Center of Mass in Special Relativity: Observer Dependence?

In summary, in SR, the concept of center of mass is not well-defined and is observer-dependent. However, the worldlines of different observers' centers of masses are parallel to each other and are at rest in the center of momentum frame. The term "center of energy" may be a more accurate description, but it also changes in a Lorentz transformation.
  • #1
Dmitry67
2,567
1
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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  • #3
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.
 
  • #4
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.
 
  • #5
Ha, thank you both (even your answers are slightly contradicting :) )
 
  • #6
Center of mass is not a useful concept in SR.
Center of energy doesn't help because it changes in a Lorentz transformation.
 

Related to Center of Mass in Special Relativity: Observer Dependence?

1. What is the concept of "center of mass" in special relativity?

The center of mass is a point in space that represents the average position of all the mass in a system. It is a concept used to describe the overall motion of a system, taking into account the mass and velocities of all the individual objects within the system.

2. Why is the center of mass important in special relativity?

In special relativity, the laws of physics are observer dependent, meaning they can appear different to different observers depending on their relative motion. The center of mass is important because it is a frame-invariant quantity, meaning it is the same for all observers regardless of their motion. This allows us to make accurate predictions and calculations in different frames of reference.

3. How does the center of mass change in special relativity?

In special relativity, the concept of "mass" changes with velocity due to time dilation and length contraction. Therefore, the center of mass also changes depending on the relative velocities of the objects within the system. This means that the center of mass can appear different to different observers, but it will always be frame-invariant.

4. Can the center of mass be outside of the system in special relativity?

No, the center of mass is always within the system in special relativity. This is because the concept of "mass" is only defined within the system, and the center of mass is calculated based on the mass and velocities of the objects within the system. If an object is outside of the system, it is not included in the calculations for the center of mass.

5. How is the center of mass calculated in special relativity?

The center of mass is calculated using the relativistic formula, which takes into account the velocities and masses of all the objects within the system. This formula is similar to the classical Newtonian formula, but it also includes factors for time dilation and length contraction. It is important to note that the center of mass is a frame-invariant quantity, so the same formula can be used by all observers regardless of their relative motion.

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