From: relativity@paulba.no   
      
   Den 09.10.2025 09:32, skrev Thomas Heger:   
   > Am Dienstag000007, 07.10.2025 um 10:51 schrieb Paul B. Andersen:   
   >>>>>   
   >> OK.   
   >> Since you are not trying to defend your statement:   
   >>   
   >>   "Other observers in other locations have a local future,   
   >>    too, but that can actually be your past."   
   >>   
   >> . . you must have realised that it is meaningless nonsense.   
   >   
   > It is an assumption.   
   >   
   > This assumption says, that time is local only.   
   >   
   > This means: the universe has not really an age, because it 'folds back   
   > into itself'.   
   >   
   > This idea is a little tricky, but imagine a Moebius strip. That has only   
   > one side, even if a sheet of paper has two.   
   >   
   > Now place something (like e.g. yourself) upon one side and walk into one   
   > direction, then you would end up upside down below your feet and would   
   > walk into the opposite direction.   
   >   
   > Now think about this phenomenon in 3D.   
      
   Enough mindless nonsense.   
      
   Let's revert to the real world.   
      
   The subject line is: The problem of simultaneity.   
      
   If you read and understand the following, your problem   
   with simultaneity will be solved.   
      
   But considering all the nonsense you have written,   
   I doubt that you are able to understand the logic.   
      
   But maybe you will surprise me?   
      
   -----------------------------   
      
   We start with this quote:   
      
   quote from § 1. Definition of Simultaneity   
   -------------------------------------------   
   |  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."   
      
   Note that this statement imply that A and B are stationary   
   relative to each other.   
      
   This definition together with the two postulates of SR means:   
          The speed of light is isotropic c by definition.   
      
   This is a definition of simultaneity, see below.   
      
   That two clocks are synchronous means that they   
   simultaneously show the same.   
   (This is the definition of "synchronous".)   
      
   Einstein made 'an imaginary physical experiment':   
   (That is a _thought experiment_)   
      
      
   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 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.   
      
   In a thought experiment measurements can be made with   
   infinite precision, and we can sit at our desks and analyse it.   
      
   The transit time is d/c where d is the distance between A and B.   
   Let clock B be F ahead of clock A, where F is between 0 and   
   a long time.   
      
   We then have: tB  = tA + d/c + F   
   and:          t'A = tB + d/c - F   
      
   so:  (tB - tA)  = d/c + F   
         (t'A - tB) = d/c - F   
      
   If (tB - tA) = (t'A - tB)  then (d/c + F) = (d/c - F),   
   which is true only if F = 0,   
   the clocks simultaneously show the same.   
      
   This means:   
      
       TB = (TA + d/c)   
     When clock B shows TB clock A simultaneously   
     shows (TA + d/c), which is the same.   
      
       t'A = (tB + d/c)   
     When clock A shows t'A clock B simultaneously   
     shows (tB + d/c), which is the same.   
      
      
   Thus:   
     In accordance with definition the two clocks are synchronous if   
          tB − tA = t′A − tB.   
      
   This is a logical consequence of the postulates of SR   
   and that the speed of light is isotropic.   
      
   Einstein's definition of simultaneity is mathematically   
   consistent.   
      
   This doesn't say anything about whether or not SR's   
   predictions are in accordance with measurements.   
   Only real experiments can do that.   
      
      
   --   
   Paul   
      
   https://paulba.no/   
      
   --- SoupGate-Win32 v1.05   
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