General Case of Relative Velocities

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The discussion centers on the concept of relative velocities in the context of relativity, specifically addressing the general case of velocity addition. Participants note a potential typo in the formula presented in the Wikipedia article, suggesting that a dot product is implied between two velocity vectors that are shown side by side without a dot. Clarification is sought on whether B or A is the observer in the context of the calculations. The correct interpretation of the formula is emphasized, particularly the need to calculate the velocity of B in the rest frame of A. The conversation highlights the importance of precise notation in understanding relative velocities.
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I was looking relative velocities and I saw General case in Relativity part.That part means every direction isn't it.
http://en.wikipedia.org/wiki/Relative_velocity
and in there B is the observer or A is the observer
Thanks
 
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Quarlep said:
I was looking relative velocities and I saw General case in Relativity part.That part means every direction isn't it.
http://en.wikipedia.org/wiki/Relative_velocity
and in there B is the observer or A is the observer
Thanks

With respect to the general case of velocity addition in the wiki, there appears to be a (typo) in the formula.

I see two vectors (velocity A and velocity B) side by side in the denominator of the fraction. Most likely this is a dot product but there is no dot between them.

Yes? No?
 
Quarlep said:
in there B is the observer or A is the observer

##\vec{v}_{BA}## is the velocity of B in the rest frame of A, which needs to be calculated; ##\vec{v}_A## and ##\vec{v}_B## are the velocities of A and B in some other frame, which are presumed to be known at the start of the calculation.

MikeLizzi said:
Most likely this is a dot product

Yes, there should be a dot between them.
 
In an inertial frame of reference (IFR), there are two fixed points, A and B, which share an entangled state $$ \frac{1}{\sqrt{2}}(|0>_A|1>_B+|1>_A|0>_B) $$ At point A, a measurement is made. The state then collapses to $$ |a>_A|b>_B, \{a,b\}=\{0,1\} $$ We assume that A has the state ##|a>_A## and B has ##|b>_B## simultaneously, i.e., when their synchronized clocks both read time T However, in other inertial frames, due to the relativity of simultaneity, the moment when B has ##|b>_B##...

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