Is Center-of-Mass Supraliminal?

[LarryS]

In Newtonian physics, the center-of-mass of a group of particles depends on the instantaneous positions of the particles, no matter how far apart they are or how fast they are moving relative to each other.

What about under SR? Is the center-of-mass of a group of particles determined instantaneously or is it delayed because of the limitation of the speed of light?

Thanks in advance.

 

[bcrowell]

I think it's instantaneous. I don't see how it could even make sense to make it not instantaneous. To determine the speed-of-light delay, you'd have to know the distance to the point in question, but you don't know the point in question yet.

 

[HallsofIvy]

The "determining" the center of mass does not involve any object actually moving so is not subject to a light speed limit.

 

[LarryS]

What about center of mass versus center of gravity? Don't gravity waves, under GR, travel at the speed of light?

 

[DrGreg]

It is my understanding that "centre of mass" is, in general, frame-dependent in relativity. All observers agree on the "centre of momentum" frame (the frame in which total momentum is zero) and that the centre of mass moves with the same velocity as the centre of momentum frame, but they may disagree on its location.

Reference: Rindler, W. (2006), Relativity: Special, General and Cosmological, 2nd ed, Oxford University Press, ISBN 978-0-19-856732-5, p.126, exercise 6.5.