Re: [SR] Their proper times will necessarily be equal

Le 21/04/2024 à 23:19, Python a écrit :

We may not have the same space-time path, and have the same proper time, the same path, and the same improper time (for other observers).

 To have the same improper time is meaningless because in a given
frame of reference there is a single time elapsed between any
two events. And there are only two events : travelers' depart
and travelers' meeting again.
 Moreover to have the same path (in the spatial sense) is a
property that is only true in a single frame of reference.
 It makes no sense (outside of a trivial one in Galilean Relativity)
to claim that a condition depending on a given chosen frame could
imply a property (equality of proper times) that does not depend
on that.
 

Note that "space-time path", I don't understand the geometric concept very well.

 It's not a big deal! It is the set of events "traveler is at this
position at that time".
 

[snip babbling]

 Your claim is directly violating the principle of Relativity. End of
Story.

Having the same improper time is on the contrary an important relativistic concept, as important as having the same proper time.
For example, in the example of the two travelers from Tau Ceti, Stella and Bella, one in Galilean mode (Vo=0.929c), the other in accelerated mode (a=1.052ly/y²), we notice that the The observer Terrence (terrestrial) will give them the same improper time. That is 12,915 years.
This means that they leave together, make the same journey, and arrive together, although the journey was never joint at any point of the journey.
This is a point that all physicists in the world accept (I hope).
It is on Bella's notion of proper time that we no longer agree because the way physicists go about it in accelerated frames of reference does not seem entirely correct or logical to me.
R.H.