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

Le 21/04/2024 à 23:07, Richard Hachel a écrit :

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).

To have the same improper time is meaningless because in a given
frame of reference there is a single time elapsed between any
two events. And there are only two events : travelers' depart
and travelers' meeting again.
Moreover to have the same path (in the spatial sense) is a
property that is only true in a single frame of reference.
It makes no sense (outside of a trivial one in Galilean Relativity)
to claim that a condition depending on a given chosen frame could
imply a property (equality of proper times) that does not depend
on that.

Note that "space-time path", I don't understand the geometric concept very well.

It's not a big deal! It is the set of events "traveler is at this
position at that time".

[snip babbling]

Your claim is directly violating the principle of Relativity. End of
Story.