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

Le 13/04/2024 à 08:36, Richard "Hachel" Lengrand a écrit :

Let us understand each other (a moment of optimism).
   The immense, the incomparable, the fantastic relativist theorist (that's me) wrote:
   "If two different observers travel an identical path in equal observable times,
then their proper times will necessarily be equal.

[note : I posted a more detailed answer on fr.sci.physique]
This claim is logically ill-founded to begin with :
1. From the point of view of any frame of reference the elapsed time
between ANY pair of events has a UNIQUE value. So "equal observable
times" is a void proposition.
2. "Identical path" i.e. "same set of locations" for different
trajectories is a condition that can be verified in a given
frame of reference but, then won't be so in other frames.
A condition that depends on a choice of frame of reference (subjective)
CANNOT implies a conclusion that does not depend on it ("objective")
(except in Galilean Relativity, of course, but then all times, proper
or not are equal, but everything implies an always true proposition,
and this is not what Lengrand claims)
So Lengrand's claim is dead in the water at first read.

  Let's set up a Galilean frame of reference, in which a Galilean mobile moves from left to right on the x axis.

...

  Let us pose another body, but this time in uniformly accelerated motion, and whose speed will be specially chosen so that To=12.915.
   This means that in R, if they leave together, they arrive together (even if they do not have the same speed between them).

...

  Their own times will be equal.

This is obviously violating the principle of Relativity. It is obvious
when you describe the situation in the inertial traveler's frame of
reference. (except, again, in Galilean Relativiy)

  It's even a very speech full of abstract religiosity.

If you call religiosity the fact that you are psychologically unable
to consider anything that went through your mind, without any sensible
justification, as wrong, this is, indeed, religiosity. This is more
correctly called "hubris".