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From: "Paul.B.Andersen" <relativity@paulba.no>
Newsgroups: sci.physics.relativity
Subject: Re: Understanding the theory of special relativity
Date: Thu, 23 Jan 2025 21:34:07 +0100
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Den 23.01.2025 09:02, skrev Richard Hachel:
> Le 22/01/2025 à 22:11, "Paul.B.Andersen" a écrit :
>> =========================================
>> There is no reciprocity in this scenario.
>> =========================================

The subject line is:"Understanding the theory of special relativity"

What SR predicts is not a matter of opinion, it is a matter of fact.

This is the fact:

https://paulba.no/pdf/TwinsByMetric.pdf
See: 2.3 "B travels with constant acceleration"
and: 2.4 "Concrete example"

> 
> There is reciprocity ; and accelerations, weight, gravity have nothing 
> to do with the theory of relativity.

Gravitation has nothing to do with The Special Theory of Relativity.
But in this scenario twin B is accelerating during the whole journey,
and an accelerated object has weight.

> There is 
> reciprocity.  Why?
> Because the theory of relativity, and more precisely the Lorentz factor, 
> which is one of the cornerstones of understanding, only relies on one 
> thing: relative speed.

The Lorenz factor depends only on their relative speed.
But their speed in an inertial frame also depends on their
_proper_ accelerations.

See equation (14)

So for the scenario to be reciprocal both their relative speed
and their proper accelerations must be reciprocal.

Their relative speed is reciprocal, but their accelerations are not.

This is the reason why their proper times are different.

Twin A ages 23.664 year
Twin B ages  9.912 year

No reciprocity.
Fact.
Nothing more to discuss.


-- 
Paul

https://paulba.no/