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

Le 12/03/2024 à 20:19, "Paul B. Andersen" a écrit :

Den 12.03.2024 10:00, skrev Richard Hachel:

We know that in accelerated frames of reference the average speed is proportional to the instantaneous speed.
 Let Vrm=(1/2)Vri

 This is meaningless without definition of the entities.
 But I can guess:
You are not talking about "speed in an accelerated frame".
 You are talking about the speed of a stationary object
in an accelerated frame, measured in an inertial frame.
 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
and the average speed from t=0 to t=t is Vrm(t) = at/2.
 So  Vrm=(1/2)Vri

That is what I am saying.
Vr=a.Tr
Vrm=(1/2)Vri

 

 We are talking about real relativistic speeds (Richard Verret's hobby).

 According to SR:
 For the above to be true, the coordinate acceleration must
be constant. This means that the proper acceleration must
increase with time.
 Let 1g = 1 c per year = 9.4998 m/s².
 To keep the coordinate acceleration a equal to  1 g
the proper acceleration A must be:
at t = 0   year   A =   1.00 g
at t = 0.8 year   A =   1.65 g
at t = 0.9 year   A =   3.33 g
at t = 0.99 year  A =  33.4  g
at t = 0.999 year A = 333.5  g
at t = 1.000 year A = infinite
 when t ≥ 1.0 year the coordinate acceleration can't
be kept equal to 1 g.
 Generally:
The coordinate acceleration a can't be kept equal to n g
when t ≥ 1/n year.
  It is obviously normal to keep the proper acceleration constant,
and then Vrm  ≠ (1/2)Vri

I don't understand what you are saying.
I think that between you and me, there is a different understanding of things.

 

 But we know that relativistic physicists do not use this notion, and it is important to remind them of the relationship between real speed and observable speed.
 Vr=Vo/sqrt(1-Vo²/c²)

 This is nonsense.
According to "relativistic physicists" there is no difference
between the "real speed" and the "observable (measurable) speed"
in the inertial frame.

That is what I am saying.
Physicists do not differentiate between Vo and Vr.

 

 This immediately leads us to Vom/sqrt(1-Vom²/c²)=(1/2)Voi/sqrt(1-Voi²/c²)
 and therefore to:
 Vom²(1-Voi²/c²)=(1/4)Voi²(1-Vom²/c²)
 Let Vom²=(1/4)Voi²+(3/4)Voi².Vom²/c²
 Hence Vom=(1/2)Voi/sqrt(1-(3/4)Vom²/c²) and, conversely, Voi=2.Vom/sqrt(1+3Vom²/c²)
  Thank you for your kind attention.

It is really a shame that a large majority of physicists are not very intelligent, they understand nothing of what they are saying,
which is dramatic since their number serves as truth.
A bit like in Nazi Germany everyone believed they were right because everyone held out their arm in front of Hitler.
Physicists are educated, but very few are intelligent.
On usenet, there are perhaps five or six people with whom we can seriously discuss relativity, without immediately falling into hysterical reactions. (Julien Arlandis, Michel Talon, Paul B Andersen...). The others not only learned anything, but answer nonsense when asked a simple problem.
A good example of this madness here is Python, as stupid as he is aggressive.
 R.H.