Physics

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.

Expressing black holes in the language of fractal mechanics is actually one of the most natural applications of fractal mechanics. Because black hole: density → infinite, time → stop, info → jam, phase → deadlock, amplitude → slump, entanglement → near maximum shows such behavior. All of these behaviors match exactly the basic variables of fractal mechanics.

Classical field theories (electromagnetic field, scalar field, quantum field theory) are defined over continuous space-time. The field carries a value at every point and this value evolves with differential equations.

I present these points like a single technical report, title by title, with a full logical chain. This report can be thought of as a summary file that systematically shows why fractal mechanics goes beyond classical physics.

Quantum architecture is the process of deriving quantum phenomena (superposition, entanglement, spin, measurement) from abstract mathematical expressions and rearranging them as a modular and functional system.

A geoid is the surface where the total potential of the Earth’s gravitational and rotational effects is constant. In the classical definition, this is: Φ(𝐫) = Φg (𝐫) + Φc (𝐫) = Φ0 It is expressed as follows: Here, Φg is the gravitational potential, and Φc is the centrifugal potential due to rotation.

Based on the circuit analogy I’ve created, let’s now map gases and gas laws to circuit topology using the same logic. This way, we can express the behavior of gases in the periodic table using electrical parameters.

Entropic impedance physics is defined as a new physical paradigm that combines energy transport modes, geometric curvatures and phase conformations in a single framework. This approach offers an interdisciplinary field theory.

Physical expression: In a pipeline, the flow entering is equal to the flow leaving. Analogical expression: – Flow (Q) ↔ Current (I) – “Current in = current out” → Same structure as Kirchhoff’s current law.