From: stargene@sbcglobal.net   
      
   [[Mod. note -- I'm sorry for the delay in processing this article,   
   which the author submitted on 2021-Sept-04.  -- jt]]   
      
   The following quote is from a sciam article titled "Black Hole   
   Computers" by Seth Lloyd and Y. Jack Ng (April 1, 2007).  They   
   are referring to satellites measuring any region with radius R   
   and certain ultimate limits to the possible accuracy which can be   
   obtained by even the most advanced civilization imaginable; lp   
   is the Planck length:   
      
   "..Mathematically, in the time it takes to map a region of radius R,   
   the total number of ticks by all the satellites is R^2/lp^2. If each   
   satellite ticks precisely once during the mapping process, the   
   satellites are spaced out by an average distance of   
   R^(1/3)lp^(2/3). Shorter distances can be measured in one sub-   
   region but only at the expense of reduced precision in some   
   other subregion. The argument applies even if space is   
   expanding.   
      
   This formula gives the precision to which distances can be   
   determined; it is applicable when the measurement apparatus is   
   just on the verge of becoming a black hole. Below the minimum   
   scale, spacetime geometry ceases to exist. That level of   
   precision is much, much bigger than the Planck length. To be   
   sure, it is still very small. The average imprecision in measuring   
   the size of the observable universe is about 10^-15 meter. Never-   
   theless, such an imprecision might be detectable by precise   
   distance-measuring equipment, such as future gravitational-wave   
   observatories--"   
      
   I don't have a concrete grasp of their conclusions-- Are they   
   saying, as an example, if we had a system (equivalent to a   
   cosmic tape measure), any attempt to measure the entire   
   universe would never have an average accuracy finer than   
   ~ 10^-15 meter?  Also, the fact of this "fineness" accuracy,   
   10^-15 meters, re: the "measure of the universe", being   
   roughly the radius of a proton, is fairly astonishing.  Also, what   
   do Lloyd and Ng mean when they say that below that minimum   
   (fineness) scale, spacetime geometry has no meaning?  Would   
   this actually conform with the notion of spacetime being   
   an emergent phenomenon outside of certain defined limits?   
   Thanks, Gene   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)