From: darshanbeniwal11@gmail.com   
      
   On Wednesday, 17 July 2019 05:17:51 UTC+5:30, Phillip Helbig (undress to   
   reply)  wrote:   
   > 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.   
      
   Is this way correct to add/subtract  velocities as velocities of   
   galaxy is about the speed of light? If we consider the velocity of   
   galaxy is equal or greater then speed of light (Not a surprise at   
   all), even then there will be a linear relation between velocity   
   and distance as Hubble stated?   
      
   [[Mod. note -- No.  -- jt]]   
      
   > 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)