Elementary modules are point-like objects and would not have many properties if the location of that point-like object would be quite stationary. Instead, at every progression instant, the elementary module gets a new location that is provided by a private stochastic mechanism. Consequently, the elementary module hops around in a stochastic hopping path and the hop landings form a location swarm. The swarm is characterized by a location density distribution. The Fourier transform of this distribution equals the characteristic function of the stochastic process that is applied by the mechanism that generates the hop locations. Therefore, the swarm owns a displacement generator and consequently at first approximation the swarm moves as one unit. The location density distribution of the swarm equals the squared modulus of the wavefunction of the elementary module.
The swarm contains a huge number of elements. Compared to the vigorous hopping of the elementary module, its representing location swarm moves quite steadily.
The Hilbert Book Model contains a section about a multi-mix algorithm that starts from the hopping path and the fact that the location swarm owns a Fourier transform. The algorithm results in an equivalent of the Lagrangian and the Hamiltonian. In fact, the multi-mix algorithm takes the reverse of Feynman's path integral, which starts from the Lagrangian. The HBM does not take all possible paths. Instead, it takes the stochastic hopping path.
Look at Report of the Hilbert Book Model Project
