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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,
Let us first clarify the purpose of string theory, and then establish how we can achieve the same goal through fractal mechanics.
Feynman diagrams are tools of quantum field theory that visually represent particle interactions; from the perspective of fractal mechanics, these diagrams can be interpreted as a projection of fractal networks that explain particle behavior through multi-scale wave-resonance motifs.
Fractal Symmetry Breaking, distinct from classical symmetry breaking, refers to an approach that accounts for the inter-scale distortion dynamics of motifs, rather than just the breaking of a symmetry at a single scale.
Fractal statics is an approach that combines the classical static concept of “equilibrium” with fractal geometry and multiscale structures. In classical statics, for an object to remain in equilibrium, the sum of forces and moments must be zero. In fractal statics, however, these equilibrium conditions are satisfied not just for a single scale, but across all sub-scales and self-repeating fractal motifs of the system.
The fine-structure constant (𝛼 ≈ 1/137) is a dimensionless constant that determines the strength of electromagnetic interactions. This constant manifests in the fine details of atomic spectra (e.g., the energy levels of hydrogen).
Fractal Magnetic Field Theory is a brand-new field theory that integrates the time-derivative structure of classical Maxwell fields with the scale-derivative structure of fractal mechanics. Below are the axioms, field equations, operators, physical interpretations, and circuit equivalents of the complete theory. This stands as the natural extension of fractal circuit theory.
This model explains the “reading” process in biological systems through spiral–fractal resonance chains. DNA decoding, enzyme substrate selection, and ribosomal protein synthesis are all unified under the same universal reading operator.
Spiral–Fractal Node Resonance is a universal framework that visualizes and mathematically models the stability analysis of triple-interaction systems.