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

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.

i'm not sure. It looks like you think same wordline means same place and
trajectory, which is false. A same path through spacetime does not mean
that.