Three previous papers in this series introduce and discuss the Scale Expanding Cosmos (SEC) theory. This paper proposes a connection between the theory's discrete, stepwise, cosmological scale expansion and quantum mechanics. Very high frequency, small amplitude, temporal excitation in the metrical coefficients of the Minkowski spacetime is modelled in general relativity. DeBroglie type matter-waves are shown to result from motion of spatially confined metrics oscillating at the Compton frequency. The momentum ?guiding function? of Bohm and de Broglie naturally follows from the geodesic equations of general relativity. A clear physical explanation to the double-slit interference experiment is given. Setting part of the Ricci scalar equal to zero gives a wave equation from which the Schr?dinger equation is derived. This possible link between general relativity theory and quantum theory explains the particle-wave duality and suggests that quantum mechanical wave functions are amplitude and phase odulations of very high frequency oscillations in general relativity's metrical coefficients.
