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## Main Question or Discussion Point

I'm stuck on this problem in the "Relativistic Particle Mechanics" section, number 26. I had no trouble with the first part... but the second part I'm stuck.

"Two identical particles move with velocities +-u along the parallel lines z=0, y=+-a in a frame S, passing x=0 simultaneously. Prove that all centroids determined by observers moving collinearly with these particles lie on the open line-segment x=z=0, |y|<ua/c"...

I had no trouble here. But now:

"Also prove that, keeping the same total (relativistic) mass and angular momentum, two such particles cannot move along lines closer than 2ua/c without breaking the relativistic speed limit."

My basic idea was to use the equation for conservation of relativistic mass leading to:

[tex] \gamma (v_1) + \gamma (v_2) = 2*\gamma (u)[/tex]

And conservation of 3-angular momentum which leads to:

[tex] \gamma (v_1)*v_1*r_1 + \gamma (v_2)*v_2*r_2 = 2*\gamma (u) * u * a[/tex]

to try and show the required inequality, but haven't been successful. I'd appreciate any help. Thanks.

"Two identical particles move with velocities +-u along the parallel lines z=0, y=+-a in a frame S, passing x=0 simultaneously. Prove that all centroids determined by observers moving collinearly with these particles lie on the open line-segment x=z=0, |y|<ua/c"...

I had no trouble here. But now:

"Also prove that, keeping the same total (relativistic) mass and angular momentum, two such particles cannot move along lines closer than 2ua/c without breaking the relativistic speed limit."

My basic idea was to use the equation for conservation of relativistic mass leading to:

[tex] \gamma (v_1) + \gamma (v_2) = 2*\gamma (u)[/tex]

And conservation of 3-angular momentum which leads to:

[tex] \gamma (v_1)*v_1*r_1 + \gamma (v_2)*v_2*r_2 = 2*\gamma (u) * u * a[/tex]

to try and show the required inequality, but haven't been successful. I'd appreciate any help. Thanks.

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