Hi Alan,
You left questions on several forums. I left answers on my blog site, but had not heard any responses from you, so I thought I should repost those responses here.
Thanks for the Congratulations.
I think this question ultimately reverts back to the question "Is Nature fundamentally Discrete or Continuous?"
I said that Reality is an effectively an intertwined "twistor-like" hybrid of both. This permits wave-particle duality, and permits us to observe "continuous realities" such as fields that are modeled as if they are continuous "ad infinitum" (as Cristi Stoica claimed), as well as "discrete realities" such as electric charges that are modeled as if they are non-divisible quanta. I liked Cristi's presentation, but I asked him to define "continuous ad infinitum" if infinity cannot exist in a finite Observable Universe (13.7 billion light years is a very large size, but it isn't infinite). The reality is that these "continuous fields" probably break down somewhere around the 10^-31 cm scale, and this is where the spacetime lattice model is required for a proper understanding of the Black Hole "singularity" (it may also be related to the Dirac Sea and Constantin Leshan's Quantum Vacuum Hole).
Ed and I traded books, and have been discussing each other's ideas since the last essay contest. I like his GEM-like ideas and agree that this could represent part of the continuous nature of reality. As a particle physicist myself, I think he is "off-base" with regard to his claim of 4 fundamental particles, but I'm also tired of arguing a point that I consider obvious. I think that Ed's model has a single triality, and therefore requires scales and S-duality to explain the two required trialities in his model: Color (he doesn't have a QCD field), and Generations (similar to Garrett Lisi's triality of generations).
I like your helical screw idea. Perhaps there is a mixing of transverse and longitudinal waves (that implies an effective mass) that includes the properties of scales. Recall that electromagnetism is ~10^40 times stronger than gravity - and this requires a scale. Ed Klingman's 10^60 also requires a scale, and I think that he has improperly modeled 10^120~(10^60)^2 rather than 10^120~(10^40)^3. Effectively, this requires your screw threads to be logarithmic - finer threads for weaker forces such as gravity and courser threads for stronger forces such as electromagnetism. In this sense, the threads for gravity may be so fine (outside of a Black Hole) that they seem to be stripped out.
I think that the unification of forces requires scales - which is why I dedicated this essay to scales and how they explain the continuous and discrete natures of relaity.
I see that you left this message in several forums. My previous answer involved scales moreso than screws, but I thought that I should explore more details about your Archimedes screw.
I think that there are details that have been largely overlooked here. First, there is the "pitch" of a screw thread. In the US, most of our screws are pitched such that we turn "right to tighten, or left to loosen", but screws with the opposite pitch can also be manufactured. About 20 years ago, many propane gas cylinder tanks had opposite threads - I guess that the assumption was that you would try to "turn left to loosen", but always tighten instead - until you read all of the safety directions and realized that you didn't know what you were doing. They have since changed propane gas cyclinder threads back to the standard pitch - I guess that you don't want people to accidently loosen a tank while they thought they were tightening it.
Conclusion - By changing the pitch of an Archimedes' screw, you can make it attractive or repulsive.
Another detail is the rotation of the screw. It should be obvious that if we change the rotation of a screw - say from Clockwise to Counter-clockwise, then the direction of the force induced by the Archimedes' screw changes.
Conclusion - By changing the rotation of an Archimedes' screw, you can make it attractive or repulsive.
I think that all of these ideas may tie into CPT symmetry. Perhaps handedness (parity) and antimatter (charge) (4 different permutations) are related to these concepts of pitch and rotation (also 4 different permutations).
Personally, I have no problem modeling a Field line or a String with an Archimedes' screw (with variable thread spacing), but realize that the resultant force could be attractive or repulsive - as is electrostatics.
Now we need to explain why gravity is strictly attractive. Is there more to gravity (say within a Black Hole or in a scale of greater complexergy) such as Quantum Gravity, Holographic Gravity, my WIMP-Gravity (see my book), or Edwin Klingman's GEM Gravity? And we only observe the attractive side? Or is this tied into CPT symmetry such that attractive gravity moves forward in time, and repulsive gravity moves backwards in time (which would look attractive and forward)? I don't know...
I think there is enough that we truly don't understand about the origins of mass and gravity that we shouldn't get too overconfident in our models.
One more thought that may be significant:
Earlier, I mentioned that the Archimedes' screw needs an effective mass and longitudinal degrees-of-freedom similar to a Z boson in order to physically represent the concept of screw threads.
Photons are expected to have zero rest mass so that they can have a pure inverse-distance-squared dependance - so where is the effective mass? This may require mass-energy correspondance such that photons have an effective mass given by E = mc^2 = hf.
Have Fun!
Dr. Cosmic Ray