Re: Dualism & Micro-Macro

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

Hi Sonnet et al,
  Thank you for the enlightening discussion on the "matter" and "energy".
Let me digest and understand better what you mean to say.

  Let me add few word about the duality. The duality is a very natural 
and universal thing. From Yin-Yang to girl-boy, wave-particle,...and 
among them "matter" and "energy" as you said.

  However, the dualism I mentioned is a litle bit more than that ( 
hopefully). The dual theories, that are interrelated to each other.
Using your matter-energy pair we can have another dual theory where matter
becomes energy and energy becomes matter. There are two kinds of dualities
in such a framework. The theory duality and the component duality.

  As the theories interchange the components also. The Sonnet arguments
is just a projection of this in a specific language. Let me take a diagram
method to represent the phenomena. We have a diagram with nodes and links.
OK, nodes are matter ( or elements) and links are energies( or mor 
exactly interactions). The very usual practice in Physics is to transform 
this diagram into another diagram where nodes become links and vice versa.
Sometimes the new theory is easier to compute.

  The Maxwell Electrodynamics has also a electricity-magnetism duality.
However, at the theory level, this theory is self-dual ( if monopole is 
there). That means if you interchange electricity and magnetism you have the
same theory. The Yang-Mills theories are self-dual.

  Now, the Seiberg-Witten's duality is promissing because they try to
solve the weak-strong theories' duality via a component level duality
: i.e the soliton-basic field duality.

   The practical significance of this duality is that: the strong 
interaction is hard to studied. If the weak dual theory exists we can
studied this instead and transform the result back to the weak region.

   So the analysis should not start with a given theory, but should start
with formulation of the theory so that the further analysis is possible.

Cheers
Aiviet

PS: Let me think about the dual of money later. Maybe that is my wife:-)))
    She like s shopping.