Is the center of mass fixed in Relativity?

[fast_squirrel]

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.

 

[DaveC426913]

You will get more responses if you post your ideas directly here. Few people will open a potentially harmful attachment.

 

[PeterDonis]

Could anyone look at my attached memo and tell me if I am right or wrong.

Please use the PF LaTeX feature to post your math directly. See this page for more info:

https://www.physicsforums.com/help/latexhelp/

 

[cosmik debris]

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.

 

[PAllen]

Special Relativity or general? In general relativity, there is no way to define center of mass except for special cases.

 

[bcrowell]

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

 

[greswd]

dont worry his document is safe to open

 

[PAllen]

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.

 

[PAllen]

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.

 

[DrGreg]

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).