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

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.

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Yes, of course.
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My response differs from others because I interpret your context
differently.
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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).
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     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.]

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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?