## Main Question or Discussion Point

I am a noob! Forgive me if it sounds too stupid!

Let me say, I am in CERN right now at the LHC.
I fire a proton at 0.9c in one direction. While this happens, I also fire another proton at 0.5c in the opposite direction. Both the measurements were done considering the lab as a reference frame.

The problem is, what's the speed(or velocity) of either proton relative to one another??

Related Special and General Relativity News on Phys.org
Pengwuino
Gold Member

It will be given by $v' = {{v_1 + v_2}\over{1+{{v_1v_2}\over{c^2}}}}$

Numerically either proton will see the other shoot off at .966c

Formally you consider one of the proton's rest frame and send the lab traveling off at 0.9c/0.5c and then the other proton is shot off at 0.5c/0.9c from the lab frame.