Center of mass and center of energy

[gravityandlev]

center of mass and "center of energy"

Hi everyone,

I recently came across a little thought experiment in a book that seemed to imply that the center of mass of an isolated system is not a strictly conserved quantity. Rather, it is the "center of energy" that remains fixed. The idea of a "center of mass", then, just comes from the fact that mass energies tend to be much larger than other relevant energy scales. I've tried to write up the book's argument clearly here: http://gravityandlevity.wordpress.c...ence-of-mass-and-energy-the-center-of-energy/ I'm not fully convinced there isn't a flaw in the reasoning somewhere.

Maybe this is common knowledge, but I had never heard it before. Is the "center of energy" of a closed system strictly conserved?

 

[Bob_for_short]

Maybe this is common knowledge, but I had never heard it before. Is the "center of energy" of a closed system strictly conserved?

Yes, I think so. The motion equations of a closed system describe the energy-momentum exchanges between the constituents. Summed up, the equations give the center of energy coordinate R moving with a constant velocity. See L. Landau, E. Lifschitz, "The Classical Theory of Fields"

Bob.

 

[gravityandlev]

Thanks, Bob. I'll look it up.

Come to think of it, I have heard of this concept in the context of electromagnetic fields. I guess I just didn't think to apply it to mass energy as well. I wonder why it is not commonly taught?