Draft:Fractal Universe and Variable Planck Constants

• Comment: Draft is entirely unsourced at time of review ~Liance^talk 17:00, 10 December 2024 (UTC)

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Fractal Universe and Variable Planck Constants

Introduction

The view of the universe is constantly evolving. The theory of the multiverse challenges the idea that our universe is the only one existing. This theory connects concepts of quantum fluctuations, variable fundamental constants, and the hierarchical arrangement of the universe into a single speculative theory. A key role in this theory is played by the Planck constant (ℏ), which influences the energy, length, and time scales of each layer of the universe.

Structure of Empty Space

At first glance, the vacuum may seem like empty space, but quantum field theory shows that it is not. The vacuum is a dynamic structure full of quantum fluctuations, where virtual particles constantly emerge and disappear. These fluctuations have a measurable impact on physical reality. For example, the **Casimir effect** demonstrates how vacuum fluctuations can generate attractive forces between two nearby surfaces.

Quantum Fluctuations and the Formation of Virtual Particles

According to quantum field theory, the vacuum contains oscillating quantum fields that enable the creation and annihilation of particle-antiparticle pairs. This phenomenon is governed by the **Heisenberg uncertainty principle**:

$\Delta E\cdot \Delta t\geq \hbar$

This principle allows for the temporary "borrowing" of energy from the vacuum, leading to the formation of virtual particles. If the Planck constant (ℏ) differs in another layer of the universe, the intensity of quantum fluctuations will also change, significantly affecting the structure of that universe.

Fractal Universe and Variable Planck Constants

The theory of the fractal universe assumes the existence of an infinite hierarchy of universes, each with its own values of fundamental constants:

• **Gravitational constant (G)**
• **Speed of light (c)**
• **Planck constant (ℏ)**

These constants affect the **Planck units** as follows:

• **Planck length**: $l_{P}={\sqrt {\frac {\hbar \,G}{c^{3}}}}$
• **Planck time**: $t_{P}={\sqrt {\frac {\hbar \,G}{c^{5}}}}$
• **Planck energy**: $E_{P}={\sqrt {\frac {\hbar \,c^{5}}{G}}}$

When these constants change, the scales of length, time, and energy in a given layer of the universe also change.

How Planck Constant (ℏ) Differs in Different Layers

• **Lower layers (smaller ℏ)**: A smaller ℏ weakens quantum effects, leading to a more stable vacuum with less pronounced "quantum noise." Quantum fluctuations are weaker, and the vacuum is calmer.
• **Higher layers (larger ℏ)**: A larger ℏ amplifies quantum effects, resulting in more intense quantum fluctuations. The vacuum generates large numbers of high-energy virtual particles. Such fluctuations may even enable the creation of new universes.

Planck Units in Different Layers of the Universe

When ℏ, **G** (gravitational constant), or **c** (speed of light) change, the Planck units also change. These units are defined as follows:

• **Planck length**: $l_{P}={\sqrt {\frac {\hbar \,G}{c^{3}}}}$
• **Planck time**: $t_{P}={\sqrt {\frac {\hbar \,G}{c^{5}}}}$
• **Planck energy**: $E_{P}={\sqrt {\frac {\hbar \,c^{5}}{G}}}$

• • Example of changes in Planck units**:

Suppose ℏ is reduced by half in a lower layer of the universe. How would this affect the Planck units?

1. **Planck length ($l_{P}$)**:

  $l_{P}\propto {\sqrt {\hbar }}$  
  $l_{P}={\sqrt {\frac {0.5\,\hbar \,G}{c^{3}}}}$  
  $l_{P}={\frac {1}{\sqrt {2}}}\,l_{P}$  

  The Planck length shortens, meaning that smaller distances can be measured in this layer.

2. **Planck time ($t_{P}$)**:

  $t_{P}\propto {\sqrt {\hbar }}$  
  $t_{P}={\sqrt {\frac {0.5\,\hbar \,G}{c^{5}}}}$  
  $t_{P}={\frac {1}{\sqrt {2}}}\,t_{P}$  

  The Planck time shortens, meaning that time flows faster in this layer.

3. **Planck energy ($E_{P}$)**:

  $E_{P}\propto {\sqrt {\hbar }}$  
  $E_{P}={\sqrt {\frac {0.5\,\hbar \,c^{5}}{G}}}$  
  $E_{P}={\frac {1}{\sqrt {2}}}\,E_{P}$  

  The Planck energy decreases, which means that less energy is required to create virtual particles, increasing their frequency of appearance.

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1. 1. 1. **The Formation of a Universe from Quantum Fluctuations**

According to the **Heisenberg uncertainty principle**, significant energy can appear for short periods. If the Planck energy in a given layer is high enough, a quantum fluctuation could create a **"pocket" of space** that exponentially expands through inflation, forming an independent universe. This process is analogous to the creation of virtual particles but on a larger energy scale.

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1. 1. 1. **Multiverse and the Infinite Cycle**

The fractal universe theory suggests that our universe is just one of many universes forming a hierarchy of multiverses. Each universe has its own set of fundamental constants that define its size, duration, and physical laws.

- **Lower layers**: More stable vacuum, weaker quantum fluctuations, and faster time flow. - **Higher layers**: Intense vacuum, stronger quantum fluctuations, and slower time flow.

A moment in one layer could correspond to an extremely long period in another. Each layer may appear as a completely different reality to an observer.

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1. 1. 1. **Conclusion**

The theory of the fractal universe with variable fundamental constants provides a fresh perspective on the origin and structure of the universe. Key aspects of this theory include:

• **Variable Planck constants**, which change the scales of time, length, and energy.
• **Quantum fluctuations**, which may create new universes.
• **The concept of a multiverse**, where each universe has its own unique physical properties.

This theory opens the door to new theories that may attempt to explain not only the origin of our universe but also the potential existence of infinite, diverse worlds. It bridges quantum physics, cosmology, and fractal geometry into one coherent framework, offering a possible explanation for the universe's formation through quantum fluctuations and variable fundamental constants.