For higher level modules a similar model applies. The footprint of a module is a location swarm that is constituted of the location swarms of its components. Again this swarm is generated by an overall stochastic process that owns a characteristic function that acts as a displacement generator. Thus, at first approximation, the module moves as a single unit. The characteristic function of the stochastic process of the module is the superposition of the characteristic functions of the processes that generate hopping locations the components. The superposition coefficients may oscillate and relate to the internal positions of the components. This means that the characteristic function of the module not only controls the coherent movement of the module, it also installs the spectral binding of the components.
This spectral binding replaces the idea that forces cause the binding of elementary particles into higher order objects.
In the base model, the fact that in the scanning subspace the elementary modules only take a single quaternionic eigenvalue that contains a time-stamp and a spatial hopping location means that a single eigenvector of a dedicated operator represents the elementary particle.
The hopping location swarm covers many instances and many locations. In the base model, it is represented by a tube that smoothly travels through the background parameter space.
The modules are represented by a sublattice of the orthomodular lattice. The relations in this sublattice are more restricted than the elements that occur in the orthomodular lattice. We will call this sublattice a modular configuration lattice.
The base model contains nothing that supports the stochastic processes, which generate the hopping locations. The generation occurs as part of the embedding of the separable Hilbert space into the non-separable Hilbert space. The hopping locations represent artifacts that interact with the continuum that embeds these artifacts.The base model must be completed with a set of mechanisms. One for each elementary module. This essential ingredient introduces coherent dynamics and converts the rather dull base model into an interesting play garden.
As indicated above, not all discrete objects are modules or modular objects. This will be the subject of the next blog entry.
Please refer to https://en.wikiversity.org/wiki/Hilbert_Book_Model_Project for more details. The Wikiversity project tells a more complete story and provides the corresponding mathematics.