From: gerry@bindweed.com   
      
   In article , Iguy@myhouse.com says...   
   >   
   > Can the fact that galaxies are receding from each other faster   
   >  than light violate causality?   
      
      
   What we observe is that the galaxies are moving apart.  (And obviously   
   we have never observed a galaxy moving away from us faster than light.)   
      
   If we choose to use the conventional coordinate system (co-moving   
   coordinates) in which the galaxies are not moving, then to make this   
   compatible with observations, we must consider the space between the   
   galaxies (in the co-moving coordinate system) to be expanding.  That is   
   where 'expanding space' comes from - it really is that simple!  It's   
   just a description of the (more or less) inertial movement of the   
   galaxies.   
      
   We could choose a coordinate system in which the galaxies are exploding   
   out from a central point (essentially the Milne universe).  In this   
   coordinate system, space would not be expanding.   
      
   It is instructive to compare the two coordinate systems, as it   
   elucidates very clearly why the faster than light recession in co-moving   
   coordinates is not paradoxical.   
      
   In the Milne system, we use special relativistic coordinates to describe   
   the motion of galaxies.  In the frame of reference of our own galaxy   
   [more precisely a local group of gravitationally bound galaxies], all   
   the other galaxies are moving away, and the further away they are, the   
   faster they are moving.  Importantly, that means that - in our frame of   
   reference - they undergo time dilation.  Which means that *now*, in our   
   frame, they are younger than our galaxy.  The furthest visible ones are   
   very young, and traveling at nearly the speed of light.   
      
   Now let's see how this works in co-moving coordinates.  None of the   
   galaxies are moving, so they all age at the same rate.  That means that   
   for distant galaxies 'now' in the co-moving frame is far in the future   
   of 'now' in the Milne frame.  In the Milne frame, the plane of   
   simultaneity of the co-moving frame is an upwardly concave hyperbola.   
      
   If a galaxy in the co-moving frame is X light years away today, then in   
   a year's time it may be X + 10 light years away.  That seems   
   problematic, until you remember that in a year's time, its 'now' in the   
   co-moving frame, as described in the special relativistic Milne frame,   
   has also advanced ten years or more.  So, no paradox.   
      
   The paradox comes from forgetting that 'now' means something   
   considerably different in the two frameworks.   
      
   - Gerry Quinn   
      
   ---   
   This email has been checked for viruses by Avast antivirus software.   
   https://www.avast.com/antivirus   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)