On the origin of quantum mechanics

Action at distance in Newtonian physics is replaced by finite propagation speeds in classical post-Newtonian physics. As a result, the differential equations of motion in Newtonian physics are replaced by functional differential equations, where the delay associated with the finite propagation speed is taken into account. Newtonian equations of motion, with post-Newtonian corrections, are often used to approximate the functional differential equations. Is the finite propagation speed the origin of the quantum mechanics? In the present work a simple atomic model based on a functional differential equation which reproduces the quantized Bohr atomic model is presented. As straightforward application of the result the fine structure of the hydrogen atom is tackled.