Re: [SR] Usefulness of real velocities in accelerated relativistic frames of reference.

Le 13/03/2024 à 21:59, "Paul B. Andersen" a écrit :

Den 12.03.2024 20:42, skrev Richard Hachel:

So  Vrm=(1/2)Vri

 That is what I am saying.

 Yes. And I agree.
 NOTE THIS:
  If the object is instantly at rest at t = 0, and
  the coordinate acceleration in the inertial frame is constant a,
  Then the speed Vri(t) = at
 

 Vr=a.Tr

 Where Vr (Vri(t)) is the speed in the inertial frame,
and Tr (t) is the time coordinate in the inertial frame, and
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a is the constant coordinate acceleration in the inertial frame!
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 The consequence of this is that when t > c/a  v > c
which is impossible in SR.
 That means that the coordinate acceleration a can't be constant!

In the rocket frame, a is constant.
Always.
a=10m/s² (a=1.052ly/y²)
The rocket is at rest in its frame of reference, and the speed Vr of the surrounding space becomes Vr=a.Tr
There is no problem, the speed of the rocket, that is to say the real speed of movement of the terrestrial frame of reference, is indeed Vr.
But you know the conversion equation that I gave forty years ago: Vo=Vr/sqrt(1+Vr²/c²)
Everything is remarkably clear and of great theoretical beauty if you understand what I am saying.
R.H.