Overview of the Zero Energy Cycle Theory

The Zero Energy Cycle Theory provides a new cosmological view based on the foundational equation "0 = +∞ − ∞," where the infinite progression of energy generation and annihilation ensures energy conservation. This theory perceives the entire universe as a "universe within fluctuations" in a medium called "vacuum," where continuous energy generation and annihilation occur.

The theory posits that the universe is a fluctuation within a single medium known as the "vacuum," attributing all cosmic phenomena to these vacuum fluctuations. The vacuum serves as the basis for all energy in the universe, and its energy fluctuations are believed to drive the dynamics of the cosmos.

The Relationship Between Observation Points and Multiverse Theory

Universe Generated by Fluctuations:

The "universe generated by fluctuations" refers to the concept that the material medium generated from vacuum fluctuations is considered to be the multiverse itself, distinct from the fluctuations (e.g., galaxy formation) occurring within the universe after the Big Bang.

Observation Points A and A':

Observation Point A: The perspective from which material generated by vacuum fluctuations is observed externally.
Observation Point A': The observation point within the universe generated by fluctuations, observing the universe from within.

According to the Zero Energy Cycle Theory, concepts like time and size are relative and dependent on the observer's viewpoint. This means that even the same phenomenon might be perceived differently in time and scale depending on the observation point. For example, from Observation Point A, A' may appear as a tiny, fleeting event, while within A', the scale might seem infinite, and time might appear eternal.

The Relativity of Size and Time and Consistency with Relativity Theory

The length of time and size can vary significantly depending on the observation standpoint, such as Observation Points A and A'. These concepts are relative rather than absolute, aligning with the Theory of Relativity.

According to relativity, the size of an object and the passage of time depend on the object's speed and the strength of the gravitational field. The idea that time and space differ for each observer aligns with relativity's concept of "spacetime relativity for each observer."

The Relationship Between Energy and Vacuum Fluctuations

This theory explains how the generation and annihilation of energy through vacuum fluctuations result in a continuous cycle of cosmic phenomena.

1. Dynamic Generation and Annihilation of Energy

The zero energy state involves the merging of matter and antimatter energies, leading to their transformation into different energy states, described by:

\[E_{\text{matter}} + E_{\text{antimatter}} = 2mc^2\]

This equation shows that the energy of matter and antimatter exists in complementary forms. This energy transformation process, originating from vacuum fluctuations, triggers phenomena like the Big Bang (as a creation from nothing) and the Big Crunch (energy dissolution).

2. Generation and Complementarity of Matter and Antimatter

The material universe and the antimatter universe are generated symmetrically and engage in a relationship through energy cycles, attracting each other. This interaction explains the presence of abundant antimatter in the early universe.

Extended Analogies

1. Analogy of Electromagnets and Iron Sand

Iron Sand in an Electromagnet:

In the early stage, with weak current, iron sand remains mixed at the center, and polarity is not distinct. This represents the state of the early universe where matter and antimatter were still mingled.

As the current increases, the S and N poles become distinct, and the iron sand aligns with each pole, separating clearly. This mirrors the cosmic evolution where increasing energy leads to a clearer separation of matter and antimatter.

Zero Point Energy and Vacuum Fluctuations

\[⟨0∣H∣0⟩_{\text{ren}} = \frac{1}{2} \sum_{k=0}^{k_{\text{max}}} ℏω_k\]

This equation shows that vacuum fluctuations induce finite energy changes, with the cutoff wavenumber \(k_{\text{max}}\) introduced to prevent infinite energy divergence.

Additional Implications for Current Theories

Dark energy and cosmic expansion mechanisms are explained through differential equations that describe how energy stabilizes, potentially leading to cosmic contraction.

The Symmetry Between the Physical and Spiritual Worlds

This theory suggests a relationship between physical and non-physical phenomena, linking it with concepts from multiverse and string theories.

Conclusion

The Zero Energy Cycle Theory highlights the recurring energy transformations that sustain cosmic evolution, emphasizing how matter and antimatter interact to preserve the dynamic balance of the universe.

New Definition and Theoretical Background of Integrated Dark Matter \( \rho_X \)

One of the major mysteries in cosmology is the rapid rotation of stars and gas in the outer regions of galaxies. To explain this phenomenon, physicists have long hypothesized the existence of dark matter. However, conventional dark matter models have limitations and cannot fully explain the flattening of the rotation speeds in these outer regions.

In this paper, we propose a new definition of dark matter \( \rho_X \), based on quantum fluctuations of vacuum energy, applying Zero Theory and aiming to integrate it with quantum field theory (QFT) and general relativity (GR). Furthermore, we will explore gravitational lensing as a result of theoretical consistency and delve deeper into the mechanisms of gravity and energy transmission.

1. The Standard Einstein Equation in General Relativity

1.1 The Standard Einstein Equation

The Einstein equation in general relativity (GR) is the fundamental equation that relates the curvature of spacetime to the distribution of matter and energy:

\[ G_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu} \]

Where:

• \( G_{\mu\nu} \) is the Einstein tensor, representing the curvature of spacetime.
• \( \Lambda \) is the cosmological constant, representing uniformly distributed dark energy.
• \( G \) is the gravitational constant.
• \( c \) is the speed of light.
• \( T_{\mu\nu} \) is the energy-momentum tensor, describing the distribution of matter and energy.

2. The Expansion of the Einstein Equation through Zero Theory

2.1 Overview of Zero Theory

Zero Theory is an approach that incorporates quantum fluctuations of vacuum energy density into the gravitational field, defining dark matter \( \rho_X \) in a new way. Through this theory, the Einstein equation is expanded as follows:

\[ G_{\mu\nu} = \frac{8\pi G}{c^4} \left( T_{\mu\nu}^{\text{matter}} - \rho_X g_{\mu\nu} \right) \]

Here, \( \rho_X \) is the vacuum energy density, which directly influences the curvature of spacetime. These fluctuations in vacuum energy suggest that dark matter does not need to exist as particles, offering a key explanation of gravitational phenomena as quantum fluctuations in vacuum energy.

3. New Definition of Dark Matter \( \rho_X \) and Understanding of Observational Phenomena

3.1 Overview of the New Definition

The new definition of dark matter \( \rho_X \) is that it is a local fluctuation in vacuum energy. In this way, dark matter is understood not as a particle, but as a fluctuation in the energy of the vacuum. In other words, phenomena such as the rotation speed of galaxies and gravitational lensing can be explained through transformations in vacuum energy.

3.2 Gravitational Lensing and the Vacuum as a Medium for Energy Transmission

3.2.1 What is Gravitational Lensing?

Gravitational lensing is a phenomenon in which light from a distant source appears to bend due to the curvature of spacetime around a massive object. In general relativity, mass bends spacetime, causing light to follow a curved path. The new theory, however, adds the perspective that vacuum acts as a medium for energy transmission.

3.2.2 The Role of Vacuum

In the new theory, gravitational lensing is a phenomenon that occurs as a result of mass distorting the vacuum. The vacuum functions as a medium for energy transmission, influencing the path of photons through energy vibrations and transformations. When a massive object distorts the vacuum, light travels through the distorted vacuum, appearing bent to the observer.

From this perspective, gravitational lensing can be understood as an observational phenomenon that proves the vacuum serves as a medium for energy transmission.

4. The Relationship Between Energy Density and the Rotation Speed of Galaxies

4.1 The Mechanism for Maintaining Galactic Rotation Speed

In the outer regions of galaxies, where the matter density decreases, vacuum energy \( \rho_X \) plays a dominant role, driving the matter in these regions and maintaining a constant rotation speed. This is the result of an energy transformation process, where vacuum energy consistently influences the entire galaxy.

5. Why Gravitational Lensing Proves the Theory

5.1 Unified Understanding of E=mc² and Energy

Einstein's famous equation, E=mc², shows that mass and energy are equivalent. In the new theory, gravitational lensing and the flattening of galactic rotation speeds are all understood as results of energy transformation processes, eliminating the need for dark matter to exist as hypothetical particles. Instead, dark matter \( \rho_X \), as a fluctuation in vacuum energy, causes the observed gravitational phenomena through differences in energy density.

5.1.1 Redefinition of Dark Matter

Dark matter is redefined not as particles but as fluctuations in energy density, explaining observed phenomena like gravitational lensing. Energy affects the curvature of spacetime, bending light and resulting in observable effects.

5.1.2 Reinterpretation of Gravitons

Previously, gravitons were proposed as hypothetical particles that mediate gravity. However, in vacuum energy theory, gravitons are no longer necessary. Gravity itself is explained as the result of energy transformations in the vacuum, where the mass's influence on the vacuum is observed as "gravity."

6. Conclusion and Future Prospects

This theory provides a new perspective, where vacuum energy acts as a medium for energy transmission, offering a unified explanation for gravitational phenomena, galactic rotation speeds, and gravitational lensing. Observed phenomena are understood as results of energy transformations, establishing theoretical consistency without the need for hypothetical particles like dark matter or gravitons.

Future challenges include further clarifying how vacuum energy fluctuations contribute to quantum mechanical phenomena and energy variations. Additionally, further experimental verification is required to confirm the consistency between observational data and the theory.

In conclusion, the observed gravitational lensing and the flattening of galactic rotation speeds are all consistently explained by the theory of vacuum energy transformations.

Gravitational Lensing and Vacuum as a Medium for Energy Transmission

1. What is Gravitational Lensing?

Gravitational lensing is a phenomenon where a massive object warps the spacetime around it, causing light from distant sources to bend as observed. This effect, explained through general relativity, has widely been accepted as intuitive — light bends due to the gravitational field of the object. However, a deeper energy mechanism is at play behind this phenomenon.

2. Understanding Vacuum as an Energy Transmission Medium

The new theory posits that gravitational lensing is not simply due to mass bending light but rather a phenomenon arising because **vacuum acts as a medium for energy transmission**. Not only does mass warp spacetime, but vacuum itself acts as a "field" that transmits energy.

• **Massive objects distort the vacuum:** Large massive objects (e.g., galaxies, black holes) induce energy vibrations in the surrounding vacuum, causing the vacuum to warp. This warping causes space to ripple, affecting even the flow of time. This distortion alters the path of light, and the bending of distant light is observed as the gravitational lensing effect.
• **Photons follow the vibrations of the vacuum:** Photons, being a form of energy, follow the vacuum's energy conversion and vibrations. As a result, the path of light bends along the distorted vacuum, appearing bent to the observer. This phenomenon itself demonstrates that vacuum serves as a medium for energy transmission.

Why Gravitational Lensing Proves the Theory

1. Unified Understanding of E=mc² and Energy

Einstein's famous equation **E=mc²** shows that mass and energy are equivalent. Applying this to the new energy transformation theory, the idea emerges that all phenomena can be explained through energy transformations and transmissions.

• **The Role of Dark Matter:** In conventional physics, dark matter has been explained as particles. In the new theory, however, dark matter is reinterpreted as "vacuum energy transformations." In other words, dark matter is a phenomenon based on energy differences, and that energy induces forces like gravity through the vacuum medium. The gravitational behavior observed through gravitational lensing is evidence that dark matter manifests as differences in energy density, rather than particles.
• **The Role of Gravitons:** Gravitons have been proposed as hypothetical particles that mediate gravity. However, in the new theory, gravitons are no longer necessary. Gravity itself is the result of energy transformations and vibrations in the vacuum. The presence of mass alters the vacuum medium, which is observed as "gravity." Therefore, gravitons are replaced by the behavior of vacuum energy.

2. Gravitational Lensing as Proof of the Energy Transformation Theory

Gravitational lensing serves as observational proof that the vacuum is a medium for transmitting energy transformations. This can be understood through the following steps:

• **Mass distorts the vacuum, and energy transforms:** A massive object distorts the surrounding vacuum, triggering energy transformations. This distortion alters the structure of spacetime, and photons (energy) travel along the warped spacetime.
• **Light travels along the distorted path, leading to gravitational lensing:** The path of photons traveling through the warped spacetime is bent, and the observer sees the light of distant objects as bent. This observation demonstrates that energy transformations act through the vacuum.

3. The Phenomena Themselves Prove the Theory

In this way, gravitational lensing and other gravitational phenomena (e.g., the flattening of galaxy rotation curves) are all understood as part of the energy transformation theory. The phenomena themselves serve as evidence that **vacuum functions as a medium for energy transmission**, and based on the principle of E=mc², these phenomena can be explained without relying on hypothetical particles like dark matter or gravitons.

An Analogy for Understanding: The Vibrating String Model

To further clarify this theory, the following analogy can be used:

• **A string with ends A and B, where A vibrates:** When A vibrates, it sends waves through the string, affecting B. The stronger A vibrates, the more the string undulates, and the apparent distance between A and B may shorten. These undulations correspond to the **warping of spacetime**.
• **The string represents the vacuum of the universe:** A represents a massive object (energy density), and B represents photons or other forms of energy. As A warps the string, B follows the undulating string, and thus B’s path appears bent. This serves as an analogy for the **gravitational lensing effect**.

Conclusion: Observational Phenomena as Proof of the Energy Transformation Theory

• **Gravitational lensing** and the **flattening of galaxy rotation curves** are phenomena resulting from energy transformations transmitted through the vacuum. These phenomena can be consistently explained without the assumption of hypothetical particles like dark matter or gravitons, instead relying on the energy transformations of the vacuum.
• Based on the equivalence of mass and energy as demonstrated by **E=mc²**, the bending of light and gravitational phenomena are all caused by energy transformations, proving the nature of vacuum as a medium for energy transmission.

Thus, these observational results themselves serve as proof of the energy transformation theory, offering a new understanding that surpasses the limitations of modern physics.

1. Definition of "Field" and Equations in Current Theories

In current theories, especially electromagnetism and general relativity (GR), "field" is a fundamental concept through which forces are transmitted. Even in vacuum, where no matter exists, fields function as the medium for force transmission.

1.1 Electromagnetic Field (Maxwell's Equations)

The electromagnetic field extends throughout space, and forces are transmitted through the electric field \( \mathbf{E} \) and the magnetic field \( \mathbf{B} \). Even in a vacuum, photons propagate through this field.

Set of Maxwell's equations:

\[ \nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}, \quad \nabla \cdot \mathbf{B} = 0 \]

\[ \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}, \quad \nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \frac{1}{c^2} \frac{\partial \mathbf{E}}{\partial t} \]

These equations describe how the electric field \( \mathbf{E} \) and the magnetic field \( \mathbf{B} \) interact and transport energy. Particularly, electromagnetic waves (light) propagate as waves of these fields. It is crucial to note that these fields exist even in a vacuum where no matter is present.

• Definition of a Field: Even in a vacuum, fields form the basic structure through which energy is transmitted. Photons are expressed as waves of these fields, transmitting forces through their interaction.

1.2 Spacetime Fields in General Relativity (Einstein's Equation)

In Einstein's General Theory of Relativity, gravity is described through the curvature of spacetime as a "field." Gravity arises when matter and energy bend spacetime, and as a result, light and matter move through the curved spacetime.

Einstein's Equation:

\[ G_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu} \]

• \( G_{\mu\nu} \): Einstein tensor, representing the curvature of spacetime.
• \( T_{\mu\nu} \): Energy-momentum tensor, representing the distribution of matter and energy.
• \( \Lambda \): Cosmological constant (representing dark energy).
• \( G \): Gravitational constant.
• \( c \): Speed of light.

The transmission of **photons and gravity** occurs within this curved spacetime, with light traveling along the shortest path (the geodesic). In regions where matter or energy is present, this "field" is affected, causing spacetime to warp. However, this "field" also exists in vacuum where no matter is present.

2. Vacuum Medium and Equations in Zero Theory

In Zero Theory, the concept of a "field" is extended to view **vacuum itself as an active medium for energy transmission**. While traditional theories treat vacuum as an empty space devoid of energy, Zero Theory suggests that vacuum possesses energy and that fluctuations and transformations of this energy govern physical phenomena.

2.1 The Extended Einstein Equation in Zero Theory

In Zero Theory, because the fluctuations and transformations of vacuum energy directly affect the curvature of spacetime, the Einstein equation is modified as follows:

\[ G_{\mu\nu} = \frac{8\pi G}{c^4} \left( T_{\mu\nu}^{\text{matter}} - \rho_X g_{\mu\nu} \right) \]

• \( \rho_X \): Represents vacuum energy density, showing how energy transforms within the vacuum and governs the transmission of gravity and light.

This term indicates that **vacuum is not merely empty space but a physical entity responsible for energy transmission**.

Equation for vacuum energy density:

\[ \rho_X = \frac{\Delta E}{V} \]

• \( \Delta E \): The amount of energy transformed within the vacuum.
• \( V \): The volume of the vacuum.

This equation explains how the vacuum manages energy transformations, allowing gravity and other forces to operate even in the absence of matter.

3. Relationship with Quantum Field Theory: Field Fluctuations and Particle Generation

In quantum field theory, it is believed that the "field" of the vacuum is not static but exhibits **fluctuations**. In Zero Theory, these fluctuations play a significant role, with the fluctuations and energy variations in the vacuum being understood as fulfilling the role of dark matter.

3.1 Fluctuations in Quantum Field Theory and Dark Matter

In quantum field theory, even in vacuum, "fluctuations" exist where particles are continually created and annihilated. In Zero Theory, these fluctuations are expressed as vacuum energy density and are believed to play the role of dark matter.

\[ \langle 0 | \phi(x) \phi(y) | 0 \rangle = \int \frac{d^3p}{(2\pi)^3} \frac{1}{2E_p} e^{-ip(x-y)} \]

Here, the quantum state of the field \( | 0 \rangle \) causes fluctuations, providing a mechanism by which energy affects spacetime. This explains how gravity and the propagation of light occur even in regions of space without matter.

4. Vacuum Energy Transformations and the Integration of Dark Matter

In Zero Theory, dark matter is not understood as particles but rather as fluctuations in vacuum energy. In other words, dark matter is a result of fluctuations and transformations within the "field," with its density \( \rho_X \) described as follows:

4.1 Energy Transformations and Vacuum Energy Density

\[ \rho_X = \frac{\Delta E}{V} \]

This equation explains how vacuum energy fluctuates and how energy is transmitted through the vacuum. This energy density affects the curvature of spacetime, showing how gravity and light transmission occur even within a vacuum.

5. Comprehensive Interpretation and New Theoretical Perspectives

Zero Theory redefines the vacuum as an active medium for energy, providing a unified explanation of energy transmission, gravity, and light propagation. This extends the traditional concept of fields, offering a new framework in which the vacuum itself acts as the field for energy transformation, with these transformations fulfilling the role of gravity and dark matter.

Future theoretical development will require further integration of vacuum energy fluctuations with quantum field theory and verification of how this aligns with observational data.

Integrated Study of Vacuum Fluctuations, Matter-Antimatter Creation, and the Fractal Universe Model Based on Zero Theory

1. Introduction

Zero theory views the creation and annihilation of the universe as a dynamic energy transformation based on vacuum fluctuations. It provides a new perspective that unifies the generation of matter and antimatter, the fractal structure of the universe, dark energy, and the mechanisms of cosmic expansion and contraction through vacuum energy. In this paper, we will consider the mathematical model of zero theory and its consistency with general relativity (GR) and quantum electrodynamics (QED), proposing a multidimensional universe model based on the perspectives of observation points A and A'.

The aim of zero theory is to address the challenges faced by modern physics regarding dark energy and cosmic expansion. Traditional physical theories have yet to fully explain the dynamics of cosmic expansion and energy, creating a need for new approaches. This theory posits that vacuum energy governs all phenomena in the universe and provides dynamism through energy transformations.

2. Perspectives of Observation Points A and A'

Understanding zero theory requires two perspectives: the "observation point A (external perspective)" and the "observation point A' (internal perspective)." The difference between these viewpoints offers a multidimensional approach to deepen our understanding of the universe's structure and energy dynamics. The core of this theory lies in how these differing perspectives of the observer alter the perception of phenomena.

2.1 Observation Point A (External Perspective)

Vacuum fluctuations seen from an external viewpoint: From the perspective of observation point A, vacuum fluctuations are extremely brief and small phenomena, making it challenging to perceive the large-scale structure and energy contained within them. Based on current scientific observation techniques and frameworks, these fluctuations are considered so tiny and fleeting that they vanish almost instantaneously.

The importance of relative viewpoints and relativity theory: In this perspective, the relativity of time and space, as described by relativity theory, plays a significant role. As Einstein demonstrated, the perception of time and space can change drastically depending on the observer's position and state. Thus, it is possible that our universe, from an external viewpoint, might be nothing more than a "momentary vacuum fluctuation."

Adopting this relative viewpoint prompts a reassessment of traditional cosmology. If we have assumed that there is nothing within this fluctuation from the perspective of an external observer, it might simply be a limitation of observation or a constraint imposed by our own viewpoint.

2.2 Observation Point A' (Internal Perspective)

The universe's structure seen from within: From the perspective of observation point A', it becomes apparent that the energy of vacuum fluctuations could self-organize to form its unique spacetime. This internal viewpoint suggests that vacuum fluctuations themselves form the foundation of the universe, where energy transformations and the creation of matter and antimatter are continuously occurring.

Fractal scale and self-similarity: In this internal perspective, the universe's structure possesses fractal self-similarity, meaning that the same patterns repeat on all scales. From the viewpoint of observation point A', an endless cycle of energy transformation through vacuum fluctuations unfolds, potentially causing the entire universe to expand in a fractal manner.

Considering the principles of relativity, which state that the observation results of time and space depend on the observer's position, strongly supports this theory. If the reality seen by an internal observer differs from our understanding of the universe, dismissing that could be tantamount to imposing our own observational limitations.

3. Perspectives of Fractal Theory and Energy Transformation in Zero Theory

Zero theory conceives the universe as "fluctuations themselves" that repeat the cycle of creation and annihilation within a single medium known as "vacuum." Both the Big Bang and the Big Crunch are understood as phenomena stemming from vacuum fluctuations.

Relativity of time and scale: In zero theory, the concepts of time and space are relative to the observer, and the same phenomenon can be perceived differently in terms of time and scale depending on the observation point. When observed externally, this universe may also be perceived as a "momentary vacuum fluctuation" that is tiny and transient.

Energy transformation cycles: Changes in the entire universe and energy flows are attributed to the process of energy conversion through vacuum fluctuations. According to zero theory, the total mass of the cosmic medium (vacuum) remains constant due to these energy transformations, maintaining the overall energy balance of the universe.

3.1 Fractal Structure and Self-Similarity of Vacuum Fluctuations

The concept of self-similarity: In fractal structures, self-similarity means that similar patterns recur at every scale. From the perspective of zero theory, energy fluctuations caused by vacuum fluctuations could generate similar spacetime structures at all scales.

The multidimensional fractal model of the universe: In this fractal model, vacuum fluctuations repeatedly carry out energy conversions, creating nearly infinite cosmic structures. As a result, from the perspective of observation point A', the universe is recognized as a dynamic and multidimensional entity that continuously changes while consistently reproducing the same patterns.

3.2 Multidimensional Understanding of Zero Theory and Observation Points A and A'

By understanding the difference between observation points A and A', zero theory allows vacuum fluctuations to be redefined as not merely a temporary phenomenon but as a fundamental force governing the generation and annihilation of the entire universe. This multidimensional approach redefines vacuum fluctuations not as simple energy variations but as a part of the dynamic energy exchange cycle driving the evolution of the universe.

4. Consistency of Zero Theory with Existing Theories (GR, QED)

Consistency with General Relativity: Zero theory is expressed by incorporating vacuum energy density into the Einstein equation, clarifying the effect of vacuum on spacetime curvature.

\[ G_{\mu\nu} = \frac{8\pi G}{c^4} \left( T_{\mu\nu}^{\text{matter}} - \rho_{\text{vac}} g_{\mu\nu} \right) \]

This modification provides a theoretical foundation for explaining the mechanisms of cosmic expansion and contraction.

4.2 Consistency with Quantum Electrodynamics

Consistency with QED: Zero theory describes the wave-particle duality of photons as a manifestation of vacuum fluctuations, maintaining consistency with experimental phenomena such as the Casimir effect.

\[ a_k^\dagger |0\rangle = |k\rangle, \quad a_k |k\rangle = |0\rangle \]

This approach enables a bridge between quantum mechanics and cosmology.

5. Conclusion

Zero theory proposes a new cosmological framework that combines vacuum fluctuations, the creation of matter and antimatter, fractal cosmic structures, and multidimensional perspectives. By integrating the perspectives of observation points A and A', this multidimensional approach deepens our understanding of the universe's energy dynamics and the nature of time and space, fostering new interpretations of dark energy and dark matter.

This document provides a comprehensive cosmological consideration based on zero theory, integrating the perspectives of observation points A and A' with fractal theory, laying the groundwork for new developments in physics.

Zero Point Energy and Vacuum Fluctuations

\[⟨0∣H∣0⟩_{\text{ren}} = \frac{1}{2} \sum_{k=0}^{k_{\text{max}}} ℏω_k\]

This equation shows that vacuum fluctuations induce finite energy fluctuations. Here, the **cutoff wavenumber** \(k_{\text{max}}\) is introduced to prevent the energy from diverging to infinity. In calculating the universe's energy, the cutoff wavenumber is set to avoid infinite divergence, thereby regularizing the energy to a finite value.

Reasons for Introducing a Cutoff

**To Prevent Infinite Energy Divergence:** In the calculation of zero-point energy, if all wavenumber modes are considered, the energy diverges to infinity. To prevent this theoretical issue, the cutoff wavenumber \(k_{\text{max}}\) is introduced, limiting the range of integration to a finite value. This regularization ensures that the energy converges to a finite value and produces physically interpretable results.

Selection of the Cutoff Criterion

The appropriate cutoff criterion should be chosen based on whether the focus is on spatial scales or energy scales. The cutoff may be based on the **Planck length \( l_P \)** or the **Planck energy \( E_P \)** depending on the context.

- For wave number or spatial scale: \[k_{\text{max}} = \frac{1}{l_P}\] Where the Planck length is: \[l_P = \sqrt{\frac{\hbar G}{c^3}}\] - For energy-related topics: \[E_{\text{max}} = E_P = \sqrt{\frac{\hbar c^5}{G}}\]

Regularization of Zero-Point Energy Using the Cutoff Wavenumber

**The formula for calculating zero-point energy:**

\[E = \int_{0}^{k_{\text{max}}} \frac{\hbar \omega}{2} D(k) \, dk\]

Where \( E \) is zero-point energy, \( \hbar \) is the reduced Planck constant, \( \omega \) is the frequency, and \( D(k) \) is the distribution function (density of states) dependent on wavenumber \( k \).

Additional Implications for Current Theories

1. Dark Energy and Cosmic Expansion

The following equation expresses the dependence of dark energy density on the cosmic expansion rate \( H \):

\[\rho_{\Lambda} = \frac{3H^2}{8\pi G} - (\rho_m + \rho_r)\]

2. Energy Generation Mechanisms

\[ \frac{d\rho_{\Lambda}}{dt} = \alpha H^3 - \beta \rho_{\Lambda} H\]

This differential equation describes the rates of energy generation and annihilation, showing how dark energy density \( \rho_{\Lambda} \) evolves in response to changes in the Hubble parameter \( H \).

The Symmetry Between the Material World and the Spiritual World

This theory suggests a new relationship between physical and non-physical phenomena. For instance, the following perspectives can be considered:

- Phenomena that seem to appear and then disappear, returning to their source through vacuum fluctuations, belong to the material universe.

- Phenomena such as electromagnetic waves or photons, which do not seem to return to their source and appear to vanish, may belong to the spiritual universe.

These views reinforce concepts from multiverse theory, string theory, and fractal theory, offering new insights.

Conclusion

The Zero Energy Cycle Theory comprehensively explains the dynamics of the universe through the infinite cycle of energy generation and annihilation. This framework provides a new way of understanding the unity between matter and antimatter, physical phenomena and spiritual phenomena, and even multiverse theories.

Energy Sources of the Big Bang and Big Crunch

The Big Bang and Big Crunch can be understood as significant energy transformation phenomena that explain large-scale changes in the universe. Here, we explain the energy sources of the Big Bang and Big Crunch from the perspectives of vacuum fluctuations and fractal structures, accompanied by mathematical equations.

1. Splitting Energy and Vacuum Fluctuations

The fundamental equation of the Zero Theory, "0 = +∞ − ∞", indicates that the vacuum (0) is established by the mutual cancellation of positive infinite energy (+∞) and negative infinite energy (−∞). When this balance is disrupted, a splitting of the universe's energy occurs, leading to an energy explosion akin to the Big Bang.

In quantum mechanics and quantum field theory, the vacuum is not a state of absolute "nothingness" with no energy but exists as a fluctuating field with zero-point energy. Zero-point energy is expressed by the following equation:

\[ \langle 0 | H | 0 \rangle = \frac{1}{2} \sum_{k=0}^{k_{\text{max}}} \hbar \omega_k \]

• \(\langle 0 | H | 0 \rangle\): Expectation value of zero-point energy
• \(\hbar\): Reduced Planck constant
• \(\omega_k\): Angular frequency of mode \( k \)
• \(k_{\text{max}}\): Cut-off wave number

The cut-off wave number \(k_{\text{max}}\) is defined using the Planck length \(l_P\):

\[ k_{\text{max}} = \frac{1}{l_P} \]

The Planck length \(l_P\) is given by:

\[ l_P = \sqrt{\frac{\hbar G}{c^3}} \]

This cut-off prevents the energy calculations from diverging to infinity, ensuring convergence to a physically meaningful finite value. This makes it clear that the Big Bang is a phenomenon arising from vacuum energy fluctuations. Additionally, it leads to the idea that the entire universe forms a fractal structure within these vacuum fluctuations.

2. Decrease of Splitting Energy and Energy Stabilization

Splitting energy is crucial in the process where the universe transitions from an unstable energy state to a stable one. The splitting and stabilization of energy are considered to possess fractal self-similarity and are represented by the following equation:

\[ E(n) = E_0 \cdot r^n \]

• \(E(n)\): Energy at hierarchical level \(n\)
• \(E_0\): Initial energy
• \(r\): Scaling factor (\(0 < r < 1\))
• \(n\): Fractal hierarchical level

This equation illustrates how energy is hierarchically divided and circulates in a self-similar manner. The Big Bang and Big Crunch are processes of energy splitting and stabilization repeated at each scale of the universe, supported overall by fractal energy circulation.

As splitting progresses, energy gradually stabilizes, and the total energy decreases. In this process, positive energy and opposing energy attract each other, maintaining the universe's energy balance. This explains the stabilization of energy in the universe's evolution.

3. Universe's Contraction and the Role of Gravity

After the Big Bang, while the universe is expanding, there is also the possibility of eventual contraction. To describe the expansion and contraction of the universe, the Friedmann Equation is useful.

\[ \left( \frac{\dot{a}}{a} \right)^2 = \frac{8\pi G}{3} \rho - \frac{k}{a^2} \]

• \(a\): Scale factor (size of the universe)
• \(\dot{a}\): Time derivative of the scale factor
• \(\rho\): Energy density
• \(k\): Spatial curvature

The energy density \(\rho\) includes matter, antimatter, and vacuum energy, which influence the universe's expansion and contraction. In particular, the interaction between matter and antimatter can generate strong gravitational forces, potentially leading to the universe's contraction. Ultimately, this force is expected to drive the process of the Big Crunch, converging the universe.

4. Energy Circulation Through Pair Production and Annihilation

The interaction between matter and antimatter demonstrates the fundamental mechanisms of energy splitting and integration. The processes of pair production and annihilation are represented by the following equations:

• Pair Production:

\[ \gamma \rightarrow e^{-} + e^{+} \]

• Annihilation:

\[ e^{-} + e^{+} \rightarrow \gamma \]

High-energy photons (\(\gamma\)) generate matter and antimatter, and these particles can combine to release energy again as photons. This splitting and recombination of energy are essential for explaining matter generation after the Big Bang and the energy convergence leading to the Big Crunch.

5. Control of Finite Energy Through Cut-off

Energy calculations in the universe can potentially diverge to infinity, but physically, energy can be controlled to remain finite by introducing a cut-off. This cut-off is defined using the Planck length \(l_P\) as follows:

\[ k_{\text{max}} = \frac{1}{l_P} \]

This prevents vacuum energy and other forms of energy from expanding to infinity, ensuring convergence within a physically meaningful range. Such control demonstrates that the energy in the Big Bang and Big Crunch exists within a realistically manageable scope.

---

Summary

The energy sources of the Big Bang and Big Crunch are based on vacuum fluctuations and energy splitting, and these phenomena are understood as parts of a fractal energy circulation.

• The Big Bang is perceived as the process of vacuum energy splitting and expansion, while the Big Crunch is explained as the process of energy contraction driven by gravity.
• These phenomena demonstrate that energy circulates self-similarly at different scales, indicating that the universe's evolution is not a single event but progresses complexly within a fractal structure.
• By preventing energy from diverging to infinity through a cut-off, it becomes clear that the Big Bang and Big Crunch are physically controlled phenomena.

The Big Bang and Big Crunch are positioned as parts of a fractal energy circulation in the universe's energy dynamics, interpreted as significant energy sources in the universe's evolution.

Overview of the Zero Energy Cycle Theory

The Zero Energy Cycle Theory provides a new cosmological view, based on the foundational equation "0 = +∞ − ∞," where energy conservation is achieved through the infinite progression of energy generation and annihilation. This theory views the entire universe as "fluctuations within a vacuum," with energy continually being generated and annihilated, forming a dynamic universe within fluctuations.

The Relationship Between Observation Points and Multiverse Theory

Universe Generated by Fluctuations:

The "universe generated by fluctuations" refers to the concept that the material medium generated from vacuum fluctuations is the multiverse itself, distinct from the fluctuations (e.g., galaxy formation) occurring within the universe after the Big Bang.

Observation Points A and A':

Observation Point A: The perspective from which material generated by vacuum fluctuations is observed externally.
Observation Point A': The observation point within the universe generated by fluctuations, observing the universe from within.

The Zero Energy Cycle Theory hypothesizes that our universe could also be observed as a fluctuation in the vacuum from a higher-dimensional perspective. This implies that we might be at Observation Point A'. From Observation Point A, A' would be seen as a small, momentary phenomenon, but within A', the scale may seem infinite, and the time may seem eternal.

The Relativity of Size and Time and Consistency with Relativity Theory

Concepts like "large" and "small," and "long" and "short" in time, can vary significantly depending on the observation standpoint, such as Observation Points A and A'. These concepts are relative rather than absolute, aligning with the Theory of Relativity.

According to relativity, the size of an object and the passage of time depend on the object's speed and the strength of the gravitational field. The idea that time and space differ for each observer aligns with relativity's concept of "spacetime relativity for each observer." For instance, the universe seen from Observation Point A may appear to end quickly in a brief moment, while for an observer within A', much more time may have passed.

The Relationship Between Energy and Vacuum Fluctuations

This theory explains how the generation and annihilation of energy through vacuum fluctuations results in various unified phenomena.

1. Dynamic Generation and Annihilation of Energy

The zero energy state is a transient point where energy is cyclically generated and annihilated. This process explains the creation of something from nothing (e.g., the Big Bang) and the eventual disappearance of energy (e.g., the Big Crunch). The universe is understood to be in constant transformation through this energy cycle.

2. Generation and Complementarity of Matter and Antimatter

The material universe and the antimatter universe are generated symmetrically and are bound by a complementary relationship through energy cycles, attracting each other. This interaction explains why the early universe contained a significant amount of antimatter.

Extended Analogies

1. The Analogy of Electromagnets and Iron Sand

Iron Sand in an Electromagnet:

In the early stage, when the electric current is weak, the iron sand is mixed in the center, and the polarity is not yet clear. This is because the energy is insufficient, and the S and N poles of the electromagnet have not fully formed. This phase mirrors the state of the early universe, where matter and antimatter are mixed and not yet completely separated.

With Increased Electric Current:

As the current increases, the S and N poles become distinct, and the iron sand separates and aligns with each pole. Similarly, as energy increases (due to cosmic expansion or physical processes), matter and antimatter become distinctly separated, with matter ultimately prevailing and antimatter diminishing in certain regions of the universe.

2. The Analogy Between the Material Universe and the Antimatter Universe

The Relationship Between the Material Universe and the Antimatter Universe:

Like iron sand aligning with the poles of an electromagnet, matter and antimatter were generated symmetrically in the early universe, and their mutual attraction or repulsion caused them to separate. However, as energy imbalances and interactions occurred, matter became dominant in the universe, and antimatter diminished.

3. The Early Stage of the Universe When Antimatter Was More Abundant

Mixed Iron Sand Near the Center and the Abundance of Antimatter:

At the center of the electromagnet, the iron sand is influenced by both the S and N poles in the early stage, representing the early universe's state where matter and antimatter coexisted equally. As the current strengthens, polarity becomes clear, and matter dominates, mirroring the process where antimatter gradually disappears, and the material universe becomes dominant.

4. The Possibility of an Antimatter Universe

The Dual Polarity of Magnetic Fields:

Just as an electromagnet always has both an S and N pole, matter and antimatter also coexist in a balanced relationship. While the material universe may currently dominate, the possibility remains that the antimatter universe continues to exist.

Zero Point Energy and Vacuum Fluctuations

\[⟨0∣H∣0⟩_{\text{ren}} = \frac{1}{2} \sum_{k=0}^{k_{\text{max}}} ℏω_k\]

This equation shows that vacuum fluctuations induce finite energy fluctuations. Here, the **cutoff wavenumber** \(k_{\text{max}}\) is introduced to prevent the energy from diverging to infinity. In calculating the universe's energy, the cutoff wavenumber is set to avoid infinite divergence, thereby regularizing the energy to a finite value.

Reasons for Introducing a Cutoff

**To Prevent Infinite Energy Divergence:** In the calculation of zero-point energy, if all wavenumber modes are considered, the energy diverges to infinity. To prevent this theoretical issue, the cutoff wavenumber \(k_{\text{max}}\) is introduced, limiting the range of integration to a finite value. This regularization ensures that the energy converges to a finite value and produces physically interpretable results.

Selection of the Cutoff Criterion

The appropriate cutoff criterion should be chosen based on whether the focus is on spatial scales or energy scales. The cutoff may be based on the **Planck length \( l_P \)** or the **Planck energy \( E_P \)** depending on the context.

- For wave number or spatial scale: \[k_{\text{max}} = \frac{1}{l_P}\] Where the Planck length is: \[l_P = \sqrt{\frac{\hbar G}{c^3}}\] - For energy-related topics: \[E_{\text{max}} = E_P = \sqrt{\frac{\hbar c^5}{G}}\]

Regularization of Zero-Point Energy Using the Cutoff Wavenumber

**The formula for calculating zero-point energy:**

\[E = \int_{0}^{k_{\text{max}}} \frac{\hbar \omega}{2} D(k) \, dk\]

Where \( E \) is zero-point energy, \( \hbar \) is the reduced Planck constant, \( \omega \) is the frequency, and \( D(k) \) is the distribution function (density of states) dependent on wavenumber \( k \).

Additional Implications for Current Theories

1. Dark Energy and Cosmic Expansion

The following equation expresses the dependence of dark energy density on the cosmic expansion rate \( H \):

\[\rho_{\Lambda} = \frac{3H^2}{8\pi G} - (\rho_m + \rho_r)\]

2. Energy Generation Mechanisms

\[ \frac{d\rho_{\Lambda}}{dt} = \alpha H^3 - \beta \rho_{\Lambda} H\]

This differential equation describes the rates of energy generation and annihilation, showing how dark energy density \( \rho_{\Lambda} \) evolves in response to changes in the Hubble parameter \( H \).

The Symmetry Between the Material World and the Spiritual World

This theory suggests a new relationship between physical and non-physical phenomena. For instance, the following perspectives can be considered:

- Phenomena that seem to appear and then disappear, returning to their source through vacuum fluctuations, belong to the material universe.

- Phenomena such as electromagnetic waves or photons, which do not seem to return to their source and appear to vanish, may belong to the spiritual universe.

These views reinforce concepts from multiverse theory, string theory, and fractal theory, offering new insights.

Conclusion

The Zero Energy Cycle Theory comprehensively explains the dynamics of the universe through the infinite cycle of energy generation and annihilation. This framework provides a new way of understanding the unity between matter and antimatter, physical phenomena and spiritual phenomena, and even multiverse theories.

Details of the Zero Energy Cycle Theory

The Zero Energy Cycle Theory provides a new cosmological view, based on the foundational equation "0 = +∞ − ∞," where energy conservation is achieved through the infinite progression of energy generation and annihilation. This theory views the entire universe as "fluctuations within a vacuum," with energy continually being generated and annihilated, forming a dynamic universe within fluctuations.

The Relationship Between Observation Points and Multiverse Theory

Universe Generated by Fluctuations:

The "universe generated by fluctuations" refers to the concept that the material medium generated from vacuum fluctuations is the multiverse itself, distinct from the fluctuations (e.g., galaxy formation) occurring within the universe after the Big Bang.

Observation Points A and A':

Observation Point A: The perspective from which material generated by vacuum fluctuations is observed externally.
Observation Point A': The observation point within the universe generated by fluctuations, observing the universe from within.

The Zero Energy Cycle Theory hypothesizes that our universe could also be observed as a fluctuation in the vacuum from a higher-dimensional perspective. This implies that we might be at Observation Point A'. From Observation Point A, A' would be seen as a small, momentary phenomenon, but within A', the scale may seem infinite, and the time may seem eternal.

The Relativity of Size and Time and Consistency with Relativity Theory

Concepts like "large" and "small," and "long" and "short" in time, can vary significantly depending on the observation standpoint, such as Observation Points A and A'. These concepts are relative rather than absolute, aligning with the Theory of Relativity.

According to relativity, the size of an object and the passage of time depend on the object's speed and the strength of the gravitational field. The idea that time and space differ for each observer aligns with relativity's concept of "spacetime relativity for each observer." For instance, the universe seen from Observation Point A may appear to end quickly in a brief moment, while for an observer within A', much more time may have passed.

The Relationship Between Energy and Vacuum Fluctuations

This theory explains how the generation and annihilation of energy through vacuum fluctuations results in various unified phenomena.

1. Dynamic Generation and Annihilation of Energy

The zero energy state is a transient point where energy is cyclically generated and annihilated. This process explains the creation of something from nothing (e.g., the Big Bang) and the eventual disappearance of energy (e.g., the Big Crunch). The universe is understood to be in constant transformation through this energy cycle.

2. Generation and Complementarity of Matter and Antimatter

The material universe and the antimatter universe are generated symmetrically and are bound by a complementary relationship through energy cycles, attracting each other. This interaction explains why the early universe contained a significant amount of antimatter.

Extended Analogies

1. The Analogy of Electromagnets and Iron Sand

Iron Sand in an Electromagnet:

In the early stage, when the electric current is weak, the iron sand is mixed in the center, and the polarity is not yet clear. This is because the energy is insufficient, and the S and N poles of the electromagnet have not fully formed. This phase mirrors the state of the early universe, where matter and antimatter are mixed and not yet completely separated.

With Increased Electric Current:

As the current increases, the S and N poles become distinct, and the iron sand separates and aligns with each pole. Similarly, as energy increases (due to cosmic expansion or physical processes), matter and antimatter become distinctly separated, with matter ultimately prevailing and antimatter diminishing in certain regions of the universe.

2. The Analogy Between the Material Universe and the Antimatter Universe

The Relationship Between the Material Universe and the Antimatter Universe:

Like iron sand aligning with the poles of an electromagnet, matter and antimatter were generated symmetrically in the early universe, and their mutual attraction or repulsion caused them to separate. However, as energy imbalances and interactions occurred, matter became dominant in the universe, and antimatter diminished.

3. The Early Stage of the Universe When Antimatter Was More Abundant

Mixed Iron Sand Near the Center and the Abundance of Antimatter:

At the center of the electromagnet, the iron sand is influenced by both the S and N poles in the early stage, representing the early universe's state where matter and antimatter coexisted equally. As the current strengthens, polarity becomes clear, and matter dominates, mirroring the process where antimatter gradually disappears, and the material universe becomes dominant.

4. The Possibility of an Antimatter Universe

The Dual Polarity of Magnetic Fields:

Just as an electromagnet always has both an S and N pole, matter and antimatter also coexist in a balanced relationship. While the material universe may currently dominate, the possibility remains that the antimatter universe continues to exist.

Zero Point Energy and Vacuum Fluctuations

\[⟨0∣H∣0⟩_{\text{ren}} = \frac{1}{2} \sum_{k=0}^{k_{\text{max}}} ℏω_k\]

This equation shows that vacuum fluctuations induce finite energy fluctuations. Here, the **cutoff wavenumber** \(k_{\text{max}}\) is introduced to prevent the energy from diverging to infinity. In calculating the universe's energy, the cutoff wavenumber is set to avoid infinite divergence, thereby regularizing the energy to a finite value.

Reasons for Introducing a Cutoff

**To Prevent Infinite Energy Divergence:** In the calculation of zero-point energy, if all wavenumber modes are considered, the energy diverges to infinity. To prevent this theoretical issue, the cutoff wavenumber \(k_{\text{max}}\) is introduced, limiting the range of integration to a finite value. This regularization ensures that the energy converges to a finite value and produces physically interpretable results.

Selection of the Cutoff Criterion

The appropriate cutoff criterion should be chosen based on whether the focus is on spatial scales or energy scales. The cutoff may be based on the **Planck length \( l_P \)** or the **Planck energy \( E_P \)** depending on the context.

- For wave number or spatial scale: \[k_{\text{max}} = \frac{1}{l_P}\] Where the Planck length is: \[l_P = \sqrt{\frac{\hbar G}{c^3}}\] - For energy-related topics: \[E_{\text{max}} = E_P = \sqrt{\frac{\hbar c^5}{G}}\]

Regularization of Zero-Point Energy Using the Cutoff Wavenumber

**The formula for calculating zero-point energy:**

\[E = \int_{0}^{k_{\text{max}}} \frac{\hbar \omega}{2} D(k) \, dk\]

Where \( E \) is zero-point energy, \( \hbar \) is the reduced Planck constant, \( \omega \) is the frequency, and \( D(k) \) is the distribution function (density of states) dependent on wavenumber \( k \).

Additional Implications for Current Theories

1. Dark Energy and Cosmic Expansion

The following equation expresses the dependence of dark energy density on the cosmic expansion rate \( H \):

\[\rho_{\Lambda} = \frac{3H^2}{8\pi G} - (\rho_m + \rho_r)\]

2. Energy Generation Mechanisms

\[ \frac{d\rho_{\Lambda}}{dt} = \alpha H^3 - \beta \rho_{\Lambda} H\]

This differential equation describes the rates of energy generation and annihilation, showing how dark energy density \( \rho_{\Lambda} \) evolves in response to changes in the Hubble parameter \( H \).

The Symmetry Between the Material World and the Spiritual World

This theory suggests a new relationship between physical and non-physical phenomena. For instance, the following perspectives can be considered:

- Phenomena that seem to appear and then disappear, returning to their source through vacuum fluctuations, belong to the material universe.

- Phenomena such as electromagnetic waves or photons, which do not seem to return to their source and appear to vanish, may belong to the spiritual universe.

These views reinforce concepts from multiverse theory, string theory, and fractal theory, offering new insights.

Conclusion

The Zero Energy Cycle Theory comprehensively explains the dynamics of the universe through the infinite cycle of energy generation and annihilation. This framework provides a new way of understanding the unity between matter and antimatter, physical phenomena and spiritual phenomena, and even multiverse theories.

Overview of the Zero Energy Cycle Theory

The Zero Energy Cycle Theory provides a new cosmology based on the fundamental equation "0 = +∞ − ∞," proposing that energy conservation is achieved through the infinite progression of energy generation and annihilation. This theory perceives the entire universe as "a universe within fluctuations," where it continually generates and annihilates itself within a medium called "vacuum."

Relationship Between Observation Points and Multiverse Theory

Universe Created by Fluctuations:

The "universe created by fluctuations" refers to a concept where the material medium generated from vacuum fluctuations is assumed to be the multiverse itself, distinct from the fluctuations that occur within the universe after the Big Bang (e.g., galaxy formation).

Observation Point A and A':

Observation Point A: The viewpoint of observing the material generated from vacuum fluctuations from the outside.
Observation Point A': The viewpoint from within the universe that was created by fluctuations, observing the universe from within.

In Zero Theory, our universe is hypothesized to be observed from a higher dimension as a fluctuation within the vacuum. This suggests the possibility that we are at Observation Point A'. From Observation Point A, Point A' may appear minuscule and be measured as a brief phenomenon. However, within Point A', what seems like infinite size and eternal time may be experienced.

Relativity of Size and Time and Consistency with Relativity Theory

The relative length of size and time may vary greatly depending on the observer's perspective, such as between Observation Points A and A'. In other words, the concepts of "large," "small," "long," and "short" are not absolute but relative. This is consistent with Relativity Theory.

In Relativity Theory, the size of an object and the passage of time depend on the object's speed and the strength of the gravitational field. The idea that time and space differ between observation points aligns with the "spacetime relativity depending on the observer," as demonstrated in Relativity Theory.

Relationship Between Energy and Vacuum Fluctuations

This theory explains a variety of phenomena through the continuous cycle of energy generation and annihilation caused by vacuum fluctuations.

1. Dynamic Generation and Annihilation of Energy

The zero-energy state is a passing point where energy repeatedly generates and annihilates. Through this process, phenomena like the Big Bang, where existence is created from nothing, and the Big Crunch, where energy disappears, can be explained.

2. Generation and Interaction of Matter and Antimatter

The matter universe and the antimatter universe are symmetrically generated, with each exerting a mutual pull through energy cycles. This interaction explains the coexistence of a matter-dominated universe and an antimatter universe, as well as why the early universe contained much antimatter.

Expansion of the Analogy

1. The Analogy of Electromagnets and Iron Filings

The Arrangement of Iron Filings with an Electromagnet:

In the initial stage, when the current is weak, the iron filings are scattered in the center, and the polarity is not distinct. This is because the energy is insufficient to fully form the S-pole and N-pole of the electromagnet.

2. The Analogy of the Matter Universe and the Antimatter Universe

The Relationship Between the Matter Universe and the Antimatter Universe:

Just as iron filings are drawn to the S-pole and N-pole of an electromagnet, matter and antimatter were symmetrically generated in the early universe, and each was drawn by forces of attraction and repulsion.

3. The Early Stage When the Matter Universe Contained Abundant Antimatter

The Mixing of Iron Filings Near the Center and the Abundance of Antimatter:

Near the center of the electromagnet, in the early stage, both the S-pole and N-pole influence the arrangement of iron filings, resulting in a mixed state. This symbolizes the coexistence of matter and antimatter in the early universe, where antimatter was also abundant.

4. The Possibility of the Existence of an Antimatter Universe

The Bipolarity of the Magnetic Field:

The relationship between the matter universe and the antimatter universe suggests a possible mutual existence. While the matter universe is currently dominant, the antimatter universe may still exist.

Zero-Point Energy and Vacuum Fluctuations

$$⟨0∣H∣0⟩_{\text{ren}} = \frac{1}{2} \sum_{k=0}^{k_{\text{max}}} \hbar \omega_k$$

This equation shows that vacuum fluctuations cause finite energy fluctuations. Here, the cutoff wavenumber \(k_{\text{max}}\) is introduced to prevent infinite energy divergence. In the calculation of the universe's energy, a cutoff wavenumber is set to avoid infinite divergence, normalizing the energy to a finite value.

The Reason for Introducing a Cutoff

Prevention of Infinite Energy Divergence: In the calculation of zero-point energy, considering all wavenumber modes leads to infinite energy divergence. The cutoff wavenumber \(k_{\text{max}}\) is introduced to limit the integration range to a finite value.

Relation to the Speed of Light: The cutoff wavenumber \(k_{\text{max}}\) can be set based on the speed of light \(c\). Setting the cutoff wavenumber based on the speed of light prevents energy from diverging to infinity.

Normalization of Zero-Point Energy by Cutoff Wavenumber

The zero-point energy formula:

$$E = \int_{0}^{k_{\text{max}}} \frac{\hbar \omega}{2} D(k) \, dk$$

Supplementation and Application to Current Theories

1. Dark Energy and Cosmic Expansion

$$\rho_{\Lambda} = \frac{3H^2}{8\pi G} - (\rho_m + \rho_r)$$

This equation shows that the dark energy density \(\rho_{\Λ}\) is derived depending on the rate of cosmic expansion \(H\).

2. Energy Generation Mechanism

$$\frac{d\rho_{\Lambda}}{dt} = \alpha H^3 - \beta \rho_{\Lambda} H$$

This differential equation shows how dark energy density \(\rho_{\Λ}\) changes with variations in the Hubble parameter \(H\).

Symmetrical Structure of the Physical and Spiritual Worlds

This theory suggests a new relationship between physical and non-physical phenomena. For example, the following perspectives can be considered:

• Phenomena generated by vacuum fluctuations and then annihilated are part of the physical energy universe.
• Phenomena like electromagnetic waves, which seem to disappear without returning to the source, belong to the spiritual universe.

Conclusion

The Zero Energy Cycle Theory explains the dynamics of the universe through the infinite cycle of energy generation and annihilation. This presents a new framework for understanding interactions between matter, antimatter, and even physical and spiritual phenomena.