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 theory. Planck constants play a key role in this concept, as they determine the energy, length, and time scales of each layer of the universe.

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, although short-term, have a real 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

Quantum field theory shows that the vacuum is a "boiling soup" of oscillating quantum fields that enable 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 allows for the creation of virtual particles. If the values of fundamental constants, such as the Planck constant (ℏ), differ in other layers of the universe, quantum fluctuations can occur with different intensities, significantly affecting the structure of the given universe.

Fractal Universe and Variable Planck Constants

The theory of the fractal universe assumes that universes form an infinite hierarchy of layers, with each layer having its own fundamental constants, such as:

• Gravitational constant ($G$)
• Speed of light ($c$)
• Planck constant ($\hbar$)

These constants directly affect Planck units:

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

How Planck Constant (ℏ) Differs in Different Layers

• **Lower layers (smaller ℏ)**: If ℏ is smaller, quantum effects are weaker. As a result, quantum fluctuations in the vacuum would have less intensity, possibly leading to a more stable and calmer vacuum. In such a universe, "quantum noise" would be less pronounced.
• **Higher layers (larger ℏ)**: If ℏ is larger, quantum effects become more pronounced. This could lead to extremely strong quantum fluctuations where the vacuum constantly generates large amounts of virtual particles with higher energy. This could potentially allow for the creation of new universes from a single quantum fluctuation.

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 by the following equations:

• **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, ℏ is reduced by half. What happens to the Planck units?

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

  :$l_{P}={\sqrt {\frac {\hbar G}{c^{3}}}}\implies l_{P}\sim {\sqrt {\frac {0.5\cdot \hbar \cdot G}{c^{3}}}}={\frac {1}{\sqrt {2}}}\cdot l_{P}$

  This means that the Planck length is shortened, indicating that the smallest possible length in this universe is smaller than in our universe.

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

  :$t_{P}={\sqrt {\frac {\hbar G}{c^{5}}}}\implies t_{P}\sim {\frac {1}{\sqrt {2}}}\cdot t_{P}$

  The Planck time is also reduced, which means that the time scale in this universe runs faster than in our universe.

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

  :$E_{P}={\sqrt {\frac {\hbar c^{5}}{G}}}\implies E_{P}\sim {\frac {1}{\sqrt {2}}}\cdot E_{P}$

  Planck energy decreases, which means that the amount of energy required to create a virtual particle is lower. 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 ($l_{P}\to {\frac {1}{\sqrt {2}}}l_{P}$) | Smaller particles and shorter distances. | | **Planck time** | Decreases ($t_{P}\to {\frac {1}{\sqrt {2}}}t_{P}$) | Time runs faster. | | **Planck energy** | Decreases ($E_{P}\to {\frac {1}{\sqrt {2}}}E_{P}$) | Lower energy needed to create particles. |

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The Formation of a Universe from Quantum Fluctuations

Heisenberg's uncertainty principle allows a large amount of energy to be created even on very short time scales. If the Planck energy in a particular layer of the universe is high enough, a quantum fluctuation can create a new "pocket" of space that 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.

Multiverse and the Infinite Cycle

According to this theory, our universe is just one of countless universes forming a hierarchy of multiverses. Each of these universes has different constants that affect its size, duration, and physical laws.

• **Lower layers**: More stable vacuum, weaker quantum fluctuations, faster time flow.
• **Higher layers**: Intense vacuum, strong quantum fluctuations, slower time flow.

An interesting aspect is that what may appear as a moment in one layer may be a long period in another layer. Thus, each layer can appear to the observer as a completely different reality.

Expansion of the Universe and Its End

The expansion of the universe, driven by dark energy, may be the result of 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.

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 include:

• Quantum fluctuations can create a new universe in other layers of the fractal multiverse.
• Variable Planck constants affect the time, length, and energy scales of individual layers.
• The multiverse is a hierarchy of layers, each with its unique physical properties.

This view of the universe opens the door to new theories that could explain not only the origin of our universe but also the infinite diversity of other worlds that may exist beyond our reach.