CPQ Theory: De Broglie Wave as a Volume Response of the Matrix

Within CPQ theory, we propose that the de Broglie wave is a real volume response of the matrix, generated by the gradient coupling -λ(∇· T)V in the full Matrix Lagrangian [1] during the motion of a topological defect. A moving defect (particle) has a spatially varying torsion structure T, whose divergence, through the coupling, excites a perturbation δ V in the surrounding matrix. The perturbation has a causal front limited by the speed c, while its phase velocity in the massive regime is vₚₕ = c^2/v. The de Broglie relation λ = h/p appears in this picture as a consequence of the dispersion of the volume sector and energy-momentum matching between the defect and the perturbation it excites. From this picture naturally follow the interpretation of the double-slit experiment, the Schrödinger equation as a low-energy effective limit, and Born's rule as a natural interpretation of the δ V field density. Numerical verification of the δ V trail behind a moving defect was carried out in [1] (Sim 6). Porschová, A. (2026). CPQ Theory — A Unified Framework from Spacetime Quanta to Cosmology (Books I–III). Zenodo. https://doi.org/10.5281/zenodo.18686137 Porschová, A. (2026). CPQ Field Theory — Applications (Books 01–03). Zenodo. https://doi.org/10.5281/zenodo.19100819 Porschová, A. (2026). The Matrix — Parameters and Dynamics: Foundation of CPQ Theory (3.1). Zenodo. https://doi.org/10.5281/zenodo.19431867