From: nospam@de-ster.demon.nl   
      
   Tom Roberts  wrote:   
      
   > On 5/31/22 2:54 AM, Luigi Fortunati wrote:   
   > > In accelerated reference frames, the clocks do not stay synchronized   
   > > with each other.   
   >   
   > Hmmm. Clocks that are at the same "altitude" relative to the   
   > acceleration do remain synchronized.   
   >   
   > Note also that "accelerated frame" is an oxymoron -- "frame" implies a   
   > set of four mutually-orthogonal coordinate axes, which can occur ONLY   
   > for inertial coordinates.   
   >   
   > > Yet on Earth, which is an accelerated reference frame,   
   >   
   > No, it is not. On the surface of the earth, a "small" region of   
   > spacetime can be considered to be equivalent to an accelerated system in   
   > flat spacetime, but larger regions on the surface are nowhere close to   
   > an accelerated system in flat spacetime. Here "small" depends on one's   
   > measurement accuracy.   
   >   
   > > all the clocks that are at the same altitude remain perfectly   
   > > synchronized with each other wherever they are, why?   
   >   
   > Because in weak gravity, "gravitational time dilation" depends on the   
   > gravitational potential, which primarily depends on altitude (as in an   
   > accelerated system in flat spacetime). This is only approximate: when   
   > measured very accurately, the potential at a given altitude depends on   
   > the density of the material below, and on the positions of sun, moon,   
   > and planets above -- at 15,000 feet above earth's geoid, the potential   
   > over Pike's Peak is measurably different from that over Death Valley.   
      
   Certainly, but one should realise that there is no such thing   
   as an absolute value of the Newtonian potential.   
   It depends on which masses you consider to be relevant,   
   at your level of approximation.   
   Or in other words, where you consider a practical 'at infinity' to be.   
      
   Fortunati says correctly that all clocks on a Newtonian equipotential   
   system, calculated with respect to all masses on the Earth,   
   will remain synchronised. (for all practical purposes, on Earth)   
   But they will not remain synchronised when you also consider   
   the (as yet unobservably small) gravitational effects of the Sun   
   at diferent places on Earth.   
      
   In practical terms, for all 'sub-lunar' calculations   
   the relativistically corrected TCG timescale will do.   
   (which takes only terrestrial relativistic corrections into account)   
   If you want to go further out in the Solar system you need TCB,   
   which corrects for solar gravitational effects.   
      
   BTW, for practical purposes all those relativistic time scales   
   are computed as corrections to TAI,   
      
   Jan   
      
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