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

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

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

1. The Standard Einstein Equation in General Relativity

1.1 The Standard Einstein Equation

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

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

Where:

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

2. The Expansion of the Einstein Equation through Zero Theory

2.1 Overview of Zero Theory

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

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

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

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

3.1 Overview of the New Definition

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

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

3.2.1 What is Gravitational Lensing?

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

3.2.2 The Role of Vacuum

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

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

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

4.1 The Mechanism for Maintaining Galactic Rotation Speed

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

5. Why Gravitational Lensing Proves the Theory

5.1 Unified Understanding of E=mc² and Energy

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

5.1.1 Redefinition of Dark Matter

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

5.1.2 Reinterpretation of Gravitons

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

6. Conclusion and Future Prospects

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

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

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

Gravitational Lensing and Vacuum as a Medium for Energy Transmission

1. What is Gravitational Lensing?

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

2. Understanding Vacuum as an Energy Transmission Medium

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

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

Why Gravitational Lensing Proves the Theory

1. Unified Understanding of E=mc² and Energy

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

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

2. Gravitational Lensing as Proof of the Energy Transformation Theory

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

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

3. The Phenomena Themselves Prove the Theory

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

An Analogy for Understanding: The Vibrating String Model

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

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

Conclusion: Observational Phenomena as Proof of the Energy Transformation Theory

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

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

Overview of the Zero Energy Cycle Theory

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

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

The Relationship Between Observation Points and Multiverse Theory

Universe Generated by Fluctuations:

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

Observation Points A and A':

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

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

The Relativity of Size and Time and Consistency with Relativity Theory

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

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

The Relationship Between Energy and Vacuum Fluctuations

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

1. Dynamic Generation and Annihilation of Energy

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

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

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

2. Generation and Complementarity of Matter and Antimatter

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

Extended Analogies

1. Analogy of Electromagnets and Iron Sand

Iron Sand in an Electromagnet:

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

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

Zero Point Energy and Vacuum Fluctuations

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

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

Additional Implications for Current Theories

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

The Symmetry Between the Physical and Spiritual Worlds

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

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

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

1. Introduction

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

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

2. Perspectives of Observation Points A and A'

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

2.1 Observation Point A (External Perspective)

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

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

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

2.2 Observation Point A' (Internal Perspective)

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

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

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

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

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

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

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

3.1 Fractal Structure and Self-Similarity of Vacuum Fluctuations

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

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

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

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

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

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

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

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

4.2 Consistency with Quantum Electrodynamics

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

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

This approach enables a bridge between quantum mechanics and cosmology.

5. Conclusion

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

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

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 a theory based on the idea that the expansion and contraction of the universe are driven by energy exchange processes, maintaining the total energy of the universe at zero. As an alternative to the conventional ΛCDM model, this theory presents the following key characteristics.

1.1 Fractal Structure and Energy Conservation

In the Zero Theory, the large-scale structure of the universe is considered to have 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 linked to the law of conservation of energy across the entire universe.

According to this theory, the total energy of the universe is kept at zero by the mutual cancellation of matter energy, antimatter energy, and gravitational energy. This dynamic exchange of energy between expansion and contraction is expressed by 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, keeping the universe's energy always at zero.

1.2 Role of Observation Points A and A'

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

- Observation Point A (External Perspective): This is a viewpoint observing our universe from the outside, where processes like the creation of matter and antimatter through vacuum fluctuations and energy exchanges with the antimatter universe can be observed.

- Observation Point A' (Internal Perspective): This viewpoint observes the distribution of matter and antimatter and the fractal structure within the universe. This helps evaluate the relationship between the universe's energy exchange processes and the external viewpoint.

Through these multidimensional observation perspectives, 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. Interactions driven by gravity and energy exchange organize galaxies and galaxy clusters hierarchically, facilitating efficient energy distribution. This structure is expressed by the following scaling laws:

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

Here, \(M(R)\) represents the mass within radius \(R\), and \(N(R)\) represents the number of galaxies within radius \(R\), with \(D\) being the fractal dimension. This scaling law demonstrates that the distribution of galaxies has a fractal structure, which explains the efficient energy distribution in the evolution of the universe.

1.4 Reinterpretation of Dark Energy

The interpretation of dark energy in the Zero Theory differs significantly from the current ΛCDM model. In the ΛCDM model, dark energy is considered the primary factor causing the accelerated expansion of the universe, while in the Zero Theory, it is interpreted as a 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 itself is driven by external factors, and the term corresponding to dark energy, \( \rho_{\text{energy exchange}} \), represents the energy exchange that occurs as a result of expansion. As the universe expands, energy is generated from vacuum fluctuations caused by fluctuations in the matter and antimatter densities, and energy is exchanged.

- In the ΛCDM model, dark energy is considered to exist uniformly throughout the universe and is viewed as the main factor driving expansion. The ΛCDM model posits that dark energy directly causes the expansion of the universe and is seen as the fundamental cause of expansion.

The Zero Theory suggests that energy exchange does not directly trigger expansion, but rather occurs as a result of expansion caused by external factors. This mechanism of energy exchange explains the process by which energy is generated and annihilated between matter and antimatter.

2. Equations and Theoretical Background of the Zero Theory

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, as shown below:

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

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

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 and pressure of matter and antimatter contribute to the accelerated expansion or contraction of the universe.

3. Energy Fluctuations due to the Uncertainty Principle

The uncertainty principle of quantum mechanics influences the universe's energy exchange process, introducing fluctuations into 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 expansion and contraction of the universe form an unstable pattern without a perfect cycle.

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

In the Zero Theory, the universe is assumed to have a shape close to a sphere, but its internal structure is flat. As a result, the propagation of light continues in a straight line, and the conventional concept of light bending due to curvature is not considered.

Moreover, even if the universe has curvature, it is difficult to detect relative changes in curvature because both the observer and the photons follow the same reference frame. Local phenomena such as the bending of light due to distortions around black holes or galaxies are interpreted as different 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 also 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.

A New Concept of Dark Energy

Dark Energy and the Expansion-Contraction Cycle in Zero Theory

Interpretation of Energy Exchange in the Zero Theory

In the Zero Theory, the expansion of the universe is triggered by external factors, and the term corresponding to dark energy, \(\rho_{\text{energy exchange}}\), represents the energy exchange resulting from this expansion. This energy exchange is activated by vacuum fluctuations accompanying changes in the density of matter and antimatter. Due to these fluctuations, pairs of particles and antiparticles are generated and annihilated, forming the basis of the energy exchange process.

The energy density from vacuum fluctuations usually diverges to infinity. To address this, a cutoff at the Planck energy is introduced to make the energy density based on vacuum fluctuations finite and physically meaningful. Specifically, the energy density is calculated as follows:

\[ \rho_{\text{vacuum fluctuations}}(t) = \int_{0}^{E_P} \frac{g(E) E}{(2\pi)^3} dE \]

Here, \( E_P \) represents the Planck energy, a cutoff based on physical scales. This cutoff prevents the vacuum energy density from diverging to infinity, maintaining the consistency of the theory.

Specifically, as the universe expands, the density decreases, leading to the occurrence of vacuum fluctuations. These fluctuations are similar to those that occurred just after the Big Bang and involve the generation and annihilation of energy. As the expansion progresses, energy is exchanged between matter and antimatter, potentially influencing the formation of large-scale structures and the distribution of matter in the universe.

In equations, the energy exchange process is described as follows:

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

- \(f(a(t))\) is a function dependent on the scale factor \(a(t)\), indicating the influence of vacuum fluctuations during expansion.
- \(\rho_{\text{vacuum fluctuations}}(t)\) is the energy density caused by vacuum fluctuations.

This energy exchange process is a dynamic one where energy is generated and annihilated between matter and antimatter, occurring as a result of the expansion. In the Zero Theory, this energy exchange is equivalent to dark energy, though it does not directly cause the expansion itself. The expansion is triggered by external factors, and energy exchange is activated as a result.

Interpretation of Dark Energy in the Current ΛCDM Model

In the current ΛCDM model, dark energy is introduced to explain the accelerated expansion of the universe. Dark energy \(\rho_{\text{dark energy}}\) is considered to be uniformly distributed throughout the universe and is the main cause of the acceleration of cosmic expansion. Dark energy is directly incorporated into the Friedmann equation, playing the role of driving the accelerated expansion.

Comparison of Interpretations Reflecting the Theoretical Differences

Summary of the Theories

In the Zero Theory, the energy exchange equivalent to dark energy is a secondary phenomenon arising from the expansion of the universe. Vacuum fluctuations occur due to changes in the density of matter and antimatter, leading to energy exchange. This process is similar to the fluctuations that occurred after the Big Bang and affects the evolution of the universe, but it does not cause the expansion itself.

Based on this idea, the Friedmann equation in the Zero Theory is described as follows:

\[ H^2(t) = \frac{8\pi G}{3} \left[ \rho_{\text{matter}}(t) + \rho_{\text{radiation}}(t) + f(a(t)) \cdot \rho_{\text{vacuum fluctuations}}(t) \right] - \frac{k}{a^2(t)} \]

This equation specifically represents the impact of energy exchange due to vacuum fluctuations on the expansion of the universe. In contrast, in the ΛCDM model, dark energy is considered the primary driver of cosmic expansion, directly causing the acceleration.

Summary of the Theories

Introduction of the Equation of State

It is also essential to consider the equation of state for dark energy. In the ΛCDM model, the equation of state parameter for dark energy \( w \) is always \( w = -1 \), meaning that the density of dark energy remains constant. However, in the Zero Theory, the equation of state parameter \( w \) is allowed to vary with time or depend on the scale factor \( a(t) \).

The equation of state is expressed as follows:

\[ p = w \rho \]

Here, \( p \) represents pressure, and \( \rho \) represents energy density. In the Zero Theory, the time variability of \( w \) or its dependence on the scale factor plays a role in describing the dynamic nature of dark energy.

Modeling Energy Conservation and Energy Exchange

Energy Exchange Dependent on the Scale Factor

By incorporating energy exchange into the law of energy conservation (continuity equation), the dynamics of energy conservation in the universe can be explained. The energy conservation equation in the Zero Theory is represented as follows:

\[ \dot{\rho}_{\text{total}} + 3H (\rho_{\text{total}} + p_{\text{total}}) = Q(t) \]

Here, \( Q(t) \) is a source term for energy exchange, indicating how energy exchange is involved in the law of energy conservation.

To quantitatively model the energy exchange process, the following equation is used:

\[ Q(t) = \gamma \cdot \rho_{\text{energy exchange}}(t) \cdot H(t) \]

This equation expresses that energy exchange occurs in proportion to the Hubble parameter \( H(t) \) and energy density. \( \gamma \) is a constant representing the efficiency of energy exchange.

Energy Exchange Dependent on the Scale Factor

Introduction of the Function

In the Zero Theory, the strength of energy exchange is considered to depend on the scale factor \( a(t) \). The function \( f(a(t)) \), dependent on the scale factor, describes how energy exchange decays over time.

The following function is introduced to model this:

\[ f(a(t)) = e^{-\beta a(t)} \]

Here, \( \beta \) is a constant representing the decay rate of energy exchange. This model shows that energy exchange decreases exponentially as the scale factor increases.

New Theory: The Role of Vacuum Energy in Unifying All Phenomena through Energy Conversion

The new theory reinterprets the individual concepts of traditional physics (photons, gravity, dark energy, dark matter, gravitons, etc.) through the perspective that "everything can be explained by energy conversion." This approach, based on Einstein's famous energy-mass equivalence equation \(E=mc^2\), understands physical phenomena as a series of processes of energy conversion. Additionally, by applying Zero Theory to Einstein's equations, it delves deeper into how vacuum energy density influences the curvature of spacetime. This article elaborates on this new perspective, focusing on the dynamic role of vacuum energy, forces arising from energy conversion, the transmission of photons and gravity, the reinterpretation of dark energy and dark matter, the understanding of quantum entanglement, and the redefinition of the law of energy conservation.

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1. Reinterpretation of Vacuum Energy

1.1 The Dynamic Role of Vacuum Energy as Energy Conversion

In traditional physics, the vacuum is often considered an empty space without energy. However, the new theory interprets the vacuum as a field with zero-point energy fluctuations, viewing the vacuum itself as the primary stage for energy conversion. This perspective posits that fluctuations in the vacuum's energy density are the foundation for all physical phenomena.

Equation:

The expectation value of zero-point energy is expressed as follows:

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

This equation indicates that vacuum fluctuations cause finite energy variations. Here, the cutoff wave number \( k_{\text{max}} \) is set using the Planck length \( l_P \), preventing the divergence of vacuum energy to infinity.

\[k_{\text{max}} = \frac{1}{l_P}, \quad l_P = \sqrt{\frac{\hbar G}{c^3}}\]

This setting shows how energy conversion occurs at the smallest physical scale (Planck length), providing the foundation for the new theory.

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2. Extension of Einstein's Equation with Zero Theory

2.1 Application of Zero Theory to Einstein's Equation

Applying Zero Theory to Einstein's equation clarifies that vacuum energy density directly influences the curvature of spacetime. In traditional general relativity, the distribution of matter and energy determines the structure of spacetime, but Zero Theory adds the influence of vacuum energy to this relationship.

Extended Einstein's Equation with Zero Theory:

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

This equation shows that in addition to the distribution of matter and energy, the vacuum energy density \(\rho_{\text{vac}}\) contributes to the curvature of spacetime. It emphasizes that vacuum energy is not merely a background energy but a dynamic element actively shaping the structure of spacetime.

2.2 Relationship between Dark Energy and the Cosmological Constant

In this extended equation, the dynamic changes in vacuum energy density play the role of dark energy, providing a deeper understanding beyond the traditional static cosmological constant \(\Lambda\). This naturally explains the accelerated expansion of the universe as a result of energy conversion.

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3. Forces Arising from Energy Conversion

3.1 Definition: Attractive Forces Generated by Distortion of Cosmic Medium through Energy Conversion

Attractive forces that arise from the distortion of the cosmic medium caused by energy conversion.

3.2 Concept: The Mechanism by which Energy Conversion Distorts the Medium (Spacetime), Generating Attractive Forces

Energy conversion distorts the medium (spacetime), resulting in the generation of attractive forces. This mechanism demonstrates that local changes in energy affect the entire medium. The mechanisms of these two forces are based on different energy conversions and interactions within the framework of Zero Theory, making them essential elements for explaining the dynamics of the universe.

3.3 Analogy between General Relativity and Zero Theory

3.3.1 Explanation of Gravity in General Relativity

Curvature of Space:

In Einstein's general relativity, mass and energy curve spacetime, and this curvature exerts gravitational forces on other objects. The heavier an object, the more it curves the surrounding spacetime, causing other objects to move along these curves.

3.3.2 Analogy in Zero Theory

Thread and Pattern Analogy:

In Zero Theory, the universe is likened to a "medium" like a thread, with energy conversions "weaving" patterns into it. By weaving patterns into the thread, the surrounding energy and matter are drawn in, creating gravitational-like forces. These patterns represent the vibrations or conversions of energy within the medium, illustrating the mechanism by which attractive forces are generated.

3.4 Detailed Explanation of the Analogy

Vibrations of the Thread and Gravity:

In Zero Theory, energy conversion causes the medium (thread) to vibrate, creating "patterns" that manifest as gravitational-like phenomena. These vibrations influence the entire universe, explaining how energy conversions lead to the attraction between objects. This perspective views energy conversion as altering the properties of the medium, resulting in the emergence of gravitational forces.

Universality of the Medium:

In Zero Theory, the medium (thread) exists throughout the universe, and energy conversions within this medium distort it, generating forces similar to gravity. This universal presence allows energy conversions to influence the structure of spacetime consistently, providing a unified explanation for gravitational phenomena and energy interactions.

3.5 Understanding Gravity in Zero Theory

3.5.1 Origin of Attractive Forces:

In Zero Theory, attractive forces arise from the interaction between the cosmic medium and energy conversions. Here, the "cosmic medium" represents the state of energy conversion and fluctuations within the universe.

3.5.2 Macroscale Phenomena:

At cosmic scales, the attraction is considered a result of the circulation and conversion of energy within Zero Theory. Attractive forces are derived from the distortions and energy distributions in the medium, understood as phenomena observable at macroscopic scales.

3.6 Examination of Theoretical Consistency

3.6.1 Consistency within the Framework of Zero Theory

Energy Conversion and Attraction:

Zero Theory views the universe as a "medium," with energy conversions and fluctuations generating attractive forces. The explanation that attractive forces are a result of energy redistribution and conversion is consistent within the theory.

Fluctuations of the Medium:

In this theory, attractive forces emerge as interactions within the cosmic medium, meaning that fluctuations and energy variations within the medium directly generate these forces. This explains how attractive forces are produced as a consequence of energy transformations within the medium.

3.6.2 Consistency with Other Theories

Consistency with Relativity:

Gravity, explained by the curvature of spacetime in relativity, and gravity described in Zero Theory as vibrations or conversions in the cosmic medium, contribute to explaining the same phenomenon (gravity) through different mechanisms. While the mechanisms differ, both aim to describe the gravitational force's effects.

Consistency with Quantum Mechanics:

If quantum entanglement and state changes based on Zero Theory's energy conversion, they must align with established results in quantum mechanics. How Zero Theory integrates these phenomena within its framework is crucial for maintaining consistency with quantum theory.

3.6.3 Experimental Verification

Confirmation of Theoretical Consistency:

Alignment with experimental data is essential. Whether the forces and energy conversions predicted by Zero Theory match observations and experimental results is critical.

New Experimental Approaches:

To verify the new predictions of Zero Theory, new experiments and observations are required. This includes precise measurements of energy conversions and the resulting forces within the cosmic medium.

3.7 Conclusion

The interpretation of attractive forces within Zero Theory conceptualizes the universe as a "medium," with energy conversions and fluctuations generating these forces. This approach explains how attractive forces emerge as a result of energy redistribution and conversion within the medium, providing a clear explanation of how these forces influence the motion and dynamics of matter.

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4. Relationship between Zero Theory and Dark Energy, Dark Matter

4.1 Dark Energy: Cosmic Expansion as Energy Conversion

Concept:
Dark energy is the energy responsible for the accelerated expansion of the universe. It is uniformly distributed throughout the cosmos and affects space itself.

Relation to Zero Theory:

- Energy Vibrations:
In Zero Theory, changes in cosmic expansion and gravitational variations are explained by the vibrations and conversions of energy within the cosmic medium. The effects of dark energy can potentially be understood as energy conversions within Zero Theory's cosmic medium.

- Relation to Gravity:
While dark energy works against the effects of gravity, Zero Theory explains gravity as arising from energy vibrations and conversions within the medium. The influence of dark energy could also be explained through these energy conversions within the medium.

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4.2 Dark Matter

Concept:
Dark matter is traditionally considered a hypothetical substance that accounts for the missing mass required to form and sustain galaxies. It interacts through gravity but is invisible and does not emit, absorb, or reflect light.

Relation to Zero Theory:

- Energy Vibrations:
In Zero Theory, the presence and behavior of matter and gravity are explained by energy vibrations and conversions within the cosmic medium. The gravitational effects of dark matter can be understood as the influence of energy conversions within Zero Theory's medium.

- Relation to Gravity:
Dark matter interacts gravitationally with ordinary matter, and in Zero Theory, gravity is generated by vibrations and conversions in the cosmic medium. Thus, the effects of dark matter can be explained based on the changes in the medium's energy.

\[\nabla^2 \Phi = 4\pi G \left( \rho_m + \delta \rho_{\text{vac}} \right)\]

Here, \(\delta \rho_{\text{vac}}\) represents fluctuations in vacuum energy density, understood not as a material entity but as a distortion in spacetime, characterized by the Planck length \( l_P \).

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5. Redefinition of Gravitons: Understanding as Mediators of Energy Conversion

Gravitons are traditionally considered quantum particles that mediate gravity in quantum mechanics. However, the new theory reinterprets them as part of the energy conversion process itself. Gravity is seen as a phenomenon transmitted through fluctuations in vacuum energy, eliminating the need to assume the existence of gravitons as virtual particles.

In this new interpretation, vacuum energy itself acts as the medium of space, with distortions in space manifesting as increases in density, observed as gravity. Thus, the conversion of vacuum energy directly shapes the structure of spacetime and generates gravitational phenomena.

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6. Reinterpretation of Quantum Entanglement and Vacuum Energy

6.1 The Role of Non-Local Correlation and Vacuum Energy

Quantum entanglement is interpreted as a phenomenon where energy states mutually influence each other through the vacuum energy field. This perspective explains why the correlation between entangled particles is maintained regardless of distance, from the viewpoint of energy conversion.

\[\langle \psi_1 | \hat{O} | \psi_2 \rangle = \int e^{-i\omega t} \delta \rho_{\text{vac}}(x, t) dx\]

This equation indicates that fluctuations in vacuum energy play a role in maintaining the correlation between entangled particles.

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7. Unified Understanding through Vacuum Energy Conversion

7.1 Common Mechanism of Photons and Gravity

Photons and gravity are understood as phenomena transmitted through the conversion of vacuum energy. This common mechanism explains how energy state transformations are linked to various physical phenomena.

\[E_{\text{photon}} = \hbar \omega, \quad G_{\mu\nu} = 8\pi G \rho_{\text{vac}} g_{\mu\nu}\]

This shows that both photons and gravity rely on the fluctuations in vacuum energy through a shared mechanism.

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8. Conclusion: Consistency of the New Theory from the Perspective of Energy Conversion

The new theory aims to explain all physical phenomena through processes of energy conversion, providing a consistent framework for understanding photons, gravity, dark energy, dark matter, and quantum entanglement. By applying Zero Theory, the impact of vacuum energy density on the curvature of spacetime is clearly articulated in mathematical terms, enabling a unified understanding that maintains consistency with current physical theories while offering new interpretations. This approach returns to the foundations of Einstein's \(E=mc^2\), offering a simpler and more coherent theoretical system.

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Appendix: Importance of Theoretical Consistency and Experimental Verification

To ensure the consistency and reliability of the new theory, the following points are essential:

1. Detailed Mechanism Elucidation:
   Strengthening the physical basis of the theory by providing detailed explanations of energy conversion processes and mechanisms.
2. Examination of Consistency with Observational Data:
   Comparing the theory's predictions with observational data (e.g., cosmic microwave background radiation, galaxy rotation curves, gravitational lensing effects) to ensure alignment.
3. Theoretical Predictions and Experimental Verification:
   Enhancing the theory's practicality and reliability by outlining specific predictions and how they can be experimentally verified.
4. Clarification of Terminology:
   Defining and explaining unique terms and concepts within the new theory to facilitate reader understanding.
5. Theory's Limitations and Future Prospects:
   Discussing the current limitations of the new theory and outlining future research directions to address unresolved challenges.

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The above content provides a detailed explanation with mathematical equations necessary to comprehensively describe the new theory. By integrating Zero Theory with the new theory, a comprehensive physical model based on energy conversion is presented, offering a new perspective on existing physical theories. Future research and experimental verification are expected to further elucidate the validity and consistency of this theory.

Transmission of Photons and Gravity
Using the Vacuum as a Medium

New Theory: The Role of Vacuum Energy in Unifying All Phenomena through Energy Conversion

The new theory reinterprets the individual concepts of traditional physics (photons, gravity, dark energy, dark matter, gravitons, etc.) through the perspective that "everything can be explained by energy conversion." This approach, based on Einstein's famous equation \(E=mc^2\), understands physical phenomena as a series of processes of energy conversion. Additionally, by applying Zero Theory to Einstein's equation, it further explores how vacuum energy density influences the curvature of spacetime. This article elaborates on this new perspective, focusing on the dynamic role of vacuum energy, the transmission of photons and gravity, the reinterpretation of dark energy and dark matter, the understanding of quantum entanglement, and the redefinition of the law of energy conservation.

1. Reinterpretation of Vacuum Energy

1.1 The Dynamic Role of Vacuum Energy as Energy Conversion

In traditional physics, the vacuum is often considered an empty space without energy. However, the new theory interprets the vacuum as a field with zero-point energy fluctuations, viewing the vacuum itself as the primary stage for energy conversion. This perspective posits that fluctuations in the vacuum's energy density are the foundation for all physical phenomena.

Equation:

The expectation value of zero-point energy is expressed as follows:

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

This equation indicates that vacuum fluctuations cause finite energy variations. Here, the cutoff wave number \( k_{\text{max}} \) is set using the Planck length \( l_P \), preventing the divergence of vacuum energy to infinity.

\[k_{\text{max}} = \frac{1}{l_P}, \quad l_P = \sqrt{\frac{\hbar G}{c^3}}\]

This setting shows how energy conversion occurs at the smallest physical scale (Planck length), providing the basis for the new theory.

2. Extension of Einstein's Equation with Zero Theory

2.1 Application of Zero Theory to Einstein's Equation

Applying Zero Theory to Einstein's equation reveals that vacuum energy density directly influences the curvature of spacetime. In traditional general relativity, the distribution of matter and energy determines the structure of spacetime, but Zero Theory adds the influence of vacuum energy to this relationship.

Extended Einstein's Equation with Zero Theory:

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

This equation shows that in addition to the distribution of matter and energy, the vacuum energy density \(\rho_{\text{vac}}\) contributes to the curvature of spacetime. It emphasizes that vacuum energy is not merely a background energy but a dynamic element actively shaping the structure of spacetime.

2.2 Relationship between Dark Energy and the Cosmological Constant

In this extended equation, the dynamic changes in vacuum energy density play the role of dark energy, providing a deeper understanding beyond the traditional static cosmological constant \(\Lambda\). This naturally explains the accelerated expansion of the universe as a result of energy conversion.

3. Unified Explanation of Photons and Gravity

3.1 Reinterpretation of the Wave-Particle Duality of Photons

While photons are traditionally known to possess both wave-like and particle-like properties, the new theory views the existence of photons as a transient phenomenon resulting from the dynamic conversion of vacuum energy. The wave and particle nature of photons are reinterpreted as energy states arising from local fluctuations in vacuum energy density.

\[E = h\nu\]

This equation shows that the energy of photons is determined by the conversion of vacuum energy, explaining how the propagation of light depends on the energy density of the vacuum.

3.2 Relationship between Gravity and Energy Conversion

In the new theory, gravity is also interpreted as a result of the energy conversion of the vacuum. Gravitational potential depends on fluctuations in vacuum energy density, which cause the curvature of spacetime.

\[\nabla^2 \Phi = 4\pi G \left( \rho_m + \delta \rho_{\text{vac}} \right)\]

Here, \(\delta \rho_{\text{vac}}\) represents the fluctuation in vacuum energy density, clearly showing that gravity is not a material entity but a curvature of spacetime based on energy conversion.

4. Reinterpretation of Dark Energy and Dark Matter

4.1 Dark Energy: Cosmic Expansion as Energy Conversion

Dark energy is traditionally understood as the energy responsible for the accelerated expansion of the universe. However, the new theory interprets it as energy conversion resulting from temporal fluctuations in vacuum energy. This approach explains dark energy based on the fluctuations in the universe's energy density.

\[\rho_{\text{vac}}(t) = \rho_{\text{vac},0} \left( \frac{a_0}{a(t)} \right)^n\]

This equation demonstrates that the effects of dark energy stem from the dynamic variations in vacuum energy. As the universe expands, the vacuum energy density decreases, leading to fluctuations in the vacuum, which serve as the source of energy, manifesting as dark energy.

4.2 A New Understanding of Dark Matter: Energy Conversion of the Vacuum

Dark matter has traditionally been considered a hypothetical substance needed to account for the mass required to form and maintain galaxies. However, the new theory reinterprets dark matter not as a form of matter but as local fluctuations in vacuum energy density. These fluctuations create distortions in spacetime, observed as gravitational effects.

Furthermore, this approach supports the hypothesis that "dark matter equals the vacuum itself." In other words, the vacuum itself compensates for the missing mass required for galaxy formation and maintenance through energy conversion. This perspective allows dark matter to be understood not as a hypothetical substance but as a phenomenon originating from the energy conversion of the vacuum.

\[\nabla^2 \Phi = 4\pi G \left( \rho_m + \delta \rho_{\text{vac}} \right)\]

Here, \(\delta \rho_{\text{vac}}\) represents fluctuations in vacuum energy density, understood not as a material entity but as a distortion in spacetime, characterized by the Planck length \( l_P \).

5. Redefinition of Gravitons: Understanding as Mediators of Energy Conversion

Gravitons are traditionally considered quantum particles that mediate gravity. However, the new theory reinterprets them as part of the energy conversion process itself. Gravity is seen as a phenomenon transmitted through fluctuations in vacuum energy, eliminating the need to assume the existence of gravitons as virtual particles.

In this new interpretation, vacuum energy itself acts as the medium of space, with the distortion of space manifesting as an increase in density, observed as gravity. Thus, vacuum energy conversion is directly responsible for forming the structure of spacetime and generating gravitational phenomena.

6. Reinterpretation of Quantum Entanglement and Vacuum Energy

6.1 The Role of Non-Local Correlation and Vacuum Energy

Quantum entanglement is interpreted as a phenomenon in which energy states mutually influence each other through the vacuum energy field. This perspective explains why the correlation between entangled particles is maintained regardless of distance, from the viewpoint of energy conversion.

\[\langle \psi_1 | \hat{O} | \psi_2 \rangle = \int e^{-i\omega t} \delta \rho_{\text{vac}}(x, t) dx\]

This equation indicates that fluctuations in vacuum energy play a role in maintaining the correlation between entangled particles.

7. Unified Understanding through Vacuum Energy Conversion

7.1 Common Mechanism of Photons and Gravity

Photons and gravity are understood as phenomena transmitted through the conversion of vacuum energy. This common mechanism explains how energy state transformations are linked to various physical phenomena.

\[E_{\text{photon}} = \hbar \omega, \quad G_{\mu\nu} = 8\pi G \rho_{\text{vac}} g_{\mu\nu}\]

This shows that both photons and gravity rely on the fluctuations in vacuum energy through a shared mechanism.

8. Conclusion: Consistency of the New Theory from the Perspective of Energy Conversion

The new theory aims to explain all physical phenomena through processes of energy conversion, providing a consistent framework for understanding photons, gravity, dark energy, dark matter, and quantum entanglement. By applying Zero Theory, the impact of vacuum energy density on the curvature of spacetime is clearly articulated in mathematical terms, enabling a unified understanding that maintains consistency with current physical theories while offering new interpretations. This approach returns to the foundations of Einstein's \(E=mc^2\), offering a simpler and more coherent theoretical system.

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 Uncertainty 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.