schmiereck/hex_field_map: Relativistic Quantum Mechanics from Lattice Geometry: Emergent Speed of Light, Mass, and Time Dilation on an Equilateral Triangular Lattice

This work investigates the emergence of relativistic quantum mechanics from fundamental geometric principles on a discrete equilateral triangular lattice. By formulating a discrete path integral framework, we demonstrate how continuous relativistic phenomena—specifically a strictly bounded emergent speed of light (c), inertial mass generation, and kinematic time dilation—arise directly from the lattice geometry and transition probabilities without assuming continuous spacetime or Lorentz symmetry a priori. Key Highlights & Findings: * Discrete Path Integral Formulation: Extension of lattice path summation to an equilateral triangular topology with 6-fold rotational symmetry. * Emergent Invariant Speed: Natural upper bound on propagation velocity defined by discrete step intervals and lattice geometry. * Mass & Dispersion: Inertial properties emerging from direction-reversal amplitudes (zitterbewegung analog). * Numerical Verification: Accompanied by open-source simulation code verifying wave packet dynamics and geometric time dilation. Repository & Simulation Code: Source code, simulation framework, and LaTeX sources are available on GitHub: https://github.com/schmiereck/hex_field_map