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From: "Paul.B.Andersen" <relativity@paulba.no>
Newsgroups: sci.physics.relativity
Subject: Re: The problem of relativistic synchronisation
Date: Sun, 1 Sep 2024 11:58:17 +0200
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Den 31.08.2024 23:14, skrev Richard Hachel:
> Le 31/08/2024 à 22:10, "Paul.B.Andersen" a écrit :
>> Den 31.08.2024 09:05, skrev Richard Hachel:
> 
> 
>> https://paulba.no/pdf/Mutual_time_dilation.pdf
> 
> ? ? ?

Thanks to Python, I see that you fail to understand
the very first equation in the paper.

https://ibb.co/7C0S4nJ

It probably won't help, but I will point out what is clearly
defined in the paper.

https://paulba.no/pdf/Mutual_time_dilation.pdf

Quote:
| Event E₂: clock A and clock B' are adjacent
| In frame K', A will be at the position -d when B' shows  t₂'= d/v

I considered this to be obvious for a reasonable knowledgeable reader.

Explanation for the less knowledgeable reader:
-----------------------------------------------
In frame K' the clock A has moved from the position X' = 0
to the position x' = -d with the speed v.
Since t' = 0 when A was at  x' = 0, t' = d/v when A is at x' = -d.

So the coordinates of event E₂ in K' are  x₂'= -d, t₂' = d/v
In frame K the temporal coordinate will be:

t₂ = γ⋅(t₂' + (v/c²)⋅x₂') = equation (1) in the paper

The spatial coordinate was irrelevant, but it would be:

x₂ =  γ⋅(x₂' + v⋅t₂') = γ⋅(-d + v⋅d/v) = 0

which is a trivial result since clock A is stationary at x = 0.

--------------

Your d' is probably the distance between the clocks in K measured
in frame K', and vice versa.
But this 'contacted' distance is never used, and is irrelevant.

In the Lorentz transform you never use contacted distances and
dilated times. You _only_ use proper distances and proper times.

Didn't you know that?

-- 
Paul

https://paulba.no/