joy: question for you, in context of the above.
is it *really* the case that space may be concluded to be an quaternionic 3-sphere, or is that purely limited to the local interactions of matter?
by that i mean that, from what i have seen of dr randell mill's work, the group that you've come up with (which after doing a google search "SU(2)xU(1)xU(1)" comes up with some veerry interesting publications... dating back to *1977* (1)) could be said to be a solution of maxwell's equations for mobius elliptically-polarised light (2) (3).
by virtue of the quite reasonable statement that *not every* photon is elliptically-polarised, we may logically surmise that the work that you did *only* applies to photons (aka "particles") which *are* elliptically-polarised mobius double-exponentials... and thus, logically refute the assertion that we "live in a quarternionic 3-sphere".
now, please please note: i am simply asking the question. if you were to go into detail to the level which would satisfy people with experience at the level of mathematics that you and they will comprehend, you will lose me *instantly*
however, the question still stands, as best i can ask it. and i have to say that even if the answer turns out to be "oops, yes you're right", the fact that you've discovered a group which can help solve elliptically-polarised mobius light superposition maxwell's equations is... well... absolutely fantastic and (understatement, here) an incredibly important breakthrough in its own right.
(1) Progress of Theoretical Physics, Vol. 58, No. 6, December 1977
SU(2) X U(l) X U(l) Gauge Theory of Weak
and Electromagnetic Interactions in a Unified SU(6) Scheme
Kenzo INOUE, tl Akira KAKUTO, * Hiromasa KOMATSU and Y oshimasa NAKANO
note IN PARTICULAR equation (10) which involves sin2 which means double the angle which means "mobius" topology. randall mills (4) also uses sin2 in a formula representing the neutrino... just in pure maxwell's equations, no "groups"... but it's the same thing.
(2) Multi-twist optical Mobius strips
Isaac Freund
arxiv:0910.1663
and other papers by freund.
(3) Optical Polarization Mobius Strips and Points of Purely Transverse Spin Density
Thomas Bauer,1, 2 Martin Neugebauer,1, 2 Gerd Leuchs,1, 2, 3 and Peter Banzer1, 2, 3,
arxiv:1601.06072
note especially figure 2(b) BUT, remember: the nonradiating condition has NOT been applied in this work (nor in freund's work).
(4)
http://brilliantlightpower.com/book-dow ... streaming/ - current edition sep 2016
http://brilliantlightpower.com/wp-conte ... ok-Web.pdf
joy: question for you, in context of the above.
is it *really* the case that space may be concluded to be an quaternionic 3-sphere, or is that purely limited to the local interactions of matter?
by that i mean that, from what i have seen of dr randell mill's work, the group that you've come up with (which after doing a google search "SU(2)xU(1)xU(1)" comes up with some veerry interesting publications... dating back to *1977* (1)) could be said to be a solution of maxwell's equations for mobius elliptically-polarised light (2) (3).
by virtue of the quite reasonable statement that *not every* photon is elliptically-polarised, we may logically surmise that the work that you did *only* applies to photons (aka "particles") which *are* elliptically-polarised mobius double-exponentials... and thus, logically refute the assertion that we "live in a quarternionic 3-sphere".
now, please please note: i am simply asking the question. if you were to go into detail to the level which would satisfy people with experience at the level of mathematics that you and they will comprehend, you will lose me *instantly* :)
however, the question still stands, as best i can ask it. and i have to say that even if the answer turns out to be "oops, yes you're right", the fact that you've discovered a group which can help solve elliptically-polarised mobius light superposition maxwell's equations is... well... absolutely fantastic and (understatement, here) an incredibly important breakthrough in its own right.
(1) Progress of Theoretical Physics, Vol. 58, No. 6, December 1977
SU(2) X U(l) X U(l) Gauge Theory of Weak
and Electromagnetic Interactions in a Unified SU(6) Scheme
Kenzo INOUE, tl Akira KAKUTO, * Hiromasa KOMATSU and Y oshimasa NAKANO
note IN PARTICULAR equation (10) which involves sin2 which means double the angle which means "mobius" topology. randall mills (4) also uses sin2 in a formula representing the neutrino... just in pure maxwell's equations, no "groups"... but it's the same thing.
(2) Multi-twist optical Mobius strips
Isaac Freund
arxiv:0910.1663
and other papers by freund.
(3) Optical Polarization Mobius Strips and Points of Purely Transverse Spin Density
Thomas Bauer,1, 2 Martin Neugebauer,1, 2 Gerd Leuchs,1, 2, 3 and Peter Banzer1, 2, 3,
arxiv:1601.06072
note especially figure 2(b) BUT, remember: the nonradiating condition has NOT been applied in this work (nor in freund's work).
(4) http://brilliantlightpower.com/book-download-and-streaming/ - current edition sep 2016 http://brilliantlightpower.com/wp-content/uploads/theory/GUT-CP-2016-Ed-Book-Web.pdf