Re: It's not the same thing.

Le 29/04/2024 à 03:41, Richard Hachel a écrit :

Jean-Pierre Messager alleging that the comparison of the reference frames of Bella and Stella between them,
in the famous problem of the double traveler of Tau Ceti, it was the same thing (he considers that in the Terrence-Bella report, it is the same phenomenon that occurs as in the Stella-Bella report, because, he says , Terrence like Stella are in Galilean frames of reference, and that there is therefore the same phenomenon which links them.
 In short, he wants us to treat Stella the way we treat Terrence.
 I understand his grievances.

No you don't. My point is not about comparing Terrence-Bella (i.e.
Bella's trajectory in Terrence's frame) to Stella-Bella (i.e.
Bella's trajectory in Stella's frame).

I'll explain to him how it works.
 In the first frame of reference, that of Terrence, the departure takes place in A and the arrival in B. But A and B are not spatially in the same place for the two participants.
 In the second, events A and B are in the same place for both speakers.
 It's not the same thing.
 Furthermore, I have said and repeated that if the start was not made at rest, the equality of clean times was no longer assured in Terrence's case.
 Now, the highlight of the show and the beauty of reasoning.
 The first diagram shows what happens between Terrence and his two sisters, and we can already see that the two sisters will have equal time.
  <http://news2.nemoweb.net/jntp?45YM3ho2qHlFfZEkhlnrNslahOY@jntp/Data.Media:1>
  The other shows what is happening between Bella and Stella (and vice versa) and the equality of proper tenses, as in the first diagram (otherwise it would be absurd).
 <http://news2.nemoweb.net/jntp?45YM3ho2qHlFfZEkhlnrNslahOY@jntp/Data.Media:2>
 Je vous remercie de votre attention.

Let me explain, again (sigh) my argument :
Terrence is at rest in Earth frame.
Stella is traveling to Tau Ceti at constant velocity [w.r.t Earth]
Bella is traveling with constant acceleration to Tau Ceti,
with a initial velocity of zero w.r.t Earth.
Both leave Earth and arrive at Tau Ceti together.
You claim is that Stella and Bella will record the same duration
(proper times) for their journeys.
Anyone who studied Relativity knows that this is false: proper
duration along an inertial space-time path is always strictly
longer than in any non-inertial path.
But I don't even need to invoke SR to show you are contradicting
yourself (and also the Principle of Relativity) :
Consider Bella's trajectory in Stella's inertial frame of reference,
Bella is leaving at a given non null speed, then decelerate gradually
and travel back to Bella at increasing speed.
Now consider another traveler, say Paula, who has, in Earth frame of
reference, *exactly* the same kind of trajectory Bella has w.r.t
Stella in the Tau Ceti previous scenario.
When asked what would be proper times on Earth clock and on Paula's
clock you agreed that they will differ.
As Paula's cinematic in Earth frame and Bella's cinematic in Bella's
frame, and both Earth frame and Bella's frame are inertial you are
obviously contradicting yourself.
Moreover you are violating the Principle of Relativity which states
that the same experiments in different inertial frames of reference
have necessarily the same outcomes.