XPost: sci.physics.relativity   
   From: relativity@paulba.no   
      
   Den 15.09.2025 08:38, skrev Thomas Heger:   
   >   
   > It starts with the lack of a proper definition of t_A and t_B.   
   >   
   > If disconnected local times are meant with 'A-time' and 'B-time' and t_A   
   > was measured in 'A-time' and t_B by means of 'B-time', than   
   > t_B-t_A would be an illegal operation to begin with.   
   >   
   > Therefore t_A and t_B must be based on 'A-time' only. And that in turn   
   > would make 'B-time' irrelevant.   
   >   
   > That isn't bad at all, because the clock in B shall be synchronized with   
   > the clock in A, anyhow.   
   >   
      
   quote from § 1. Definition of Simultaneity   
   -------------------------------------------   
   | "If at the point A of space there is a clock, an observer   
   |  at A can determine the time values of events in the immediate   
   |  proximity of A by finding the positions of the hands which   
   |  are simultaneous with these events.   
   |  If there is at the point B of space another clock in all   
   |  respects resembling the one at A, it is possible for an observer   
   |  at B to determine the time values of events in the immediate   
   |  neighbourhood of B."   
      
   An observer at A can determine the time value of the clock at A.   
   An observer at B can determine the time value of the clock at B.   
   Got it?   
      
   quote from § 1. Definition of Simultaneity   
   -------------------------------------------   
   | "But it is not possible without further assumption to compare,   
   |  in respect of time, an event at A with an event at B.   
   |  We have so far defined only an “A time” and a “B time.”   
      
   It is not possible to compare the time of events at A and   
   the time of event at B without further assumptions.   
   Got it?   
      
   So we have to make further assumptions:   
      
   quote from § 1. Definition of Simultaneity   
   -------------------------------------------   
   | "We have not defined a common “time” for A and B, for   
   |  the latter cannot be defined at all unless we establish   
   |  by definition that the “time” required by light to travel   
   |  from A to B equals the “time” it requires to travel from   
   |  B to A."   
      
   The _definition_ of simultaneity is that light uses the same   
   time to go from A to B and to go from from B to A.   
   Got it?   
      
   quote from § 1. Definition of Simultaneity   
   -------------------------------------------   
   | "Let a ray of light start at the “A time” tA from A towards B,   
   | let it at the “B time” tB be reflected at B in the direction   
   | of A, and arrive again at A at the “A time” t′A."   
      
   tA, tB and t'A  are precisely defined as:   
   tA is the time shown by the clock at A when the ray leave A.   
   tB is the time shown by the clock at B when the ray hits B.   
   t'A is the time shown by the clock at A when the reflected ray hits A.   
   Got it?   
      
   quote from § 1. Definition of Simultaneity   
   -------------------------------------------   
   | " In accordance with definition the two clocks synchronize if   
   |       tB − tA = t′A − tB."   
      
   For this equation to be true must   
     tB = (tA + t′A)/2 = tA + (t'A - tA)/2   
      
   Note that Einstein says nothing about how to make   
   asynchronous clocks synchronous. He only says that   
   if  tB − tA = t′A − tB (or TB = tA + (t'A - tA)/2)   
   then the clock at A and the clock at B are synchronous.   
   This is a definition of simultaneity, not a description   
   of how to synchronise clock.   
   --------   
      
   How to synchronise clocks depend on a lot of circumstances,   
   and it would be stupid of Einstein to define a method   
   which should be applicable for all cases in all future.   
      
   To illustrate this problem let's ask:   
   How do we synchronise TAI and UTC clocks?   
      
   Let two clocks A and B be stationary at the geoid at equator.   
   Clock B is a distance L east of clock A.   
   We know that clock A is synchronous with UTC, and we want to   
   synchronise clock B to UTC.   
      
   How do w do it?   
   The problem is that TAI and UTC clocks are synchronous in   
   the non rotating Earth centred frame of reference (ECI-frame),   
   they are NOT synchronous in the ground frame.   
   But the clocks A and B are moving in the ECI-frame,  and   
   we can't stop the spinning of the Earth to sync the clocks.   
      
   The following calculations are made in the ECI frame.   
   v = 465.1 m/s  v/c = 1.55e-6   
      
   We assume that at t = 0 the clocks are synonymous and show 0.   
   That is at t = 0, tA = 0 and TB = 0.   
   If we send a light pulse from clock A to clock B, clock B   
   will move away from clock at the speed v.   
   We can calculate the time the light pulse will use to hit B:   
     ct = L + vt  =>  t = L/(c-v) = (L/c)⋅(1 + 1.55e-6)   
      
   That means that if clock A showed t1 when the light pulse   
   was emitted, then, to be synchronous with clock A, clock B   
   must show t1 + (L/c)⋅(1 + 1.55e-6) when the pulse hits it.   
      
   TAI clocks are routinely synced after the basic principle shown above.   
   (The details are different of course. Satellites, optic fibre, radio)   
      
   --   
   Paul   
      
   https://paulba.no/   
      
   --- SoupGate-Win32 v1.05   
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