Is the center of mass fixed in Relativity?

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Discussion Overview

The discussion revolves around the concept of the center of mass in the context of relativity, exploring whether it is fixed or invariant compared to classical physics. Participants examine implications in both special and general relativity, and the conversation includes references to specific literature and definitions.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants propose that the center of mass is not fixed in relativity, contrasting it with classical physics.
  • Others argue that the center of mass may be invariant under Lorentz boosts, relating this to Noether's theorem.
  • There is a distinction made between special relativity and general relativity, with some noting that a center of mass cannot be defined in general relativity except in special cases.
  • One participant mentions that in special relativity, the concept of center of mass is replaced by center of energy, which leads to different conclusions based on relativistic definitions.
  • Another participant questions the validity of conclusions drawn from scenarios where momentum is not conserved, suggesting that such conclusions may be meaningless.
  • A reference is made to Rindler's work, which defines the center of energy and discusses its frame-dependence in systems of particles in relative motion.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the center of mass in relativity, with no consensus reached on whether it is fixed or invariant. The discussion remains unresolved, with multiple competing perspectives presented.

Contextual Notes

Some claims rely on nonstandard definitions and assumptions, and there are references to specific literature that may not be universally accepted. The discussion also highlights the complexity of the topic and the potential for varying interpretations.

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I think that the center of mass is not fixed in Relativity (unlike in classical physics). Could anyone look at my attached memo and tell me if I am right or wrong.
 

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I haven't read your document so I may misunderstand but I think that the centre of mass is invariant under Lorentz boosts. This is a consequence of Noether's theorem in the same way that momentum is invariant under spatial translation and energy under time translation.
 
Special Relativity or general? In general relativity, there is no way to define center of mass except for special cases.
 
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PAllen said:
Special Relativity or general? In general relativity, there is no way to define center of mass except for special cases.

This is why we can get things like relativistic gliders.

"Swimming in Spacetime: Motion in Space by Cyclic Changes in Body Shape" Jack Wisdom 2003, Science , 299 , 1865. http://groups.csail.mit.edu/mac/users/wisdom/

"The relativistic glider," Eduardo Gueron and Ricardo A. Mosna, Phys.Rev.D75:081501,2007. http://arxiv.org/abs/gr-qc/0612131

"'Swimming' versus 'swinging' in spacetime", Gueron, Maia, and Matsas, http://arxiv.org/abs/gr-qc/0510054
 
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dont worry his document is safe to open
 
Your document is wildly over complex and uses nonstandard definitions, leading to nonstandard conclusions. In special relativity one replaces center of mass with center of energy. Each term is m*gamma*(c squared), for a particle, and simply E for photon or light pulse.
 
While I am not willing to review your document in detail, I wonder if you are just saying that if momentum isn't conserved, then center of energy isn't frame independent. However, any process must conserve energy-momentum, so a conclusion based on a violation is meaningless.
 
  • #10
In an exercise in his book Relativity: Special, General and Cosmological (2nd ed, 2006, exercise 6.5 p. 126), Rindler defines the centre of energy (which he calls "centre of mass", as he is one of the few authors who still uses "mass" to mean "relativistic mass" a.k.a. energy). He asks the reader to prove that the centre of energy of a system of two particles in relative motion is frame-dependent and that, nevertheless, for any system in which the only forces are collision forces, all inertial frames agree that the velocity of the centre of energy equals the velocity of the "centre of momentum frame" (the frame relative to which the total momentum is zero).
 

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