Having advanced the principles of generative orders, we find ourselves in a situation somewhat similar to that faced by quantum theorists after wave-particle duality was advanced. A number of experiments appeared to violate the principles of Classical Mechanics (i.e. – the double-slit experiment, electronic excitations of the hydrogen atom, and the photoelectric effect). Progress was achieved by generalizing the methods of classical mechanics (Hamiltonian and Lagrange equations) into differential equations through Fourier analysis.
The problem in the case of generative orders is more difficult. The principle does not generalize existing theory into new realms of application – it serves to supplant existing theories, stretching back to Special Relativity and quantum mechanics. Additionally, the enumerated principles are abstract. They do not drive us to a specific formulation of physics in one dimension. A number of alternatives may be mathematically feasible.
Lacking a definite starting point for analysis, nothing short of an intellectual Big Bang would produce a fully elaborated theory that explains everything that is known about particle physics and cosmology. That does not exclude thoughtful exploration of specific possibilities. In this section, we consider a simple model (narrative here), elaborated to the point that conceptual correspondence with known phenomenology is established. The model is sufficient to support development of model potentials (as outlined in the research program), and therefore to advance theoretical insight and analysis methods that can be applied to other models.
- The initial state of the universe is a disordered but “cold” (at least as compared to Big Bang theories) collection of one-dimensional structures.
- Physics of one dimension includes a mechanism of segmentation (or quantization). The W/Z mass may establish a scale for this segmentation (see item 8 in this list).
- Folding or bonding on segmentation boundaries produces higher-dimensional structures. Geometrically, we know that triangles are the most stable of these structures.
- Higher-dimensional structures are self-associative, building lattices of distinct dimensionality. Tiling a plane with triangles is trivial. The structure of higher-order lattices is a an extrinsic property of the lattice potential.
- Lower-order lattices may exist in the empty spaces between cell layers. This is again an extrinsic property of the lattice potential
- Lattice formation is spontaneous. Orientation of expanding lattices is random.
- Surface energy at the boundaries between merging lattices of different orientation (a la grain boundaries in metals) provides the energy to compress structures into lower order, producing quasars and super-massive black holes at the center of galaxy formation. In this model, a black hole in three dimensions is a volume bounded by a two-dimensional lattice.
- Parthogenesis occurs through the expulsion of residual lower-order structures from the enclosed surface. In the reference model, these are one-dimensional structures (termed “threads” below). Threads may pass around the polygonal subunits of the lattice or through them. Threads that penetrate the lattice sub-units are localized, creating loci that we identify with fermions. Fermions interact strongly with similarly localized threads, giving rise to the non-gravitational forces. The potential barrier of the W and Z mass corresponds to a thread-exchange process, which requires reconfiguration of the sub-units.
- Captured threads locally distort the lattice. Gravity is a side-effect of the lattice energetics that localizes the distortion.
- Dark energy corresponds to the potential energy of lattice compression.
This illustrates how the principles of generative orders can be used to build a simple one-component model of the early universe. Geometrical models are presented in Chapter 4 of Love Works.
Certain details of particle phenomenology appear superficially to be accessible in the context of this model.
- Charge corresponds to the number of threads that penetrate a lattice sub-unit (which naturally has three degrees of freedom). Sign is simply a way of characterizing the tendency of fermions to attract fermions with different degrees of thread penetration.
- Mass arises naturally when threads pull on each other, causing the loci of thread capture to be dragged through the lattice. From the properties of the first particle family, it would appear that asymmetrical thread configurations must be more disruptive than symmetrical configurations. The equivalence of gravitational and kinetic mass is natural, as both effects correspond to lattice distortions. The equations of special relativity suggest the velocity-dependence of kinetic distortions.
- Particle families correspond to distortions of a particle’s lattice sub-unit from its normal configuration.
- Conservation of momentum could result from lattice dynamics that tends to reject disturbances, forcing energy back onto moving fermion. Analogies in material science include superfluidity and superconductivity.
- Light could be a self-propagating disturbance in the lattice, achievable only through fermion kinematics. Assuming that gravitational packing of particles causes re-orientation of the lattice at the surface of large bodies, the constancy of the speed of propagation is a local phenomenon (i.e. – a massive body “drags” space around with it).
- Light may interact with the lattice as it propagates, causing energy loss that manifests as a shift to lower frequencies. This may explain the microwave background radiation.
- A soul is a complex configuration of threads that are supported by but only tenuously bound to the lattice.
These configurations store energy as potential energy due to the associated distortion of the lattice.
Obviously, all of these are conceptual possibilities, whose validity can only be established through construction of a model of the energetics of the interactions between one-dimensional structures. As will become clear in the description of the research program, the list is by no means exhaustive. It is presented to provide a sense of the naturalness of fit between phenomenology and theories that might be elaborated using the principles of generative order.