ABSTRACT.

Over the past hundred years, the mathematical apparatus of algebra has been successfully and rapidly developed, to some extent bypassing the methodology of natural-philosophical thought and creating a certain imbalance in physics as a science of the nature of things. The observed imbalance is expressed primarily in the fact that the proposed theories, developed on the basis of the apparatus of algebra, lose their ontological content. They are slender and beautiful in themselves, but often they have no real application to reality and cannot offer a solution to a number of intractable questions of physics, among which the question of gravitation in general and its presence in the micro-world remains unresolved.

The geometric approach covered in this article offers a new look at the issues of gravitation interconnection and quantum entanglement, as well as a rather general schematic simple solution in explaining their nature based on the geometry of Clifford's parallels. The result of the successive geometric transformations covered is also the proposal of a new atomic model, which is in accordance with the line atomic emission-absorption spectra and is devoid of the contradictions that the existing model, established in the theoretical views of physics, has.

The proposed geometric approach can be a key aspect for answering many intractable questions in creating an ontological foundation for building a Unified Theory of Everything.

Keywords: Clifford`s program, spatial curvature geometry, Clifford`s parallels, Mцbius Pattern, monopole, dipole, Pauli bifurcation, Clifford-Hopf fibration, phases of fibration, “unified theory for the “proton-electron” together”, gravitational interconnection – lever balance with moving axis, quantum entanglement, polarization orientation in the radial direction, center-periphery, atom based on Mцbius dipoles, four-point function, ontology of the principle of complementarity, geometrization of physics, Unified Theory of Everything, moral aspects.

The December 2020 article “Determining the fine structure constant to within 81 parts per trillion” (authors Leo Morel, Zhibin Yao, and Saida Jelati) noted in Nature:

“The Standard Model of particle physics is surprisingly successful because it agrees with (almost) all experimental results. However, it cannot explain dark matter, dark energy, and the imbalance between matter and antimatter in the universe. Given that discrepancies between the predictions of the Standard Model and experimental observations can provide evidence for new physics, an accurate assessment of these predictions requires very precise values of fundamental physical constants.” [1]

Once the Nobel laureate Max Planck was asked the question: “In short, what do physicists do?” Answer: “In short, they clarify the constants!”

As far as the Standard Model (SM) is concerned, the main success of the SM is based on carefully described fundamental "forces", the nature of which remains unknown. The SM model describes three of the four fundamental interactions – electromagnetic, weak and strong nuclear forces, i.e. everything is believed to be the forces of nature, excluding gravitation.

All theories of the Standard Model describe the interactions between particles within the framework of a single picture, where the "particles" of matter (fermions) do not come into direct contact with each other, but exchange "particles"-intermediaries (bosons), called carriers of interactions. These are the theoretical representations of the SM today. How close they are to reality or far from it, no one knows yet. But the theory exists and attempts are being made to confirm it with the help of experiments conducted at colliders.

At the same time, no one sees the Standard Model as the final theory, since it is good only as an intermediate auxiliary tool and is not able to give scientists answers to many very serious questions regarding the number and properties of the fundamental "particles" of nature. And still within the framework of the SM no one has managed to squeeze gravity into the micro-world, which is proposed to be neglected there. The main success of the SM is most likely due to significant achievements in the development of the mathematical apparatus of algebra and the demonstration of its harmony and capabilities.

If we talk about the fact that discrepancies between theory and experimental data may indicate a new physics, then it is worth paying attention to some scientific prophecies that were made by the great physicists-mathematicians of the recent past.

The English mathematician and thinker William Kingdon Clifford clearly indicated that in the “hydrodynamic” picture of the world that he intends to build, literally everything that seems to us to be reality and its physics of variously interacting objects, ultimately turns out to be “curvature in the geometry of space and their movements like waves."

In 2000, on the pages of a specialized scientific journal, entirely devoted to applied aspects of Clifford mathematics, a note of purely historical value was published – "Scientific Prophecy of W.C. Clifford" [2]

This short article contains a note by Clifford with theses compiled by a scientist in an unknown year and for what purpose. But if we evaluate the document from the standpoint of scientific achievements of the late XX century, we can see that in the scientific plans of Clifford (1845-1879) the ideas of creating a common platform for combining all research from different fields of science are clearly visible, and in particular, the scientist focuses on gravity, which in his opinion, connects very different phenomena together, and the ether provides a bridge between these phenomena.

“This explains the laws of electric and magnetic attraction/repulsion, the action of electric currents on magnets and on each other, the laws of induction, the derivation of the speed of charges and the polarization of light, the rotation of the plane of polarization by a magnetic field. All these things must be deduced from the knowledge of the geometrical forms of the atoms and their relationship with the ether, thus indicating the relationship between the kinetic theory [of particles] and the wave theory [of ether].”[2]

In February 1870, a young and brilliantly gifted English mathematician, William Kingdon Clifford, gave an astonishing report to colleagues in the academic community at the University of Cambridge. The title of the report was as follows: "On the Spatial Theory of Matter".

The content of Clifford's speech and the ideas he voiced about the structure of nature sounded extremely unusual not only for the enlightened public of that time, but even today are perceived by many scientists as "bright dreams of the coming Theory of Everything based on the geometrization of physics."

In its full form, the text of W. Clifford's report for the history of science has not been preserved. But there are author's theses of this speech, published in the "Reports of the Cambridge Philosophical Society" and giving a very clear idea of ​​the innovative ideas of the scientist. [3]

Clifford highly appreciated the results and discoveries of Bernhard Riemann in the field of non-Euclidean geometry of curved spaces and compared them with natural phenomena already known to science in the field of physics of light, electricity and magnetism. As a result of his analytical comparisons, the mathematician came to the conclusion that the geometry of curved spaces could naturally explain these phenomena.

In Clifford's report summarizing these primary studies, the new theory was succinctly formulated in 4 idea points, something like this:

1). [Every smooth sheet of paper, upon closer examination, has local irregularities, scars and grooves. Similarly,] There are local areas of curvature in space, similar to small hills or pits on the surface. In these areas, the usual laws of plane geometry are inapplicable.

2). The pattern of local curvature is not static, but essentially dynamic. Any deformation or curvature of space is like a wave of perturbation, freely moving from one part of space to another.

3). This kind of change in the local curvature of space is the real nature of the phenomena that we perceive as the movement of matter. Moreover, this idea equally concerns both weighty matter and ethereal matter that forms space.

4). In reality, nothing else happens in the physical world, except for such changes in the geometry of space, possibly obeying the law of continuity.

This program of Clifford to some extent anticipated the emergence of science's views on gravity almost half a century before the advent of Einstein's general relativity. But in the picture of the world presented by Clifford, one can see not only the gravitational force of gravity generated by curvature. According to the above theses, in fact EVERYTHING that happens in nature comes down to dynamic changes in the geometry of space.

Therefore, it is natural and convenient to study and describe this dynamics, relying on the geometric methods of mathematics.

In the Afterword to Chisholm's book on Silver Streams, Nobel Laureate Roger Penrose writes about the personal contribution of the mathematician William Kingdon Clifford to scientific thought:

“Clifford's writings have strongly influenced the direction of my own research, not to mention the research of many other mathematicians and physicists. The main mathematical contribution of William Clifford is considered to be the introduction to science of what is now known as the "Clifford algebra". [5]

Clifford's remarkable property of the three-dimensional sphere (i.e., a spherical three-dimensional "surface" in four-dimensional space) has a particularly deep mathematical significance. This is the concept of what is now called Clifford's parallels.

Such "parallels" are actually circles that are parallel in the sense that they never get closer to each other or further away from each other as we move along these circles. And the circles are linked to each other. Clifford discovered that the entire 3D sphere could be filled with these sort of non-intersecting "parallel" circles, each of which was linked to each of the others.

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