QM Series #2 / 7

Emergent Wave-Particle Duality and the Schrödinger Equation from DI Bit Flows in the 600-Cell Lattice

Derives both wave-particle duality and the time-dependent Schrödinger equation as the continuum limit of discrete DI bit diffusion under SSV potentials.

Thomas Lee Abshier, ND· Hyperphysics Institute

Grok (x.AI)

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Abstract

In Conscious Point Physics (CPP), wave-particle duality and the time-dependent Schrödinger equation emerge naturally from the propagation and diffusion of Displacement Increment (DI) bits along 600-cell lattice geodesics. Particles are localized CP aggregates; their associated waves arise as coherent probability currents of DI bit ensembles. The Schrödinger equation \(i\hbar \partial_t \psi = \left[-\frac{\hbar^2}{2m}\nabla^2 + V(\mathbf{r})\right]\psi\) is derived as the continuum limit of discrete bit diffusion under Space Stress Vector (SSV) potentials. No fundamental wavefunction or Hilbert space is postulated — \(\psi(\mathbf{r},t) \sim \sqrt{\rho_\text{bit}(\mathbf{r},t)} \, e^{i\phi(\mathbf{r},t)}\), where \(\rho_\text{bit}\) is the DI bit density and \(\phi\) is the accumulated lattice phase.

ψ = √ρ e^iφ

Wavefunction from Bits

No Hilbert space postulated

iℏ∂_tψ

Schrödinger Derived

Continuum limit of diffusion

~10¹⁰ Hz

Lattice Artifacts

Testable deviations

DI Bit Dynamics on the 600-Cell Lattice

Propagation Rules

DI bits move along lattice edges according to local rules determined by nearby CP charges and SSV gradients. Each bit carries phase information accumulated along its path, with phase increment per edge \(\Delta\phi \propto\) lattice angle and SSV potential.

Geodesic Paths and Multi-Path Summing

The 600-cell lattice supports multiple geodesic paths between any two points. Coherent bit flows along these paths interfere at the destination vertex, producing wave-like patterns.

Bit Density and Probability

The DI bit density \(\rho_\text{bit}(\mathbf{r},t)\) at vertex \(\mathbf{r}\) gives the probability density: \(P(\mathbf{r},t) = \rho_\text{bit}(\mathbf{r},t) / N_\text{total}\). The associated amplitude is \(\psi(\mathbf{r},t) \sim \sqrt{\rho_\text{bit}} \, e^{i\phi}\).

Phase Accumulation

Phase per edge depends on lattice geometry (golden-ratio angles) and SSV:

\[\Delta\phi = \frac{2\pi}{\lambda_\text{lattice}} \Delta s + \frac{V(\mathbf{r})}{\hbar} \Delta t + \Delta\phi_\text{geom}\]

where the geometric phase contribution \(\Delta\phi_\text{geom}\) arises from 600-cell dihedral angles and golden-ratio edge-length ratios. This carries over the phase interference framework established in the Electroweak series (SSV fields, phase interferences, bit compression).

Derivation of the Schrödinger Equation

In the continuum limit, the discrete bit diffusion equation becomes the time-dependent Schrödinger equation. The kinetic term \(-\frac{\hbar^2}{2m}\nabla^2\psi\) emerges from the lattice Laplacian of bit density, while the potential term \(V(\mathbf{r})\psi\) comes from SSV gradients acting on DI bits:

\[i\hbar \frac{\partial \psi}{\partial t} = \left[-\frac{\hbar^2}{2m}\nabla^2 + V(\mathbf{r})\right]\psi\]

This reproduces free-particle dispersion, potential scattering, and predicts testable deviations at high energies (~10¹⁰–10¹² Hz) in precision optical lattices and atomic clocks, where the discrete lattice structure becomes detectable through precision phase measurements.