Center or mass in SR

1. Sep 12, 2010

Dmitry67

I know that in GR center of mass is not well defined.
Whats about SR?
Is a worldline of center of mass observer-dependent or not?

P.S.
As rest mass is not conserved, as I understand, it makes sense to talk about center of relativistic mass = center of energy?

2. Sep 12, 2010

bcrowell

Staff Emeritus
3. Sep 12, 2010

Jonathan Scott

In SR, energy and momentum are well-defined and the center of mass of a closed system moves in a straight line at constant velocity with constant energy.

4. Sep 12, 2010

DrGreg

It is an exercise in Rindler: Relativity: Special, General & Cosmological (2nd ed, ex. 6.5) to show that the "centre of mass" $\Sigma(E\textbf{x})/\Sigma E$ is observer-dependent. But the worldlines of all the different observers' centres of masses are all parallel to each other, and are all at rest in the centre of momentum frame (the frame in which the total momentum is zero).

I guess it could be better described as "centre of energy". Rindler is one of the few academics who still use "mass" to mean relativistic mass.

5. Sep 13, 2010

Dmitry67

Ha, thank you both (even your answers are slightly contradicting :) )

6. Sep 13, 2010

Meir Achuz

Center of mass is not a useful concept in SR.
Center of energy doesn't help because it changes in a Lorentz transformation.

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