From: tjroberts137@sbcglobal.net   
      
   On 6/23/18 11:46 AM, Luigi Fortunati wrote:   
   > Twin A is at the base of the tower where the watch  of twin B goes   
   > slower than that at the top.   
      
   	[This is garbled -- is B at the top or bottom? which   
   	 watch goes slower than which? -- Let me stipulate   
   	 that A is at the bottom and B is at the top, and your   
   	 claim is that A's watch goes slower than B's.]   
      
   Not in GR. 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).   
      
   	[This also applies to SR, for watches moving differently.   
   	 Note that this English phrasing implies we are discussing   
   	 the watches' intrinsic tick rates, and NOT how someone   
   	 else might observe them.]   
      
   Note that if one COMPARES their watches' ticking via light signals that   
   carry ticks from one to the other, one finds that watch A ticks more   
   slowly than SIGNALS from B, and also watch B ticks faster than SIGNALS   
   from A [#]. This statement is very different from yours.   
      
   Other methods of comparison are possible; all physically realizable ones   
   yield the same result, including a very different approach: start with   
   them together and synchronized, move them slowly to the tower's top and   
   bottom, wait a while, move them slowly back together, and compare their   
   displayed times.   
      
   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 (relative to anything) [@]. Relativity is more subtle, and   
   more complicated, than those books and discussions can capture (because   
   they make a fundamentally wrong assumption about clock tick rates,   
   essentially ignoring the first postulate of SR).   
      
   	[#] Interestingly, since light signals follow null   
   	geodesics, the signals are not affected, either. The   
   	entire difference comes from the geometrical projections   
   	involved in the measurements, and the fact that those   
   	projections occur at locations with different values   
   	of the metric. GR is subtle, and at base geometrical.   
      
   	[@] After all, one calculates the interval between ticks   
   	by integrating the metric along the (timelike) path of   
   	the clock. Ticks always occur the same time-interval   
   	apart (that's what we mean by "clock").   
      
   > [... the moderator answered the rest.]   
      
   Tom Roberts   
      
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