Re: What is interesting in Physics

[Tuan Anh Tran <tat1821@unix.tamu.edu>]

On Mon, 17 Mar 1997, Ha Le wrote:

> 
> Hi Ba'c A'i Vie^.t,
> Thanks much for answering my question. I do need some time to digest what 
> you wrote and besides, i would like to hear from the "pro".
>    
>   I personally, don't believe in any TOE ( Theory of everything)...
> 
> As i understand, "everything" here just mean a unification theory, it 
> does not mean "everything" i.e the end of Physics. In this respect, is 
> string theory has any chance? 
> 

There are five different string theories. Since you don't believe in 
TOE, there is no problem. If you want to have a unification theory, five 
string theories are gonna be too many candidates. I personally don't 
think that string theories will be a candidate of unification theory.  

> 
>   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. 
> 
> i'm not sure if i understand here, so you mean that istead of considering 
> each "individual" anomaly, they consider a kind of moduli space of all 
> anomalities by throwing in more dimensions?   
> 
> The way to go from a multi-dimensional 
> theory to the usual 4-dim field theory is through a process called 
> dimesion reduction. 
> 
>  Do you have any simple example of this "dimension reduction" process?
> 
> 

Tough question. Naively, you can think as follows:

let us take a plan which is 2-dimensional space (x,y). -infinity< x 
<+infinity, -infinity< y < +infinity. Then we identify -infinity and 
+infinity of x-axis (for example). The x-axis becomes a cirle of 
infinite radius (R=infinity).  If you can let R-->0, the x-axis will be 
disappeared and this procedure reduces your plane (2-dim) to a line 
(1-dim) namely y-axis only. In fact, what people do is to take an axis 
(let say X) and assume that X=X+2*pi*interger.  


> It is believed widely that duality is universal.( You can think of Jing-Jang as 
> a very good and simple model for the world).
> 
> If i remember correctly, one of Hilbert's problem is to describe the 
> so-called "universal duality" - I dont' really understand what it means, 
> but it seems that he wanted a kind of axiommatic approach to duality 
> phenomena so that for example if something is true, then we get for free its 
> "duality" is also true !?
> 
> Btw, Can you explain the phenomenon "Cu+.c du+o+ng sinh a^m (and vise 
> versa) " in terms of say, perhaps entropy? 
> cheers!
> Ha
>