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General Balance in the Six-Dimensions of Space-Time

Authors:

Abstract

This paper presents a comprehensive theory that expresses the theories of quantum mechanics and general relativity in a unified framework. The study investigates events over a specific duration in the Euclidean six-dimensional space-time (𝑅6=𝑥1+𝑥2+𝑥3+𝑡1+𝑡2+𝑡3). Notably, the relationship between the inherent properties of matter, fundamental constants, and quantum mechanics phenomena with space-time geometry has not been thoroughly explored in previous research. The proposed theory provides deterministic predictions for the probabilistic outcomes of quantum mechanics. This prediction is based on a metric derived from the Eccentricity of the Ellipse, influenced by the density of objects over time. Furthermore, the article presents novel insights into the cause and nature of dark matter and dark energy.
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https://doi.org/10.32388/QT9EZE
General Balance in the Six-Dimensions of Space-Time
Seyed Kazem Mousavi1
Department of Physics University of isfahan
Abstract:
This paper presents a comprehensive theory that expresses the theories of quantum mechanics and general
relativity in a unified framework. The study investigates events over a specific duration in the Euclidean
six-dimensional space-time (!6="1+"2+"3+#1+#2+#3). Notably, the relationship between the inherent
properties of matter, fundamental constants, and quantum mechanics phenomena with space-time geometry
has not been thoroughly explored in previous research. The proposed theory provides deterministic
predictions for the probabilistic outcomes of quantum mechanics. This prediction is based on a metric
derived from the Eccentricity of the Ellipse, influenced by the density of objects over time. Furthermore,
the article presents novel insights into the cause and nature of dark matter and dark energy.
Keywords: quantum mechanics, general relativity, space-time geometry, dark matter, dark energy
1 Correspondence: kazem.mousavi92@yahoo.com
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https://doi.org/10.32388/QT9EZE
1. Introduction
In the past century, significant efforts have been dedicated to reconciling quantum mechanics and
general relativity. The inherent non-deterministic nature of quantum mechanical phenomena has
posed a fundamental challenge to the compatibility of these two pillars of modern physics. At the
heart of this incompatibility lies the unreality of quantum mechanical phenomena, which stands in
stark contrast to the deterministic framework of general relativity. This discrepancy has been a
subject of intense theoretical and experimental investigation, reflecting the profound implications
for our understanding of the fundamental nature of reality. Albert Einstein, a key figure in the
development of both quantum mechanics and general relativity, articulated a perspective that sheds
light on this fundamental issue. According to Einstein, the reality of a physical quantity is
contingent upon the ability to predict that reality with certainty, without inducing any disruption
or disorder within the system. This criterion, rooted in the classical determinism of physics,
underscores the challenge posed by the inherently probabilistic nature of quantum mechanics [1].
To unite two theories, the two theories must share identical attitudes towards physical quantities.
Understanding the phenomenon of quantum mechanics can be achieved through a comprehensive
knowledge of the origins of mass, spin, electric charge, and other related factors. This
understanding is crucial for the integration of theories and the advancement of scientific
knowledge in the field.[2][3][4][5][6]. The exploration of time's nature has become increasingly
crucial in the ongoing development of the theory of everything, particularly in light of the
remarkable successes of quantum mechanics. As we strive towards a comprehensive
understanding of the universe, it is imperative to consider the fundamental nature of time and its
role in shaping the fabric of reality. By delving into the intricacies of temporal dynamics, we can
gain valuable insights that may ultimately lead to a more unified and comprehensive theoretical
framework. This endeavor holds great promise for advancing our understanding of the cosmos and
represents a pivotal strategy in the evolution of scientific thought [7]
A new approach to understanding quantum mechanics phenomena involves reexamining the nature
of space-time. Describing events outside of the constraints of time is a novel area of study that
offers a fresh perspective in the field of physics. This new outlook provides a different vantage
point from which to explore the universe. Research and scholarly work in this area is centered on
defining different metrics within a six-dimensional space. This shift in perspective opens up new
possibilities for comprehending the fundamental principles that govern the behavior of particles at
the quantum level [8][9][10][11][12]. The incorporation of six-dimensional space as a framework
for understanding space-time presents certain challenges, yet it proves to be highly advantageous
in elucidating various phenomena within the realm of quantum mechanics [13]. The concept of
space-time metric, described in terms of elliptical eccentricity, offers a compelling solution to
several longstanding problems in the field of astrophysics and cosmology. This innovative
approach provides a new framework for understanding the fundamental nature of space-time and
its impact on the behavior of celestial bodies. One of the key advantages of employing elliptical
eccentricity in the metric description of space-time is its ability to account for the non-uniform
distribution of mass and energy throughout the universe. Traditional models often struggle to
accurately represent the complex gravitational interactions that occur in systems with significant
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asymmetry or irregularity. By incorporating elliptical eccentricity into the metric, scientists can
more effectively capture the dynamic and intricate nature of these systems, leading to more
accurate predictions and explanations of observed phenomena.
Furthermore, this approach has the potential to address discrepancies between theoretical
predictions and observational data related to the motion of celestial bodies. The incorporation of
elliptical eccentricity into the space-time metric offers a more nuanced understanding of
gravitational effects, allowing for better alignment between theoretical calculations and empirical
evidence. This has significant implications for our ability to model and interpret the behavior of
objects ranging from individual stars to entire galaxies. In addition, the use of elliptical eccentricity
in the metric description of space-time has implications for our understanding of the fundamental
structure of the universe. By providing a more comprehensive framework for incorporating the
effects of mass and energy distribution, this approach has the potential to shed light on
longstanding mysteries such as dark matter and dark energy. It may also offer new insights into
the behavior of black holes and other exotic astronomical phenomena. Overall, the incorporation
of elliptical eccentricity into the metric description of space-time represents a promising avenue
for advancing our understanding of the cosmos. By providing a more accurate and comprehensive
model of gravitational interactions, this approach has the potential to revolutionize our ability to
explain and predict a wide range of astrophysical phenomena. As researchers continue to explore
and refine this innovative framework, it is likely to yield discoveries and deepen our appreciation
for the intricate interplay between space, time, and the forces that shape the universe [14][15]. In
this six-dimensional space-time framework, quantum mechanics offers a comprehensive and
elegant way to describe the behavior of particles and their interactions. By incorporating both the
three dimensions of space and the three dimensions of time, this approach provides a more
complete picture of the dynamics of quantum systems. The concept of six-dimensional space-time
has profound implications for our understanding of phenomena such as quantum entanglement,
particle-wave duality, and the behavior of subatomic particles. It allows for a more nuanced and
sophisticated description of these phenomena, shedding light on the underlying principles that
govern the behavior of the quantum world [16]. The concept of time as an independent dimension
from space allows for the definition of a unique type of 'motion' in time itself. When considering
extrinsic geometry, this motion in time can be understood as a 'real' distance. The unidirectional
nature of time is expressed by the time arrow, and it is observed that objects move at varying
speeds within this dimension. The rate of an object's movement through time is directly related to
its mass, with denser objects moving more slowly in the time dimension. This relationship between
mass and movement through time is further exemplified by phenomena such as gravitational time
dilation and time dilation for moving objects. These occurrences express the change in density of
an object within the space-time continuum, resulting in a slower movement through time for denser
objects. The balance theory delves into the equilibrium of events and quantities across the three
dimensions of time and the three dimensions of space within the six dimensions of space-time
[17]. This theory provides a framework for understanding the interplay between temporal and
spatial dimensions, offering insights into the dynamic nature of the universe. In conclusion, the
consideration of time as an independent dimension opens up new avenues for understanding
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motion and the interplay between mass, space, and time. It provides a framework for exploring the
intricacies of the universe and offers valuable insights into the fundamental nature of reality. The
paper addresses several key defects in a particular theory, aiming to establish a balance and parity
between time, space, and physical quantities. Its theories the concept of mass resulting from
movement in both time dimensions and space, emphasizing the interconnectedness of these
fundamental aspects. The proposition that time can be disregarded in the sub-atomic realm is
explored, with examples illustrating particle behavior within different time dimensions.
Furthermore, the paper discusses the relationship between particle state entanglement and higher
dimensions, highlighting the intriguing closeness of particles despite spatial separation.
Additionally, the article explores the potential independence of three-time dimensions from three
space dimensions and their deep interconnections for analyzing quantum mechanics and general
relativity phenomena. The nature and cause of quantum mechanical phenomena are attributed to
the relationship between fundamental constants and key mathematical numbers. Finally, the paper
emphasizes the significance of a geometrical interpretation for unifying quantum mechanics with
general relativity.
2. Six-dimensional space-time
Space-time is a Euclidean space 3+3 consisting of three space dimensions (x, y, z) and three-time
dimensions (t-, t, t+). (2.1). Time dimensions are imaginary 3-dimensional from the perspective of
a supervisor and they are observed only in one dimension. (1.2) (2.2)
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The dimensions y and z are imaginary for creatures one-dimensional on a circle. This circle is
embedded in the surface of a 3-dimensional sphere. Also, this sphere is expanding. Figure 1.
Consequently, of the parallaxes of one -dimensional creatures, two imaginary dimensions are
observed in the direction of one imaginary dimension. also, Time has an internal dimension as
well.
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Figure 1. The circle on the surface of the sphere is also expanded with the expansion of the sphere, and as
a result, the dimensions y & z are observed from the perspective of the points on the circle's surface in the
form of an imaginary dimension.
Time dilation depends on the mass and speed of the observer. Time dilation (the speed of
movement in the time dimension) depends on the mass and speed of the observer. The mass and
speed of the observer are directly related to the eccentricity of the ellipse. Figure 2. Eccentricity in
the space dimensions has an effect on the time dimensions as well. From the perspective of
extrinsic geometry, the time dilation of the moving object and also Gravitational time dilation in
the gravitational field are expressed based on the angle θ. (2.3). Figure 2. Density or speed can
create eccentricity in space-time dimensions.
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Figure 2: Time dilation of the moving object and gravitational time dilation express the direct relationship
between mass & density with time.
The passed distance in space is real six-dimensional from the perspective of space-time. But the
distance from the perspective of 4 or 5-dimensional space-time is expressed in hyperbolic
geometry. (2.4) (2.5)
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Eccentricity in one axis causes eccentricity in other axes. As a result of this eccentricity, the path
traversed in space-time has a rotation equal to ¼ of the circumference of the hypothetical circle
with the radius of the density (field). Figure 3
Figure 3: Eccentricity in space causes to create time dilation for the moving object compared to the 2-time
axles.
As a result of defining the passed distance in space-time, is dependent on the space-time expansion,
the light speed as well as eccentricity in six-dimensional space-time. (2.6)
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In six-dimensional space, there are five degrees of freedom. From the perspective of 4–
dimensional space-time, two-time dimensions are observed in one dimension. Consequently, the
two angles, related to eccentricity are expressed by the angle θ. The angle κ is also for expansion
and final movement in time. Figure 4
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Figure 4: The density of each object has a length in the time dimension and it is embedded around a
sphere with a radius equal to the density which is called a “mass field”.
While moving the rigid object in space, the radius of the field and object lengths change which is
proportional to density. The angles related to eccentricity exist in equilibrium in the two-time
dimensions. (2.7)
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With consideration of the two-time axles, the matter is stressed by space–time. The exerted stress
on the matter from time dimensions is twice the exerted stress from space dimensions. This twice
proportion has a direct connection with the golden constant. (2.8)
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Figure 5: Two dimensions of time are seen from the perspective of three-dimensional space in one
dimension, and as a result, this causes the material to experience double stress from the time dimensions.
From the perspective of extrinsic geometry, the illusory dimension of time is a real dimension.
And the distance traveled in space-time is a real path over time. (2.9)
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The angles θ and ϕ indicate the extent of eccentricity. The metric of space-time is expressed
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The matter with a 3-dimensional nature creates heterogeneity in the space density with higher
dimensions. As a result of this heterogeneity, matter moves in space–time. Meanwhile,
heterogeneity is a factor in creating eccentricity and stress to the material. Based on creating
heterogeneity in space–time structure by matter and energy, density can be expressed in the form
of passed distance in space–time. The oscillation of heterogeneity in space-time creates
gravitational mass. Mass cannot exist in the past or future; therefore, expressing negative density
is necessary for the Energy momentum tensor (2.11).
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Möbius space is a concept that transfers the properties of lower dimensions to higher dimensions.
This phenomenon is similar to the Möbius strip, a famous example of a two-dimensional structure
existing in three-dimensional space. The Möbius strip is constructed by taking a long strip of paper,
giving it a half-twist, and then joining the ends together. The Möbius strip is a tangible
representation of Möbius space, In Möbius space, the properties of lower dimensions with rotating
are "transferred" to higher dimensions, leading to unexpected and counterintuitive phenomena.
This concept has profound implications for our understanding of space, time, and the fundamental
nature of reality.
Objects in space-time rotate around a field with a radius that matches their density radius in higher
dimensions. This radius is equivalent to the density in two dimensions of one radian. Figure 6. The
matter field is rotating and moving simultaneously by rotating around a field its radius varies with
space expansion as well. Figure 7. The length of density or heterogeneity is like the length of one
Radian on the circle circumference. A sum of density and the negative of density in the 2-
dimensions is equal to ¼ of the circle circumference. Based on Figure 3, the object route in one
dimension is changed in the direction of geodesics of space–time in another dimension as well.
Thus, the object rotates equal to ¼ of the circle circumference in 3-dimensional space. This rotation
was generalized to higher dimensions. (2.12). This rotation is due to the constancy of object density
and causes to create eccentricity in other space–time expansion axles. Figure 3
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Figure 6: The rigid body is rotating in a field with a radius equal to the object density simultaneously by
spacetime expansion. Negative density is meaningful with time. Also, Möbius space is a concept that
transfers the properties of lower dimensions to higher dimensions
3. Geometry and fundamental constants of physics
The rotating of objects in 5-dimensional space was expressed by the Golden proportion. (3.13)
Golden constant, π, and e have a geometrical connection with physics fundamental constants like
the gravity constant and Planck constant in 6-dimensional space-time. (3.13)
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The resulting force from rotating objects around the field and then the performed work in six-
dimensional space were calculated by the Planck constant coefficient. (3.14) The Planck constant
is about object movement in space-time and the gravity constant is about object resistance versus
expansion of space-time. Figure7
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Figure 7: The object field in the space-time expanding is rotating and moving by the two forces
perpendicular to each other.
Two forces are exerted on the rigid object by the higher dimensions. One force causes the object
to move perpendicular to the axis of expansion, and the other force applies force to the object
against the direction of expansion of space-time. As a whole, the object is rotating around a field,
and the field is also rotating around an expanding sphere. Changing angles of ɑ and β indicate rigid
object motion around a field with higher dimensions. (3.15)
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Cosmology constant has a direct connection with the Planck constant, the gravity
constant, and 3 natural numbers. (3.16)
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Observations related to the planet's movement express a deep geometrical relationship between
fundamental constants. (3.17)
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The radius of the object field in space–time has a direct relationship with exerted force by the
higher dimensions. Due to this direct relationship, the proportions between these forces have a
constant with density. These proportions follow the golden constant, Euler's number, and π.
Figure 8
Figure 8: The proportion of exerted stress from spacetime has a relationship with the object density. This
proportion has a relationship with three natural numbers of π, e, and)4.
4. Wave function
The wave function in quantum mechanics has expanded over time. Concerning the object field,
the eccentricity of space-time dimensional, negative density, object rotation around the field, and
field rotation, the structure of wave function was expressed in the 6-dimensional space-time
(4.18) Quantization depends on two types of rotations in space. Figure 9
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Figure 9: Quantization has been entangled in space-time structure, and it depends on the object's
momentum.
Concerning affine transformation, elliptic parametric equation, Fourier Series eccentricity of
elliptic, and metric of 6-dimensional space-time, the relationship between wave function and
wave tensor was expressed. (4.19) Meanwhile, the tensor Ψ expresses the created rotation stress
by space-time to the matter. (4.19). Positive and negative amounts that have a relationship with
object rotation in higher dimensions are variable depending on the phase, speed, and density.
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5. Field structure and force
The electrical load has a direct relationship with the phase of object field rotation. Particles with
no mass or without loads have two opposite rotation phases. Photons transport energy and follow
from the geodesics of quantized space-time. the photons can be decomposed into a pair couple of
electron-positron fields. Each pack of energy has a particular geometric structure, and on this basis,
the field radius and the 2nd radius can be calculated with consideration of the performed work in
space and time. (5.20) Electrical load has a direct relationship with the phase of the field in higher
dimensions. Figure 10
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consist of two particles with opposite phases.
Changing the speed of rotation phases in the electromagnetic field is more than other space-time
points. Each particle follows space-time geodesics within the limits of an electrical field.
Eccentricity, in the gravitational field and electromagnetic fields, creates phase-changing speed.
Figure 11
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15
https://doi.org/10.32388/QT9EZE
Figure 11: Phase changing speed is greater in electrical and magnetic fields compared to the gravitational
field, and the effective range of the gravitational field is more compared to electrical and magnetic fields.
The mass obtained from motion in space is (inertial mass) and the mass obtained from motion in
time is (gravitational mass). The exerted stress from space-time to matter concerns the Planck
constant and gravitation constant. This stress intensity is very insignificant. However, the exerted
stress is observable concerning the rotation around the field and the passage of time. Tensor for
space-time stress based on Planck constant, gravitation constant, and cosmology constant indicate
the quantum Structure of space-time. (5.21) (5.22). The “K” tensor expresses the exerted stress to
matter in space-time with higher dimensions. This Stress is, therefore, a factor in producing spin,
electrical load & electromagnetic fields. K tensor has a direct relationship with wavelength and
cosmology constant. (5.22) The radius equal to density length (field radius) is ‘r_x’ and the radius
for the variable of field rotation is ‘r_t’. It is not able to be greater than a specific amount that is
dependent on the object's mass. Consequently, 'r_t’ is periodic.
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constant and gravitational constant is specified with the cosmology constant. (5.23)
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more complete. (5.24). Mass in space-time can cause inhomogeneity, which is represented by
negative density. (5.25)
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Ricci tensor expresses curvature in 4-dimensional space-time; by adding two Dimensions of time
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tensor and Ricci tensor in six-dimensional space-time may not be comprehensive. (6.26)
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Concerning space rotation, the Ricci tensor expresses curvature in the time dimension length, and
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dimensional tensor can only be defined during the time in the case of existing various masses.
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https://doi.org/10.32388/QT9EZE
Einstein tensor, Scalar Ricci, and Ricci tensor were obtained using Christoffel symbols. (6.30)
(6.31) Geometrical connection is hidden between space curvature and time length curvature in
Scalar Ricci. (6.30)
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Hilbert space is a complex of various states for a particle in a time loop. A particle rotates around
the field with a density radius in higher dimensions. In a moment a particle can have two upper
and lower spins. Measurement reduces the dimensions of a particle to four dimensions. Figure 12
19
https://doi.org/10.32388/QT9EZE
Figure 12: when a particle is in the time loop around a field, it exists in Hilbert space.
Measuring a phenomenon in higher dimensions causes the wave function to collapse to the lower
dimensions, resulting in different observable states. Figure 13
Figure 13: With continuous changing of supervisor states or objects in space, each time a new result
measurement is created.
Despite the distance of the two objects from each other, they can have similar states. Regarding
the masses with similar densities, these states are contrariwise. Figure 14
Figure 14: Particles with different charge and mass can have similar states in space simultaneously.
Due to the direct relationship of mass and momentum with wave function and the direct
relationship of the wave function with space-time structure, the whole similar particles like
electrons, photons, and protons, follow space geodesics. When one of the entangled particles is
measured, another particle’s all states can be predicted with certainty. Figure 15
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https://doi.org/10.32388/QT9EZE
Figure 15: In case of having sufficient information from mass and particle speed, other states can be
predicted as well.
Before measuring a particle, there is no orientation in 3-dimensional space. Measuring in the time
state π/3 causes the particle’s dimension to collapse into a four-dimensional space; for this reason,
we select the states from the tensor Ψ which are constant for all the particles with a specific
momentum. As a result, entanglement will never occur between two particles in the coordinate
system of relativistic. Entanglement has been institutionalized in the space-time structure. Bell's
Inequality defect is due to the existence of similar states in the space-time rotating structure. (7.33)
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8. Results and Discussion
The study of the relationship between fundamental physics constants and mathematical constants
such as π, φ, and ɐ reveals a deep connection between electromagnetic fields and the geometry of
space-time. This relationship sheds light on the inherent properties of matter, including spin, mass,
polarization, and load, within the framework of space-time geometry and electromagnetic fields.
One of the key insights from this relationship is the concept of mass, which can be understood as
resulting from motion in both space (inertial mass) and time (gravitational mass). This duality
reflects the equilibrium that exists within the symmetrical space-time, where the interplay of
various physical quantities is balanced. Furthermore, the investigation of events within space-time
yields important principles such as orthogonality, separability, and reality. These principles
underpin our understanding of the behavior of physical systems over time. Additionally, concepts
such as the uncertainty principle, commutative property, and Bell inequality violation are shown
to be intricately linked to the passage of time. Drawing from both quantum mechanics and general
relativity, it becomes apparent that an electromagnetic field rotating in space-time has the capacity
to generate a positive or negative gravitational field. This insight not only deepens our
understanding of the interplay between electromagnetic and gravitational forces but also provides
a potential avenue for further exploration and experimentation. Moreover, the study of space-time
geometry also has implications for our understanding of dark matter and dark energy. These
enigmatic components of the universe are directly related to the underlying geometry of space-
time, hinting at a deeper connection between the structure of the universe and the fundamental
forces that govern it. In conclusion, the relationship between fundamental physics constants,
mathematical constants, and the geometry of space-time offers a rich tapestry of insights into the
nature of our universe. By delving into this relationship, we gain a deeper understanding of the
interconnectedness of physical phenomena and pave the way for new discoveries and
advancements in our comprehension of the cosmos.
22
https://doi.org/10.32388/QT9EZE
Acknowledgements:
The author would like to express their gratitude to Professor Masoud Naseri, Dr. M.T, Dr. Lh. Razazi and
E.t.S. Sattar for their helpful discussions.
Conflicts of Interest:
The author declares that there are no conflicts of interest. The author takes full responsibility for the content
and writing of this article.
The data statement
The data that support the findings of this study are openly available in [ Preprints.org ] at
https://doi.org/10.20944/preprints202308.1112.v1
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This paper presents a proof of Riemann's hypothesis by utilizing the golden ratio and the eccentricity of the ellipse in six dimensions. This proof extends across all scientific fields. this research introduces logical and mathematical principles for the distribution, recognition, and categorization of prime numbers. It also explores the relationship between prime numbers and the complex conjugate of five prime numbers in various dimensions. Accordingly, it delves into the classification of even numbers based on prime numbers. In this study, the proof of Riemann's hypothesis is examined from a geometric dimension's perspective. And based on this, the mathematical structure of an integrated theory is defined. properties and principles associated with prime numbers reveal connections between quantum mechanics and general relativity.
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