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 - (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 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 v₏₇ = c²/v. The de Broglie relation = 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 V field density. Numerical verification of the 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