Dear Rafael,
I was hesitant to present all of the details of my ideas, because some are a bit maverick, and probably too detailed for this type of essay. I competed in the second FQXi essay contest, was in the top five after the public and community votes, but didn't finish in the top 18 - I attributed this to the fact that that essay was very mathematical.
In my "The Interrelationship of Spin and Scales" paper, I suggested that the Multiverse (or super-Cosmic) scale is the largest scale from which we can feel effects. If a larger scale exists, we may never know. The Multiverse scale is related to the Graviton (and the origin of gravity), and is a continuous (boson-like) space. Complexity of this scale may be infinite, although this also implies an infinite Multiverse.
Below the Multiverse scale is a Cosmic Scale. This Cosmic Scale is related to the Gravitino, and is a discrete(?) (fermion-like) space. This discrete structure may exhibit itself as cosmic strings and their effects. Perhaps the discrete Holographic Principle occurs at this scale. The mass distribution of our Universe is not isotropic and homogeneous, but is coursely grained. Complexity of this scale may be based on the number of possible string vacua of ~10^500.
You said "I have been thinking about the idea of a hierarchical cosmos wherein the cosmic subsystems have alternating periods of densification and attenuation that establish the upper and lower limits for the quantization of the particulate cosmos. My idea is that gravity gathers and densifies the cosmic subsystems, and eventually, with their increased mass-energy, each cosmic subsystem is taken by its own increased orbital momenta towards an orbital apex that initiates a period of attenuation with the cosmic subsystem getting fragmented. This renders a picture of an expanding and spiralling cosmos but with cosmic mass-density accordingly maintained and the particles multiplied."
I think that our ideas are complementary, and perhaps even identical.
Below the Cosmic Scale is the very familiar Classical Scale. The Classical Scale is related to Vector Bosons, and is a continuous (boson-like) space. Complexity of this scale is based on Dirac's Large Number of ~10^41.
Below the Classical Scale is the Quantum Scale. The Quantum Scale is related to normal matter Fermions, and is a discrete (fermion-like) space. Complexity of this scale may be of order 496 ~ SO(32) ~ E8xE8*.
Below the Quantum Scale is the sub-Quantum or Dirac Sea Scale. This Dirac Sea Scale is related to Scalar Bosons, the so-called Higgs Mechanism and the origin of mass, and is a continuous (boson-like) space. Complexity of this scale may be of order 32.
You said "My idea regarding particles is that the waves/motions get wrapped or folded into the particulate essence - perhaps in somewhat the same manner as that of the loops of space of Astekhar, Smolin and Rovelli, only that I see loops of motion instead of space."
Of course position and momentum space are reciprocal lattices, and conjugate variables. We may have quantization of position such as Kissing Spheres or Causal Dyanamical Triangulation that provides lattices and their reciprocal scaled lattices (that appear continuous because of the large number of states). OR we may have quantization of momentum such as String Loops or String Winding modes that provides lattices and their reciprocal scaled lattices (that appear continuous because of the large number of states).
I agree that it is a Chicken-Egg type of question, that both continuous waves and discrete particles are fundamental, and the existance of either probably necessitates the existance of the other.
Along the lines of this wave-particle duality, I think that fields require mediating bosons and vice versa. The Electric Field required the Photon with fine-structure constant of 1/137, whereas the magnetic field requires the magnetic monopole with coupling of 137/4 (with an apparant S-Duality). My Quantum Statistical Grand Unified Theory does not predict a force of strength 137/4, nor have we observed the magnetic monopole. Thus the question should be 1) Does the magnetic monopole exist at a scale we haven't yet observed? or 2) Did the magnetic monopole degrees-of-freedom get absorbed into another physical effect (such as my interpretation of Edwin Klingman's ideas whereby the gravitational magnetic monopole degrees of freedom may explain the CKM and/or PMNS matrices).
I know that my ideas are maverick, but I also think that we are a long way from a TOE without some radical thinking.
Have Fun!
Dr. Cosmic Ray
