From: tjroberts137@sbcglobal.net   
      
   On 6/24/18 3:29 PM, Gregor Scholten wrote:   
   > Tom Roberts wrote:   
   >> In GR, the local laws of physics are the same everywhere, including the   
   >> laws that govern the ticking of watches. So the two watches tick at the   
   >> same rate (assuming they are identical).   
   >   
   > Measured in the proper time of an observer, the clock of this observer   
   > always ticks with the same rate, that is correct.   
      
   Yes. This is essentially a tautology -- that's what those words mean.   
      
   This discussion is as much an issue of English word usage as it is   
   physics.   
      
   > However, one can consider two clocks on different positions in a   
   > gravitational field - e.g. one clock at the bottom of a tower and the second   
   > clock at the top of that tower - and construct a coordinate system, e.g.   
   > Schwarzschild coordinates, to describe the spacetime region around the two   
   > clocks, and see one clock ticking slower compared to the coordinate time   
   > than the other clock.   
      
   Certainly. But don't think you are comparing clock tick rates,   
   because you are clearly comparing clocks to coordinate time.   
   Coordinates are arbitrary, and one could construct coordinates   
   relative to which either clock ticks more slowly than coordinate   
   time, or they tick the same.   
      
   >> All too many elementary books and discussions talk about "clocks ticking   
   >> slower" than other clocks. In GR this is just plain wrong -- all clocks   
   >> tick at their usual rate, no matter where they are located or how they   
   >> might move   
   >   
   > Once again: this holds for the tick rate of a clock measured in the clock's   
   > own proper time.   
      
   Yes. That is what we MEAN by "a clock's tick rate". That phrase   
   does not mention anything but the clock, so measuring it must not   
   include anything other than the clock itself -- certainly not signals   
   from the clock to a measuring instrument, or some arbitrary coordinate   
   system.   
      
   > But it does not hold e.g. when comparing the clock's proper time to the   
   > coordinate time of some coordinate system.   
      
   Of course not -- coordinate systems are arbitrary. But if that's   
   what you are doing, YOU SHOULD SAY SO. Just saying "moving clocks   
   run slow" or "higher clocks run fast" is just plain wrong -- they   
   all run at the same rate, because that is what these words mean.   
      
   As I said to Mr. Vroom: a clock's tick rate can only be measured   
   by a co-located and co-moving observer; anything else involves   
   signals, not just the clock.   
      
   Tom Roberts   
      
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