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Articles such as this one follow in the footsteps of great educators such as David Hilbert. Your work here might inspire someone to invent a 3D interferometer... and with that comes the discovery of a spacetime structure to fit a unified field.
A Mobius band will be oriented either left or right handed depending on which way the 1/2 twist is made. As with a spring, the twist and the closing of the loop locks in energy; in this respect the Mobius band resembles a unit of 1/2 spin (as it pertains to subatomic physics). If we cut this "spin unit" down the middle it becomes a spin of 1 (a full twist). Cutting the band off center makes a spin of 1 and 1/2. Gluing two bands together should make a spin of net zero or plus/minus 1... my math skills fall short at that point.
The Penrose Twistor is envisioned as an nth dimensional extension of vectors & tensors, and seems to become a Mobius/Klein type of topology; this could be the unified field model long sought by physicists, yet the math proved too difficult even for Roger Penrose.
I might have a way of simplifying the math in either case. This requires a redefinition of pi as the square root of 6 times Reimann's Zeta(1) value. However, the term 6 represents a structure of six Klein bottles interconnected/looped at their handles as to form a type of xyz axial system that allows all three axes to represent complex numbered coordinates. This pushes the difficult/impossible math toward the center (at the handles), and makes the exterior (pseudospheres of the Klein bottles) as simple as adding complex numbers.
With three values, 81, the speed of light, and a secret "uncertainty" number, I can make this 6lobed structure mathematically represent any Lepton or Quark (by spin, mass, and charge). Pretty neat, huh? The only great difficulty is finding empirical evidence of such a 6lobed structure in nature (doh!). That won't happen until someone invents the detector, a similarly 6lobed interferometer!
rd4ji2@live.com
PS a couple of other difficulties are we need 3.14 space dimensions and the value of pi gets smaller (becomes 2) at the center of the structure.