From: jos.bergervoet@xs4all.nl   
      
   On 7/23/2017 9:01 AM, Sylvia Else wrote:   
   > On 23/07/2017 5:17 AM, Jos Bergervoet wrote:   
   >> On 7/22/2017 6:00 PM, Sylvia Else wrote:   
   >>> On 22/07/2017 9:41 PM, LuigiFortunati wrote:   
       ...   
     ..   
   >>>>> Sylvia   
   >>>>>   
   >>>>> [*] Strictly, about 24 hours minus four minutes, because he's   
   >>>>> observing sidereal days, not solar days.   
   >>>>   
   >>>>       Obviously, for the traveling twin, rotations and earth revolutions   
   do   
   >>>> not appear to be regular.   
   >>>>   
   >>>>       As time expands, they take place always more slowly than the   
   >>>> terrestrial brother.   
   >>>   
   >>> Whether the travelling twin is moving away from Earth, or moving towards   
   >>> Earth, time on Earth passes more slowly in the travelling twin's frame   
   >>> that does his time (and vice versa, of course).   
   >>   
   >> If the twin uses the time coordinate in its own inertial   
   >> frame. But the twin could of course use another concept of   
   >> "time on earth". Some options are:   
   >> 1) Using the twin's own time coordinate for the Earth's world-   
   >>       line (as mentioned above).   
   >> 2) Using Earth's time coordinate (which the twin knows) for   
   >>       the Earth's world line (a bit like if we would use the   
   >>       Chinese calendar to answer "What year is it China?")   
   >> 3) Use the time on Earth when the light signals left that are   
   >>       currently reaching the twin's space ship.   
   >> And probably many more..   
   >   
   > The time on Earth in the travelling twin's frame is just a number that   
   > can be plugged into the laws of nature in the twin's frame so as to   
   > predict the outcomes of experiments.   
      
   Yes but any other coordinate system (with other numbers) can   
   also give the right prediction. Using the coordinates of the   
   traveling twin's frame may be most natural for experiments   
   done locally, but perhaps not for very distant and fast moving   
   locations like Earth.   
      
   > In particular, it allows a prediction of what the travelling twin will   
   > see when he points a telescope at Earth.   
   >   
   >>   
   >>> However, in the frame of the travelling twin, time on Earth makes an   
   >>> abrupt jump forwards when the twin reverses direction,   
   >>   
   >> That is when you use option 1) *and* if you make the twin   
   >> reverse direction abruptly. (Which would be an even greater   
   >> achievement than merely make her travel at relativistic speed!)   
   >   
   > If you find it objectionable, then we can arrange for a second   
   > spacecraft to be travelling in the opposite direction but same speed   
   > relative to Earth. It passes the first spacecraft at the nominal reverse   
   > point and information about the state of the travelling twin's clocks is   
   > transferred.   
      
   But then we need triplets instead of twins!   
      
   Anyhow, what I would prefer is a smooth, uniform de-/accceleration.   
   It would of course be most natural for the traveling twin to use   
   Rindler coordinates during that phase. The Rindler coordinates   
   seamlessly match the Minkowski space coordinates at the points   
   where the turn-around phase starts and stops. In fact, Rindler   
   coordinates for the twin can be computed simply as Minkowski coordinates   
   with the speed parameter in the Lorentz transform   
   continuously changing.   
      
   This gives a continuous description without any jumps (it could   
   also be done for the acceleration phase at departure from Earth   
   and later at re-arrival).   
      
   >    The clocks on the second space craft when it arrives at   
   > Earth will reflect the age the travelling twin would have had, had he   
   > (and the spacecraft) been able to survive his jumping between them.   
      
   A smooth ride with Rindler coordinates will save his or her life!   
      
   >>>      whereas in the   
   >>> frame of Earth, time for the travelling twin makes no such abrupt jump.   
   >>> The moderator alludes to that below. Not that the travelling twin   
   >>> observes any such jump through the telescope - all he sees is that the   
   >>> rotation rate of Earth appears to increase.   
   >>   
   >> Of course, because the telescope shows time according to   
   >> definition number 3) above, not 1).   
   >>   
   >>>> [[Mod. note -- It's important to remember that when the travelling   
   >>>> twin reverses her direction, her   
   >>>> lines-of-simultaneity-in-a-Minkowski-diagram change.  There's a nice   
   >>>> diagram of this at   
   >>>>       https://en.wikipedia.org/wiki/Twin_paradox#Relativity   
   of_simultaneity   
   >>>> This means that the "earthly revolutions" she observes accumulate at   
   >>>> what she measures to be a very NON-uniform rate, so the "average" the   
   >>>> the author refers to is averaging over a very disparate set of   
   >>>> observations.   
   >>>> -- jt]]   
   >>   
   >> Yes, but I really do expect the twin to be aware that insisting   
   >> that this really defines the time on Earth is a bit, well,   
   >> provincial!   
   >>   
   >   
   > SR can be viewed as a projection of one space-time frame onto a second   
   > one.   
      
   And Rindler coordinates continuously change between different   
   projections based on the changing speed of the accelerating   
   twin. That's about as far as you can stretch SR to describe   
   something which is essentially GR (acceleration).   
      
   --   
   Jos   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)