From: helbig@asclothestro.multivax.de   
      
   In article <0c7a7059-b37b-4024-aad4-93536e301d1d@googlegroups.com>,   
   Savin Beniwal  writes:   
      
   > I have questions regarding the Cosmological Principle that usually we   
   > study universe is SPATIALLY homogeneous and isotropic(around every   
   > point) at large scale (>150MPC).  Here homogenous means--> No special   
   > location and Isotropic means-->No special point. Also, this was   
   > confirmed by Hubble in 1929 that if distances are expanding (or   
   > contracting), the speed must be proportional to distance =E2=80=93 Hubble=   
   's Law   
   > is inevitable.   
   >   
   > But my questions is that if there were a proportionality relation   
   > between velocity and square of distance rather than a linear relation   
   > between r and v. Even then can we understand the homogenous and   
   > isotropic concept from Hubble's law under this nonlinear relation?   
      
   No.   
      
   Say you are at the origin, at distance 1 velocity is 1, at distance 2   
   velocity is 4, at distance 3 velocity is 9, and so on.  For an observer   
   at distance 1, your distance 2 is just 1 unit of distance away, but its   
   speed relative to the observer at 1 is 3 (4-1), whereas it should be 1   
   if the distance is 1.   
      
   In short, homogeneity and isotropy demand a linear velocity--distance   
   law, since otherwise homogeneity and isotropy couldn't persist.  (Note   
   that this is purely kinematics, no dynamics, hence this does not depend   
   on general relativity in any way.)   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)