Fractal-like structure of the universe
Big Bang, Big Crunch

1. Overview of the Zero Theory and Fractal Structure of the Universe

The Zero Energy Cycle Theory is based on the principle that the expansion and contraction of the universe are driven by energy exchange processes, keeping the total energy of the universe at zero. As an alternative to the conventional ΛCDM model, it introduces the following key features.

1.1 Fractal Structure and Energy Conservation

In the Zero Theory, the large-scale structure of the universe is thought to possess fractal properties, where self-similar structures are repeated on different scales. The fractal structure is based on the interaction between the matter universe and the antimatter universe and is tied to the law of conservation of energy throughout the universe.

In this theory, the total energy of the universe is kept at zero through the cancellation of matter energy, antimatter energy, and gravitational energy. This dynamic energy exchange between expansion and contraction is expressed in the following equation:

\[ E_{\text{total}} = E_{\text{matter}} + E_{\text{antimatter}} + E_{\text{gravity}} = 0 \]

This equation indicates that matter and antimatter cancel each other out, maintaining the universe’s energy at zero.

1.2 Role of Observation Points A and A'

The Zero Theory introduces external and internal perspectives to observe the universe’s expansion and contraction.

- Observation Point A (External Perspective): Observes our universe from the outside, allowing for the observation of processes such as the creation of matter and antimatter through vacuum fluctuations and energy exchange with the antimatter universe.

- Observation Point A' (Internal Perspective): Observes the distribution of matter and antimatter and the fractal structure within the universe, helping to evaluate the relationship between energy exchange processes and the external perspective.

By using these multidimensional observation points, the Zero Theory deepens the understanding of the universe’s fractal structure and energy circulation.

1.3 Fractal Structure and Self-Organization

The fractal structure of the universe is formed through self-organization. Through interactions involving gravity and energy exchange, galaxies and galaxy clusters are hierarchically organized, leading to efficient energy distribution. This structure is described by the following scaling laws:

\[ M(R) \propto R^D \quad \text{and} \quad N(R) \propto R^D \]

- \(M(R)\) is the mass within a radius \(R\).

- \(N(R)\) is the number of galaxies within a radius \(R\).

- \(D\) is the fractal dimension.

This scaling law demonstrates that the distribution of galaxies has a fractal structure, explaining the efficient energy distribution during the evolution of the universe.

1.4 Reinterpretation of Dark Energy

The interpretation of dark energy in the Zero Theory differs greatly from that of the current ΛCDM model. In the ΛCDM model, dark energy is considered the main factor driving the accelerated expansion of the universe, whereas in the Zero Theory, it is interpreted as the result of energy exchange.

\[ \rho_{\text{dark energy}}(t) = f(a(t)) \cdot \rho_{\text{energy exchange}}(t) \]

- In the Zero Theory, the expansion of the universe is caused by external factors, and the term corresponding to dark energy, \( \rho_{\text{energy exchange}} \), represents energy exchange that occurs as a result of expansion. As the expansion progresses, energy is generated from vacuum fluctuations due to fluctuations in matter and antimatter density, leading to energy exchange.

- In the ΛCDM model, dark energy is uniformly distributed throughout the universe and is seen as the primary driver of expansion. In this model, dark energy directly causes the universe’s expansion and is considered the root cause of expansion.

In the Zero Theory, energy exchange processes do not directly trigger expansion but occur as a result of expansion caused by external factors. This mechanism explains how energy is generated and annihilated between matter and antimatter.

2. Equations and Theoretical Background of the Zero Theory

2.1 Friedmann Equation for Expansion and Contraction

In the Zero Theory, the Friedmann equation is modified to quantitatively describe the expansion and contraction of the universe:

\[ \left(\frac{\dot{a}}{a}\right)^2 = \frac{8 \pi G}{3} \left(\rho_{\text{matter}} + \rho_{\text{antimatter}} + \rho_{\text{energy exchange}}\right) - \frac{k}{a^2} \]

- **Left Side**: \(\left(\frac{\dot{a}}{a}\right)^2\) represents the rate of change of the scale factor \(a(t)\) over time, indicating the rate of the universe's expansion.

- **Right Side**: Includes contributions from the energy of matter (\(\rho_{\text{matter}}\)), antimatter (\(\rho_{\text{antimatter}}\)), and energy exchange (\(\rho_{\text{energy exchange}}\)), all of which influence the universe's expansion or contraction.

- **\(\frac{k}{a^2}\)**: Represents the curvature of space, where \(k\) is the curvature constant (positive, negative, or zero).

This modified Friedmann equation demonstrates that the universe’s expansion and contraction are controlled by the energy of matter, antimatter, and energy exchange.

2.2 Acceleration Equation for Expansion and Contraction

The acceleration of the universe’s expansion and contraction is described by the following equation:

\[ \frac{d^2 a}{dt^2} = - \frac{4 \pi G}{3} \left(\rho_{\text{total}} + 3p_{\text{total}}\right) \]

This equation shows how the energy density (\(\rho_{\text{total}}\)) and pressure (\(p_{\text{total}}\)) of matter and antimatter contribute to the acceleration or deceleration of the universe’s expansion or contraction.

3. Energy Fluctuations due to the Uncertainty Principle

The uncertainty principle in quantum mechanics impacts the universe's energy exchange processes, introducing fluctuations in the cycle of expansion and contraction.

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

This principle introduces random fluctuations in the efficiency and timing of energy exchange, explaining why the universe’s expansion and contraction do not follow a perfect, stable cycle.

4. A New Perspective on the Propagation of Light and the Curvature of the Universe

In the Zero Theory, it is assumed that the overall shape of the universe is close to a sphere, but its internal structure is flat. As a result, light propagates in straight lines, and the conventional concept of light bending due to curvature is not considered.

Furthermore, even if curvature exists in the universe, it is difficult to detect relative changes because both the observer and the photons follow the same reference frame. Local phenomena, such as the bending of light due to distortions caused by black holes or galaxies, are interpreted as distinct from the overall curvature of the universe.

5. Observational Consistency and Challenges of the New Theory

The Zero Theory explains the expansion and contraction of the entire universe based on the law of conservation of energy. By introducing external energy exchange processes, it may naturally explain the differences in expansion rates observed in local and distant regions of the universe (the Hubble tension problem). However, this theory still requires observational evidence and theoretical validation, and further research is needed.

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.

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. Specifically, the cutoff criterion here is defined by the Planck length \( l_P \). This can be expressed as:

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

Where the Planck length is given by:

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

By using the Planck length as a cutoff, we ensure that the energy and information conversion process converges to a finite number of modes while maintaining Lorentz invariance. Thus, the horizon is not merely a storage location but functions as a place where energy and information are transformed and move on 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. The energy scale related to this conversion uses Planck energy \( E_P \) as a cutoff:

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

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. Here again, the Planck length \( l_P \) is used as a cutoff.

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. This process, being energy-related, uses Planck energy \( E_P \) as a cutoff.

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. The Planck length \( l_P \) is also used as needed in this context.

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. The Planck length \( l_P \) is used as a cutoff in this context, as it relates to wave numbers and spatial scales.

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. To maintain Lorentz invariance, Planck length \( l_P \) or Planck energy \( E_P \) are appropriately used as cutoff criteria.

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. In this context, both the Planck length \( l_P \) and Planck energy \( E_P \) are used as needed.

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.

The Universe and Consciousness:
Fractal Multidimensional Evolution and the Holographic Theory

The essence of our universe and consciousness may go beyond mere physical phenomena, possibly based on multidimensional connections such as fractal structures, quantum mechanics, multidimensional universes, and the holographic theory. By integrating science and spiritual philosophy, we explore how consciousness transcends matter, expands, and resonates with the vastness of the universe. Here, we consider how consciousness and energy are preserved and evolve multidimensionally, like a hologram.
 
 

1. Multidimensionality of Consciousness and Fractal Structures

 
The multidimensionality of consciousness may not be limited to mere material reactions within the brain, but rather connected to other dimensions on a quantum level. Quantum entanglement demonstrates that matter can exchange information instantaneously across distances, and it is conceivable that consciousness might also exist in dimensions beyond matter. If our consciousness extends beyond the constraints of matter, it can be hypothesized that it is entangled with other dimensions and the universe as a whole, in a quantum sense.
The Schrödinger equation in quantum mechanics describes the wave-like behavior of matter, but if this wave is connected to the multidimensional energy underlying consciousness, a new understanding of consciousness becomes possible.

Schrödinger equation:

$$ i \hbar \frac{\partial}{\partial t} \Psi(\mathbf{r}, t) = \hat{H} \Psi(\mathbf{r}, t) $$

2. Fractal Structures and the Expansion of Consciousness

Fractal theory
 
emphasizes the importance of self-similar patterns repeating at different scales. The large-scale structure of the universe, the neural networks within living organisms, and the spiral structure of DNA are all self-organized and evolving in a fractal manner. Our consciousness may also possess a fractal-like expansion, existing in different dimensions. This structure suggests that consciousness expands multidimensionally in conjunction with the evolution of the universe.
Consciousness, like a fractal, maintains self-similarity while expanding and connecting with the entire universe, building connections that transcend dimensions through quantum entanglement.
 
 

3. Holographic Theory: Preservation of Information and Consciousness

 
The holographic theory suggests that phenomena occurring on the event horizon of black holes imply that three-dimensional information may be preserved on a two-dimensional surface. When extended to consciousness, it raises the possibility that the information of our life and consciousness might also be preserved as a hologram in another dimension of the universe. This suggests that our information may be transferred to a spiritual dimension or an antimatter universe, beyond physical reality.
Just as material energy and information are preserved in holographic dimensions through black holes, our consciousness may also transcend matter, recorded as a hologram in other dimensions.
 
 

4. Multidimensional Energy Conversion in Black Holes

At the event horizon of black holes,
material energy undergoes fluctuations, and through Hawking radiation, it is emitted outward. However, this information may not be entirely lost but transferred to other dimensions. The energy conversion occurring in this process may not merely represent the collapse of matter but could be understood as a multidimensional entanglement of consciousness through quantum energy conversion.
Black holes serve as places where material energy is preserved across dimensions, suggesting that information is transferred to other dimensions. This process may be key to understanding how consciousness and the universe connect and evolve multidimensionally.
 
 

5. Expansion of Consciousness and a Holographic Future

 
As suggested by fractal structures and the holographic theory, the evolution of our consciousness and the universe possesses a multidimensional expansion that transcends material constraints. Through extreme cosmic phenomena like black holes, material and consciousness undergo new energy exchange processes, continually preserved in other dimensions.
As the boundaries between matter and consciousness blur, and energy and information continue to expand fractally, the science of our future will be required to focus beyond material limitations and toward the multidimensional evolution of consciousness.
 
 

Conclusion: Integration of Fractal Multidimensional Evolution and the Holographic Theory

 
Based on fractal structures and the holographic theory, the evolution of our consciousness and the universe suggests an exchange of multidimensional energy and information that transcends matter. Black holes function as gateways to these dimensions, where the information of matter and consciousness is preserved multidimensionally and connected to the antimatter universe or spiritual dimensions.
This perspective provides a new direction for us to transcend material reality, connect with the entire universe through the expansion of consciousness and spiritual growth, and aim for a new fusion of science and philosophy.