Sujet : [SR] Usefulness of real velocities in accelerated relativistic frames of reference.
De : r.hachel (at) *nospam* tiscali.fr (Richard Hachel)
Groupes : sci.physics.relativityDate : 12. Mar 2024, 10:00:29
Autres entêtes
Organisation : Nemoweb
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User-Agent : Nemo/0.999a
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)
Thank you for your kind attention.
R.H.