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

Den 15.03.2024 15:30, skrev Richard Hachel:

Le 15/03/2024 à 15:11, "Paul B. Andersen" a écrit :

I suppose you are referring to my "false" equations:
Speed:            Vr(t) = a⋅t/√(1+(a⋅t/c)²)
Average speed     Vm(t) = c²⋅(√(1+(a⋅t/c)²)-1)/a⋅t
>
where your "correct" equations are:
Speed:  Vr(t) = a⋅t
Average speed  Vm(t) = a⋅t/2
>
:-D

 The speed of the accelerated mobile or particle
is a function of time.
The more time passes, the greater the speed.
Everyone agrees on that

Indeed! Vr increases with time.
Den 12.03.2024, skrev Richard Hachel:
| In the rocket frame, a is constant. Always.
| 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.
This means that Vr is the relative speed between the rocket
and the terrestrial frame. Since the terrestrial frame is
inertial while the rocket is accelerating this means that
Vr is the speed of rocket in the inertial terrestrial frame.
So there is no problem: Vr = a.Tr
where a is the proper acceleration of the rocket
and Vr is the speed of the rocket in the inertial frame.
Den 16.03.2024 skrev Richard Hachel:
| When I say Vr(Tr)=a.Tr, it IS Newtonian relativity.
| However, the equation is correct.
| Warning! Tr is a proper time.
OK.
This is Newtonian (Galilean) relativity.
Tr is the proper time of the rocket and the time coordinate
in the inertial (terrestrial) frame.
There is no limit for the speed of the rocket.
We can conclude:
================
Richard Hachel's equations:
  Speed of rocket in inertial frame:             Vr=a.Tr
  Average speed of rocket in the inertial frame: Vrm=(1/2)Vr
Are correct only in Newtonian Mechanics with Galilean relativity.
So Richard Hachel's theory is identical to Newtonian Mechanics.
--
Paul
https://paulba.no/