Center of Mass in Special Relativity: Observer Dependence?

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Discussion Overview

The discussion revolves around the concept of center of mass in the context of Special Relativity (SR) and its observer dependence. Participants explore whether the worldline of the center of mass is observer-dependent and the implications of relativistic mass and energy in this framework.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants note that in General Relativity (GR), the center of mass is not well defined and question its status in SR.
  • There is a suggestion that the worldline of the center of mass may be observer-dependent, with references to the center of relativistic mass being equated to the center of energy.
  • One participant cites an exercise from Rindler's work indicating that the center of mass is observer-dependent, but asserts that the worldlines of different observers' centers of mass are parallel and at rest in the center of momentum frame.
  • Another participant expresses skepticism about the utility of the center of mass concept in SR, stating that the center of energy also varies under Lorentz transformations.
  • Participants acknowledge slight contradictions in the responses provided, indicating a lack of consensus on the topic.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the center of mass is a useful concept in SR, and there are competing views regarding its observer dependence and the relevance of the center of energy.

Contextual Notes

There are limitations regarding the definitions of mass and energy in relativistic contexts, as well as the implications of Lorentz transformations on these concepts. The discussion reflects varying interpretations and assumptions about the nature of mass in SR.

Dmitry67
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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?
 
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Dmitry67 said:
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?

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.
 
Dmitry67 said:
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?

It is an exercise in Rindler: Relativity: Special, General & Cosmological (2nd ed, ex. 6.5) to show that the "centre of mass" [itex]\Sigma(E\textbf{x})/\Sigma E[/itex] 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.
 
Ha, thank you both (even your answers are slightly contradicting :) )
 
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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