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Subject: [SR] Usefulness of real velocities in accelerated relativistic frames of 
 reference.
Newsgroups: sci.physics.relativity
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Date: Tue, 12 Mar 24 09:00:29 +0000
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From: Richard Hachel <r.hachel@tiscali.fr>
Bytes: 1994
Lines: 28

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.