Series Paper — QM-Line
Quantum Mechanics Series
QM-1: Quantum Mechanics in CPP: The Schrödinger Equation from Phase-Carrying DI-Bit Hopping on the 600-Cell Lattice
Schrödinger's equation emerges in the continuum limit from discrete complex amplitude hopping on the lattice
Abstract: QM-1 derives the time-dependent Schrödinger equation in Conscious Point Physics from the hopping of phase-carrying Displacement Increment bits on the 600-cell lattice. Each DI bit carries a complex amplitude at each Grid Point, where the phase is geometrically accumulated at velocity c, and the discrete evolution over one Absolute Moment tick involves a complex hopping Hamiltonian with off-diagonal amplitude T = hbar^2 / (4 m Δs^2) derived from the DI-bit velocity and the icosahedral coordination z=12. The graph Laplacian of the 600-cell satisfies a continuum-limit identity yielding exactly i hbar partial_t psi = [-hbar^2 nabla^2 / (2m) + V] psi. The imaginary unit arises physically from DI-bit phase accumulation per hop, not from diffusion, and Madelung decomposition shows the quantum pressure term emerges automatically from complex hopping without being postulated. Lattice corrections are of order (l_P/lambda)^2 and unobservable at laboratory wavelengths.
- Schrödinger equation exact in continuum limit of lattice hopping
- Quantum pressure (Madelung Q-term) emerges, not postulated
- Imaginary unit physical: DI-bit phase per hop