with its surrounding objects.

It is therefore necessary to take a further dimension into account: time. Particles, or the energy that constitutes them, move at a finite speed, following the paths determined by state level configurations, whereas state levels oscillate synchronously with the particles’ mutual position. This twofold behavior implies that space geometry must be dealt with simultaneously at the atemporal and temporal levels.

The units of measure we use are not rational for quantum space either, as they are based on geocentric (and anthropocentric) parameters, and therefore require the constant use of such approximate centers to correlate all phenomena with one another and on a universal scale. In order to greatly facilitate our calculations and to avoid misleading approximations, we should use a system based on the appropriate units of measure of quantum space, such as the speed of light expressed in a quantum distance and time unit of measure (see chapter on SPACE-TIME in QUANTUM SPACE).

Also our current computing instrument are not really adequate to fulfill the requirements that the above-mentioned operating conditions imply; such instruments have in fact great potentials but they are structured to work mainly in a sequential manner. The nature of the problems we are dealing with instead forces us to carry out a huge amount of operations in parallel and in constant atemporal correlation.

The creation of computing instruments which can adequately manage quantum space geometry is not easy, but not out of reach for our technology: the integration on a large scale of a high number of bus connected parallel processors, so to allow the simultaneous flow of data, with connections rigorously of equal lengths, and with the appropriate software adaptations, would succeed in neutralizing all distortions caused by time delays, allowing numerical simulations in real-time.

Computer simulations will be very helpful, both for the development of mathematical procedures, and for the representation of space geometry. But also in this area our creativity will be put to the test, since instruments will have to be invented capable of providing real three-dimensional image delivery, or, even better, with the four space dimensions necessary to describe quantum space.

Fractal geometry will also constitute an excellent instrument to represent and support simulations. However, it will only be fully effective when it can operate in holographic projection allowing complete three-dimensional and dynamic delivery, in conjunction with images operating in real-time simulations.

The model of the universe I have described is at the same time extremely simple – made up of only two elements, quantum space and energy – and extraordinarily more complex than we had ever thought, because of its articulated and dynamic geometry, its structure of systems ordered on hierarchic scales, its absolute and perfect organization expressed in the very space quanta which surround the systems, and the constant and equal interaction among all of its components, at a universal level, from the smallest up to the largest.

There’s another important characteristic this model lacks in order to be complete: an hypothesis capable of describing the quantum mechanical nature of energy in accordance with the observed interactions with quantum space. A possible direction to follow might be the development of the theory of preons and their dynamic, but if I will not be able to formulate a theory capable of describing the nature of energy, I am sure somebody else will take on the challenge and complete the work I have begun.

Paradoxically, the complexity of the universe – which these theories have greatly enhanced even more than Relativity and quantum mechanics had done – does not complicate its comprehension; on the contrary, it makes it more appropriate and compatible with our logic. A more careful analysis shows that the higher complexity can account for those elements that our observations had not detected, which makes the theories complete and consistent with the needs of our deterministic logic.

This seems to confirm my anthropic conviction that the logic developed naturally by our brain, which is part of the universe, in accordance with its structure, could not have developed differently from the universal logic, in a contrasting way.

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1) Nature and origin of mass, of energy, of charges, of fields, distribution and modes of field spreading, etc. (GO BACK)

2) It might be a paradox if we think that any energy exchange is attributed to the action of intermediate bosons, while very little or nothing at all is foreseen to modulate the utterly invasive action of fields. (GO BACK)

3) With roles consequently less important. (GO BACK)

4) The relativity criterion is once again essential. (GO BACK)

5) It is very likely that in future, with a well-aimed research, both experimental detections and mathematical calculations will be able to better highlight the behavior of material particles in quantum space. (GO BACK)

6) We are led to suppose that particles without an internal structure could originate from the interaction between energy and a clump of space quanta, instead of just one, by the muon and tau decays. This hypothesis however must not be ruled out a priori, although no other hint has confirmed its validity. (GO BACK)

7) The validity of these ideas could be verified by exerting high "pressures" on the space occupied by the particle for a longer period of time, through the use of laser beams concentrated on the particle. This way the state level following the impact will be prolonged with photon bombardment. Another experiment might offer important clues: beams of accelerated particles from different directions could be channeled onto one specific point. Their spherical distribution would allow us to go beyond the mere effects of frontal impacts, the limitation of current linear accelerators. (GO BACK)

8) See the papers on complex systems by Ilya Prigogine and the ideas of Henry Laborit on organization levels, a different definition of what I refer to as hierarchies of complex systems. (GO BACK)

9) See the recent proposal of Hooft for the construction of models based on "computerized" cells made up of _causally related elements, to determine relations within complex systems. (GO BACK)

10) See fig. 5 which outlines the crossing of concentric spheres at a uniform state level around charge or energy concentrations. (GO BACK)

11) The discrete amount of energy might be such only because discrete is the amount that can/must be acquired by space quanta to become observable particles. (GO BACK)

12) The electromagnetic force, in positive and negative form, is effective until the charge and polarity differences among systems or their inside have a value capable of modulating the surrounding space in a relevant way. When distances among systems are such that the charges' effect on state levels is compensated, or when their algebraic sum is below the gravitational level, the electromagnetic force is obviously no longer effective. (GO BACK)

13) The idea of relation has already been perceived and proposed in various ways, although it then has not been totally integrated into scientific theories. In this respect we can recall the remote spectral action proposed by Einstein, the instantaneous propagation of the gravitational force proposed by Newton, or the "non-locality" hypothized by Penrose. Recent experiments show a correlation between the behavior of photons emitted by a source in opposite directions, which can provide a partial confirmation of relation. (GO BACK)

14) The different destiny of two equal systems is attributed to external causes or to intrinsic flaws which englobe and conceal the causes due to different space collocation. (GO BACK)

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Aldo PIANA   -   Corso Monte Grappa n. 13   -    10146  TORINO  (Italy)


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