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Kulak L.A.
2. Quantum entaglement. Möbius geometry. The "yin-yang" symble. Phases of fibration

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"Quantum physics urgently needs new images and ideas, which can only arise from a profound revision of the principles that underlie it." Nobel laureate Louis de Broglie.

"Of all the services that can be rendered to science, the introduction of new ideas is the most important." Nobel laureate Joseph John Thomson

"Geometry exists for this very reason, so that knowledge may not be divorced from spatial contemplation." P.A. Florensky

"It is precisely the ethereal matter of space (masked by the obviously inappropriate term "vacuum") that, according to the conviction of truly knowledgeable scientists, should become the basis for bringing all the forces of nature into a single self-consistent picture." [80]


In my author`s monograph "Substance. Atom. Theory of Everything" [72] I proposed a self-consistent concept based on the ontology of the complementarity principle. The concept is proposed as a new platform for generalizations and covers the issues of the structure of the supporting Cosmic Medium, the basic element of nature and the atomic model based on it, the method of formation of atoms and the actualization of structural interrelations that hold system formations together as a whole, as well as the fractally-identical transfer of the general universal structural scheme to scaling levels. The monograph uses the methodology of Fractal Synthesis and lays the foundations of Linguistic Physics.

Speaking about the ontology of the complementarity principle, it should be noted that this principle has been known since ancient times.

For quantum mechanics, it was formulated by Nobel laureate N. Bohr in 1927 and is its most important principle.

Subsequently, the principle of complementarity was generalized in science, which led to the creation of the concept of complementarity, which covers not only physics, but also biology, psychology, cultural studies and, in fact, all areas of knowledge in general.

B. Mandelbrot's fractal geometry, discovered in 1967, has its roots in the ontology of the principle of complementarity.

The ontology of the complementarity principle also underlies the holographic principle, introduced into modern science in 1993 by theoretical physicist G. 't Hooft as a hypothesis about the general property of quantum gravity – a theory that aims to create a quantum description of gravitational interaction and bring theoretical achievements closer to the creation of a general Theory of Everything.

Experience and the accumulation of knowledge show that the comprehensive essence of the complementarity principle implies the existence of its equivalent in everything and is a universal natural duality. And the main conclusion is that it is the original and fundamental principle, mediating a unified formula, a unified equation and a unified geometry. And if in all reasoning we start from its original essence, then we can get significant simplifications both in chains of logical reasoning and in mathematical calculations.

A more detailed restatement of the theoretical view proposed in the monograph is grouped by me into four main articles in accordance with current topics of theoretical physics, and several articles published earlier are also added to this. In physics, experiment plays a decisive role in the construction of theories. Therefore, in the format of the proposed concept, not only a number of basic questions of theoretical physics are considered, but also the results of existing theoretical proposals and experiments are included, confirming both the correctness of the chosen starting point of the concept and the conclusions made on its basis, which can be classified as a fundamental work.

"The fundamental nature of the theory is determined by the degree of penetration into the secrets of nature and is determined not by the cumbersomeness of its mathematical apparatus, but by the degree of connection with materialistic philosophy and proximity to the boundaries of the knowable." Kuligin V.A. [77]


At this point, it is important to emphasize that the existing paradigm of particles still has its place due to the fact that at the stages of cognition, scientific thinking creates a vector of dividing a single spatial structure into separate fragments, peculiar puzzles, which are much easier to learn and describe by the apparatus of algebra separately.

Nevertheless, the fullness of time comes when differentiation has already exhausted itself, the fragments are known and a feeling of a dead end and a state of crisis arises. It is then that the stage of integration and synthesis of already acquired knowledge into the overall picture begins, the picture which is most clearly visible at the current stage of cognition. This picture forms a new fundamental theory, which requires both a new platform of generalizations and new mathematics.

Experimental results applied to the theoretical field of the new concept proposed by me increase the weight of the arguments in favor of the conclusions made, and are also the evidence link that is extremely necessary for the theoretical view to acquire the status of reflecting the reality of natural phenomena. And in this regard, the experiment is the fact that supports and confirms the theory.

In physics, it is the experiment that plays the decisive role in constructing a theory.” Academician of the Russian Academy of Natural Sciences G.I. Shipov [89]


For the theoretical presentation I used a geometric approach, which, as is known, helps to make quite significant simplifications and often leads to the goal faster than the path laid out by the apparatus of algebra. Also, the geometric approach contributes to visualization and the creation of figurative pictures, which theoretical physics experienced an acute shortage in the period of the creation of quantum mechanics, and is also experiencing also experiences the same deficit at the current stage of development.

The foundation of the geometric approach in the new proposed concept is the geometric analogue of the principle of complementarity. As a geometric analogue, the Mobius strip or Mobius ring is considered. The basis for this is the correspondence of this geometry and its properties to the ontological content of the principle of complementarity as a universal duality mediating the dynamics and forms of movement, as well as to the pictorial display in ancient symbolism.

The representation of a physical point in space in the form of a Mobius ring and its consideration as a magnetoelectric circuit provides the key to the analysis of the processes of Cosmogenesis, which can bring many theoretical views to a common denominator. In this regard, the universalism of the principle of complementarity as a natural duality, presented in the format of Mobius Geometry, can be laid down as the basis for creating the Unified Theory of Everything and, in all likelihood, is the most effective way to achieve this goal.

The author's monograph and articles also note hypothetical assumptions and elements of theoretical proposals in which scientists in the history of science, at the level of guesses or partial conclusions, touched upon the method of explaining a number of theoretical aspects using the geometry of the Mobius strip.

However, to date, no scientist has considered the properties of Möbius geometry in application to the fundamental and intractable questions of physics so broadly as to obtain their resulting or exhaustive explanation, as well as to link the scaling levels into a unified paradigm on this basis and to show the universality of the interrelations that mediate interactions and determine the forces in them, that is, to create a Unified Theory of Everything. A number of questions of theoretical physics in electrodynamics and quantum mechanics still have no explanation. The proposed geometric format demonstrates how these difficult questions can be resolved.

A more detailed presentation of the questions of physics in the theoretical view I propose in the format of Möbius Geometry is grouped into four articles:

"1. Quantum Medium. Möbius Geometry. Magnetic Monopole."

"2. Quantum Entanglement. Möbius Geometry. «Yin-Yang» Symbol. Phases of Fibration".

"3. The Basic Element of Nature. Mobius Geometry. Gravity. Model of the Atom".

"4. Hydromagnetic Dynamo. Mobius Geometry. The Method of Formation of the Atom".


To these four articles several articles published earlier are attached:

5. "Experiments of Thomson and Rutherford", ("Time out") [82]

6. "Clifford`s parallels", [71]

7. "Fibration of the Mobius Pattern. Formation of the Atom" [81]


This article is a continuation of the article "1. Quantum Medium. Mobius Geometry. Magnetic Monopole", which examined the issues of the structure of the etheric Quantum Medium as a supporting Cosmic Medium and proposed the following conclusions:

1. The main driving mechanism mediating the method of universal torsion (UNI-VERCE) is INVERSION (mirror asymmetry), enclosed in the topology of the geometry of the Mobius strip. This inversion mediates the interrelation between complementary components and determines the universal law of the dynamics of their interaction.

2. The supporting Cosmic Medium is a physical medium and represents the initial state of matter – the primordial matter – in the form of a dynamic cellular (matrix) structure of vortex magnetoelectric nodes, closed according to the complementary principle, which mediates the phenomenon of magnetism as such and oscillating self-motion – spinning.

3. Magnetism is the physical embodiment of the comprehensive principle of complementarity, which determines its universality and generality of manifestation.

4. The matrix structure gives the supporting etheric medium the property of granularity and, according to fractal similarity, it is characterized by effects occurring in granular materials.

5. The magnetic field of such nodes is not externally manifested as bipolarity, since their polarity has a closure in one topology, and is in a monopolar (monopole) state – two in one, closed in antiphase. The nodes of etheric matter are magnetic monopoles. Such an initial physical state of matter is magnetoelectrically "invisible" or unmanifested. It represents a monopole hidden duality. A monopole does not mean unipolar, but has an internal closure of the polarities of magnetism. It represents a monopole hidden duality.

6. The geometric visualization of such a magnetic monopole is a Mobius strip with a minimum aspect ratio of a plane closed through an inverse turn of 180 degrees.

The Mobius Magnetic Monopole (MMM) contains a natural antiphase duality, as well as the duality of symmetry and mirror asymmetry, combining them into one whole.

In essence, this is the original form of a quantum phenomenon, which determines discreteness. The InfoGen of the original antiphase duality and the symmetry-asymmetry duality is transmitted to all subsequent generations in a universal copying method. Magnetism as a physical embodiment of this duality has the property of transmitting its InfoGen to all subsequent generations.

7. In the state of closure through inversion and due to the internal magnetic reconnection, the etheric monopoles perform continuous and non-stop oscillations, which are an act of their internal spinning in the form of Mobius torsion, which is the simultaneous execution of two cyclorotations:

- rotation of inversion around a conditional internal center along the middle of the Mobius curvature line and

- cyclorotations of inversion around a conditional external center located inside the Mobius ring.

This double type of cyclo-turnover is transmitted InfoGenetically to all system formations generated by the etheric Quantum Medium, and is a universal type of torsion UNI-VERSE, as evidenced by the entire cosmos and the names of the Universe in English, as well as Russian. [72]

8. The Mobius Magnetic Monopole is a spinning quantum-mechanical unit that performs continuous and non-stop oscillations and produces sub-micro-monopole radiation, as well as the absorption of portions of magneto-plasma as a phase of quantum breathing. MMM is the original fundamental unit. The geometric shape, metrics and dynamics of the MMM cycle rotation contain a relationship with numerical values close to three constants: φ = 1.618, π = 3.1415 and e = 2.718281828459.

9. According to the description, such a vortex matrix of the supporting Cosmic Medium will create turbulence effects and, accordingly, a hydromagnetic dynamo will be generated in it.

10. Magnetoelectric oscillations of magnetic etheric monopoles are a reciprocal quantum process of "radiation-absorption", in other words, a process of oscillating quantum breathing of the etheric Medium, which is also transmitted InfoGenetically to all the creatures of the environment from small to large as a process of breathing of life and at each level of scaling and in each plane of being has its own way of expression. This breathing of life is performed by both sub-micro-units of the etheric Quantum Medium, and atoms, bioorganisms, stellar-planetary systems, galaxies and the Universe as a whole.

11. The process of quantum breathing of the supporting Medium creates a sub-micro-vibrational background and is that high-vibrational carrier mediating all processes of interactions in the supporting Medium, the transfer of information and the implementation of the background principle.

12. The spinning substrate of the etheric Quantum Medium is an etheric magneto-plasma – a kind of superfluid plasma liquid from sub-micro-monopole radiations-absorptions, that is, active living matter.

13. At ultra-low temperatures of outer space, the etheric magneto-plasma is a special kind of condensed medium, a kind of mega-quantum object, in which a variety of collective effects are observed both of the entire object as a whole and of its individual areas interacting as a whole. Such a medium is characterized by the movement of arrays of “text phrases”, and not individual “letter units” of universal binary coding.

14. The processes occurring in the superfluid etheric-plasma medium will obey the laws of hydrodynamics similar to the processes occurring in water and air environments.

15. According to the laws of hydrodynamics:

- In a hydrodynamic environment, any arc discharge, whether occurring in technological power plants or in natural conditions, can curl up into an electron vortex.

- As a result of external influences, a vortex ring can decrease the toroidal velocity and increase the annular velocity, turning either into a vortex disk or a cylindrical vortex (thick or thin). The opposite transformation is also possible. A vortex ring in the form of a Hill vortex can form a vortex funnel in the form of a cone (jet).

- Individual electron streams can separate from the surface of the vortex, quickly disintegrating into sparks.

- A vortex ring can deform, passing through small holes, and restore its shape after deformation.

- Vortex objects can divide spontaneously or under sudden external influence. The surface of an electron vortex can spontaneously delaminate into parallel electron beams.

- Dynamic interaction is possible between vortex objects – they play leapfrog, dance in a circle, merge together, etc.

- Vortices can form Karman paths. [34]

16. In accordance with the law of hydrodynamics on the spontaneous division of a vortex object or its division under a sharp external influence, it is proposed to further consider the phases of the process of bifurcation/fibration of a vortex monopole formation closed through an inverse turn, which geometrically represents the original Mobius strip as a special case of Clifford parallels.

In this article, in continuation of the coverage of the format of the application of Möbius Geometry to questions of theoretical physics, quantum entanglement and the fibrational phases of the Möbius Magnetic Monopole are considered.


The Nobel Prize in Physics 2022 was awarded to three physicists: Alain Aspect from Paris, John F. Clauser from California, and Anton Zeilinger from Vienna. The prize was awarded "for experiments with entangled photons, the establishment of the violation of Bell's inequality, and pioneering quantum information science." [60]

According to opinion of Chris Ferry, a lecturer at the Centre for Quantum Software and Information at the University of Technology Sydney, “Quantum entanglement is a complex phenomenon in physics that is usually poorly described as an invisible link between distant quantum objects that allows one to instantly affect the other. Albert Einstein famously dismissed this idea of entanglement as “spooky action at a distance.” In reality, entanglement is better understood as information, but that’s admittedly bland. So nowadays, every news article, explainer, opinion piece and artistic interpretation of quantum entanglement equates the phenomenon with Einstein’s spookiness.

The situation has only worsened with the 2022 Nobel Prize in Physics going to Alain Aspect, John F. Clauser and Anton Zeilinger for quantum entanglement experiments. But it’s time to cut this adjective loose. Calling entanglement spooky completely misrepresents how it actually works and hinders our ability to make sense of it.” [88]

Chris Ferry says that quantum entanglement is better understood as information. Of course, if quantum theory still lacks a picture of the representation of a quantum phenomenon as such and, accordingly, the form of the original quantum unit that creates this phenomenon has not been identified, then in the search for a picture of representation, it is worth grasping the understanding of this phenomenon as information, so that at least in some form it can be represented. Without an appropriate figurative representation, thought simply cannot move in the right direction, much less comprehend the phenomenon being studied and its application in practice.

In essence, the same phenomenon, which represents the original substantial essence, has its individual projections in different spheres. An example of this is the complementary corelation, which in the field of information, where its transmission occurs by binary coding, can be represented by two symbols – "0" and "1", in the field of electromagnetism – a magnetic field and electric current, in the field of electrical engineering – "+" and "-", in the field of cell biology – two strands of DNA, in the field of species biology – division into two sexes, and so on. All these are different forms of expression of one substantial essence – complementarity. Therefore, it is possible to understand and study it in different planes of being, while remembering their fractal-holographic identity.

Regarding the phenomenon of quantum entanglement, according to the holographic principle, it is also possible to study and understand it in various applications. And there is a weighty basis for this, because its nature is embedded in the original form of the quantum phenomenon, which was discussed in the work "1. Quantum Medium. Mobius Geometry. Magnetic Monopole".

The initial form of a quantum phenomenon is proposed to be considered a unit of the etheric Quantum Medium, which is considered as a sub-micro-magnetoelectric circuit in the form of a Mobius strip with one inversion. The absence of figurative pictures in quantum theory from the very beginning of its inception elevated the section of quantum physics to the category of some exception from the category of classical laws and thus gave rise to a number of unfavorable tendencies in it. Nevertheless, the quantum world is not an exception to the general rules and laws of physics, all of which are applicable to the sphere of quantum phenomena. The question is how to apply and how to represent. It is precisely in the absence of figurative pictures of representation that difficulties arise.

I believe that this absence was the reason why, when Erwin Schrödinger coined the term entanglement in 1935, he emphasized that “not one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of though”t. In fact, before quantum theory, "classical lines of thought" simply did not address these issues. The time had not yet come for their discovery.

“The EPR argument concerns the everyday notion of reality as a collection of things in the world with physical properties waiting to be revealed through measurement. This is how most of us intuitively understand reality. Einstein’s theory of relativity fits into this understanding, and says reality must be local, meaning nothing can influence anything else faster than the speed of light. But EPR showed that quantum physics isn’t compatible with these ideas—that it can’t account for a theory of local reality. In other words, quantum physics was missing something. To complete quantum physics, Einstein suggested scientists should look for a “deeper” theory of local reality”. [88]

This deeper theory of local reality begins precisely in the area of ​​quantum phenomena. Quantum phenomena concern everyday life to the same extent as the things we see, touch, and hear. The difference is that the quantum sphere is more perceptible to us not through the senses, but through intuitive sensations. And if quantum physics speaks of measurable dimensions at the level of the Planck length, then why shouldn't this "quantum length" have "physical properties awaiting their revelation through measurement"?

As for the fact that "nothing can influence anything else faster than the speed of light", I raised this question in the previous article "1. Quantum Medium. Mobius Geometry. Magnetic Monopole" and concerns the way light propagates in the ethereal Quantum Medium. The article presents arguments and the results of an experiment regarding the slowing down of the speed of light, and proposes a revision of the method of light propagation in the format of applying Mobius Geometry to the structure of the ethereal cosmic medium.

Based on the concept I proposed, if the propagation of light is assumed to be instantaneous, as the ancients believed, and Descartes, Kepler and Fermat also adhered to this opinion, then all questions related to locality and non-locality disappear by themselves. The basis for the instantaneous propagation is embedded in the matrix structure of the ethereal Quantum Medium, as well as in the geometry and properties of its individual pixels. The main question is always how we imagine this or that phenomenon. The virtuosity of algebra is practically capable of confirming any of the ideas with calculations. But in mathematics there is also geometry, which is just an intermediary between the theoretical studies of algebra and reality.

Let's say that according to Gödel's incompleteness theorem, in any theory built on the basis of first principles, it is always possible for such statements and facts to appear that are not deduced from them, but which are of fundamental importance. That is, any fundamental theory will always be incomplete, no matter how many facts and statements are added to it. This must always be kept in mind and expected. And also, some facts of the science of physics, which are already considered fundamental, may in fact be particular solutions of broader fundamental ideas that are expanding in scientific consciousness in each era. And there is no need to resist this expansion and assume that we have known everything for a long time.

Proposing a generalized concept in the format of Mobius Geometry, I am not afraid to introduce new statements, as well as to revive old ones, but forgotten for a number of objective reasons. Therefore, in contrast to the prevailing opinion about the exclusivity of quantum physics, as well as the explanation of “how quantum physics works, and how it departs from the classical world, from the perspective of information, not physics”, I assert that quantum physics is the original part of the “classical world,” its organic inclusion, does not depart from physics even from the point of view of information, and information is always associated with a material carrier, whatever it may be. If it is not a magnetic card or tape, not a paper carrier, not a computer or server, not cosmic ether, then only one thing remains - our head. And we should not forget about this. There is no information in some immaterial form. If someone still thinks differently, then it is worth twisting this thought until you understand this truth.

Therefore, quantum entanglement as a phenomenon of the quantum world has both its physical representation and explanation. Everything else is “from the evil one” or due to the incompleteness of knowledge at the current time. In this work I have mostly shown the actualization of quantum entanglement during the formation of an atomic structure in the process of fibration of etheric monopoles and growth of the structure from the inside out, in other words, in the process of transformation of "dark matter" into baryonic matter. Before directly moving on to this issue, it is necessary to touch upon the current trend and its experimental part.

Today, the facts from the life of the scientific preprint archive (arxiv.org) are such that since 2010, the theoretical section of high-energy particle physics "hep-th" has seen an exponential growth of articles devoted to the phenomenon of quantum entanglement.

The preprint site has shown a steady increase in the number of publications on quantum entanglement since 2009-2010 in the sections on condensed matter physics [cond-mat], high-energy particle physics [hep-th], and general relativity and quantum cosmology [gr-qc]. This fact was noted earlier by John Preskill in the blog of the Institute for Quantum Information and Matter. [11]


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Kulak L.A., 2. Quantum entaglement. Möbius geometry. The "yin-yang" symble. Phases of fibration // «Àêàäåìèÿ Òðèíèòàðèçìà», Ì., Ýë ¹ 77-6567, ïóáë.29435, 03.04.2025

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