Hello Mr. Garrett!,
I would like you to comment on this. The guy who pointed you some mistakes (Jacques Distler), made several more remarks about your theory, specially after DEC 9TH. He seems to be changing his mind every day, maybe he is confused.
He is still seems to be very hostile to your theory. But if you discuss with him, it would be profitable, as his got some new maths. He is saying you are not even getting the 1st generation right
http://golem.ph.utexas.edu/~distler/blog/archives/001505.html#AlittleU4
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Update (11/29/2007):
David Vogan, from MIT, wrote me to point out that I was too fast in saying that G does not embed in F 4×G 2. It is possible to find such an embedding, but it necessarily leads to a completely nonchiral “fermion” representation (and hence contains no copies of R). I simply didn’t bother considering such embeddings, when I was preparing this post. For the record, though
F 4(−20)⊃Spin(8,1)⊃Spin(3,1)×Spin(5)⊃SL(2,ℂ)×SU(2)×U(1)
and
F 4(4)⊃Spin(5,4)⊃Spin(3,1)×Spin(2,3)⊃SL(2,ℂ)×SU(2)×U(1)
In the latter case, one obtains
26=1+9+16 =(1,1) 0+(4,1) 0+(1,3) 0+(1,1) 2+(1,1) −2 +(2,2) 1+(2,2) −1+(2¯,2) 1+(2¯,2) −1 52=36+16 =(Adj,1) 0+(1,3) 0+(1,1) 0+(1,3) 2+(1,3) −2+(4,3) 0+(4,1) 2+(4,1) −2 +(2,2) 1+(2,2) −1+(2¯,2) 1+(2¯,2) −1
In the former case, there are two distinct embeddings of SU(2)×U(1)⊂Spin(5). For the one under which 4=2 1+2 −1, one obtains the same result as above. For the one under which 4=2 0+1 1+1 −1, one obtains
26 =2(1,1) 0+(4,1) 0+(1,2) 1+(1,2) −1 +(2,2) 0+(2,1) 1+(2,1) −1+(2¯,2) 0+(2¯,1) 1+(2¯,1) −1 52 =(Adj,1) 0+(1,3) 0+(1,1) 0+(4,1) 0+(1,1) 2+(1,1) −2+(1,2) 1+(1,2) −1+(4,2) 1+(4,2) −1 +(2,2) 0+(2,1) 1+(2,1) −1+(2¯,2) 0+(2¯,1) 1+(2¯,1) −1
Putting these, together with the embedding of SU(3)⊂G 2,
7 =1+3+3¯ 14 =8+3+3¯
into (3), one obtains a completely nonchiral representation of G.
Update (12/10/2007):
For more, along these lines, see here
http://golem.ph.utexas.edu/~distler/blog/archives/001532.html
Correction (12/11/2007):
Above, I asserted that I had found an embedding of G with two generations. To do that, I had optimistically assumed that there is an embedding of SL(2,ℂ) in a suitable noncompact real form of A 4, such that the 5 decomposes as 5=1+2+2. This is incorrect. It is easy to show that only 5=1+2+2¯ arises. Thus, instead of two generations, one obtains a generation and an anti-generation. That is, the spectrum of “fermions” is, again, completely non-chiral. I believe (but haven’t proven) that this is a completely general result: for any embedding of G in either noncompact real form of E 8, the spectrum of “fermions” is always nonchiral. Let’s have a contest, among you, dear readers, to see who can come up with a proof of this statement.I apologize if I’d gotten anyone’s hopes up, with the above example. Not only can one never hope to get 3 generations out of this “Theory of Everything”; it appears that one can’t even get one generation.
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And here is a post apparently claiming a final blow (not his words, but my emotional interpretation). A certain mark refers to Smolin and you almost as crackpots (again, not his words, but my emotional interpretation)
http://golem.ph.utexas.edu/~distler/blog/archives/001532.html#more
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There it is Garrett. Would you have some comments about that?
. Problem is this is a wait for prices and technology to converge issue. I'm reasonably certain a 16way AMD64 system will be fairly cheap to build in about 18 months.
