Draft:Fractal Universe and Variable Planck Constants

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 existing one. This theory connects the concepts of quantum fluctuations, variable fundamental constants, and the hierarchical arrangement of the universe into a single speculative framework. The Planck constant (ℏ) plays a key role in this concept, as it determines the energy, length, and time scales of each layer of the universe.

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Structure of Empty Space

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

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Quantum Fluctuations and the Formation of Virtual Particles

Quantum field theory shows that the vacuum contains oscillating quantum fields, which allow for the creation and annihilation of particle-antiparticle pairs. This phenomenon is governed by **Heisenberg's uncertainty principle**:

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

This principle allows for the short-term "borrowing" of energy from the vacuum, which enables the creation of virtual particles. If the Planck constant (ℏ) is different in another layer of the universe, the intensity of quantum fluctuations changes accordingly, significantly affecting the structure of that universe.

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Fractal Universe and Variable Planck Constants

The fractal universe theory proposes the existence of an infinite hierarchy of universes, with each having its own set of fundamental constants, such as:

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

These constants directly affect the so-called **Planck units**:

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

If these constants change, the scales of length, time, and energy also change accordingly in each layer of the universe.

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How Planck Constant (ℏ) Differs in Different Layers

• **Lower layers (smaller ℏ)**: A smaller value of ℏ weakens quantum effects, leading to a more stable and calmer vacuum with less "quantum noise." As a result, quantum fluctuations are weaker, and the vacuum appears more stable.
• **Higher layers (larger ℏ)**: A larger value of ℏ strengthens quantum effects. This leads to intense quantum fluctuations where the vacuum generates a large number of virtual particles with higher energy. Such fluctuations may even allow for the creation of new universes from a single quantum fluctuation.

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Planck Units in Different Layers of the Universe

If 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**: $E_{P}={\sqrt {\frac {\hbar c^{5}}{G}}}$

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1. 1. 1. **Example of Changes in Planck Units**

Imagine that in a lower layer of the universe, the value of ℏ is reduced by half. How does this affect the Planck units?

1. **Planck length (lₚ)**

  \[
  l_P \propto \sqrt{\hbar} \implies l_P \to \frac{1}{\sqrt{2}} \, l_P
  \]
  A shorter Planck length implies that the smallest possible distance in this universe is shorter than in our universe.

2. **Planck time (tₚ)**

  \[
  t_P \propto \sqrt{\hbar} \implies t_P \to \frac{1}{\sqrt{2}} \, t_P
  \]
  Planck time is also reduced, which means that time in this layer of the universe flows faster than in our universe.

3. **Planck energy (Eₚ)**

  \[
  E_P \propto \sqrt{\hbar} \implies E_P \to \frac{1}{\sqrt{2}} \, E_P
  \]
  Planck energy decreases, meaning that less energy is required to create a virtual particle. As a result, more virtual particles could appear in this universe.

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1. 1. 1. **Summary of Changes**

| **Planck Unit** | **Change** | **Effect** | |-----------------|----------------------------------------|-----------------------------------------------| | **Planck length** | Decreases ($l_{P}\to {\frac {1}{\sqrt {2}}}l_{P}$) | Shorter distances, smaller particles. | | **Planck time** | Decreases ($t_{P}\to {\frac {1}{\sqrt {2}}}t_{P}$) | Time flows faster. | | **Planck energy** | Decreases ($E_{P}\to {\frac {1}{\sqrt {2}}}E_{P}$) | Less energy needed to create particles. |

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Formation of a Universe from Quantum Fluctuations

Heisenberg's uncertainty principle allows for large amounts of energy to be created even over extremely short time scales. If Planck energy in a particular layer of the universe is sufficiently high, a quantum fluctuation can create a **"pocket" of space**, which exponentially expands due to inflation and becomes an independent universe. This process is analogous to the creation of virtual particles but on a much larger energy scale.

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Multiverse and the Infinite Cycle

According to the theory of the fractal universe, our universe is just one of many in a hierarchy of multiverses. Each of these universes has different fundamental constants that affect its size, duration, and physical laws.

• **Lower layers**: Stable vacuum, weaker quantum fluctuations, faster time flow.
• **Higher layers**: Intense vacuum, stronger quantum fluctuations, slower time flow.

What may seem like a moment in one layer can be an extremely long period in another layer. Thus, each layer can appear to the observer as a completely different reality.

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Expansion of the Universe and Its End

The expansion of the universe, driven by dark energy, may result from interactions with higher layers of the fractal universe. As our universe continues to expand at an accelerating rate, individual regions of space become isolated, which could lead to its "end." At this point, all particles lose the ability to interact, time loses its meaning, and all borrowed energy returns to the vacuum.

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Conclusion

The theory of the fractal universe with variable fundamental constants provides a fascinating view of the origin and structure of the universe. The key aspects of this theory include:

• **Variable Planck constants**, which change the scales of time, length, and energy.
• **Quantum fluctuations**, which can give rise to new universes.
• **The concept of a multiverse**, where each universe has unique physical properties.

This perspective opens the door to new theories that could attempt to explain not only the origin of our universe but also the possibility of an infinite diversity of other worlds. This theory connects quantum physics, cosmology, and fractal geometry into a coherent framework capable of explaining the origin of the universe through quantum fluctuations and variable fundamental constants.

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