Sorry, Verlan, I don't think you have that right. Here's
how you really add relativistic velocities.

Your math error is actually a very common one. You assume that the squareroot of the sum of two squares is equal to the sum. It is not.

Another way you to write your formula for v_3 is as follows

v_3=sqrt(v_1^2+v-2^2-(v_1*v_2/c)^2)

If this is nonrelativistic v_1*v_2 much less than c^2, we get from your equation that

v_3=sqrt(v_1^2+v_2^2)

Which isn't true... in fact...

v_3=v_1+v_2

It's very clear why you are having a problem with negative versus positive velocities, which are the cases for which the above two equations are the most drastically different (since the square of a negative number is positive). Using your logic would lead us to believe that if point A and point C were travelling at the same velocity and we stuck a point B in between them travelling at a different velocity, we would measure a "relativistic" velocity that was equal to (roughly) twice the velocity of B instead of zero.

My recommendation to you is to look over the site I posted and derive the correct equation for v_3 from there. You will find that there is no paradox after all.

<font size=-1>[ This Message was edited by: JS Princeton on 2002-10-11 00:36 ]</font>