Re: Cayley algebra - Octonions. What is interesting now in Physics (For Non-experts again)

[Aiviet Nguyen <aiviet@cat.syr.edu>]

Hi Anh Hale,
 I have already have a non-expert review on string and high-dim theories 
on VNSA in the thread "Can we understand smart guys".
  I personally, don't believe in any TOE ( Theory of everything). In 
principles, I see it as an effort of a crazy man who tries to lift himself
up by pulling his hair.
  In fact in late eighties, people were excited about strings and their 
promises. Strings geneRATED a generation of physicists thinking in a 
string way. You could have found job without strings. Today, stringists 
have switched to Computer Physics or went to Wall Street ( they were 
among the cleverests). However, I should say here that good ideas will 
never die. They will find a new form of existence to survive.
  The passion of strings was revived by John Schwartz   at Caltech and 
exactly atracted attention by explaining why the dimension is 10 or 26.
It was discovered that when a field theory is quantized, some troubles
emerge ( so called anomaly). In the mathematical terms, quantum anomalies
have origin in the index theorems. I will not go into details here.
 There is a possibility that the anomalies can have opposite sign and 
they can cancelled each other if the theory has more components. The 
multi-dimensional theories are one way to introduce multi-fields as 
components of an unique object. The way to go from a multi-dimensional 
theory to the usual 4-dim field theory is through a process called 
dimesion reduction. Similarly, string theory can also be expanded into a 
series and in a low energy limit few first terms will give field theories.
  By a mystery, the strong theory in 26 dim and superstring in 10-dim 
has no anomaly ( trouble). If we believe that God does not like trouble 
when he built the World we suspect that the theory of everything should 
not have trouble. So 10 and 26 dims are very specific.
 The early nineties lost the passion on too complicated theories ( mainly 
because of the shrinking budget) and looked for phenomenological models.
Stringists generated a lot of phenomenological models "derived" from 
string theories.
  Recently, the noisiest fashion in Physics is the Seiberg-Witten duality.
It leads to amazing developements in String theories. I am sorry that I 
cannot follow up the latest trends. However, the duality has a very deep
and profound significance in any discipline. The promise of this theory 
to Physics is to solve the Strong Interaction problem. In Mathematical terms,
if you add some small term into a solved equation you can always use the 
perturbative series to solve it. With a big term ( strong interaction) 
there is no way to do the calculation than to solve it directly and in 
most case it is impossible.
  The duality is a relationship that connect a weak coupling theory with 
a strong coupling theory. It maybe possible a so called duality 
transmation that transforms one theory into the other and vice versa.
If it is the case, you can transform a strong coupling theory into and 
the dual weak theory., solve the weak theory perturbatively and use the 
duality transformation to trnsform the solutions back into the strong theory.
 They found the supertsymmetric N=2 QCD is in fact a dual theory. It is 
believed widely that duality is universal.( You can think of Jing-Jang as 
a very good and simple model for the world).
  I heard that recently they found a lot of new solutions including 
blackholes that may have very important implications for Physics thanks 
to duality.
  Somebody else may know more than me.
Anyway, in my personal opinion, in the whole Physics this maybe the only 
point you can expect a break through the current conceptual crisis.
 Cheers
  Aiviet


 On Thu, 13 Mar 1997, Ha Le wrote:

> 
> Cha`o Ba'c A'i Vie^.t,
> 
> Ba'c no'i Cayley algebra thi` to^i ngo^. ra ro^`i. To^i bi. ma('c 
> ke.t o+? ca'i dda^`u octo-, nghi~ ra(`ng chu' na`y pha?i 10 dim la` i't :-)
> ca?m o+n Ba'c nhie^`u.
> 
> Btw, recently i read a book named "Superstring theory - a TOE?", a kind 
> of "for the dummies" series. After all the praises and optimistic 
> statements, three most "sensitive" problems are pointed out: 
> First, it can not yet explain why the model have 9 or 10 or whatever 
> dimension. Second, It can not yet tell what the topology of a point ( 
> which is very thick!) look like.  And finally, it is too unrigorous (sp?)
> in the sense that usually, a theory is accepted if it can predict something 
> and is later confirmed by the experimenters. So far, it has not 
> made any kind of prediction!
> 
> The book is dated back in 88', so it would be wonderful if our string 
> theorists can explain to me about the current "state of the art" of this 
> theory (or these theories, i'm not so sure :-)).
> 
> TQ
>