Is Center-of-Mass Supraliminal?

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Discussion Overview

The discussion revolves around the concept of center-of-mass in the context of Newtonian physics and special relativity (SR). Participants explore whether the determination of center-of-mass is instantaneous or affected by the speed of light, as well as the relationship between center-of-mass and center-of-gravity.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants assert that in Newtonian physics, the center-of-mass is determined by the instantaneous positions of particles, regardless of their relative motion.
  • One participant believes that the determination of center-of-mass in special relativity is instantaneous, questioning how a delay could be conceptualized without knowing the point in question.
  • Another participant argues that determining the center of mass does not involve any physical movement and thus should not be subject to light speed limitations.
  • A participant raises a question about the distinction between center of mass and center of gravity, noting that gravity waves in general relativity (GR) travel at the speed of light.
  • One participant mentions that the center of mass is frame-dependent in relativity, highlighting that observers may disagree on its location while agreeing on the center of momentum frame.

Areas of Agreement / Disagreement

Participants express differing views on whether the center-of-mass is determined instantaneously or subject to delays due to the speed of light. There is no consensus on the relationship between center-of-mass and center-of-gravity, nor on the implications of frame dependence in relativity.

Contextual Notes

Some limitations include the dependence on definitions of center-of-mass and center-of-gravity, as well as the unresolved implications of relativistic effects on the determination of center-of-mass.

LarryS
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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.
 
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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.
 
The "determining" the center of mass does not involve any object actually moving so is not subject to a light speed limit.
 
What about center of mass versus center of gravity? Don't gravity waves, under GR, travel at the speed of light?
 
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.
 

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