PDF version : twistorspin.pdf

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Introduction on the origins of twistor theory by Professor Sir Roger Penrose

^{1}and a public talk:

George Musser

^{2 }also writes about twistor/string theory as a useful continuation.________________

The twistor particle programme published hitherto

^{3}includes examples from 2 spin classes (fermion, boson): electron/neutrino/quark: spin 1/2 = 2^{-1}=_{2}i^{2 }=_{2}e^{iπ}and higgs/photon/gluon/graviton: spin 0, 2^{0}, 2^{1}. Yet the scope of available spin classes triangulated by Andrew Kels^{4}is Cardinal and spin is a measurable property in/of space-time (Martens & de Muynck^{5}).________________

Basically, shedding light on dark matter has great theoretical scope.

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Which, if any, of these unobserved-hitherto spinning, Kelsian realnesses will interest physicists for a while? Discussions with David Falconer

^{6}and Phil Jones^{7}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 = 2^{1/2}=_{2}2^{-1 }and its reciprocal 1/√2 = 2^{1/2}/2 =_{2}2^{-1}/2________________

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Such objects (named rottons for their infinite precision) are distinct from both Weinstein spin 3/2 (e.g. M. du Sautoy

^{8}) and other generic trions^{9}. 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 2^{Fiat Lux}____________

A plane right triangle of unit height and base has hypoteneuse ± 2

^{1/2 }=_{2}2^{-1}Projected rotton spin values 2

^{1/2}(“boson-like”) and 2^{1/2}/2 (“fermion-like”, 2 identical copies, projected < or >, tangentiality over a 2-sphere of radius 2^{1/2}/2) follow holomorphism. Lisa Randall*et al*^{9 }Double Disk Dark Matter emerges, naturally._____________

Next, the plane right triangle of unit height and hypoteneuse 2 has base ± 3

^{1/2 }=_{3}2^{-1}Hey, prongo! 4-off rottons (3ons) with spin 3

^{1/2}(b-like), 2.3^{1/2}/3 (unlike), 3^{1/2}/2 (f-like) and 3^{1/2}/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 identical^{11}with 3^{1/2}/2._____________

The boson-like rotton

_{2}2^{-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 Nylander^{12 }and Frank Jones^{13}, 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:

_{2}2^{-1 }<-> 2 x [_{2}2^{-1 }/2] and, as far as i can imagine,_{2}2^{-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|

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PhysOrg has a fine connection to fluid dynamics here: http://phys.org/news/2013-07-fluid-dynamics-mimic-quantum-mechanics.html

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References

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

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