Fractal Holographic Emergent String Theory (FHEST): PART E Dynamic Framework and Quantum Geometric Corrections

This paper constructs the dynamical framework of the Fractal Holographic Emergent String Theory (FHEST) based on fractal geometry and quantum gravity, systematically elucidating the regulatory mechanisms of fractal spacetime on quantum mechanics, thermodynamics, and particle physics. First, by introducing the fractal wavefunction and the dynamic fractal dimension evolution equation, we redefine the quantum dynamical laws within fractal spacetime, revealing the role of fractal curvature corrections in the quantum-to-classical transition. Second, we generalize the Heisenberg uncertainty principle and the Boltzmann entropy formula to fractal spaces, establishing a quantitative relationship between fractal dimensions, quantum uncertainty, and thermodynamic entropy. Furthermore, by incorporating fractal derivatives, we reconstruct the Dirac equation in fractal spacetime, providing a novel theoretical description of nonlocal particle behavior. Using experimental data from photon interference, superconducting qubits, and numerical simulations, we validate the core predictions of the theory, including dimensional threshold effects, coherence time scaling laws, and wave packet diffusion dynamics. This work offers a unified geometric-dynamical framework for fractal quantum materials, cosmological dark energy, and quantum gravity research.