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Subject: Re: [SR] Their proper times will necessarily be equal
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From: Richard Hachel   <bts.orange@licorne-bleue.fr>
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Le 21/04/2024 à 16:48, Python a écrit :
> Le 21/04/2024 à 15:53, Ross Finlayson a écrit :
>> On 04/20/2024 09:52 AM, Tom Roberts wrote:
>>> On 4/13/24 1:36 AM, Richard Hachel wrote:
>>>> "If two different observers travel an identical path in equal
>>>> observable times, then their proper times will necessarily be equal.
>>>
>>> Yes, of course.
>>>
>>> My response differs from others because I interpret your context
>>> differently.
>>>
>>> Since you mention "proper times", your context must be relativity; it
>>> does not matter whether SR or GR, because "travel an identical path"
>>> means they travel along a single worldline through spacetime -- i.e.
>>> they are always co-located and co-moving, so of course their elapsed
>>> proper times are equal (counting from any event on their worldline).
>>>
>>>      Your "in equal observable times" is redundant. For any
>>>      observer this directly follows from them following the
>>>      same worldline through spacetime.
>>>
>>> Note this is essentially the first time I agree with Hachel. I doubt
>>> that he understands why what he wrote is actually correct, because he
>>> followed it with a bunch of obfuscatory nonsense.
>>>
>>>> [... enormous amount of gibberish ignored.]
>>>
>>> Tom Roberts
>> 
>> Can you help further explain for the rest of us why
>> this isn't necessarily the usual interpretation or
>> why it sort of doesn't arrive at the same results of
>> some of the usual thought experiments like the traveling twins?
> 
> In the twins scenario, twins does not share the same
> space-time path.

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).
Note that "space-time path", I don't understand the geometric concept very 
well.
Relativist theorists must say clear things if they want to be understood. 
However, I see that their geometry is not entirely clear and easily 
understandable. Above all, I see results that are as false as they are 
strange appearing at the end of the race. All this is not normal and 
deserves more serious reflection.

R.H.