Draft:Theory of Everything and Equation

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Fluctuation Theory of Vacuum

Author: Jan Šági

Abstract

This document presents a new theory on the origin and structure of the universe based on vacuum fluctuations. Unlike the traditional Big Bang model, this theory describes the origin of the universe as a result of the collective behavior of vacuum oscillations, where the interactions of these fluctuations play an essential role. This theory redefines the concept of matter, gravity, and dark energy. A key contribution is a new equation of everything, which describes the dynamics of matter, dark energy, and interactions in the context of the wave field.

1. Introduction

Modern cosmology is based on the Big Bang model and the existence of invisible dark matter and dark energy. This paper proposes a new approach that replaces the concept of the Big Bang and introduces the term "vacuum fluctuations" as the key mechanism for the origin and structure of the universe.

2. Origin of the Universe

According to this theory, the universe was not created by a singularity but by the spontaneous fluctuation of the vacuum. The energy present in vacuum fluctuations can concentrate in certain areas and create regions with extremely high energy density:

$E_{\text{vac}}=\underset{\text{volume}}{\int }(\frac{1}{2}{\epsilon }_0|\overrightarrow{E}{|}^2+\frac{1}{2{\mu }_0}|\overrightarrow{B}{|}^2)dV$

3. Nature of Matter

Material particles are not fundamental objects but represent local undulations in a larger vacuum wave field. The mass of a particle is directly related to its energy:

$m=\frac{E_{\text{loc}}}{c^2}$

4. Origin of Elementary Particles

Vacuum fluctuations can cause the creation of particle-antiparticle pairs through the following principle:

$E_{\text{osc}}\ge 2m{c}^2$

5. Dynamics of Dark Energy

Dark energy is explained as a result of the transformation of wave energy in a vacuum. The density of dark energy is described by the following equation:

${\rho }_{\text{dark}}={\rho }_{\text{vac}}-\alpha \underset{\text{volume}}{\int }|\mathrm{\nabla }\phi {|}^{2}dV$

6. Gravity as an Emergent Phenomenon

Gravity is described as a consequence of the gradient of phase changes in the wave field. This fact can be expressed by the equation:

$\overrightarrow{g}=-\mathrm{\nabla }\mathrm{\Phi }$

7. Rotational Speed of Galaxies

The theory offers a new way to describe the rotation of galaxies without the need for dark matter. The equation for the maximum rotation speed of a galaxy is:

$v_{\text{max}}^2=\frac{GM}{R}+\frac{\delta E_{\text{vac}}}{\delta r}$

8. Equation of Everything

The theory unifies vacuum energy, dark energy, and matter into a single general equation:

$E_{\text{tot}}=\underset{\text{volume}}{\int }(\frac{1}{2}|\mathrm{\nabla }\phi {|}^2+\frac{1}{2}{m}^2{\phi }^2+{\rho }_{\text{dark}})dV$

9. Strengths of the Theory

• No need for dark matter: Gravity is a natural consequence of phase changes in the vacuum wave field.
• No singularities: The theory does not require a singularity like the Big Bang.
• Unified view of energy: Dark energy, gravity, and matter result from the same mechanism.

10. Weaknesses of the Theory

• Complex simulations: It requires advanced numerical simulations with high computational demands.
• Independent verification: The theory has no direct experimental evidence so far.
• Lack of predictions: To be accepted, the theory needs to present verifiable predictions.

11. Conclusion

The fluctuation theory of vacuum presents a new perspective on the origin and structure of the universe. This theory provides a mechanism for the creation of particles, dark energy, and gravity from a single unified principle. The newly introduced equation of everything combines all these aspects into a single relationship that can be tested through numerical simulations. If this model proves to be correct, it could rewrite modern cosmology.

References

• Hawking, S. "A Brief History of Time", 1988.
• Einstein, A. "Special Theory of Relativity", 1905.