The Central Order Theory: Deriving the Schrödinger Equation from Symmetric Metamatter and Fractal Time
Sepiashvili, David
This work proposes a minimal structural framework for the foundations of quantum mechanics based on the existence of a symmetric, atemporal informational substrate — the Central Order. Within this framework, time is defined as the sequential emergence of minimal fractal differentiations of an underlying symmetry. A quantum state is interpreted as a configuration of incomplete differentiation, which naturally gives rise to superposition, interference, and entanglement. From these geometric–informational principles we derive the necessity of linearity, complex structure, norm preservation, and operator-based evolution. It is shown that (i) additivity of differentiations enforces linearity, (ii) the fractal nature of temporal steps requires a first-order time derivative, (iii) preservation of the norm follows from the global symmetry of origin, and (iv) the generator of evolution must be anti-Hermitian, yielding an Hermitian Hamiltonian. Taken together, these constraints uniquely lead to the Schrödinger equation. Classical behavior and quantum nonlocality emerge as different limits of the same process of differentiation. In this formulation, quantum mechanics ceases to rely on postulates and instead arises as the structurally inevitable dynamics of fractal symmetry-breaking.
•Dec 6, 2025•0 citations