Wu-Yang Dictionary
And what about Jim Simons? Other than Chern Simons he did amazing stuff. Wu-Yang ...and that holonomy theorem of Berger was first rate.
Anyone else appreciate that Jim Simons redoing Berger's list of holonomy groups to prove intrinsic sphere transitivity? An artist's theorem.
Someone else I admire: Dan Freed at Austin. Dan never gets all the credit he deserves. Every paper nails some loose end for the community.
In Econ. Krugman is the master chef who can start with deadly pufferfish and dependably prepare elegant fugu thats safe to eat.
1/ APRIL FOOLS' SCIENCE: Theory into Practice.
I was challenged by someone as to why I wasn't taking my own medicine referenced in the sub-tweet below this April 1st. Ok. Here goes.
What I believe about the universe that is quite different and why I don't talk about it much... https://t.co/RjqRGc5J9m
2/ When I was around 16-17, I learned of a story that fascinated me much more than it seemed to captivate any other mathematician or physicist. It was the story of the discovery of the "Wu-Yang" dictionary around 1975-6, involving 3 super-minds: Jim Simons, CN Yang & Is Singer.
3/ What was learned was that the Quantum of Planck, Bohr & Dirac was built on an internal Geometry, just as surely as General Relativity was built on an external geometry of space-time. Only the two geometries weren't the same! One was due to B Riemann; the other to C Ehresmann.
4/ Further the 2 geometries had different advantages. Riemann's geometry allowed you to compress the curvature & measure the 'torsion' while Ehresmann's encouraged "Gauge Rotation"... as long as you didn't do either of those two things. So I asked could the geometries be unified?
5/ This would be a change in physics' main question. Instead of asking if Einstein's gravity could fit within Bohr's quantum, we could ask "Could Einstein's structures peculiar to Riemann's geometry be unified & rotated within Ehresmann's?" The answer was almost a 'No!'
Almost.
6/ While physicists said the Universe was known to be chiral, I came to believe it was fundamentally symmetric. While we seemed to observe there being 3 or more generations of matter, I came to believe that there were but 2 true generations, plus an improbable "imposter." etc...
7/ In short a great many things had to be slightly off in our picture of the world in the 1980s to get the two geometric theories into a "Geometric Unity." Then in 1998, it was found that neutrinos weren't massless! This started to tip the scales towards the alterations I needed.
8/ In short the April 1st "trick" that is being played on me is that I see a *natural* theory where chirality would be emergent (not fundamental), the number of true generations would be 2 not 3, there would be 2^4 and not 15 Fermions in a generation, and the geometries unify.
9/ I spoke on this nearly 5 years ago; I have been slow to get back to it as I found the physics response bewildering. I have now decided to return to this work & to disposition it. So over the coming year, I'll begin pushing out "Geometric Unity" (as a non-physicist) to experts.
END/ I am sorry that this was a bit technical for lay folks and not technical enough for experts, but it's twitter. I may begin to say more in the weeks and months ahead that may be clarifying.
If you are interested, do stay tuned. Until then, I thank you for your time.