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:

It is obviously normal to keep the proper acceleration constant,
and then Vrm  ≠ (1/2)Vri

We know that in accelerated frames of reference the average speed is proportional to the instantaneous speed.
 Let Vrm=(1/2)Vri
 We are talking about real relativistic speeds (Richard Verret's hobby).
 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 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)
R.H.