From: ram@zedat.fu-berlin.de   
      
   ram@zedat.fu-berlin.de (Stefan Ram) writes:   
   >Now a scientist comes along and says: I formally extend this world   
   >to a two-dimensional world with the coordinates (x,y).   
      
     To explain why I made this post, which introduces what appears   
     to be a redundant coordinate:   
      
     The unit circle is typically defined as a set of points in a   
     plane whose distance from a central point is equal to 1 (one).   
      
     Accordingly, using polar coordinates, the unit circle is the set   
     {(r, phi)|r = 1}.   
      
     I think of the circle as a world and the coordinate system as a   
     tool introduced to describe that world.   
      
     The coordinate "phi" seems redundant since the world does not   
     depend on it; one could omit it and just use { r | r=1 } to   
     describe this world.   
      
     It appears that the notion of rotational symmetry being a   
     symmetry operation may arise due to the redundancy present   
     within the coordinate system (r, phi).   
      
     After sending my previous post, I discovered some sources   
     expressing ideas similar to mine:   
      
   |Gauge symmetries are redundancies in the mathematical description   
   |of a physical system rather than properties of the system itself.   
   |[...] The difficulty of making these laws explicit in a natural   
   |and non-redundant way is the reason for "gauge symmetry".   
   Symmetry and Emergence (2018) - Edward Witten (1951/)   
      
     If what Witten says is true, then it is not surprising that   
     in some cases a physical system has no symmetry until one   
     considers its mathematical description!   
      
     Witten also gives an example, here it is in the words of Seiberg:   
      
   |It is often the case that a theory with a gauge symmetry is dual to   
   |a theory with a different gauge symmetry, or no gauge symmetry at   
   |all. A very simple example is Maxwell theory in 2+1 dimensions. This   
   |theory has a U(1) gauge symmetry, and it has a dual description in   
   |terms of a free massless scalar without a local gauge symmetry.   
   Emergent Spacetime (2005) - Nathan Seiberg (1956/).   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)