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

Le 21/04/2024 à 23:31, Richard Hachel a écrit :

Le 20/04/2024 à 19:07, Python a écrit :

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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You interpret path as a path in space-time while Hachel is considering
path in space only (so it is true in only ONE reference frame)
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For instance, he claims that if two travelers would go from Earth
to Tau Ceti, one at constant velocity w.r.t Earth the other one
with a constant acceleration both will measure the same (proper)
time for their trips.

 Yes, this is entirely correct.
 If two different protagonists use different frames of reference to join Tau Ceti (12al), and if we notice that in the terrestrial frame of reference the travel times are similar and the path is similar (direct path), then the two proper times will be similar.

The equality of travel times in any frame is always true. There is
a single value for the time elapsed between two events. You are
ridiculous, Richard.
The path being the same is only true in a single inertial frame,
and false in all others.
It is logically unsound that a property that depends on a
chosen frame of reference could imply a property that does
not. This is basic logic.
Moreover It is obvious that your claim is violating the principle of
Relativity: just consider the situation from the frame of reference of
the inertial traveler.
This is quite pathetic that you're unable to grasp such a
simple argument.