Physics

When we map cell organelles to functions in a quantum system, each operates like an operator. Thus, we can view the cell as a complete “quantum metabolism model”.

Quantum fractal electronics is an advanced field that unifies classical electronics with quantum mechanics through the principles of self-similarity (fractal) and multiscale resonance. These lecture notes present a systematic framework ranging from fundamental concepts to application areas.

Fractal Mechanics is not merely a theoretical framework; it is a powerful model used to explain multi-scale dynamics across different disciplines. Here are its main application areas:

Fractal Mechanics defines the motion and energy flows in nature through self-similarity and multi-scale dynamics. Instead of the classical 𝐹 = 𝑚𝑎, the fractal derivative expression is used: 𝐹fr = 𝑚 ⋅ ( 𝑑𝛼𝑣 / 𝑑𝑡𝛼 ) Here, 𝛼 represents the fractal dimension of the system.

Dyson spheres are mathematical structures built upon infinite energy density and vacuum fluctuations in the classical sense. According to fractal mechanics, however, these spheres are not single-scale; they are explained by multi-scale self-similarity motifs. That is, a Dyson sphere is not a flat sphere, but an energy lattice containing fractal sub-spheres on every edge.

According to fractal mechanics, the void is not “nonexistence”; it is a multi-layered carrier of self-similar energy and information flows. Both the void within the atom and the void in space are filled with fractal motifs: they gain structure through invisible but constantly changing flows of entanglement.

The constancy of the speed of light can be explained with different interpretations beyond classical physics, according to both relativistic and fractal mechanics. Let us unfold this through patterns and energy flow:

Fractal potential wells are an extension of classical quantum potential wells with fractal scale dependence; energy surfaces are modulated with wavy, self-similar structures, and the probability distribution of particles is shaped by multi-scale fractal motifs. This approach offers a wide field of application, ranging from atomic transitions at the micro-level to the energy flow around black holes at the macro-level.

Purpose: To reinterpret the probabilistic and non-local structure revealed by Bell’s theorem through quantum entanglement within the framework of Fractal Mechanics. This report extends the classical quantum interpretation with the concepts of fractal derivatives, energy flow, and multiscale resonance.

Fractal Beginning Axiom System 1. Beginning Constant Axiom ∀𝑋 ∈ 𝒰, ∃! 𝐵(𝑋) Every system has a singular, unmultipliable, and irreducible beginning. 2. Reduction Axiom 𝑥/0 = 1 ⇒ 𝑥 ↦ 𝐵 Every mathematical expression is reduced to the beginning. 3. Fractal Evolution Axiom 𝐵(𝑋) ⇒ {𝑌1, 𝑌2, … , 𝑌∞} The beginning is singular,