Black Hole Singularity and Energy Conversion Theory

A New Theoretical Approach Using the Proportional Constant \( \alpha \)

Introduction The energy conversion process near black holes is one of the unresolved critical challenges in physics. Particularly at the singularity of black holes, the gravitational field diverges to infinity, which general relativity cannot adequately explain. This theory introduces the proportional constant \( \alpha \), aiming to explain energy conversion inside and outside black holes by viewing the black hole singularity as an energy baseline \( E_0 = \langle 0 | H | 0 \rangle \).

The proportional constant \( \alpha \) is a parameter to adjust the intensity of the gravitational field and energy conversion. By introducing it, the black hole singularity can be viewed not only as a point of energy concentration but also as the origin of energy conversion, offering a potential unified understanding of the entire energy structure of black holes.

1. A New Perspective on Energy Conversion at the Singularity

Quantum Interpretation of the Singularity

In general relativity, the black hole singularity is considered a point where spacetime curvature reaches infinity. However, from a quantum mechanical perspective, the singularity can be interpreted as an energy baseline \( E_0 = \langle 0 | H | 0 \rangle \). This \( E_0 \) corresponds to the quantum vacuum energy and plays a critical role in explaining the unified energy conversion near the singularity.

The total energy of the black hole can be expressed as the energy fluctuation \( \Delta E \) relative to the baseline energy \( E_0 \) as follows:

\[ E_{\text{BH}} = E_0 + \Delta E \]

This equation indicates that the energy of the black hole can be understood as a fluctuation from the baseline energy.

2. The Role of the Proportional Constant \( \alpha \)

What is the Proportional Constant \( \alpha \)?

The proportional constant \( \alpha \) is a parameter to adjust the intensity of the gravitational field and energy conversion processes in black holes. The standard strength of the gravitational field depends on the distance \( r \) from the black hole and the mass \( M \), expressed by the following equation:

\[ g(r) = \frac{GM}{r^2 \left( 1 - \frac{r_s}{r} \right)} \]

Here, \( G \) is the gravitational constant, and \( r_s \) is the Schwarzschild radius. According to this equation, the gravitational field becomes stronger as one approaches the black hole and diverges to infinity near the singularity.

In the new approach, the proportional constant \( \alpha \) is introduced to modify the strength of the gravitational field as follows:

\[ g(r) = \alpha \frac{GM}{r^2 \left( 1 - \frac{r_s}{r} \right)} \]

In this equation, the strength of the gravitational field can be adjusted by the value of \( \alpha \).

α > 1: The gravitational field is enhanced, and energy conversion progresses rapidly.

α < 1: The gravitational field is weakened, and energy conversion proceeds more gently.

By introducing this proportional constant, the energy conversion near the singularity can be explained more flexibly.

3. The Role of Vacuum Energy

Zero-point Fluctuations and Energy Conservation

Vacuum energy plays a critical role in the energy conversion near black holes. Zero-point fluctuations influence black hole evaporation and energy conversion within the framework of energy conservation.

Zero-point energy is expressed as follows:

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

Here, the cutoff \( k_{\text{max}} \) is based on the **Planck length \( l_P \)** or the **Planck energy \( E_P \)**.

For scales related to wavenumber or spatial dimensions, the Planck length \( l_P \) is used as the cutoff:

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

where the Planck length is:

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

For energy-related processes, the Planck energy \( E_P \) is used as the cutoff:

\[ E_{\text{max}} = E_P = \sqrt{\frac{\hbar c^5}{G}} \]

In some cases, using both scales is optimal. Introducing both Planck length and Planck energy as appropriate cutoffs allows for more precise descriptions of energy conversion.

This modification helps suppress the infinite divergence of vacuum energy, providing a more physically consistent explanation of black hole evaporation and Hawking radiation.

4. Energy Conversion Processes and Mathematical Representation

Matter-Antimatter Annihilation

Near black holes, matter-antimatter annihilation is a primary mechanism for energy radiation. For example, when electrons \( e^- \) and positrons \( e^+ \) annihilate, gamma-ray photons are emitted.

\[ e^- + e^+ \rightarrow \gamma_1 + \gamma_2 + \gamma_{\text{unseen}} \]

Here, \( \gamma_1 \) and \( \gamma_2 \) are observable gamma rays, while \( \gamma_{\text{unseen}} \) represents unobserved energy radiation.

Based on the law of energy conservation, this can be expressed as follows:

\[ E_{e^-} + E_{e^+} = E_{\gamma_1} + E_{\gamma_2} + E_{\gamma_{\text{unseen}}} \]

5. A New Relationship Between Gravitational Potential and Mass Density

The proposed gravitational potential equation is as follows:

\[ \nabla^2 \Phi(x) = \alpha \nabla^2 \rho(x) \]

Here, \( \Phi(x) \) is the gravitational potential, \( \rho(x) \) is the mass density, and \( \alpha \) is the proportional constant.

Moreover, the gravitational acceleration \( g \) is proportional to the gradient of the mass density \( \rho \):

\[ g = -\alpha \nabla \rho \]

6. Vacuum Energy Density Relationships

Changes in vacuum energy density may affect other physical quantities. In particular, variations in vacuum energy density are related to energy conversion processes and contribute to the stability of the energy baseline \( E_0 \).

7. Application of the Law of Energy Conservation

Energy conversion near black holes progresses based on the law of energy conservation. This means that even if the black hole converts absorbed matter and antimatter into radiative energy, the total energy remains conserved.

\[ E_{\text{total}} = E_{\text{matter}} + E_{\text{antimatter}} = E_{\text{radiation}} + E_{\text{unseen}} \]

8. Considerations on Undetected Energy and Noise

Interference Noise and Information Preservation

High-energy fluctuations near black holes generate interference noise, suggesting the operation of the law of information preservation in energy conversion. Noise analysis may help elucidate the complexity and diversity of energy conversion near black holes.

9. The Influence of the Uncertainty Principle

Near the black hole singularity, the uncertainty principle of quantum mechanics affects the energy conversion process.

\[ \Delta E \cdot \Delta t \geq \frac{\hbar}{2} \]

This principle implies that energy conversion near the singularity can only be described probabilistically.

10. The Potential for Integration with Quantum Gravity Theories

String theory and loop quantum gravity theory offer solutions to the problem of infinities at the black hole singularity. These theories describe energy conversion at the singularity in a quantum framework, where the law of energy conservation remains valid.

Specifically, theories in string theory and loop quantum gravity propose avoiding the infinite state at the black hole singularity, suggesting that energy conversion occurs as it passes through the baseline energy \( \langle 0 | H | 0 \rangle \). This provides a new integrated perspective while maintaining the consistency of physics, demonstrating that energy is conserved inside and outside the black hole through quantum energy conversion, rather than becoming infinitely strong.

11. Conclusion

This theory introduced the proportional constant \( \alpha \) to explain energy conversion processes at the black hole singularity from a new perspective. By considering the roles of zero-point fluctuations and vacuum energy, as well as integrating string theory and loop quantum gravity, the issue of infinities is avoided while enhancing the consistency of energy conversion theories. Furthermore, introducing the Planck length \( l_P \) or Planck energy \( E_P \) as appropriate cutoffs allows for a physically consistent description of energy conversion, paving the way for further theoretical refinements and experimental verification.

Phenomena Occurring at the Event Horizon of a Black Hole: Energy Conversion and Information Preservation

This article provides a detailed explanation of what occurs at the event horizon of a black hole from the perspective of energy conversion processes and information preservation. At the event horizon, absorbed energy is transformed through fractal cycles, and the holographic principle preserves information. Additionally, the singularity defined as ⟨0∣H∣0⟩_ren functions as a waypoint in the energy conversion process, offering a new perspective on the mechanism of information preservation.

Accumulation of Matter and Energy in Black Holes and Passage to ⟨0∣H∣0⟩

Why, despite the enormous accumulation of matter and energy inside a black hole, does information converge and pass through ⟨0∣H∣0⟩ via energy conversion? The answer lies in the view of energy conversion and fractal cycles from the perspective of zero theory.

At the event horizon of a black hole, not only are matter and energy accumulated in one direction, but they are also gradually dispersed through energy conversion, dynamically retaining information. This process considers the possibility that energy is transferred across dimensions or to other universes or anti-matter universes. Ultimately, matter and energy do not accumulate infinitely but converge to the finite vacuum expectation value of ⟨0∣H∣0⟩.

Energy conversion progresses through a process known as the fractal cycle. A fractal structure is one that repeats the same pattern self-similarly, and inside a black hole, energy is similarly divided and converges toward a finite state. As a result, energy inside the black hole does not expand infinitely, but eventually converges to a finite number of modes, with energy continuing to convert within a limited range. Thanks to this convergence, information passes through ⟨0∣H∣0⟩ and moves to the next stage.

Furthermore, zero theory suggests the possibility that matter and energy accumulated inside a black hole could be transferred to anti-matter universes or other dimensions. This transfer proceeds through quantum entanglement, functioning as a gateway through which information is moved to different universes or dimensions. Thus, the information accumulated inside the black hole does not infinitely expand but is preserved across dimensions while converging through energy conversion.

Basics of Energy Conversion: Convergence to ⟨0∣H∣0⟩

Energy conversion in a black hole is explained by the following unified equation:

\[ \sum_{k=0}^{k_{\text{max}}} \hbar \omega_k = \langle 0 \mid H \mid 0 \rangle \]

This equation shows that energy conversion inside the black hole progresses through fractal cycles, terminating at a finite number of modes \(k_{\text{max}}\), without expanding infinitely. Energy is accumulated sequentially at each frequency \(\omega_k\) corresponding to mode \(k\), ultimately reaching the vacuum expectation value ⟨0∣H∣0⟩.

This unified equation forms the basis for the entire energy conversion model of a black hole, ensuring that energy does not accumulate infinitely and ultimately converges to a finite state. This enables efficient energy conversion to ⟨0∣H∣0⟩_ren, suggesting that not only is information preserved at the black hole’s event horizon, but it can also be transferred across dimensions to other universes.

Formalization of the Holographic Principle Based on Zero Theory

Zero theory further develops the holographic principle, clearly explaining energy conversion occurring at the event horizon of a black hole. This theory suggests that information preservation at the horizon is part of a dynamic energy conversion process and involves the transfer of information across dimensions.

- **Energy Preservation at the Horizon: ⟨0∣H∣0⟩_ren**

The event horizon of a black hole functions as a waypoint in energy conversion, emphasizing that information preservation is not merely static 2D preservation but a dynamic process involving energy conversion. Energy preservation at the horizon is expressed by the following equation:

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

This equation shows that energy at the event horizon of a black hole converges to a finite number of modes, and energy and information proceed to the next stage through conversion.

Interaction Between Energy Conversion and Information Preservation

Zero theory defines information preservation at the event horizon of a black hole not as static 2D preservation but as a dynamic process preserved through energy conversion. This introduces a new perspective to the conventional holographic principle, suggesting the possibility of preserving information across dimensions.

- **Energy Conversion of Information**

As information passes through the event horizon of a black hole, it continues to be preserved through energy conversion processes. This conversion forms a fractal cycle, with energy converging at a finite number of modes \(k_{\text{max}}\). As a result of energy conversion, information is preserved not only inside and outside the black hole but also across dimensions.

- **Entanglement and Transfer to an Anti-Matter Universe**

During energy conversion, information forms an entangled state, resulting in the possibility of transfer to an anti-matter universe. Zero theory suggests that the event horizon of a black hole functions as a "gateway" for transferring energy and information to other dimensions, rather than merely being a place where information is stored. This avoids information loss within the black hole and proposes a new theory where information is transferred across dimensions.

Mechanism of Information Preservation Based on the Energy Conversion Process

An important point of the holographic principle in zero theory is how energy conversion contributes to information preservation. The energy conversion that occurs at the event horizon of a black hole functions as a mechanism for preserving and transferring information across dimensions.

- **Fractal Energy Conversion**

Energy conversion at the event horizon of a black hole forms a fractal cycle, converging at a finite number of modes without expanding infinitely. This process prevents infinite accumulation of energy, providing a mechanism for safely preserving information.

- **Transdimensional Information Preservation**

Information preservation within a black hole is not merely a closed system within this universe; through entangled states, information is suggested to transfer to other dimensions or anti-matter universes. This emphasizes a mechanism in which information is preserved beyond the problem of information loss, extending across the universe.

Information Transfer to the Anti-Matter Universe

In the holographic principle based on zero theory, the possibility is raised that information is transferred to the anti-matter universe during the energy conversion process. This introduces a new perspective, wherein the event horizon of a black hole functions as a "gateway" for transferring energy and information.

- **Mechanism of Transfer to the Anti-Matter Universe**

Energy conversion inside a black hole triggers entanglement, which in turn becomes the trigger for transferring information to the anti-matter universe. As energy progresses across dimensions through fractal cycles, information is transferred to the anti-matter universe, maintaining its preservation.

- **Toward Resolving the Black Hole Information Paradox**

In this model, information is not trapped inside the black hole, but is transferred to the anti-matter universe through entanglement, potentially solving the problem of information loss. This new theory redefines the role of black holes not only as places for information storage but as venues for transdimensional information transfer.

Relation to String Theory

The new perspective on the holographic principle based on zero theory aligns with the multidimensional structure of the universe as described in string theory. The event horizon of a black hole functioning as a "gateway" for energy and information transfer across dimensions corresponds with the brane structure and interdimensional interactions in string theory.

- **A Waypoint for Multidimensional Energy Conversion**

The event horizon of a black hole not only serves as a place for 2D preservation of energy and information but also functions as a "passage point" for transfer to other dimensions. This suggests the possibility of energy conversion impacting other dimensions, leading to interdimensional energy interactions.

Consistency with Current Theories and New Perspectives

The redefinition of the holographic principle based on zero theory maintains consistency with current theories such as relativity and string theory, while offering a new solution to the black hole information paradox.

- **Consistency with Relativity**

The event horizon of a black hole functions as a waypoint for energy conversion, maintaining consistency with the relativity of spacetime as described by relativity theory. Different perspectives are obtained depending on the position and speed of the observer, ensuring that the mechanisms of energy preservation and information preservation are interpreted consistently from all viewpoints.

- **Relation to Dark Energy**

Zero theory suggests that energy conversion inside a black hole may contribute to cosmic expansion, potentially influencing the generation of dark energy. A new mechanism is proposed where energy impacts cosmic expansion during the process of transdimensional information transfer.

Conclusion

The redefinition of the holographic principle based on zero theory shows that information preservation at the event horizon of a black hole occurs dynamically through energy conversion and transdimensional information transfer. This new perspective reinterprets information preservation as part of a dynamic energy conversion process, opening a new path toward resolving the black hole information paradox.

Additionally, the possibility of information being transferred to anti-matter universes or other dimensions is raised, redefining black holes as venues for transdimensional information transmission. This theory fundamentally reconstructs the processes of information preservation and energy conversion inside and outside black holes, offering new perspectives in physics and cosmology.

Black Hole Singularities and Information Transfer

1. Fractal Energy Conversion Cycles

To understand the mechanisms of energy and information conservation in the material universe and the antimatter universe, we first introduce the concept that energy conversion has a fractal structure. This fractal structure is the key to explaining how energy and information infinitely circulate, being reconstructed each time they pass through singularities.

The process of energy conversion can be represented by the following equation:

\[\langle 0 | H | 0 \rangle_{\text{ren}} = \sum_{n=0}^{\infty} \left( \frac{1}{2^n} \sum_{k=0}^{k_{\text{max}}} \hbar \omega_k^{(n)} \cdot \rho_k^{(n)} \right)\]

Here, \( n \) denotes the hierarchical level of the energy conversion cycle, with energy at each level decaying by a scale factor of \( \frac{1}{2^n} \) while being reconstructed. \( \omega_k^{(n)} \) represents the energy modes at each level, and \( \rho_k^{(n)} \) includes the coefficients reflecting entanglement. This equation indicates that energy and information possess an infinite fractal structure, repeatedly reorganized while preserving information in each cycle.

This fractal energy conversion cycle symbolizes a process in which information is not statically conserved but dynamically transformed. This cyclic transformation underpins the flow of energy and information between the material universe and the antimatter universe.

2. Information Transfer via Black Hole Singularities

Next, we explore how information is transferred between the material universe and the antimatter universe through the mechanism of black hole singularities. Singularities act as crucial boundaries where energy and information are concentrated and then dispersed. Quantum tunneling plays a central role in the transfer of information in this process.

The continuity of the wave function at the singularity is expressed as follows:

\[\psi_{\text{M}}(x_0) = \psi_{\text{AM}}(x_0)\]

Here, \( x_0 \) denotes the position of the singularity, signifying that information is seamlessly continuous between the material universe and the antimatter universe. Moreover, the probability of information passing through the singularity is given by the tunneling equation:

\[T = e^{-2 \int_{x_1}^{x_2} \kappa(x) dx}\]

This transmission probability explains the quantum transfer process of information from the material universe to the antimatter universe. The black hole singularity functions as a physical gateway, facilitating the exchange of energy and information between the two universes without any loss of information.

3. Laws of Energy and Mass Conservation

Having understood the mechanisms of fractal energy conversion and information transfer through black hole singularities, we now discuss the principles of energy and mass conservation. The idea that the material universe and the antimatter universe conserve energy with each other can be represented by the following equation:

\[E_{\text{total}} = E_{\text{M}} + E_{\text{AM}} = 0\]

This equation indicates that the sum of the energies of the material universe and the antimatter universe equals zero, confirming the principle of total energy conservation. Additionally, based on the law of mass conservation, the masses of the material universe and the antimatter universe also counterbalance each other, maintaining a constant total mass.

4. Quantum Entanglement and Information Preservation Mechanism

Another critical component supporting the mechanism of fractal energy conversion and information transfer at black hole singularities is quantum entanglement. The material universe and the antimatter universe are in a quantum entangled state, which ensures that information is shared and preserved between them.

The entangled state can be expressed by the following equation:

\[|\Psi_{\text{total}}\rangle = \sum_{i} c_i |\psi_i^{\text{M}}\rangle \otimes |\phi_i^{\text{AM}}\rangle\]

This equation demonstrates that the states of the material universe and the antimatter universe are mutually dependent. In this entangled state, a change in the information of one universe instantly affects the other, ensuring the preservation of information without loss.

5. Information Sharing through Density Matrices and Entropy

Finally, to quantify the preservation of information rigorously, we introduce the concepts of density matrices and entropy. The density matrices of the material universe and the antimatter universe are defined as follows:

\[\rho_{\text{M}} = \text{Tr}_{\text{AM}}(\rho_{\text{total}})\]

\[S(\rho_{\text{M}}) = S(\rho_{\text{AM}})\]

The equality of entropy shows that information is symmetrically preserved between the material universe and the antimatter universe. Using density matrices, we can mathematically explain how the quantum states of information are maintained, aligning with the discussions of fractal energy conversion and entangled states.

6. Conclusion and Future Prospects

This paper has discussed the mechanisms of fractal energy conversion cycles and information transfer through black hole singularities, focusing on the conservation of information and energy between the material universe and the antimatter universe. We clarified that these mechanisms are supported by quantum entanglement and entropy conservation, ensuring overall consistency.

Future research should aim to refine these theories further and validate them through observational data and experimentation. Specifically, seeking experimental evidence of fractal energy conversion and information transfer at black hole singularities will strengthen the reliability of this theory and aim for its integration with current physical theories.

Mathematical Framework for Holographic Transfer Between Material and Antimatter Universes

1. Total Energy Conservation of the Material and Antimatter Universes

First, we consider the conservation of total energy in the combined system of the material universe and the antimatter universe. Let \( E_{\text{M}} \) be the energy of the material universe and \( E_{\text{AM}} \) be the energy of the antimatter universe. The total energy \( E_{\text{total}} \) is expressed as:

\[E_{\text{total}} = E_{\text{M}} + E_{\text{AM}} = 0\]

Here, we assume that the energy of the antimatter universe has the opposite sign to that of the material universe. This hypothesis is based on the idea that the sum of all energies is zero, thus maintaining the conservation of energy across the entire universe.

2. Extended Hamiltonian Representation

Let \( H_{\text{M}} \) and \( H_{\text{AM}} \) denote the Hamiltonians of the material universe and the antimatter universe, respectively. The Hamiltonian of the entire system, \( H_{\text{total}} \), is given by:

\[H_{\text{total}} = H_{\text{M}} + H_{\text{AM}}\]

where each Hamiltonian describes the energy and information of its respective universe.

2.1 Introduction of Entangled States

Assume that the material universe and the antimatter universe are in a quantum entangled state. The state of the entire system, \( |\Psi_{\text{total}}\rangle \), can be expressed as:

\[|\Psi_{\text{total}}\rangle = \sum_{i} c_i |\psi_i^{\text{M}}\rangle \otimes |\phi_i^{\text{AM}}\rangle\]

where \( |\psi_i^{\text{M}}\rangle \) represents the states of the material universe, \( |\phi_i^{\text{AM}}\rangle \) represents the states of the antimatter universe, and \( c_i \) are complex coefficients representing the degree of entanglement.

2.2 Calculation of Energy Expectation Values

The energy expectation value of the entire system is:

\[\langle \Psi_{\text{total}} | H_{\text{total}} | \Psi_{\text{total}} \rangle = \langle H_{\text{total}} \rangle = 0\]

This indicates that the energies of the material universe and the antimatter universe cancel each other out.

3. Mathematical Representation of Information Preservation and Transfer

3.1 Information Description Using Density Matrices

Let the density matrices of the material universe and the antimatter universe be \( \rho_{\text{M}} \) and \( \rho_{\text{AM}} \), respectively. The total density matrix \( \rho_{\text{total}} \) of the system is defined as:

\[\rho_{\text{total}} = |\Psi_{\text{total}}\rangle \langle \Psi_{\text{total}} |\]

3.2 Shared Information via Partial Traces

Information in the material universe is entangled with that of the antimatter universe. By taking a partial trace over the antimatter universe, the density matrix of the material universe becomes:

\[\rho_{\text{M}} = \text{Tr}_{\text{AM}}(\rho_{\text{total}})\]

Similarly, by tracing out the material universe, we have:

\[\rho_{\text{AM}} = \text{Tr}_{\text{M}}(\rho_{\text{total}})\]

This demonstrates that information is shared between both universes.

3.3 Entropy and Information Conservation

Quantum entropy (von Neumann entropy) is used to evaluate the preservation of information:

\[S(\rho_{\text{M}}) = -\text{Tr}(\rho_{\text{M}} \ln \rho_{\text{M}})\]

\[S(\rho_{\text{AM}}) = -\text{Tr}(\rho_{\text{AM}} \ln \rho_{\text{AM}})\]

From the purity of the entire system, it follows that:

\[S(\rho_{\text{total}}) = 0\]

Thus, we find that:

\[S(\rho_{\text{M}}) = S(\rho_{\text{AM}})\]

indicating that the entropies of the material and antimatter universes are equal, suggesting that information is preserved and shared between them.

4. Fractal Energy Conversion Cycle Model

4.1 Hierarchical Structure of Energy Conversion

We revisit the fractal energy conversion formula presented earlier:

\[\langle 0 | H | 0 \rangle_{\text{ren}} = \sum_{n=0}^{\infty} \left( \frac{1}{2^n} \sum_{k=0}^{k_{\text{max}}} \hbar \omega_k^{(n)} \cdot \rho_k^{(n)} \right)\]

where \( n \) denotes the cycle's hierarchical level, \( \omega_k^{(n)} \) represents the energy modes at the \( n \)-th level, and \( \rho_k^{(n)} \) includes coefficients representing the degree of entanglement.

4.2 Creation and Annihilation from the Vacuum

To describe the generation and annihilation of energy at each cycle, we consider the canonical commutation relations in field theory. Using creation operators \( a_k^{\dagger} \) and annihilation operators \( a_k \):

\[H = \sum_{k} \hbar \omega_k \left( a_k^{\dagger} a_k + \frac{1}{2} \right)\]

These operators describe the energy's emergence from the vacuum and its convergence into singularities.

5. Mass Conservation and Zero Total Energy

5.1 Relation Between Mass and Energy

According to special relativity, mass and energy are related by:

\[E = mc^2\]

Let the mass of the material universe be \( m_{\text{M}} \) and the mass of the antimatter universe be \( m_{\text{AM}} \):

\[E_{\text{M}} = m_{\text{M}} c^2\]

\[E_{\text{AM}} = m_{\text{AM}} c^2\]

Given that the total energy is zero:

\[m_{\text{M}} + m_{\text{AM}} = 0\]

Therefore:

\[m_{\text{M}} = -m_{\text{AM}}\]

demonstrating that the sum of masses also equals zero.

5.2 Application of Mass Conservation Law

The masses of matter and antimatter counterbalance, maintaining the law of mass conservation throughout the entire universe. This indicates that energy and information transfer to the antimatter universe occurs within the framework of mass conservation.

6. Mathematical Description of Information Sharing via Singularities

6.1 Boundary Conditions at Singularities

Assuming that the material universe and the antimatter universe are connected at singularities (e.g., the center of a black hole), the continuity of the wave function at this boundary can be expressed as:

\[\psi_{\text{M}}(x_0) = \psi_{\text{AM}}(x_0)\]

where \( x_0 \) denotes the position of the singularity.

6.2 Information Transfer via Tunneling Effect

Using the quantum tunneling effect, the probability of information passing through a singularity is calculated as follows. The transmission probability \( T \) is generally given by:

\[T = e^{-2 \int_{x_1}^{x_2} \kappa(x) dx}\]

where \( \kappa(x) \) is the decay constant, depending on the potential barrier height and particle energy.

7. Conclusion and Integrated Possibilities

This mathematical framework explains the following possibilities:

1. Energy and Mass Conservation: The energies and masses of the material and antimatter universes sum to zero, conserving both across the entire system.

2. Information Sharing and Preservation: The two universes are quantum-entangled, with information shared and preserved through density matrices and entropy.

3. Transfer via Singularities: Information and energy are transferred between the material and antimatter universes through singularities using boundary conditions and tunneling effects.

4. Fractal Energy Conversion: Energy conversion cycles occur in a fractal manner, with each layer contributing to information preservation through entanglement and energy modes.

Future Prospects

This theoretical framework outlines the potential for information preservation and energy conversion between the material and antimatter universes. Future research should refine these models and compare them against observational data to validate these hypotheses.

Phenomena Occurring at the Event Horizon of a Black Hole: Energy Conversion and Information Preservation

This article provides a detailed explanation of what happens at the event horizon of a black hole from the perspectives of energy conversion processes and information preservation. At the event horizon, absorbed energy undergoes transformation through a fractal cycle, while crucial phenomena such as the preservation of information through the holographic principle take place.

1. Basics of Energy Conversion: Convergence to ⟨0∣H∣0⟩

Energy conversion in a black hole can be described by the following unified equation:

\[ \sum_{k=0}^{k_{\text{max}}} \hbar \omega_k = \langle 0 \mid H \mid 0 \rangle \]

This equation demonstrates that energy conversion inside a black hole progresses through fractal cycles and concludes with a finite number of modes \(k_{\text{max}}\), without expanding infinitely. Energy accumulates sequentially according to the frequency \(\omega_k\) associated with each mode \(k\), eventually converging to the vacuum expectation value ⟨0∣H∣0⟩.

This unified equation forms the foundation of the entire energy conversion model of a black hole, ensuring that energy does not accumulate infinitely but instead converges to a finite state.

2. Planck Length and Planck Energy as Cutoffs

To properly constrain energy conversion inside a black hole, the Planck length \(l_P\) or Planck energy \(E_P\) is introduced as a cutoff.

- When related to wavenumber or spatial scale, the Planck length \(l_P\) is used as the cutoff. The Planck length provides the smallest scale inside a black hole, preventing infinite energy accumulation.

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

The Planck length is defined as:

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

- For themes related to energy, the Planck energy \(E_P\) is set as the cutoff. This energy scale prevents infinite energy accumulation inside the black hole and ensures that energy conversion converges within a finite range.

\[ E_{\text{max}} = E_P = \sqrt{\frac{\hbar c^5}{G}} \]

By introducing the Planck scale, the energy conversion process inside the black hole is properly controlled, preventing infinite expansion and ensuring energy conversion remains within a physically valid range.

3. Fractal Energy Conversion Process

Energy conversion inside a black hole progresses through a fractal cycle. Energy accumulates in a self-similar manner, with its frequency \(\omega_k\) corresponding to the mode \(k\). This conversion process describes how a black hole absorbs energy from the outside and gradually accumulates it.

This energy accumulation is constrained by the Planck length or Planck energy cutoff, preventing infinite expansion. Ultimately, the fractal energy conversion converges at a finite number of modes, ensuring it remains within a physically observable range.

4. Energy Convergence to the Vacuum Expectation Value ⟨0∣H∣0⟩

The energy absorbed by a black hole gradually accumulates and ultimately converges to the vacuum expectation value ⟨0∣H∣0⟩. This vacuum expectation value represents the ground energy state in quantum mechanics, a finite energy state achieved through the fractal cycle.

Energy inside the black hole does not expand infinitely but converges to a finite state due to the Planck energy or Planck length cutoff. Therefore, black holes do not possess infinite energy, but rather accumulate energy within an observable range, ultimately reaching the finite energy state represented by ⟨0∣H∣0⟩.

5. Holographic Principle and Information Preservation

At the event horizon of a black hole, the holographic principle applies. This principle explains how the energy and information absorbed by the black hole are preserved on the event horizon. Information on the event horizon is preserved through the energy conversion process and can be observed from the outside.

This holographic preservation occurs as energy is accumulated during the energy conversion process constrained by the Planck scale, ensuring that information is not infinitely dispersed but retained, potentially resolving the black hole information paradox. Even as energy converges to ⟨0∣H∣0⟩, information is holographically preserved, preventing information loss inside the black hole.

6. Resolution of the Paradox: Energy Conversion and ⟨0∣H∣0⟩

Although black holes accumulate mass and energy, the phenomenon where they ultimately converge to the vacuum expectation value ⟨0∣H∣0⟩ may seem paradoxical. However, this paradox is resolved through the fractal cycle and Planck scale cutoffs.

Through the fractal cycle, energy inside the black hole accumulates sequentially but does not reach infinity. The energy is limited by the Planck length or Planck energy, so the energy inside the black hole ultimately converges to a finite range. As a result, the energy conversion process within the black hole does not progress indefinitely but converges in a finite state, resolving the paradox.

7. String Theory and Dimensional Considerations

The introduction of the Planck length \(l_P\) aligns with the concept of higher dimensions in string theory. Considering the multidimensional nature and membrane structure within the black hole, the application of the Planck length as a cutoff prevents the collapse of spacetime, ensuring stability.

This guarantees that energy conversion proceeds stably across dimensions, without infinite expansion. This also suggests a stronger connection between string theory and the physical phenomena occurring inside black holes.

8. Connection to Dark Energy

In theories related to the generation of dark energy and the expansion of the universe, both the Planck length and Planck energy play significant roles. The expansion of energy scales is controlled by the Planck energy, while the spread of spacetime is limited by the Planck length, preventing dark energy from expanding infinitely. As a result, the energy balance of the universe is maintained, and energy conversion proceeds in a constrained manner.

Conclusion

The mechanisms of energy conversion and information preservation in black holes can be explained consistently by introducing the Planck length and Planck energy as cutoff criteria. These cutoffs limit infinite energy or information accumulation inside the black hole, ultimately converging to the vacuum expectation value ⟨0∣H∣0⟩. Additionally, the holographic principle preserves information, potentially resolving the black hole information paradox.

Furthermore, connections to string theory and dark energy are also indicated, providing a coherent explanation of the processes of energy conversion inside and outside the black hole through these theoretical frameworks. By introducing cutoff criteria, theories concerning the growth, energy conversion, and disappearance of black holes are strengthened, offering paths to resolving major problems in modern physics.

Black Hole Singularity and Energy Conversion Theory

A New Theoretical Approach Using the Proportional Constant α for Black Hole Singularity and Energy Conversion Theory

Introduction Understanding the energy conversion processes near black holes remains one of the unresolved challenges in modern physics. Particularly at the singularity at the center of a black hole, the gravitational field diverges to infinity, and general relativity (GR) cannot fully describe its behavior. This theory introduces the proportional constant α and aims to explain energy conversion within and outside black holes by considering the singularity as an energy baseline 𝐸₀=⟨0∣𝐻∣0⟩.

The proportional constant α is a parameter for adjusting the intensity of the gravitational field and energy conversion, offering a new perspective by understanding the infinite gravitational field at the singularity not merely as a point of energy concentration, but as the starting point for energy conversion. Furthermore, although constrained by the uncertainty principle and difficult to specify with concrete equations, this energy conversion may provide a unified explanation of the overall energy structure of black holes.

1. A New Perspective on Energy Conversion at the Singularity

Quantum Interpretation of the Singularity

In general relativity, the singularity of a black hole is a point where spacetime curvature diverges to infinity, rendering physical laws inapplicable. However, from a quantum mechanical viewpoint, the singularity can be regarded as the energy baseline 𝐸₀=⟨0∣𝐻∣0⟩, suggesting that this point is the origin of energy conversion. Here, 𝐸₀ corresponds to the energy of the quantum vacuum, serving as a key to the unified explanation of energy conversion near the singularity.

The total energy of a black hole can be expressed by adding the external energy fluctuation Δ𝐸 to this baseline energy 𝐸₀ as follows:

𝐸_BH = 𝐸₀ + Δ𝐸

This equation indicates that the energy of the black hole can be interpreted as a fluctuation relative to the baseline energy.

2. The Role of the Proportional Constant α

What is the Proportional Constant α?

The proportional constant α is a parameter used to adjust the intensity of the gravitational field and the energy conversion processes in black holes. The current gravitational field strength depends on the distance 𝑟 from the black hole and its mass 𝑀, as expressed by the following equation:

𝑔(𝑟) = \(\frac{𝐺𝑀}{𝑟²}(1 - \frac{𝑟ₛ}{𝑟})\)

Here, 𝐺 is the gravitational constant, and 𝑟ₛ is the Schwarzschild radius. In this equation, the gravitational field becomes stronger as the black hole is approached, diverging to infinity as 𝑟 approaches 𝑟ₛ.

In the new approach, the proportional constant α is introduced to adjust the strength of the gravitational field as follows:

𝑔(𝑟) = \(\alpha \frac{𝐺𝑀}{𝑟²}(1 - \frac{𝑟ₛ}{𝑟})\)

This equation shows that the strength of the gravitational field can be adjusted by the value of α.

α > 1: The gravitational field is enhanced, and energy conversion progresses more rapidly.

α < 1: The gravitational field is weakened, and energy conversion progresses more gently.

By introducing the proportional constant α, the energy conversion processes of the black hole are adjusted, and the details of energy conversion near the singularity can be more clearly explained.

3. The Role of Vacuum Energy

Zero-point Fluctuations and Energy Conservation

Vacuum energy plays an important role in energy conversion processes near black holes. Zero-point fluctuations are believed to affect black hole evaporation or disappearance, advancing energy conversion within the framework of energy conservation. In this process, zero-point energy serves as a key reference.

Zero-point energy can be expressed by the following equation:

⟨0∣𝐻∣0⟩ = \(\frac{1}{2} \sum_{𝑘=0}^{𝑘_{max}} ℏ𝜔ₖ\)

A cutoff is imposed by the speed of light, preventing unbounded, chaotic infinite expansion. As a result, ordered, finite energy conversion within the universe is carried out, deeply related to Hawking radiation and black hole evaporation.

4. Energy Conversion Processes and Mathematical Representation

Energy Radiation by Matter-Antimatter Annihilation

Near black holes, the annihilation of matter and antimatter is a major mechanism for energy radiation. Electrons (𝑒⁻) and positrons (𝑒⁺) annihilate each other, emitting gamma-ray photons as energy.

𝑒⁻ + 𝑒⁺ → 𝛾₁ + 𝛾₂ + 𝛾_unseen

Here, 𝑒⁻ is an electron, 𝑒⁺ is a positron, 𝛾₁ and 𝛾₂ are observable gamma-ray photons, and 𝛾_unseen represents unobserved energy radiation (such as neutrinos or unknown particles).

The law of energy conservation is applied as follows:

𝐸_𝑒⁻ + 𝐸_𝑒⁺ = 𝐸_𝛾₁ + 𝐸_𝛾₂ + 𝐸_𝛾unseen

5. A New Relationship Between Gravitational Potential and Mass Density

The proposed gravitational potential equation is as follows:

∇²Φ(𝑥) = 𝛼∇²𝜌(𝑥)

Here, Φ(𝑥) is the gravitational potential, 𝜌(𝑥) is the mass density, and 𝛼 is the proportional constant.

Furthermore, gravitational acceleration 𝑔 is proportional to the gradient of the mass density 𝜌:

𝑔 = −𝛼∇𝜌

6. Relationship Between the Speed of Light and Vacuum Energy Density

It is suggested that variations in vacuum energy density cause slight fluctuations in the speed of light.

𝑐' = 𝑐 \(\left( 1 + \frac{𝛾 𝜌_{vac}}{𝜌_m} \right)\)

Here, 𝑐' is the fluctuated speed of light, 𝑐 is the standard speed of light, 𝛾 is the proportional constant, 𝜌_vac is the vacuum energy density, and 𝜌_m is the matter energy density.

7. Application of the Law of Energy Conservation

Energy conversion near black holes is described by the law of energy conservation. That is, the total energy absorbed by the black hole, whether from matter or antimatter, is conserved even when transformed into other forms.

𝐸_total = 𝐸_matter + 𝐸_antimatter = 𝐸_radiation + 𝐸_unseen

8. Considerations on Undetected Energy and Noise

Interference Noise and Information Preservation

High-energy fluctuations near black holes generate interference noise. This noise, in turn, plays a role in preserving the law of information conservation associated with energy conversion, providing a means to understand energy conversion processes around black holes through analysis. Particularly, the simultaneous action of both serial and parallel information conservation laws suggests that the diversity and complexity of energy conversion can be elucidated through noise analysis.

9. The Influence of the Un certainty Principle

Near the singularity of a black hole, the uncertainty principle of quantum mechanics plays an important role.

Δ𝐸⋅Δ𝑡≥\(\frac{ℏ}{2}\)

This uncertainty principle indicates that energy conversion over a short period can only be described probabilistically, suggesting that energy fluctuations occur probabilistically.

10. The Possibility of Integration with Quantum Gravity Theories

Current general relativity explains how gravity increases rapidly toward the center of a black hole but does not sufficiently describe the "infinitely strong" state beyond. In contrast, string theory and loop quantum gravity theory provide comprehensive insights into energy conversion at the black hole singularity.

Specifically, theories within string theory and loop quantum gravity propose avoiding the infinite state at the black hole singularity, suggesting that energy conversion occurs as it passes through the baseline energy ⟨0∣𝐻∣0⟩. This provides a new integrated perspective while maintaining consistency in physics, demonstrating that energy is conserved inside and outside the black hole through quantum energy conversion rather than becoming infinitely strong.

11. Conclusion

By regarding the black hole singularity as the energy baseline 𝐸₀=⟨0∣𝐻∣0⟩ and introducing the proportional constant α, the energy conversion process can be explained in a unified manner. Considering the effects of vacuum energy and zero-point fluctuations on black hole evaporation and energy conversion, the diversity and complexity of energy conversion may be elucidated through noise analysis.

Furthermore, integration with string theory and loop quantum gravity theory can avoid the issue of infinite energy at the black hole singularity, strengthening the consistency of energy conversion theories. Future developments will aim to refine these theories, with experimental verification and observational support expected.

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Holographically Encoded

The Horizon as a Transition Point for Energy Conversion in ⟨0∣H∣0⟩_ren

The Horizon as a Transition Point for Energy Conversion

In traditional holographic principles, the black hole's horizon was perceived as a surface where information is merely stored on a two-dimensional plane. However, the horizon defined as ⟨0∣H∣0⟩_ren here is understood as a process where information "passes through" via energy conversion. In other words, the horizon functions not as a static storage but as a part of a dynamic energy conversion process.

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

This equation indicates that the energy conversion at the horizon converges to a finite number of modes. Thus, the horizon is not merely a place where information is stored but functions as a transition point where energy and information are converted and progress to the next stage.

Mechanism of Information Preservation in Energy Conversion

Interaction Between Energy Conversion and Information

In the new definition, the horizon based on ⟨0∣H∣0⟩_ren emphasizes that information changes its nature while passing through energy conversion. At this transition point, energy conversion converges to a finite number of modes in a fractal-like cycle, and information is preserved throughout this process.

In this conversion process, energy exists two-dimensionally on the horizon, and subsequently, the information may further be converted and transferred to other dimensions or even to an antimatter universe.

Role as a Two-Dimensional Horizon

The new role of the horizon differs from the static storage of information holographically encoded; instead, it is a dynamic transition point of energy conversion, with the horizon itself existing two-dimensionally as ⟨0∣H∣0⟩_ren. This two-dimensionality is an essential process for the energy conversion within the black hole to converge into a finite number of modes.

Potential for Transfer to an Antimatter Universe

Entanglement and Transfer to the Antimatter Universe

As energy conversion progresses, there is a possibility that information may be transferred to an antimatter universe. This process is realized by the preservation of information in quantum entangled states, with parts of it transitioning from the matter universe to the antimatter universe.

The transfer to an antimatter universe is considered one mechanism by which information, while changing its nature, remains preserved at the transition point of energy conversion at the horizon. Here, the black hole's horizon functions not as a keeper of information but as a "gate" that converts and sends it elsewhere.

Relationship Between the Horizon and the Antimatter Universe

By passing through the energy conversion transition point defined by ⟨0∣H∣0⟩_ren, the possibility of transferring information to the antimatter universe increases. This process acts as a transition mechanism for sending energy and information into a new form of preservation in another dimension, thus creating an interaction between the matter universe and the antimatter universe.

Connection with String Theory

Role of Energy Conversion and the Horizon in String Theory

In string theory, the universe is structured multidimensionally, with entities like branes and membranes playing a crucial role in the exchange of information and energy. The definition of the horizon based on ⟨0∣H∣0⟩_ren emphasizes its role as a place where information is transferred to the next dimension through energy conversion, aligning with string theory's view of a multidimensional universe.

Connection Between the Two-Dimensional Transition Point of Energy Conversion and String Theory

The new definition of the horizon existing two-dimensionally closely resembles the branes and dimensional structures in string theory. In particular, the idea that energy and information move through branes to other dimensions corresponds with the mechanism of energy conversion and information preservation defined by ⟨0∣H∣0⟩_ren.

Consistency with Current Theories and New Perspectives

Consistency with the Theory of Relativity

In this new definition, the progress of energy conversion allows for different perspectives depending on the observer’s position or velocity. Since the horizon functions as a transition point for energy conversion, it harmonizes with the relativity of spacetime as shown in the theory of relativity, confirming that the mechanism of information preservation remains consistent from various observation points.

Connection with Dark Energy

The mechanism for generating dark energy may also be associated with the energy conversion process defined by ⟨0∣H∣0⟩_ren. In the process where energy conversion contributes to the expansion of the universe and the generation of dark energy, transferring information to other dimensions or an antimatter universe might help solve the mystery of dark energy.

Conclusion

The reconsideration of the holographic principle based on the new definition emphasizes that the horizon, as ⟨0∣H∣0⟩_ren, is a transition point of energy conversion, where information is preserved while being dynamically converted in two dimensions. In this process, information is not statically stored but is transferred beyond dimensions through fractal-like energy conversion.

Key Points:

1. The horizon as a transition point of energy conversion (⟨0∣H∣0⟩_ren) plays a role in transcending dimensions through conversion rather than merely storing information holographically.

2. Transfer to the antimatter universe: There is a possibility that information is transferred to other dimensions or an antimatter universe through energy conversion.

3. Integration with string theory: The role of the horizon as a transition point for energy conversion aligns with the multidimensional structures of string theory, explaining the process of information transfer.

This new understanding based on the new definition provides deeper insights into the dynamic relationship between energy and information at the black hole's horizon, offering new perspectives in physics, string theory, and cosmology. Future research will require specific models and observations to verify the energy conversion mechanisms.

Phenomena Occurring at the Event Horizon of a Black Hole

Energy Conversion and Information Preservation

This article provides a detailed explanation of what happens at the event horizon of a black hole from the perspectives of energy conversion processes and information preservation. At the event horizon, absorbed energy undergoes transformation through a fractal cycle, while crucial phenomena such as the preservation of information through the holographic principle take place.

1. Basics of Energy Conversion: Convergence to ⟨0∣H∣0⟩

Energy conversion in a black hole can be described by the following unified equation:

\[ \sum_{k=0}^{k_{\text{max}}} \hbar \omega_k = \langle 0 \mid H \mid 0 \rangle \]

This equation demonstrates that the energy conversion inside a black hole progresses through fractal cycles and concludes with a finite number of modes, \(k_{\text{max}}\), without expanding infinitely. Energy accumulates sequentially according to the frequency \(\omega_k\) associated with each mode \(k\), eventually converging to the vacuum expectation value ⟨0∣H∣0⟩.

This unified equation forms the foundation of the entire energy conversion model of a black hole, ensuring that energy does not accumulate infinitely but instead converges to a finite state.

2. The Speed of Light as a Cutoff

The speed of light \(c\) functions as a cutoff, preventing the infinite propagation of energy and information both inside and outside the black hole. This cutoff ensures that energy conversion within the black hole does not proceed indefinitely but is confined to a finite range.

The role of the speed of light cutoff physically limits energy accumulation at the black hole's event horizon, preventing the occurrence of infinite energy in the observable universe. By serving as a cutoff, the speed of light controls the propagation of energy and information, ensuring they converge without spreading infinitely.

3. Fractal Energy Conversion Process

The energy conversion inside a black hole progresses through a fractal cycle. Energy accumulates in a self-similar manner, with its frequency \(\omega_k\) corresponding to the mode \(k\). This conversion process describes how a black hole absorbs energy from the outside and gradually accumulates it.

Ultimately, this fractal energy conversion is limited by the speed of light cutoff, preventing it from reaching infinity and resulting in the energy converging at a finite number of modes. This finite convergence guarantees that the energy inside the black hole remains within a physically observable range.

4. Energy Convergence to the Vacuum Expectation Value ⟨0∣H∣0⟩

The energy absorbed by a black hole gradually accumulates and ultimately converges to the vacuum expectation value ⟨0∣H∣0⟩. This vacuum expectation value represents the ground energy state in quantum mechanics, a finite energy state achieved through the fractal cycle.

The energy inside the black hole does not expand infinitely but instead converges to a finite state due to the speed of light cutoff. Therefore, black holes do not possess infinite energy, but rather accumulate energy within an observable range, ultimately reaching the finite energy state represented by ⟨0∣H∣0⟩.

5. Holographic Principle and Information Preservation

At the black hole's event horizon, the holographic principle applies. This principle explains how the energy and information absorbed by the black hole are preserved on the event horizon. Information on the event horizon is preserved through the energy conversion process and can be observed from the outside.

Since information is holographically preserved during the energy conversion process that converges to ⟨0∣H∣0⟩, information does not disappear within the black hole. This mechanism resolves the black hole information paradox, explaining how energy and information are consistently preserved.

6. Resolution of the Paradox: Energy Conversion and ⟨0∣H∣0⟩

Despite the fact that a black hole accumulates mass and energy, the phenomenon where it ultimately converges to the vacuum expectation value ⟨0∣H∣0⟩ may appear paradoxical. However, this paradox is resolved by the fractal cycle.

Through the fractal cycle, energy inside the black hole accumulates sequentially but does not reach infinity. The energy is limited by the speed of light cutoff, so the energy inside the black hole eventually converges to a finite range. As a result, the energy conversion process within the black hole does not progress indefinitely but converges in a finite state, resolving the paradox.

Conclusion

The energy conversion model based on the black hole and the speed of light cutoff is structured by the following unified equation:

\[ \sum_{k=0}^{k_{\text{max}}} \hbar \omega_k = \langle 0 \mid H \mid 0 \rangle \]

This equation demonstrates that energy conversion inside and outside a black hole does not expand infinitely but converges to a finite range due to the speed of light cutoff. Energy accumulates sequentially through fractal cycles and ultimately converges to the vacuum expectation value ⟨0∣H∣0⟩. This convergence ensures that no infinite energy occurs inside the black hole, establishing a mechanism by which energy and information are holographically preserved.

This approach provides a consistent explanation of the growth, energy conversion, and eventual disappearance of a black hole, resolving issues such as the black hole information paradox and energy conservation. Additionally, this theory offers a simple and intuitive framework for understanding the energy conversion within a black hole, presenting a powerful tool for interpreting physical phenomena.

Energy Sources of the Expansion and Contraction of the Universe

1. Overview of the Theory

The Zero-Energy Cycle Theory presents a new view of the universe based on the fundamental equation "0 = +∞ − ∞," where the generation and annihilation of energy proceed infinitely, maintaining energy conservation. This theory conceptualizes the entire universe as "fluctuations" within a single medium called "vacuum," where continuous cycles of creation and annihilation occur. These fluctuations generate the dynamic and fractal structure of the universe.

The creation (Big Bang) and annihilation (Big Crunch) of the universe are understood as processes where energy passes through a zero state. The zero-energy state is not a static endpoint but a dynamic and relative state. The phenomena of the Big Bang and Big Crunch are explained as processes where energy, in its journey of creation and annihilation, passes through the zero state — with the transition from nothing to something identified as the Big Bang, and the return to zero as the Big Crunch.

2. Relationship between Energy and Vacuum Fluctuations

Generation of Matter and Antimatter through Vacuum Fluctuations

Vacuum fluctuations generate matter and antimatter, splitting energy into \( E_{\text{matter}} \) and \( E_{\text{antimatter}} \), creating symmetrical entities that recombine and annihilate.

Complementarity of the Universe and Antimatter Universe

Within vacuum fluctuations, symmetrical entities such as a fractal-structured universe and an antimatter universe are generated simultaneously. The matter-dominated universe and the antimatter universe are connected through a cycle of energy exchange.

Understanding of the Same Phenomenon in Different Dimensions and Scales

The generation and recombination of energy due to vacuum fluctuations manifest differently in the dimensions and scales of matter, antimatter, the universe, and the antimatter universe. The Zero-Energy Cycle Theory encompasses these phenomena.

Unified Explanation of the Beginning and End of the Universe

The Big Bang and Big Crunch are described as energy circulation phenomena driven by vacuum fluctuations, leading to the understanding that the universe continuously experiences the dynamic generation and annihilation of energy.

3. Role and Details of Dark Energy

In the Zero-Energy Cycle Theory, dark energy differs in origin and function from traditional cosmological interpretations. It does not cause expansion but instead provides energy to the expanding space as a result of that expansion.

Mechanism of Dark Energy Generation

Dark energy is understood as a form of energy generated from vacuum fluctuations. Specifically, the decrease in energy density associated with the expansion of the universe destabilizes the vacuum state, intensifying these fluctuations. This fluctuation leads to the splitting of energy into \( E_{\text{matter}} \) and \( E_{\text{antimatter}} \), generating dark energy. Crucially, the generation of dark energy is a process of energy conversion, ensuring the total amount of energy remains conserved.

Mathematical Representation

The generation process of dark energy can be expressed by the following differential equation:

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

• \(\rho_\Lambda\): Dark energy density
• \(H\): Hubble parameter (rate of cosmic expansion)
• \(\alpha\): Constant representing the rate of energy generation

This equation quantitatively illustrates how the strengthening of vacuum fluctuations due to the increasing Hubble rate \( H \) leads to the generation of dark energy. The energy generation term \(\alpha H^3\) suggests that the rate of energy generation from fluctuations is proportional to the cube of the expansion rate.

Formulating the Variation of Vacuum Energy with Cosmic Expansion

The decrease in energy density due to the expansion of the universe affects the stability of the vacuum state. Specifically, as the universe expands and energy density decreases, fluctuations in the vacuum become more pronounced, promoting the generation of dark energy.

Based on the Friedmann equation, the generation of dark energy density \(\rho_\Lambda\) is formulated as follows:

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

• \(\rho_m\): Matter energy density
• \(\rho_r\): Radiation energy density
• \(G\): Gravitational constant

Furthermore, by differentiating the Friedmann equation with respect to time, the changes in the Hubble rate \( H \) and the energy density over time are linked. The generation of dark energy is modeled as the time variation of energy density with a generation term introduced.

Consistency with Observational Data and New Predictions

Current observational data (e.g., supernova observations, measurements of cosmic background radiation, distribution of galaxy clusters) indicate the accelerated expansion of the universe, interpreted as dark energy. The dark energy density \(\rho_\Lambda\) in the Zero-Energy Cycle Theory is based on the Friedmann equation and matches the actual observational data.

The Zero-Energy Cycle Theory provides new predictions based on the mechanism of dark energy generation:

• Dynamic Variation of Dark Energy: As the cosmic expansion rate \( H \) changes, the dark energy density \(\rho_\Lambda\) also dynamically fluctuates. This suggests that, in the future, the dark energy density might increase or decrease over time.

These predictions are expected to be verified by future observational data (e.g., more precise supernova observations, measurements of gravitational lensing effects, analyses of large-scale cosmic structures).

4. Integration of Equations and Their Interpretation

The Zero-Energy Cycle Theory redefines all cosmic phenomena as cyclic processes where energy can be generated and annihilated. By reinterpreting energy conservation, this theory provides a framework for understanding phenomena such as black holes, dark energy, and gravity from a new perspective. Moreover, the Zero-Energy Cycle Theory aligns with multiverse theories and holographic theories, offering a comprehensive understanding of the fundamental dynamics of the universe.

Overview of the Zero Energy Cycle Theory

The Zero Energy Cycle Theory offers 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 views the entire universe as "fluctuations within a vacuum," where the universe 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 the vacuum's 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 the vacuum's 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 also 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" and "small" or "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 is consistent with the "relativity of spacetime depending on the observer," as shown by Relativity Theory.
• For instance, from the perspective of Observation Point A, the universe at Point A' might appear as a fleeting phenomenon that ends quickly, but for an observer inside Point A', a long period may be perceived. This is explained by the relativity of time, where the passage of time is affected by the observer's speed and gravity.

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. The universe is understood to possess a dynamic quality where it is continually transformed by this cycle of energy.

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 why a matter-dominated universe and an antimatter universe coexist, as well as why the early universe contained much antimatter. Matter and antimatter, despite their opposing properties (e.g., charge and spin), are thought to be strongly bound by symmetry, interacting through energy.

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.
• This stage resembles the mixing of matter and antimatter in the early universe. In the early universe, matter and antimatter coexisted equally and were not yet fully separated.

Increased Current Leading to Clear Separation of Poles:

• As the current increases, the S-pole and N-pole become clear, and the iron filings are drawn to both poles, separating them. At this stage, the polarity is distinctly divided, and the mixed state is resolved.
• Applying this to the evolution of the universe, as energy increases (such as through cosmic expansion and physical processes), matter and antimatter become clearly separated, eventually leading to matter dominance, with antimatter diminishing in the universe.

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. However, due to energy imbalances and interactions, matter became dominant in the universe while antimatter diminished.

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: Just as the S-pole and N-pole of an electromagnet exist and influence each other, 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, the cutoff wavenumber is set to avoid infinite divergence, normalizing the energy value to a finite number. This normalization allows energy calculations to be confined to a physically meaningful range.

The Reason for Introducing a Cutoff

• Prevention of Infinite Energy Divergence: In the calculation of zero-point energy, considering all wavenumber modes causes the energy to diverge to infinity. This presents a theoretical issue and lacks physical meaning, so the cutoff wavenumber \(k_{\text{max}}\) is introduced to limit the range of integration to a finite value.

Zero-Point Energy Normalization Through Cutoff Wavenumber

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

Conclusion

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

Energy Sources of the Expansion and Contraction of the Universe

The Zero-Energy Cycle Theory presents a new view of the universe based on the fundamental equation "0 = +∞ − ∞," where the generation and annihilation of energy proceed infinitely, maintaining energy conservation. This theory conceptualizes the entire universe as "fluctuations" within a single medium called "vacuum," where continuous cycles of creation and annihilation occur. These fluctuations generate the dynamic and fractal structure of the universe.

The creation (Big Bang) and annihilation (Big Crunch) of the universe are understood as processes where energy passes through a zero state. The zero-energy state is not a static endpoint but a dynamic and relative state. The phenomena of the Big Bang and Big Crunch are explained as processes where energy, in its journey of creation and annihilation, passes through the zero state — with the transition from nothing to something identified as the Big Bang, and the return to zero as the Big Crunch.

1. Overview of the Theory

2. Relationship between Energy and Vacuum Fluctuations

Generation of Matter and Antimatter through Vacuum Fluctuations

Vacuum fluctuations generate matter and antimatter, splitting energy into \( E_{\text{matter}} \) and \( E_{\text{antimatter}} \), creating symmetrical entities that recombine and annihilate.

Complementarity of the Universe and Antimatter Universe

Within vacuum fluctuations, symmetrical entities such as a fractal-structured universe and an antimatter universe are generated simultaneously. The matter-dominated universe and the antimatter universe are connected through a cycle of energy exchange.

Understanding of the Same Phenomenon in Different Dimensions and Scales

The generation and recombination of energy due to vacuum fluctuations manifest differently in the dimensions and scales of matter, antimatter, the universe, and the antimatter universe. The Zero-Energy Cycle Theory encompasses these phenomena.

Unified Explanation of the Beginning and End of the Universe

The Big Bang and Big Crunch are described as energy circulation phenomena driven by vacuum fluctuations, leading to the understanding that the universe continuously experiences the dynamic generation and annihilation of energy.

3. Role and Details of Dark Energy

In the Zero-Energy Cycle Theory, dark energy differs in origin and function from traditional cosmological interpretations. It does not cause expansion but instead provides energy to the expanding space as a result of that expansion.

Mechanism of Dark Energy Generation

Dark energy is understood as a form of energy generated from vacuum fluctuations. Specifically, the decrease in energy density associated with the expansion of the universe destabilizes the vacuum state, intensifying these fluctuations. This fluctuation leads to the splitting of energy into \( E_{\text{matter}} \) and \( E_{\text{antimatter}} \), generating dark energy. Crucially, the generation of dark energy is a process of energy conversion, ensuring the total amount of energy remains conserved.

Mathematical Representation

The generation process of dark energy can be expressed by the following differential equation:

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

• \(\rho_\Lambda\): Dark energy density
• \(H\): Hubble parameter (rate of cosmic expansion)
• \(\alpha\): Constant representing the rate of energy generation

This equation quantitatively illustrates how the strengthening of vacuum fluctuations due to the increasing Hubble rate \( H \) leads to the generation of dark energy. The energy generation term \(\alpha H^3\) suggests that the rate of energy generation from fluctuations is proportional to the cube of the expansion rate.

Formulating the Variation of Vacuum Energy with Cosmic Expansion

The decrease in energy density due to the expansion of the universe affects the stability of the vacuum state. Specifically, as the universe expands and energy density decreases, fluctuations in the vacuum become more pronounced, promoting the generation of dark energy.

Based on the Friedmann equation, the generation of dark energy density \(\rho_\Lambda\) is formulated as follows:

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

• \(\rho_m\): Matter energy density
• \(\rho_r\): Radiation energy density
• \(G\): Gravitational constant

Furthermore, by differentiating the Friedmann equation with respect to time, the changes in the Hubble rate \( H \) and the energy density over time are linked. The generation of dark energy is modeled as the time variation of energy density with a generation term introduced.

Consistency with Observational Data and New Predictions

Current observational data (e.g., supernova observations, measurements of cosmic background radiation, distribution of galaxy clusters) indicate the accelerated expansion of the universe, interpreted as dark energy. The dark energy density \(\rho_\Lambda\) in the Zero-Energy Cycle Theory is based on the Friedmann equation and matches the actual observational data.

The Zero-Energy Cycle Theory provides new predictions based on the mechanism of dark energy generation:

• Dynamic Variation of Dark Energy: As the cosmic expansion rate \( H \) changes, the dark energy density \(\rho_\Lambda\) also dynamically fluctuates. This suggests that, in the future, the dark energy density might increase or decrease over time.

These predictions are expected to be verified by future observational data (e.g., more precise supernova observations, measurements of gravitational lensing effects, analyses of large-scale cosmic structures).

4. Integration of Equations and Their Interpretation

The Zero-Energy Cycle Theory redefines all cosmic phenomena as cyclic processes where energy can be generated and annihilated. By reinterpreting energy conservation, this theory provides a framework for understanding phenomena such as black holes, dark energy, and gravity from a new perspective. Moreover, the Zero-Energy Cycle Theory aligns with multiverse theories and holographic theories, offering a comprehensive understanding of the fundamental dynamics of the universe.