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We observe the universe only from the scale permitted by the gravitational volume we inhabit. That is why we assume physical laws are universal. In reality, relativity is a local limit, while the universe is a fractal-scale structure. Dark matter and dark energy are products of this scale illusion.
Quantum mechanics carries three major mysteries:
Wave–particle duality
The uncertainty principle
Collapse of the probability wave
Fractal mechanics explains these three mysteries through scale dependence.
In the definition of fractal space, completely new phenomena appear that classical physics could never predict. And these are not just “possible”—they are inevitable as a consequence of the mathematics of fractal mechanics.
I will explain in full, complete and architectural integrity how fractal mechanics, with its own internal logic, explains Dark Energy and Dark Matter. I maintain the fEnt(n) (Dark Energy) tag everywhere. This explanation will be the most powerful cosmological interpretation of fractal mechanics.
This report covers the application of atomic-level circuit motifs to biochemical molecule design. Basic assumption: Each atomic bond is the physical equivalent of a circuit element; each functional group is a circuit segment; Each molecule is a fractal scaled circuit architecture. This approach provides isomorphic coupling of biochemical functions with the Elementary Circuit Topology I developed. The analgesic effect is a low-pass filter + gain reduction + feedback function in the biological circuit. Therefore, the circuit response of the molecule to be designed must also carry these functions.
Fractal mechanics redefines all the fundamental concepts of classical physics. Each magnitude is derived from the trio of motif + phase + entanglement. So fractal mechanics: Quantum mechanics, Wave mechanics, Classic mechanics. It is a wider frame that fits over it.
Now I establish how fractal mechanics redefines Newton’s laws in a fully technical, fully systematic and fully consistent framework. This chapter is one of the strongest building blocks for showing how fractal mechanics generalizes classical mechanics.
Classic Standard Model (SM): electromagnetic force (U(1)), weak force (SU(2)), strong force (SU(3)), Higgs field, fermions and bosons it is based on. Fractal Standard Model (FSM) is: motif area, spin field, entanglement field, fractal gauge fields, fracton particles, fractal Higgs field, fractal mass generation it is built on. FSM is the fractal generalization of classical SM.
This work defines Fractal Mechanics, a new physical theory derived from fractal trigonometric functions, analogous to wave mechanics derived from the sine and cosine functions of classical trigonometry. The basic building block is the Unit Fractal Kernel (UFK), defined in the Fractal Behavior Mapping System (FBMS):
In quantum field theory (QFT): Field → is the fundamental physical object, Particle → is the quantum of the field, Interaction → is the algebra of field operators. Fractal Field Theory (FFT) is: Field → motif + spin + entanglement trio, Evolution → iterative transformation occurs with T(n), Norm → entanglement is determined by fEnt(n). Therefore, the quantization of FFT is a fractal generalization of classical QFT.