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From: "Paul B. Andersen" <relativity@paulba.no>
Newsgroups: sci.physics.relativity
Subject: Re: [SR] Usefulness of real velocities in accelerated relativistic
 frames of reference.
Date: Thu, 14 Mar 2024 15:04:13 +0100
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Den 14.03.2024 03:09, skrev Richard Hachel:
> Le 13/03/2024 à 21:59, "Paul B. Andersen" a écrit :
> 
>> Understand this:
>> What SR predicts is not a matter of opinion,
>> it is a matter of fact.

The subject line is:
"SR: Usefulness of real velocities in accelerated relativistic frames of 
reference."

I take this to mean that you are stating what you claim SR predicts.

> 
> Above all, we must prioritize experimentation.
> And if two theories face each other, we must take the one which has the 
> approval of the experimenters.

Indeed.
And you know of course that SR is confirmed by innumerable
experiments and falsified by none.
Some of them:
https://paulba.no/paper/index.html

But the issue is:
Does SR predict what you claim it predicts?

> 
> If we take Einstein's RR, which is taken from the Poincaré equation and 
> the Minkowski metric, and which is called "local", we realize that two 
> enormous problems appear.
> - The Langevin paradox (which we camouflaged, but which resurfaces using 
> apparent speeds, that is to say what we would observe if we had very 
> good telescopes and sufficient rocket technology).
> - The principle of non-locality of Aspect and its contradiction with 
> instantaneous transfers of information.

Your opinion of SR is irrelevant.

SR is a consistent theory, and the issue is:
"Does SR predict that accelerated objects will behave as
  you claim they do?"

> 
> These contradictions do not exist with me, and I have never seen a 
> single fact contradicting everything I have said for 40 years.

This is probably true, because it is obvious that you never
read the contradicting facts.

So let us review your claims and the contradicting facts.

PLEASE READ THEM FOR THE FIRST TIME IN 40 YEARS!

The scenario as defined by you:
"In the rocket frame, a is constant. The rocket is at rest
  in its frame of reference, and the speed Vr of the surrounding
  space becomes Vr=a.Tr."

A bit more precisely put:
A rocket is accelerating at the constant proper acceleration a.
An inertial frame of reference K(x,t) is at the time t = 0
instantly co-moving with the rocket.

You claim:
According to SR the speed of the rocket in K is Vr(t) = a⋅t
===========================================================

Note that this means that Vr > c when t > c/a
which according to SR is impossible.

Contradicting fact:
-------------------
So this is wrong.
You can see the correct derivation here:
https://paulba.no/pdf/TwinsByMetric.pdf
See chapter 2.3, equation (15)

Vr(t) = a⋅t/√(1+(a⋅t/c)²)

Note that:
  Vr → a⋅t when t → 0
  Vr → c   when t → ∞


Your problem is that you do not understand the difference
between proper acceleration of the rocket, and the rocket's
coordinate acceleration in the inertial frame.

If A is the coordinate acceleration in K, we have:

A = dVr/dt = a/(√(1+(a⋅t/c)²))³

Note that:
  A → a when t → 0
  A → 0 when t → ∞

So  Vr(t) = ∫(from 0 to t)A⋅dt = a⋅t/√(1+(a⋅t/c)²)

You claim:
According to SR is the average speed of the rocket Vm(t) = Vr(t)/2
=====================================================================

Contradicting fact:
-------------------
This is wrong.

Vr(t) = a⋅t/√(1+(a⋅t/c)²)

The average speed Vm at the time t is:
Vm = (integral from t=0 to t=t of Vr(t)dt)/t
Vm = c²⋅(√(1+(a⋅t/c)²)-1)/a⋅t

Note that:
  Vm → a⋅t/2 when t → 0
  Vm → c     when t → ∞

So:
  Vm/Vr  → 1/2  when t → 0
  rm/Vr  → 1    when t → ∞

So for any t > 0   Vm > Vr/2

It is not possible to make SR predict anything else!
====================================================

-- 
Paul

https://paulba.no/