From: tjroberts137@sbcglobal.net   
      
   On 11/6/19 2:08 AM, PengKuan Em wrote:   
   > The local frame at any point in general relativity is a locally inertial   
   > frame. In such frame, relativity of simultaneity applies, so the time of   
   > point 1 and 2 are different. Suppose they are t'1 and t'2 and   
   > dt'=t'2-t'1 in frame 1. then, in frame 2 next to frame 1, we have   
   > dt'=t'3-t'2. So, we have   
   > t'2=dt'+t'1 in frame 1. Suppose t'1=0. Then,t'2=dt'. Then, we have   
   successively,   
   > t'3=dt'+t'2=2*dt' in frame 2   
   > t'4=dt'+t'3=3*dt' in frame 3   
   > ...   
   > t'(n+1)=dt'+t'n=n*dt' in frame n   
   >   
   > So, the time of the satellite n+1 is n*dt' even in GR. But satellite n+1   
   > is satellite 1 and its time should be 0. Hence, even in GR, relativity   
   > of simultaneity leads to contradiction.   
      
   As I said before, each of those differences is in a DIFFERENT LOCALLY   
   INERTIAL FRAME. You cannot combine them like that.   
      
   You fooled yourself by erroneously using a single prime everywhere, when   
   in fact the differences are:   
       dt' = t'2-t'1   
       dt'' = t''3-t''2   
       dt''' = t'''4-t'''3   
       ... etc.   
       (the number of primes indicates which clock's instantaneously   
        co-moving inertial frame is used)   
   Attempting to add dt' to dt'' makes no sense as it involves frame   
   jumping. Ditto for each of the other pairs.   
      
   There is no contradiction, this is just the well-known Sagnac effect --   
   it directly implies that you cannot consistently synchronize clocks   
   around the circumference of a rotating system. Of course the GPS never   
   does that. Nor does anyone who understands SR.   
      
   Tom Roberts   
      
   --- SoupGate-Win32 v1.05   
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