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Subject: Re: [SR] Their proper times will necessarily be equal
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Date: Sun, 21 Apr 24 21:42:24 +0000
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From: Richard Hachel   <bts.orange@licorne-bleue.fr>
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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.