PDF version : twistorspin.pdf
Introduction on the origins of twistor theory by Professor Sir Roger Penrose1
and a public talk:
George Musser2 also writes about twistor/string theory as a useful continuation.
The twistor particle programme published hitherto3 includes examples from 2 spin classes (fermion, boson): electron/neutrino/quark: spin 1/2 = 2-1 = 2i2 = 2eiπ and higgs/photon/gluon/graviton: spin 0, 20, 21. Yet the scope of available spin classes triangulated by Andrew Kels4 is Cardinal and spin is a measurable property in/of space-time (Martens & de Muynck5).
Basically, shedding light on dark matter has great theoretical scope.
Which, if any, of these unobserved-hitherto spinning, Kelsian realnesses will interest physicists for a while? Discussions with David Falconer6 and Phil Jones7 leads one to suggest the next, “totally tautological and qualitative” (Falconer, personal communication) real numbers beyond the standard model are given rationally (barring supersymmetry – Oooh, get me, girlfriend!) by the irrational, positive square-root of 2 = √2 = 21/2 = 22-1 and its reciprocal 1/√2 = 21/2/2 = 22-1/2
Such objects (named rottons for their infinite precision) are distinct from both Weinstein spin 3/2 (e.g. M. du Sautoy8) and other generic trions9. Rottons appear from the projective nature of twistor geometry, if and only if this view from the back-wood-side-line-hill-sides isn’t just 2Fiat Lux
A plane right triangle of unit height and base has hypoteneuse ± 21/2 = 22-1
Projected rotton spin values 21/2 (“boson-like”) and 21/2/2 (“fermion-like”, 2 identical copies, projected < or >, tangentiality over a 2-sphere of radius 21/2/2) follow holomorphism. Lisa Randall et al9 Double Disk Dark Matter emerges, naturally.
Next, the plane right triangle of unit height and hypoteneuse 2 has base ± 31/2 = 32-1
Hey, prongo! 4-off rottons (3ons) with spin 31/2 (b-like), 2.31/2/3 (unlike), 31/2/2 (f-like) and 31/2/3 (unlike) project, again holomorphically. There exists a compound object which already displays one of these rotton spins in nature. The electrically neutral hydrogen atom has a total spin angular momentum identical11 with 31/2/2.
The boson-like rotton 22-1 transforms into twistor space T as a flag-plane pointer on the unit Riemann sphere, but i don’t have the mathematical sophistication to describe mathematically “inside a Riemann sphere”. Paul Nylander12 and Frank Jones13, however, seem to have some of the necessary ideas and wit. Further and greater imagination than mine alone is required to project the insides of a stringy meatball, sausage-sectionally etc.
Measured physically? How, when and where?
Path integrals (QED-like Feynman diagrams) for such a boson include: 22-1 <-> 2 x [ 22-1 /2] and, as far as i can imagine, 22-1 -> 4 x spin 1/2 (e.g. 2 fermions and 2 antis).
The unit pentagon yields 2 “Golden ratio” rottons, namely (1 + √5)/2 and |(1 – √5)/2|
PhysOrg has a fine connection to fluid dynamics here: http://phys.org/news/2013-07-fluid-dynamics-mimic-quantum-mechanics.html
1. Roger Penrose, 1987 : http://users.ox.ac.uk/~tweb/00001/
2. George Musser, 2010 : http://www.scientificamerican.com/article.cfm?id=simple-twist-of-fate
4. Andrew P. Kels, 2013 : http://arxiv.org/pdf/1302.3025.pdf
5. Hans Martens and Willem M. de Muynck, 1994 : http://www.phys.tue.nl/ktn/Wim/bohrfopl1.pdf
10. Double Disk Dark Matter : http://arxiv.org/pdf/1303.1521v1.pdf
12. Paul Nylander, 2005 : http://nylander.wordpress.com/2005/05/19/loxodromes-on-riemann-sphere/
13. Frank Jones, 2005 : http://www.owlnet.rice.edu/%7Efjones/loxo.html