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

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.
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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.