From: tjoberts137@sbcglobal.net   
      
   On 7/24/23 10:22 AM, Julio Di Egidio wrote:   
   > On Monday, 24 July 2023 at 09:06:24 UTC+2, Stefan Ram wrote:   
   >> The length of each of these world lines, measured in the metric of   
   >>  spacetime, gives the the time that has passed for each of them.   
   >   
   > No, [...]   
      
   Yes. That path length is the elapsed proper time of each twin, because   
   these are timelike paths through spacetime.   
      
   > it gives the time *it takes* to each of them,   
      
   That's just another way of saying the same thing. The elapsed proper   
   time along a path is indeed the time it takes along that path.   
      
   > whence they do not in fact get to the "rendez-vous" point at the same   
   > time,   
      
   PUN ALERT -- you did not specify what you mean by "time". This is   
   apparently the source of your confusion.   
      
   Note that to twin 1, twin 2 arrives at their rendezvous simultaneously   
   with their own arrival. Ditto for 1<=>2. Ditto for any other observer or   
   coordinate system. Because that rendezvous is a single event in spacetime.   
      
   > the travelling twin getting there "earlier" and meeting *a future   
   > (along their worldline, whence older) version of* the twin that   
   > stayed, and, conversely, the twin that stayed getting there "later"   
   > and meeting *a past (whence younger) version of* the twin that   
   > travelled.   
      
   This is just plain wrong. You are attempting to compare values in two   
   different coordinate systems as if they were comparable. They aren't.   
   This is directly related to the PUN above -- you are using two different   
   meanings for "time" (one for each twin) and then comparing them. That's   
   invalid.   
      
   The twins reunite at a single event in spacetime. That rendezvous is   
   necessarily simultaneous to any observer/coordinates. There is no sense   
   in which one twin arrives "earlier" or "later" than the other, because   
   they arrive TOGETHER.   
      
   Yes, the elapsed proper times along their paths are different. That is   
   the timelike version of the difference in spatial path lengths between   
   (path 1) Chicago to New York and (path 2) Chicago to New Orleans to New   
   York.   
      
   > And I understand that that is not "orthodox", but please let me   
   > propose that it is the correct reading of Einsteinian Relativity,   
   > under the notion of "proper time" as "locally universal" time,   
      
   I have no idea what you are talking about. Making up new concepts   
   ("locally universal") is not useful, especially in a theory as well   
   known as SR. But no matter -- the twins reunite at a single event.   
      
   Moreover, the twin paradox shows that proper time is not "universal".   
      
   > together with the "clock postulate", i.e. that all working clocks   
   > indeed tick at the same rate (the proper time rate) in their own   
   > frame of reference.   
      
   That is as much a definition as an hypothesis. But it seems unrelated to   
   your claims of "earlier" and "later".   
      
   Tom Roberts   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)