Principle of Generative Order
In this section we motivate the principle of generative order and define a reference model to serve as a framework for exploring the challenges in elaborating the principle into a model capable of explaining the known characteristics of particles and their interactions.
The preceding survey of the deficiencies of GI theories, culminating with lists of unexplained first-order phenomenology and axiomatic contradictions, is a powerful motivation to search for new principles to guide the construction of alternatives. In proposing generative orders (to be developed below), the author was motivated by the following observations. The observations span the scale of phenomenology from the quantum to the cosmological, in recognition of the connection between these scales established by current physical theory.
The Preponderance of Threes
As observed, we inhabit a universe with three spatial dimensions. The three particle families (of which the first is summarized below) consist of four fermions, with three charge states (the fourth state being uncharged). Finally, the non-gravitational forces (electromagnetic, weak and color) have group-theoretical ranks of 1, 2 and 3.
Following this correspondence, it seems natural to suggest that the principles that explain our reality of threes should also be able to explain realizable physical realities based upon one, two and four and higher dimensions. This is the fundamental principle of generative order.
In the table above, it is also interesting to note other correspondences. Only fractionally charged particles (u and d) have color, and their masses are far larger than the masses of integrally charged particles (n and e). I also note that particles with odd fractional charge repel each other, but are attracted to the remaining charged particle, of even fractional charge.
Gross Cosmological Structure
Almost all galaxies have super-massive black holes at their center (Galactic Cores, or GCs). Mechanisms for ejection of GCs have been proposed to explain those that do not. In addition, the oldest objects in the universe appear to be quasars. This tends to indicate that quasars may represent the early stages of GC formation, and so that galaxies form through a sudden and enormously violent mechanism, rather than through the gradual coalescence of intergalactic gas.
Secondly, galaxies appear to be clustered on the surface of extremely large voids, lacking any visible matter, but still capable of lensing light. This indicates that the initial stages of the universe must include mechanisms that explain variations in the uniformity of space (in the sense of General Relativity, thought not necessary through the mechanisms it allows).
The statement of generative order provided above is weak. It admits of realities in which a three-dimensional reality is independently established, but does not co-exist with realities of higher or lower dimensionality. Lacking a dynamical result that establishes preference for a three-dimensional reality, it would seem prudent to extend the basic principle of generative order with two others. The three are then:
- Realizable physical laws must exist on all orders of dimensionality.
- Orders are compositional: elements of lower order combine to produce elements of higher order.
- Orders must co-exist, and transitions between orders must be related to recognizable physical phenomena.